Subgroups — C₂₃×#61107 #19208733

Order 5888.

2624 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3586	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3585	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#577	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3291	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3290	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3289	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3288	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3069	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3068	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3067	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#471	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3022	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3021	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3020	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3019	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2957	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2955	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#585	C₂²	1	1	yes	characteristic
21	C₂₃×#585	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#578	—	2	2	no	—
25	C₂₃×#578	—	2	1	no	—
26	C₂₃×#578	C₂²	1	2	yes	complemented
27	C₂₃×#578	C₂²	1	4	yes	complemented
28	C₂₃×#577	—	2	2	no	—
29	C₂₃×#577	—	2	2	no	—
30	C₂₃×#577	—	2	2	no	—
31	C₂₃×#577	—	2	2	no	—
32	C₂₃×#577	—	2	1	no	—
33	C₂₃×#577	—	2	1	no	—
34	C₂₃×#577	C₂²	1	4	yes	complemented
35	C₂₃×#577	C₂²	1	4	yes	complemented
36	C₂₃×#577	C₂²	1	4	yes	complemented
37	C₂₃×#577	C₂²	1	4	yes	complemented
38	C₂₃×#577	C₂²	1	2	yes	complemented
39	C₂₃×#577	C₂²	1	2	yes	complemented
40	C₂₃×#576	—	2	2	no	—
41	C₂₃×#576	—	2	1	no	—
42	C₂₃×#576	C₂²	1	4	yes	complemented
43	C₂₃×#576	C₂²	1	2	yes	complemented
44	C₂₃×#575	—	2	2	no	—
45	C₂₃×#575	—	2	2	no	—
46	C₂₃×#575	—	2	2	no	—
47	C₂₃×#575	C₂²	1	1	yes	characteristic
48	C₂₃×#575	C₂²	1	1	yes	characteristic
49	C₂₃×#575	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#575	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#575	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₂₃×#137	—	2	2	no	—
53	C₂×C₂₃×#137	—	2	1	no	—
54	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
58	C₂×C₂₃×AGL(1,ℤ/8)	—	2	1	no	—
59	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₂₃×#135	—	2	2	no	—
63	C₂×C₂₃×#135	—	2	1	no	—
64	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic, complemented
66	C₂²×SD₁₆×C₂₃	—	2	1	no	—
67	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#568	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#568	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#535	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#497	C₂²	1	2	yes	complemented
75	C₂₃×#496	C₂²	1	2	yes	complemented
76	C₂₃×#495	C₂²	1	2	yes	complemented
77	C₂₃×#492	C₂²	1	2	yes	complemented
78	C₂₃×#473	C₂²	1	2	yes	complemented
79	C₂₃×#473	C₂²	1	4	yes	complemented
80	C₂₃×#472	C₂²	1	4	yes	complemented
81	C₂₃×#472	C₂²	1	2	yes	complemented
82	C₂₃×#471	C₂²	1	4	yes	complemented
83	C₂₃×#471	C₂²	1	4	yes	complemented
84	C₂₃×#471	C₂²	1	4	yes	complemented
85	C₂₃×#471	C₂²	1	4	yes	complemented
86	C₂₃×#471	C₂²	1	2	yes	complemented
87	C₂₃×#471	C₂²	1	2	yes	complemented
88	C₂₃×#456	C₂²	1	4	yes	complemented
89	C₂₃×#456	C₂²	1	4	yes	complemented
90	C₂₃×#455	C₂²	1	4	yes	complemented
91	C₂₃×#455	C₂²	1	4	yes	complemented
92	C₂₃×#454	C₂²	1	4	yes	complemented
93	C₂₃×#454	C₂²	1	4	yes	complemented
94	C₂₃×#453	C₂²	1	4	yes	complemented
95	C₂₃×#453	C₂²	1	4	yes	complemented
96	C₂₃×#444	C₂²	1	4	yes	complemented
97	C₂₃×#444	C₂²	1	4	yes	complemented
98	C₂₃×#443	C₂²	1	4	yes	complemented
99	C₂₃×#443	C₂²	1	4	yes	complemented
100	C₂₃×#430	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#421	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#421	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#421	C₂²	1	1	yes	characteristic, complemented
105	C₂₃×#421	C₂²	1	1	yes	characteristic, complemented
106	C₂₃×#413	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#413	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₂₃×#101	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×2₋¹⁺⁴	—	2	2	no	—
112	C₂₃×2₋¹⁺⁴	—	2	2	no	—
113	C₂₃×2₋¹⁺⁴	—	2	1	no	—
114	C₂₃×2₋¹⁺⁴	—	2	1	no	—
115	C₂₃×2₋¹⁺⁴	—	2	1	no	—
116	C₂₃×2₋¹⁺⁴	—	2	1	no	—
117	C₂₃×2₋¹⁺⁴	—	4	1	no	—
118	C₂₃×2₋¹⁺⁴	C₂³	1	4	yes	—
119	C₂₃×2₋¹⁺⁴	C₂³	1	2	yes	—
120	C₂₃×2₋¹⁺⁴	C₂³	1	2	yes	complemented
121	C₂₃×H(5,𝔽₂)	—	2	2	no	—
122	C₂₃×H(5,𝔽₂)	—	2	2	no	—
123	C₂₃×H(5,𝔽₂)	—	2	1	no	—
124	C₂₃×H(5,𝔽₂)	—	2	1	no	—
125	C₂₃×H(5,𝔽₂)	—	2	1	no	—
126	C₂₃×H(5,𝔽₂)	—	2	1	no	—
127	C₂₃×H(5,𝔽₂)	—	4	1	no	—
128	C₂₃×H(5,𝔽₂)	—	4	1	no	—
129	C₂₃×H(5,𝔽₂)	—	4	1	no	—
130	C₂₃×H(5,𝔽₂)	C₂³	1	2	yes	—
131	C₂₃×H(5,𝔽₂)	C₂³	1	4	yes	—
132	C₂₃×H(5,𝔽₂)	C₂³	1	2	yes	complemented
133	C₂×#41×C₂₃	—	2	2	no	—
134	C₂×#41×C₂₃	—	2	2	no	—
135	C₂×#41×C₂₃	—	2	2	no	—
136	C₂×#41×C₂₃	—	2	2	no	—
137	C₂×#41×C₂₃	—	2	1	no	—
138	C₂×#41×C₂₃	—	2	1	no	—
139	C₂×#41×C₂₃	—	2	1	no	—
140	C₂×#41×C₂₃	—	2	1	no	—
141	C₂×#41×C₂₃	—	4	1	no	—
142	C₂×#41×C₂₃	—	4	1	no	—
143	C₂×#41×C₂₃	—	4	1	no	—
144	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₂₃	—	2	1	no	—
151	C₂²×Q₈×C₂₃	—	2	1	no	—
152	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
153	C₂²×D₄×C₂₃	—	2	1	no	—
154	C₂²×D₄×C₂₃	—	2	1	no	—
155	C₂²×D₄×C₂₃	—	4	1	no	—
156	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂₃×#137	—	2	2	no	—
158	C₂₃×#137	—	2	2	no	—
159	C₂₃×#137	—	2	1	no	—
160	C₂₃×#137	—	2	1	no	—
161	C₂₃×#137	—	2	1	no	—
162	C₂₃×#137	—	2	1	no	—
163	C₂₃×#137	—	2	4	no	—
164	C₂₃×#137	—	2	4	no	—
165	C₂₃×#137	—	2	4	no	—
166	C₂₃×#137	—	2	4	no	—
167	C₂₃×#137	—	2	2	no	—
168	C₂₃×#137	—	2	2	no	—
169	C₂₃×#137	—	2	4	no	—
170	C₂₃×#137	—	2	2	no	—
171	C₂₃×#137	—	2	2	no	—
172	C₂₃×#137	—	2	4	no	—
173	C₂₃×#137	—	2	2	no	—
174	C₂₃×#137	—	2	2	no	—
175	C₂₃×#137	D₄	1	2	yes	complemented
176	C₂₃×#137	D₄	1	2	yes	complemented
177	C₂₃×#137	C₂³	1	4	yes	—
178	C₂₃×#137	C₂³	1	2	yes	—
179	C₂₃×#137	C₂³	1	2	yes	—
180	C₂₃×#137	C₂³	1	2	yes	—
181	C₂₃×#137	C₂³	1	4	yes	complemented
182	C₂₃×#137	C₂³	1	2	yes	complemented
183	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
184	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
185	C₂₃×AGL(1,ℤ/8)	—	2	1	no	—
186	C₂₃×AGL(1,ℤ/8)	—	2	1	no	—
187	C₂₃×AGL(1,ℤ/8)	—	2	1	no	—
188	C₂₃×AGL(1,ℤ/8)	—	2	1	no	—
189	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
190	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
191	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
192	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
193	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
194	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
195	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
196	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
197	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
198	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
199	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
200	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
201	C₂₃×AGL(1,ℤ/8)	D₄	1	2	yes	complemented
202	C₂₃×AGL(1,ℤ/8)	D₄	1	2	yes	complemented
203	C₂₃×AGL(1,ℤ/8)	C₂³	1	4	yes	—
204	C₂₃×AGL(1,ℤ/8)	C₂³	1	4	yes	—
205	C₂₃×AGL(1,ℤ/8)	C₂³	1	2	yes	—
206	C₂₃×AGL(1,ℤ/8)	C₂³	1	2	yes	—
207	C₂₃×AGL(1,ℤ/8)	C₂³	1	2	yes	—
208	C₂₃×AGL(1,ℤ/8)	C₂³	1	2	yes	complemented
209	C₂₃×#135	—	2	2	no	—
210	C₂₃×#135	—	2	2	no	—
211	C₂₃×#135	—	2	2	no	—
212	C₂₃×#135	—	2	2	no	—
213	C₂₃×#135	—	2	2	no	—
214	C₂₃×#135	—	2	4	no	—
215	C₂₃×#135	—	2	4	no	—
216	C₂₃×#135	—	2	4	no	—
217	C₂₃×#135	—	2	2	no	—
218	C₂₃×#135	—	2	2	no	—
219	C₂₃×#135	—	2	4	no	—
220	C₂₃×#135	—	2	4	no	—
221	C₂₃×#135	—	2	2	no	—
222	C₂₃×#135	—	2	4	no	—
223	C₂₃×#135	—	2	1	no	—
224	C₂₃×#135	—	2	1	no	—
225	C₂₃×#135	—	2	1	no	—
226	C₂₃×#135	—	2	1	no	—
227	C₂₃×#135	D₄	1	2	yes	complemented
228	C₂₃×#135	D₄	1	2	yes	complemented
229	C₂₃×#135	C₂³	1	2	yes	—
230	C₂₃×#135	C₂³	1	2	yes	—
231	C₂₃×#135	C₂³	1	4	yes	—
232	C₂×Q₁₆×C₂₃	—	2	1	no	—
233	C₂×Q₁₆×C₂₃	—	2	1	no	—
234	C₂×Q₁₆×C₂₃	—	2	2	no	—
235	C₂×Q₁₆×C₂₃	—	2	4	no	—
236	C₂×Q₁₆×C₂₃	D₄	1	1	yes	characteristic, complemented
237	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic, complemented
238	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	complemented
239	C₂×SD₁₆×C₂₃	—	2	1	no	—
240	C₂×SD₁₆×C₂₃	—	2	1	no	—
241	C₂×SD₁₆×C₂₃	—	2	1	no	—
242	C₂×SD₁₆×C₂₃	—	2	1	no	—
243	C₂×SD₁₆×C₂₃	—	2	4	no	—
244	C₂×SD₁₆×C₂₃	—	2	4	no	—
245	C₂×SD₁₆×C₂₃	—	2	2	no	—
246	C₂×SD₁₆×C₂₃	—	2	2	no	—
247	C₂×SD₁₆×C₂₃	—	2	4	no	—
248	C₂×SD₁₆×C₂₃	—	2	4	no	—
249	C₂×SD₁₆×C₂₃	—	2	1	no	—
250	C₂×SD₁₆×C₂₃	—	2	1	no	—
251	C₂×SD₁₆×C₂₃	—	2	1	no	—
252	C₂×SD₁₆×C₂₃	—	2	1	no	—
253	C₂×SD₁₆×C₂₃	D₄	1	1	yes	characteristic, complemented
254	C₂×SD₁₆×C₂₃	D₄	1	1	yes	characteristic, complemented
255	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
256	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
257	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
258	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic, complemented
259	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic, complemented
260	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	complemented
261	C₂×D₈×C₂₃	—	2	1	no	—
262	C₂×D₈×C₂₃	—	2	1	no	—
263	C₂×D₈×C₂₃	—	2	2	no	—
264	C₂×D₈×C₂₃	—	2	4	no	—
265	C₂×D₈×C₂₃	D₄	1	1	yes	characteristic, complemented
266	C₂×D₈×C₂₃	C₂³	1	2	yes	—
267	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic, complemented
268	C₂₃×#131	—	2	2	no	—
269	C₂₃×#131	—	2	2	no	—
270	C₂₃×#131	—	2	1	no	—
271	C₂₃×#131	—	2	1	no	—
272	C₂₃×#131	—	2	1	no	—
273	C₂₃×#131	—	2	1	no	—
274	C₂₃×#131	C₂³	1	2	yes	—
275	C₂₃×#131	C₂³	1	2	yes	—
276	C₂₃×#131	C₂³	1	4	yes	—
277	C₂₃×#131	C₂³	1	2	yes	complemented
278	C₂₃×#131	C₂³	1	2	yes	complemented
279	C₂₃×#131	C₂³	1	4	yes	complemented
280	C₂×M₁₆×C₂₃	—	2	2	no	—
281	C₂×M₁₆×C₂₃	—	2	2	no	—
282	C₂×M₁₆×C₂₃	—	2	1	no	—
283	C₂×M₁₆×C₂₃	—	2	1	no	—
284	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
285	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
286	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
287	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
288	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
289	C₂²×C₈×C₂₃	—	2	1	no	—
290	C₂²×C₈×C₂₃	—	2	1	no	—
291	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
292	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
293	C₂₃×#127	C₂³	1	2	yes	—
294	C₂₃×#124	C₂³	1	2	yes	—
295	C₂₃×#124	C₂³	1	2	yes	complemented
296	C₂₃×#123	—	4	1	no	—
297	C₂₃×C₂²⋊Q₈	—	4	1	no	—
298	C₂₃×#121	—	4	1	no	—
299	C₂₃×#120	—	4	1	no	—
300	C₂₃×#117	C₂³	1	1	yes	characteristic
301	C₂₃×#108	C₂³	1	2	yes	complemented
302	C₂₃×#108	C₂³	1	2	yes	complemented
303	C₂₃×#108	C₂³	1	4	yes	complemented
304	C₂₃×#104	C₂³	1	4	yes	—
305	C₂₃×#104	C₂³	1	4	yes	—
306	C₂₃×#104	C₂³	1	4	yes	complemented
307	C₂₃×#104	C₂³	1	4	yes	complemented
308	C₂₃×#101	C₂³	1	4	yes	complemented
309	C₂₃×#101	C₂³	1	2	yes	complemented
310	C₂₃×#101	C₂³	1	2	yes	complemented
311	C₂₃×#100	C₂³	1	4	yes	—
312	C₂₃×#100	C₂³	1	2	yes	complemented
313	C₂₃×#100	C₂³	1	2	yes	complemented
314	C₂₃×#97	C₂³	1	2	yes	complemented
315	C₄×C₈×C₂₃	C₂³	1	2	yes	complemented
316	C₂⁴×C₂₃	—	2	1	no	—
317	C₂⁴×C₂₃	—	4	1	no	—
318	#41×C₂₃	—	2	1	no	—
319	#41×C₂₃	—	2	1	no	—
320	#41×C₂₃	—	2	1	no	—
321	#41×C₂₃	—	2	1	no	—
322	#41×C₂₃	—	2	1	no	—
323	#41×C₂₃	—	2	1	no	—
324	#41×C₂₃	—	2	1	no	—
325	#41×C₂₃	—	2	1	no	—
326	#41×C₂₃	—	2	2	no	—
327	#41×C₂₃	—	2	4	no	—
328	#41×C₂₃	—	2	2	no	—
329	#41×C₂₃	—	2	2	no	—
330	#41×C₂₃	—	2	4	no	—
331	#41×C₂₃	—	2	2	no	—
332	#41×C₂₃	—	2	2	no	—
333	#41×C₂₃	—	2	4	no	—
334	#41×C₂₃	—	2	2	no	—
335	#41×C₂₃	—	2	2	no	—
336	#41×C₂₃	—	2	4	no	—
337	#41×C₂₃	—	2	2	no	—
338	#41×C₂₃	—	2	1	no	—
339	#41×C₂₃	—	2	1	no	—
340	#41×C₂₃	—	2	1	no	—
341	#41×C₂₃	—	2	1	no	—
342	#41×C₂₃	—	2	1	no	—
343	#41×C₂₃	—	2	1	no	—
344	#41×C₂₃	—	2	1	no	—
345	#41×C₂₃	—	2	1	no	—
346	#41×C₂₃	—	4	2	no	—
347	#41×C₂₃	—	4	2	no	—
348	#41×C₂₃	—	4	2	no	—
349	#41×C₂₃	—	4	2	no	—
350	#41×C₂₃	—	4	4	no	—
351	#41×C₂₃	—	4	2	no	—
352	#41×C₂₃	—	4	2	no	—
353	#41×C₂₃	—	4	2	no	—
354	#41×C₂₃	—	4	2	no	—
355	#41×C₂₃	—	4	2	no	—
356	#41×C₂₃	—	4	2	no	—
357	#41×C₂₃	—	4	2	no	—
358	#41×C₂₃	—	4	2	no	—
359	#41×C₂₃	—	4	4	no	—
360	#41×C₂₃	—	4	1	no	—
361	#41×C₂₃	—	4	1	no	—
362	#41×C₂₃	—	4	1	no	—
363	#41×C₂₃	—	4	1	no	—
364	#41×C₂₃	C₂×D₄	1	2	yes	—
365	#41×C₂₃	C₂×D₄	1	2	yes	—
366	#41×C₂₃	C₂×D₄	1	2	yes	—
367	#41×C₂₃	C₂×D₄	1	2	yes	—
368	#41×C₂₃	C₂⁴	1	2	yes	—
369	#41×C₂₃	C₂⁴	1	2	yes	—
370	#41×C₂₃	C₂⁴	1	2	yes	—
371	#41×C₂₃	C₂⁴	1	2	yes	—
372	C₂×Q₈×C₂₃	—	2	1	no	—
373	C₂×Q₈×C₂₃	—	2	4	no	—
374	C₂×Q₈×C₂₃	—	2	2	no	—
375	C₂×Q₈×C₂₃	—	2	4	no	—
376	C₂×Q₈×C₂₃	—	2	2	no	—
377	C₂×Q₈×C₂₃	—	2	2	no	—
378	C₂×Q₈×C₂₃	—	2	2	no	—
379	C₂×Q₈×C₂₃	—	2	1	no	—
380	C₂×Q₈×C₂₃	—	2	1	no	—
381	C₂×Q₈×C₂₃	—	2	1	no	—
382	C₂×Q₈×C₂₃	—	2	1	no	—
383	C₂×Q₈×C₂₃	—	4	1	no	—
384	C₂×Q₈×C₂₃	—	4	2	no	—
385	C₂×Q₈×C₂₃	—	4	2	no	—
386	C₂×Q₈×C₂₃	—	4	1	no	—
387	C₂×Q₈×C₂₃	—	4	1	no	—
388	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
389	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
390	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
391	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
392	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
393	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
394	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₂×D₄×C₂₃	—	2	1	no	—
396	C₂×D₄×C₂₃	—	2	1	no	—
397	C₂×D₄×C₂₃	—	2	1	no	—
398	C₂×D₄×C₂₃	—	2	1	no	—
399	C₂×D₄×C₂₃	—	2	2	no	—
400	C₂×D₄×C₂₃	—	2	4	no	—
401	C₂×D₄×C₂₃	—	2	2	no	—
402	C₂×D₄×C₂₃	—	2	2	no	—
403	C₂×D₄×C₂₃	—	2	4	no	—
404	C₂×D₄×C₂₃	—	2	2	no	—
405	C₂×D₄×C₂₃	—	2	1	no	—
406	C₂×D₄×C₂₃	—	2	1	no	—
407	C₂×D₄×C₂₃	—	2	1	no	—
408	C₂×D₄×C₂₃	—	2	1	no	—
409	C₂×D₄×C₂₃	—	2	1	no	—
410	C₂×D₄×C₂₃	—	2	1	no	—
411	C₂×D₄×C₂₃	—	2	1	no	—
412	C₂×D₄×C₂₃	—	4	2	no	—
413	C₂×D₄×C₂₃	—	4	2	no	—
414	C₂×D₄×C₂₃	—	4	1	no	—
415	C₂×D₄×C₂₃	—	4	1	no	—
416	C₂×D₄×C₂₃	—	4	2	no	—
417	C₂×D₄×C₂₃	—	4	4	no	—
418	C₂×D₄×C₂₃	—	4	2	no	—
419	C₂×D₄×C₂₃	—	4	2	no	—
420	C₂×D₄×C₂₃	—	4	4	no	—
421	C₂×D₄×C₂₃	—	4	1	no	—
422	C₂×D₄×C₂₃	—	4	1	no	—
423	C₂×D₄×C₂₃	—	4	2	no	—
424	C₂×D₄×C₂₃	—	4	2	no	—
425	C₂×D₄×C₂₃	—	4	2	no	—
426	C₂×D₄×C₂₃	—	4	2	no	—
427	C₂×D₄×C₂₃	—	4	1	no	—
428	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
429	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
430	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
431	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
432	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
433	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
434	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₂₃	—	2	1	no	—
436	C₂²×C₄×C₂₃	—	2	1	no	—
437	C₂²×C₄×C₂₃	—	2	1	no	—
438	C₂²×C₄×C₂₃	—	2	1	no	—
439	C₂²×C₄×C₂₃	—	2	1	no	—
440	C₂²×C₄×C₂₃	—	2	1	no	—
441	C₂²×C₄×C₂₃	—	2	1	no	—
442	C₂²×C₄×C₂₃	—	4	1	no	—
443	C₂²×C₄×C₂₃	—	4	2	no	—
444	C₂²×C₄×C₂₃	—	4	2	no	—
445	C₂²×C₄×C₂₃	—	4	1	no	—
446	C₂²×C₄×C₂₃	—	4	1	no	—
447	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
448	Q₁₆×C₂₃	—	2	2	no	—
449	Q₁₆×C₂₃	—	2	4	no	—
450	Q₁₆×C₂₃	—	2	4	no	—
451	Q₁₆×C₂₃	—	2	2	no	—
452	Q₁₆×C₂₃	—	2	2	no	—
453	Q₁₆×C₂₃	—	2	2	no	—
454	Q₁₆×C₂₃	—	2	1	no	—
455	Q₁₆×C₂₃	—	2	4	no	—
456	Q₁₆×C₂₃	—	2	1	no	—
457	Q₁₆×C₂₃	C₂×D₄	1	2	yes	—
458	Q₁₆×C₂₃	C₂×D₄	1	4	yes	—
459	Q₁₆×C₂₃	C₂×D₄	1	2	yes	—
460	SD₁₆×C₂₃	—	2	4	no	—
461	SD₁₆×C₂₃	—	2	4	no	—
462	SD₁₆×C₂₃	—	2	2	no	—
463	SD₁₆×C₂₃	—	2	2	no	—
464	SD₁₆×C₂₃	—	2	2	no	—
465	SD₁₆×C₂₃	—	2	2	no	—
466	SD₁₆×C₂₃	—	2	4	no	—
467	SD₁₆×C₂₃	—	2	2	no	—
468	SD₁₆×C₂₃	—	2	4	no	—
469	SD₁₆×C₂₃	—	2	2	no	—
470	SD₁₆×C₂₃	—	2	2	no	—
471	SD₁₆×C₂₃	—	2	2	no	—
472	SD₁₆×C₂₃	—	2	2	no	—
473	SD₁₆×C₂₃	—	2	2	no	—
474	SD₁₆×C₂₃	—	2	2	no	—
475	SD₁₆×C₂₃	—	2	2	no	—
476	SD₁₆×C₂₃	—	2	1	no	—
477	SD₁₆×C₂₃	—	2	1	no	—
478	SD₁₆×C₂₃	—	2	4	no	—
479	SD₁₆×C₂₃	—	2	4	no	—
480	SD₁₆×C₂₃	—	2	1	no	—
481	SD₁₆×C₂₃	—	2	1	no	—
482	SD₁₆×C₂₃	C₂×D₄	1	2	yes	—
483	SD₁₆×C₂₃	C₂×D₄	1	2	yes	—
484	SD₁₆×C₂₃	C₂×D₄	1	2	yes	—
485	SD₁₆×C₂₃	C₂×D₄	1	4	yes	—
486	SD₁₆×C₂₃	C₂×D₄	1	4	yes	—
487	SD₁₆×C₂₃	C₂×D₄	1	2	yes	—
488	D₈×C₂₃	—	2	2	no	—
489	D₈×C₂₃	—	2	4	no	—
490	D₈×C₂₃	—	2	2	no	—
491	D₈×C₂₃	—	2	4	no	—
492	D₈×C₂₃	—	2	2	no	—
493	D₈×C₂₃	—	2	2	no	—
494	D₈×C₂₃	—	2	1	no	—
495	D₈×C₂₃	—	2	4	no	—
496	D₈×C₂₃	—	2	1	no	—
497	D₈×C₂₃	C₂×D₄	1	2	yes	—
498	D₈×C₂₃	C₂×D₄	1	4	yes	—
499	D₈×C₂₃	C₂×D₄	1	2	yes	—
500	M₁₆×C₂₃	—	2	1	no	—
501	M₁₆×C₂₃	—	2	1	no	—
502	M₁₆×C₂₃	—	2	1	no	—
503	M₁₆×C₂₃	—	2	1	no	—
504	M₁₆×C₂₃	—	2	4	no	—
505	M₁₆×C₂₃	—	2	2	no	—
506	M₁₆×C₂₃	—	2	2	no	—
507	M₁₆×C₂₃	—	2	2	no	—
508	M₁₆×C₂₃	—	2	2	no	—
509	M₁₆×C₂₃	—	2	4	no	—
510	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
511	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
512	M₁₆×C₂₃	C₂⁴	1	2	yes	—
513	M₁₆×C₂₃	C₂⁴	1	2	yes	—
514	M₁₆×C₂₃	C₂⁴	1	2	yes	—
515	M₁₆×C₂₃	C₂⁴	1	2	yes	—
516	C₂×C₈×C₂₃	—	2	1	no	—
517	C₂×C₈×C₂₃	—	2	1	no	—
518	C₂×C₈×C₂₃	—	2	1	no	—
519	C₂×C₈×C₂₃	—	2	1	no	—
520	C₂×C₈×C₂₃	—	2	2	no	—
521	C₂×C₈×C₂₃	—	2	2	no	—
522	C₂×C₈×C₂₃	—	2	2	no	—
523	C₂×C₈×C₂₃	—	2	2	no	—
524	C₂×C₈×C₂₃	—	2	4	no	—
525	C₂×C₈×C₂₃	—	2	4	no	—
526	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
527	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
528	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
529	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
530	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
531	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
532	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
533	C₄⋊C₄×C₂₃	—	2	1	no	—
534	C₄⋊C₄×C₂₃	—	4	2	no	—
535	C₂²⋊C₄×C₂₃	—	2	1	no	—
536	C₂²⋊C₄×C₂₃	—	4	2	no	—
537	C₂²⋊C₄×C₂₃	—	4	2	no	—
538	C₄²×C₂₃	C₂⁴	1	2	yes	—
539	#61107	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
540	C₂³×C₂₃	—	2	1	no	—
541	C₂³×C₂₃	—	2	1	no	—
542	C₂³×C₂₃	—	2	1	no	—
543	C₂³×C₂₃	—	2	1	no	—
544	C₂³×C₂₃	—	2	1	no	—
545	C₂³×C₂₃	—	2	2	no	—
546	C₂³×C₂₃	—	2	1	no	—
547	C₂³×C₂₃	—	4	2	no	—
548	C₂³×C₂₃	—	4	2	no	—
549	C₂³×C₂₃	—	4	4	no	—
550	C₂³×C₂₃	—	4	1	no	—
551	C₂³×C₂₃	—	4	1	no	—
552	C₂³×C₂₃	—	16	1	no	—
553	C₂³×C₂₃	—	16	2	no	—
554	C₂³×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
555	Q₈×C₂₃	—	2	1	no	—
556	Q₈×C₂₃	—	2	1	no	—
557	Q₈×C₂₃	—	2	1	no	—
558	Q₈×C₂₃	—	2	1	no	—
559	Q₈×C₂₃	—	2	2	no	—
560	Q₈×C₂₃	—	2	1	no	—
561	Q₈×C₂₃	—	2	2	no	—
562	Q₈×C₂₃	—	2	1	no	—
563	Q₈×C₂₃	—	2	1	no	—
564	Q₈×C₂₃	—	2	1	no	—
565	Q₈×C₂₃	—	4	4	no	—
566	Q₈×C₂₃	—	4	2	no	—
567	Q₈×C₂₃	—	4	2	no	—
568	Q₈×C₂₃	—	4	1	no	—
569	Q₈×C₂₃	—	4	1	no	—
570	Q₈×C₂₃	C₂²×D₄	1	2	yes	—
571	Q₈×C₂₃	C₂²×D₄	1	2	yes	—
572	Q₈×C₂₃	C₂²×D₄	1	2	yes	—
573	Q₈×C₂₃	C₂²×D₄	1	2	yes	—
574	D₄×C₂₃	—	2	2	no	—
575	D₄×C₂₃	—	2	2	no	—
576	D₄×C₂₃	—	2	2	no	—
577	D₄×C₂₃	—	2	2	no	—
578	D₄×C₂₃	—	2	2	no	—
579	D₄×C₂₃	—	2	2	no	—
580	D₄×C₂₃	—	2	2	no	—
581	D₄×C₂₃	—	2	2	no	—
582	D₄×C₂₃	—	2	1	no	—
583	D₄×C₂₃	—	2	1	no	—
584	D₄×C₂₃	—	2	1	no	—
585	D₄×C₂₃	—	2	1	no	—
586	D₄×C₂₃	—	2	1	no	—
587	D₄×C₂₃	—	2	2	no	—
588	D₄×C₂₃	—	2	1	no	—
589	D₄×C₂₃	—	2	1	no	—
590	D₄×C₂₃	—	2	2	no	—
591	D₄×C₂₃	—	2	1	no	—
592	D₄×C₂₃	—	4	4	no	—
593	D₄×C₂₃	—	4	4	no	—
594	D₄×C₂₃	—	4	2	no	—
595	D₄×C₂₃	—	4	2	no	—
596	D₄×C₂₃	—	4	2	no	—
597	D₄×C₂₃	—	4	2	no	—
598	D₄×C₂₃	—	4	2	no	—
599	D₄×C₂₃	—	4	2	no	—
600	D₄×C₂₃	—	4	4	no	—
601	D₄×C₂₃	—	4	1	no	—
602	D₄×C₂₃	—	4	1	no	—
603	D₄×C₂₃	—	4	1	no	—
604	D₄×C₂₃	—	4	1	no	—
605	D₄×C₂₃	—	4	1	no	—
606	D₄×C₂₃	—	4	1	no	—
607	D₄×C₂₃	—	16	2	no	—
608	D₄×C₂₃	C₂²×D₄	1	2	yes	—
609	D₄×C₂₃	C₂²×D₄	1	2	yes	—
610	D₄×C₂₃	C₂²×D₄	1	2	yes	—
611	D₄×C₂₃	C₂²×D₄	1	2	yes	—
612	C₂×C₄×C₂₃	—	2	1	no	—
613	C₂×C₄×C₂₃	—	2	1	no	—
614	C₂×C₄×C₂₃	—	2	1	no	—
615	C₂×C₄×C₂₃	—	2	1	no	—
616	C₂×C₄×C₂₃	—	2	2	no	—
617	C₂×C₄×C₂₃	—	2	2	no	—
618	C₂×C₄×C₂₃	—	2	2	no	—
619	C₂×C₄×C₂₃	—	2	2	no	—
620	C₂×C₄×C₂₃	—	2	2	no	—
621	C₂×C₄×C₂₃	—	2	2	no	—
622	C₂×C₄×C₂₃	—	2	2	no	—
623	C₂×C₄×C₂₃	—	2	2	no	—
624	C₂×C₄×C₂₃	—	2	2	no	—
625	C₂×C₄×C₂₃	—	2	1	no	—
626	C₂×C₄×C₂₃	—	2	2	no	—
627	C₂×C₄×C₂₃	—	2	1	no	—
628	C₂×C₄×C₂₃	—	4	4	no	—
629	C₂×C₄×C₂₃	—	4	2	no	—
630	C₂×C₄×C₂₃	—	4	2	no	—
631	C₂×C₄×C₂₃	—	4	2	no	—
632	C₂×C₄×C₂₃	—	4	2	no	—
633	C₂×C₄×C₂₃	—	4	2	no	—
634	C₂×C₄×C₂₃	—	4	2	no	—
635	C₂×C₄×C₂₃	—	4	4	no	—
636	C₂×C₄×C₂₃	—	4	4	no	—
637	C₂×C₄×C₂₃	—	4	1	no	—
638	C₂×C₄×C₂₃	—	4	1	no	—
639	C₂×C₄×C₂₃	—	4	1	no	—
640	C₂×C₄×C₂₃	—	4	1	no	—
641	C₂×C₄×C₂₃	—	4	1	no	—
642	C₂×C₄×C₂₃	—	4	1	no	—
643	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
644	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
646	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
647	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
648	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
649	C₈×C₂₃	—	2	2	no	—
650	C₈×C₂₃	—	2	2	no	—
651	C₈×C₂₃	—	2	2	no	—
652	C₈×C₂₃	—	2	2	no	—
653	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
654	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
655	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
656	C₈×C₂₃	C₂²×D₄	1	4	yes	—
657	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
658	#3586	C₂×C₂₃	1	1	yes	characteristic, complemented
659	#3585	C₂×C₂₃	1	1	yes	characteristic, complemented
660	#3584	C₂×C₂₃	1	1	yes	characteristic, complemented
661	C₂×#577	C₂×C₂₃	1	1	yes	characteristic, complemented
662	#3291	C₂×C₂₃	1	4	yes	complemented
663	#3290	C₂×C₂₃	1	4	yes	complemented
664	#3289	C₂×C₂₃	1	4	yes	complemented
665	#3288	C₂×C₂₃	1	4	yes	complemented
666	#3154	C₂×C₂₃	1	1	yes	characteristic, complemented
667	#3069	C₂×C₂₃	1	1	yes	characteristic, complemented
668	#3068	C₂×C₂₃	1	1	yes	characteristic, complemented
669	#3067	C₂×C₂₃	1	1	yes	characteristic, complemented
670	C₂×#471	C₂×C₂₃	1	1	yes	characteristic, complemented
671	#3022	C₂×C₂₃	1	1	yes	characteristic, complemented
672	#3021	C₂×C₂₃	1	1	yes	characteristic, complemented
673	#3020	C₂×C₂₃	1	1	yes	characteristic, complemented
674	#3019	C₂×C₂₃	1	1	yes	characteristic, complemented
675	#2957	C₂×C₂₃	1	1	yes	characteristic, complemented
676	#2955	C₂×C₂₃	1	1	yes	characteristic, complemented
677	C₂²×C₂₃	—	2	2	no	—
678	C₂²×C₂₃	—	2	2	no	—
679	C₂²×C₂₃	—	2	2	no	—
680	C₂²×C₂₃	—	2	2	no	—
681	C₂²×C₂₃	—	4	1	no	—
682	C₂²×C₂₃	—	4	2	no	—
683	C₂²×C₂₃	—	4	1	no	—
684	C₂²×C₂₃	—	4	1	no	—
685	C₂²×C₂₃	—	4	2	no	—
686	C₂²×C₂₃	—	8	1	no	—
687	C₂²×C₂₃	—	8	1	no	—
688	C₂²×C₂₃	—	8	1	no	—
689	C₂²×C₂₃	—	8	1	no	—
690	C₂²×C₂₃	—	8	2	no	—
691	C₂²×C₂₃	—	8	1	no	—
692	C₂²×C₂₃	—	8	2	no	—
693	C₂²×C₂₃	—	16	1	no	—
694	C₂²×C₂₃	—	16	2	no	—
695	C₂²×C₂₃	—	16	2	no	—
696	C₂²×C₂₃	—	16	4	no	—
697	C₂²×C₂₃	D₄²	1	1	yes	characteristic
698	C₂²×C₂₃	D₄²	1	1	yes	characteristic
699	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
700	C₄×C₂₃	—	2	2	no	—
701	C₄×C₂₃	—	2	2	no	—
702	C₄×C₂₃	—	2	2	no	—
703	C₄×C₂₃	—	2	2	no	—
704	C₄×C₂₃	—	4	2	no	—
705	C₄×C₂₃	—	4	1	no	—
706	C₄×C₂₃	—	4	1	no	—
707	C₄×C₂₃	—	4	2	no	—
708	C₄×C₂₃	D₄²	1	1	yes	characteristic
709	C₄×C₂₃	D₄²	1	1	yes	characteristic
710	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
711	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
712	#585	C₂²×C₂₃	1	1	yes	characteristic
713	#585	C₂²×C₂₃	1	1	yes	characteristic, complemented
714	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic, complemented
715	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic, complemented
716	#578	—	2	2	no	—
717	#578	—	2	1	no	—
718	#578	C₂²×C₂₃	1	2	yes	complemented
719	#578	C₂²×C₂₃	1	4	yes	complemented
720	#577	—	2	2	no	—
721	#577	—	2	2	no	—
722	#577	—	2	2	no	—
723	#577	—	2	2	no	—
724	#577	—	2	1	no	—
725	#577	—	2	1	no	—
726	#577	C₂²×C₂₃	1	4	yes	complemented
727	#577	C₂²×C₂₃	1	4	yes	complemented
728	#577	C₂²×C₂₃	1	4	yes	complemented
729	#577	C₂²×C₂₃	1	2	yes	complemented
730	#577	C₂²×C₂₃	1	4	yes	complemented
731	#577	C₂²×C₂₃	1	2	yes	complemented
732	#576	—	2	2	no	—
733	#576	—	2	1	no	—
734	#576	C₂²×C₂₃	1	4	yes	complemented
735	#576	C₂²×C₂₃	1	2	yes	complemented
736	#575	—	2	2	no	—
737	#575	—	2	2	no	—
738	#575	—	2	2	no	—
739	#575	C₂²×C₂₃	1	1	yes	characteristic
740	#575	C₂²×C₂₃	1	1	yes	characteristic
741	#575	C₂²×C₂₃	1	1	yes	characteristic, complemented
742	#575	C₂²×C₂₃	1	1	yes	characteristic, complemented
743	#575	C₂²×C₂₃	1	1	yes	characteristic, complemented
744	C₂×#137	—	2	2	no	—
745	C₂×#137	—	2	1	no	—
746	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
747	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
748	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
749	C₂×AGL(1,ℤ/8)	—	2	2	no	—
750	C₂×AGL(1,ℤ/8)	—	2	1	no	—
751	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
752	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
753	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
754	C₂×#135	—	2	2	no	—
755	C₂×#135	—	2	1	no	—
756	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
757	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic, complemented
758	C₂²×SD₁₆	—	2	1	no	—
759	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
760	#568	C₂²×C₂₃	1	1	yes	characteristic, complemented
761	#568	C₂²×C₂₃	1	1	yes	characteristic, complemented
762	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
763	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
764	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
765	#535	C₂²×C₂₃	1	1	yes	characteristic, complemented
766	#497	C₂²×C₂₃	1	2	yes	complemented
767	#496	C₂²×C₂₃	1	2	yes	complemented
768	#495	C₂²×C₂₃	1	2	yes	complemented
769	#492	C₂²×C₂₃	1	2	yes	complemented
770	#473	C₂²×C₂₃	1	2	yes	complemented
771	#473	C₂²×C₂₃	1	4	yes	complemented
772	#472	C₂²×C₂₃	1	4	yes	complemented
773	#472	C₂²×C₂₃	1	2	yes	complemented
774	#471	C₂²×C₂₃	1	4	yes	complemented
775	#471	C₂²×C₂₃	1	4	yes	complemented
776	#471	C₂²×C₂₃	1	4	yes	complemented
777	#471	C₂²×C₂₃	1	4	yes	complemented
778	#471	C₂²×C₂₃	1	2	yes	complemented
779	#471	C₂²×C₂₃	1	2	yes	complemented
780	#456	C₂²×C₂₃	1	4	yes	complemented
781	#456	C₂²×C₂₃	1	4	yes	complemented
782	#455	C₂²×C₂₃	1	4	yes	complemented
783	#455	C₂²×C₂₃	1	4	yes	complemented
784	#454	C₂²×C₂₃	1	4	yes	complemented
785	#454	C₂²×C₂₃	1	4	yes	complemented
786	#453	C₂²×C₂₃	1	4	yes	complemented
787	#453	C₂²×C₂₃	1	4	yes	complemented
788	#444	C₂²×C₂₃	1	4	yes	complemented
789	#444	C₂²×C₂₃	1	4	yes	complemented
790	#443	C₂²×C₂₃	1	4	yes	complemented
791	#443	C₂²×C₂₃	1	4	yes	complemented
792	#430	C₂²×C₂₃	1	1	yes	characteristic, complemented
793	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic, complemented
794	#421	C₂²×C₂₃	1	1	yes	characteristic, complemented
795	#421	C₂²×C₂₃	1	1	yes	characteristic, complemented
796	#421	C₂²×C₂₃	1	1	yes	characteristic, complemented
797	#421	C₂²×C₂₃	1	1	yes	characteristic, complemented
798	#413	C₂²×C₂₃	1	1	yes	characteristic, complemented
799	#413	C₂²×C₂₃	1	1	yes	characteristic, complemented
800	C₂×#101	C₂²×C₂₃	1	1	yes	characteristic, complemented
801	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic, complemented
802	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
803	C₂×C₂₃	—	2	1	no	—
804	C₂×C₂₃	—	2	1	no	—
805	C₂×C₂₃	—	2	1	no	—
806	C₂×C₂₃	—	4	2	no	—
807	C₂×C₂₃	—	4	2	no	—
808	C₂×C₂₃	—	4	2	no	—
809	C₂×C₂₃	—	4	2	no	—
810	C₂×C₂₃	—	8	2	no	—
811	C₂×C₂₃	—	8	1	no	—
812	C₂×C₂₃	—	8	1	no	—
813	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
814	2₋¹⁺⁴	—	2	2	no	—
815	2₋¹⁺⁴	—	2	2	no	—
816	2₋¹⁺⁴	—	2	1	no	—
817	2₋¹⁺⁴	—	2	1	no	—
818	2₋¹⁺⁴	—	2	1	no	—
819	2₋¹⁺⁴	—	2	1	no	—
820	2₋¹⁺⁴	—	4	1	no	—
821	2₋¹⁺⁴	C₂³×C₂₃	1	4	yes	—
822	2₋¹⁺⁴	C₂³×C₂₃	1	2	yes	—
823	2₋¹⁺⁴	C₂³×C₂₃	1	2	yes	complemented
824	H(5,𝔽₂)	—	2	2	no	—
825	H(5,𝔽₂)	—	2	2	no	—
826	H(5,𝔽₂)	—	2	1	no	—
827	H(5,𝔽₂)	—	2	1	no	—
828	H(5,𝔽₂)	—	2	1	no	—
829	H(5,𝔽₂)	—	2	1	no	—
830	H(5,𝔽₂)	—	4	1	no	—
831	H(5,𝔽₂)	—	4	1	no	—
832	H(5,𝔽₂)	—	4	1	no	—
833	H(5,𝔽₂)	C₂³×C₂₃	1	2	yes	—
834	H(5,𝔽₂)	C₂³×C₂₃	1	4	yes	—
835	H(5,𝔽₂)	C₂³×C₂₃	1	2	yes	complemented
836	C₂×#41	—	2	2	no	—
837	C₂×#41	—	2	2	no	—
838	C₂×#41	—	2	2	no	—
839	C₂×#41	—	2	2	no	—
840	C₂×#41	—	2	1	no	—
841	C₂×#41	—	2	1	no	—
842	C₂×#41	—	2	1	no	—
843	C₂×#41	—	2	1	no	—
844	C₂×#41	—	4	1	no	—
845	C₂×#41	—	4	1	no	—
846	C₂×#41	—	4	1	no	—
847	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
848	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
849	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
850	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
851	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
852	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
853	C₂²×Q₈	—	2	1	no	—
854	C₂²×Q₈	—	2	1	no	—
855	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
856	C₂²×D₄	—	2	1	no	—
857	C₂²×D₄	—	2	1	no	—
858	C₂²×D₄	—	4	1	no	—
859	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
860	#137	—	2	2	no	—
861	#137	—	2	2	no	—
862	#137	—	2	1	no	—
863	#137	—	2	1	no	—
864	#137	—	2	1	no	—
865	#137	—	2	1	no	—
866	#137	—	2	4	no	—
867	#137	—	2	4	no	—
868	#137	—	2	4	no	—
869	#137	—	2	4	no	—
870	#137	—	2	2	no	—
871	#137	—	2	2	no	—
872	#137	—	2	4	no	—
873	#137	—	2	2	no	—
874	#137	—	2	2	no	—
875	#137	—	2	4	no	—
876	#137	—	2	2	no	—
877	#137	—	2	2	no	—
878	#137	D₄×C₂₃	1	2	yes	complemented
879	#137	D₄×C₂₃	1	2	yes	complemented
880	#137	C₂³×C₂₃	1	4	yes	—
881	#137	C₂³×C₂₃	1	2	yes	—
882	#137	C₂³×C₂₃	1	2	yes	—
883	#137	C₂³×C₂₃	1	2	yes	—
884	#137	C₂³×C₂₃	1	4	yes	complemented
885	#137	C₂³×C₂₃	1	2	yes	complemented
886	AGL(1,ℤ/8)	—	2	2	no	—
887	AGL(1,ℤ/8)	—	2	2	no	—
888	AGL(1,ℤ/8)	—	2	1	no	—
889	AGL(1,ℤ/8)	—	2	1	no	—
890	AGL(1,ℤ/8)	—	2	1	no	—
891	AGL(1,ℤ/8)	—	2	1	no	—
892	AGL(1,ℤ/8)	—	2	4	no	—
893	AGL(1,ℤ/8)	—	2	4	no	—
894	AGL(1,ℤ/8)	—	2	2	no	—
895	AGL(1,ℤ/8)	—	2	2	no	—
896	AGL(1,ℤ/8)	—	2	4	no	—
897	AGL(1,ℤ/8)	—	2	4	no	—
898	AGL(1,ℤ/8)	—	2	4	no	—
899	AGL(1,ℤ/8)	—	2	2	no	—
900	AGL(1,ℤ/8)	—	2	2	no	—
901	AGL(1,ℤ/8)	—	2	4	no	—
902	AGL(1,ℤ/8)	—	2	2	no	—
903	AGL(1,ℤ/8)	—	2	2	no	—
904	AGL(1,ℤ/8)	D₄×C₂₃	1	2	yes	complemented
905	AGL(1,ℤ/8)	D₄×C₂₃	1	2	yes	complemented
906	AGL(1,ℤ/8)	C₂³×C₂₃	1	4	yes	—
907	AGL(1,ℤ/8)	C₂³×C₂₃	1	4	yes	—
908	AGL(1,ℤ/8)	C₂³×C₂₃	1	2	yes	—
909	AGL(1,ℤ/8)	C₂³×C₂₃	1	2	yes	—
910	AGL(1,ℤ/8)	C₂³×C₂₃	1	2	yes	—
911	AGL(1,ℤ/8)	C₂³×C₂₃	1	2	yes	complemented
912	#135	—	2	2	no	—
913	#135	—	2	2	no	—
914	#135	—	2	2	no	—
915	#135	—	2	2	no	—
916	#135	—	2	2	no	—
917	#135	—	2	4	no	—
918	#135	—	2	4	no	—
919	#135	—	2	4	no	—
920	#135	—	2	2	no	—
921	#135	—	2	2	no	—
922	#135	—	2	4	no	—
923	#135	—	2	4	no	—
924	#135	—	2	2	no	—
925	#135	—	2	4	no	—
926	#135	—	2	1	no	—
927	#135	—	2	1	no	—
928	#135	—	2	1	no	—
929	#135	—	2	1	no	—
930	#135	D₄×C₂₃	1	2	yes	complemented
931	#135	D₄×C₂₃	1	2	yes	complemented
932	#135	C₂³×C₂₃	1	2	yes	—
933	#135	C₂³×C₂₃	1	2	yes	—
934	#135	C₂³×C₂₃	1	4	yes	—
935	C₂×Q₁₆	—	2	1	no	—
936	C₂×Q₁₆	—	2	1	no	—
937	C₂×Q₁₆	—	2	2	no	—
938	C₂×Q₁₆	—	2	4	no	—
939	C₂×Q₁₆	D₄×C₂₃	1	1	yes	characteristic, complemented
940	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic, complemented
941	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	complemented
942	C₂×SD₁₆	—	2	1	no	—
943	C₂×SD₁₆	—	2	1	no	—
944	C₂×SD₁₆	—	2	1	no	—
945	C₂×SD₁₆	—	2	1	no	—
946	C₂×SD₁₆	—	2	4	no	—
947	C₂×SD₁₆	—	2	4	no	—
948	C₂×SD₁₆	—	2	2	no	—
949	C₂×SD₁₆	—	2	2	no	—
950	C₂×SD₁₆	—	2	4	no	—
951	C₂×SD₁₆	—	2	4	no	—
952	C₂×SD₁₆	—	2	1	no	—
953	C₂×SD₁₆	—	2	1	no	—
954	C₂×SD₁₆	—	2	1	no	—
955	C₂×SD₁₆	—	2	1	no	—
956	C₂×SD₁₆	D₄×C₂₃	1	1	yes	characteristic, complemented
957	C₂×SD₁₆	D₄×C₂₃	1	1	yes	characteristic, complemented
958	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
959	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
960	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
961	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic, complemented
962	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic, complemented
963	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	complemented
964	C₂×D₈	—	2	1	no	—
965	C₂×D₈	—	2	1	no	—
966	C₂×D₈	—	2	2	no	—
967	C₂×D₈	—	2	4	no	—
968	C₂×D₈	D₄×C₂₃	1	1	yes	characteristic, complemented
969	C₂×D₈	C₂³×C₂₃	1	2	yes	—
970	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
971	#131	—	2	2	no	—
972	#131	—	2	2	no	—
973	#131	—	2	1	no	—
974	#131	—	2	1	no	—
975	#131	—	2	1	no	—
976	#131	—	2	1	no	—
977	#131	C₂³×C₂₃	1	2	yes	—
978	#131	C₂³×C₂₃	1	2	yes	—
979	#131	C₂³×C₂₃	1	4	yes	—
980	#131	C₂³×C₂₃	1	2	yes	complemented
981	#131	C₂³×C₂₃	1	2	yes	complemented
982	#131	C₂³×C₂₃	1	4	yes	complemented
983	C₂×M₁₆	—	2	2	no	—
984	C₂×M₁₆	—	2	2	no	—
985	C₂×M₁₆	—	2	1	no	—
986	C₂×M₁₆	—	2	1	no	—
987	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
988	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
989	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
990	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
991	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
992	C₂²×C₈	—	2	1	no	—
993	C₂²×C₈	—	2	1	no	—
994	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
995	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
996	#127	C₂³×C₂₃	1	2	yes	—
997	#124	C₂³×C₂₃	1	2	yes	—
998	#124	C₂³×C₂₃	1	2	yes	complemented
999	#123	—	4	1	no	—
1000	C₂²⋊Q₈	—	4	1	no	—
1001	#121	—	4	1	no	—
1002	#120	—	4	1	no	—
1003	#117	C₂³×C₂₃	1	1	yes	characteristic
1004	#108	C₂³×C₂₃	1	2	yes	complemented
1005	#108	C₂³×C₂₃	1	2	yes	complemented
1006	#108	C₂³×C₂₃	1	4	yes	complemented
1007	#104	C₂³×C₂₃	1	4	yes	—
1008	#104	C₂³×C₂₃	1	4	yes	—
1009	#104	C₂³×C₂₃	1	4	yes	complemented
1010	#104	C₂³×C₂₃	1	4	yes	complemented
1011	#101	C₂³×C₂₃	1	4	yes	complemented
1012	#101	C₂³×C₂₃	1	2	yes	complemented
1013	#101	C₂³×C₂₃	1	2	yes	complemented
1014	#100	C₂³×C₂₃	1	4	yes	—
1015	#100	C₂³×C₂₃	1	2	yes	complemented
1016	#100	C₂³×C₂₃	1	2	yes	complemented
1017	#97	C₂³×C₂₃	1	2	yes	complemented
1018	C₄×C₈	C₂³×C₂₃	1	2	yes	complemented
1019	C₂₃	#61107	1	1	yes	characteristic, direct product factor, Sylow
1020	C₂⁴	—	2	1	no	—
1021	C₂⁴	—	4	1	no	—
1022	#41	—	2	1	no	—
1023	#41	—	2	1	no	—
1024	#41	—	2	1	no	—
1025	#41	—	2	1	no	—
1026	#41	—	2	1	no	—
1027	#41	—	2	1	no	—
1028	#41	—	2	1	no	—
1029	#41	—	2	1	no	—
1030	#41	—	2	2	no	—
1031	#41	—	2	4	no	—
1032	#41	—	2	2	no	—
1033	#41	—	2	2	no	—
1034	#41	—	2	4	no	—
1035	#41	—	2	2	no	—
1036	#41	—	2	2	no	—
1037	#41	—	2	4	no	—
1038	#41	—	2	2	no	—
1039	#41	—	2	2	no	—
1040	#41	—	2	4	no	—
1041	#41	—	2	2	no	—
1042	#41	—	2	1	no	—
1043	#41	—	2	1	no	—
1044	#41	—	2	1	no	—
1045	#41	—	2	1	no	—
1046	#41	—	2	1	no	—
1047	#41	—	2	1	no	—
1048	#41	—	2	1	no	—
1049	#41	—	2	1	no	—
1050	#41	—	4	2	no	—
1051	#41	—	4	2	no	—
1052	#41	—	4	2	no	—
1053	#41	—	4	2	no	—
1054	#41	—	4	4	no	—
1055	#41	—	4	2	no	—
1056	#41	—	4	2	no	—
1057	#41	—	4	2	no	—
1058	#41	—	4	2	no	—
1059	#41	—	4	2	no	—
1060	#41	—	4	2	no	—
1061	#41	—	4	2	no	—
1062	#41	—	4	2	no	—
1063	#41	—	4	4	no	—
1064	#41	—	4	1	no	—
1065	#41	—	4	1	no	—
1066	#41	—	4	1	no	—
1067	#41	—	4	1	no	—
1068	#41	C₂×D₄×C₂₃	1	2	yes	—
1069	#41	C₂×D₄×C₂₃	1	2	yes	—
1070	#41	C₂×D₄×C₂₃	1	2	yes	—
1071	#41	C₂×D₄×C₂₃	1	2	yes	—
1072	#41	C₂⁴×C₂₃	1	2	yes	—
1073	#41	C₂⁴×C₂₃	1	2	yes	—
1074	#41	C₂⁴×C₂₃	1	2	yes	—
1075	#41	C₂⁴×C₂₃	1	2	yes	—
1076	C₂×Q₈	—	2	1	no	—
1077	C₂×Q₈	—	2	4	no	—
1078	C₂×Q₈	—	2	2	no	—
1079	C₂×Q₈	—	2	4	no	—
1080	C₂×Q₈	—	2	2	no	—
1081	C₂×Q₈	—	2	2	no	—
1082	C₂×Q₈	—	2	2	no	—
1083	C₂×Q₈	—	2	1	no	—
1084	C₂×Q₈	—	2	1	no	—
1085	C₂×Q₈	—	2	1	no	—
1086	C₂×Q₈	—	2	1	no	—
1087	C₂×Q₈	—	4	1	no	—
1088	C₂×Q₈	—	4	2	no	—
1089	C₂×Q₈	—	4	2	no	—
1090	C₂×Q₈	—	4	1	no	—
1091	C₂×Q₈	—	4	1	no	—
1092	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1093	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1094	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1095	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1096	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1097	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1098	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1099	C₂×D₄	—	2	1	no	—
1100	C₂×D₄	—	2	1	no	—
1101	C₂×D₄	—	2	1	no	—
1102	C₂×D₄	—	2	1	no	—
1103	C₂×D₄	—	2	2	no	—
1104	C₂×D₄	—	2	4	no	—
1105	C₂×D₄	—	2	2	no	—
1106	C₂×D₄	—	2	2	no	—
1107	C₂×D₄	—	2	4	no	—
1108	C₂×D₄	—	2	2	no	—
1109	C₂×D₄	—	2	1	no	—
1110	C₂×D₄	—	2	1	no	—
1111	C₂×D₄	—	2	1	no	—
1112	C₂×D₄	—	2	1	no	—
1113	C₂×D₄	—	2	1	no	—
1114	C₂×D₄	—	2	1	no	—
1115	C₂×D₄	—	2	1	no	—
1116	C₂×D₄	—	4	2	no	—
1117	C₂×D₄	—	4	2	no	—
1118	C₂×D₄	—	4	1	no	—
1119	C₂×D₄	—	4	1	no	—
1120	C₂×D₄	—	4	2	no	—
1121	C₂×D₄	—	4	4	no	—
1122	C₂×D₄	—	4	2	no	—
1123	C₂×D₄	—	4	2	no	—
1124	C₂×D₄	—	4	4	no	—
1125	C₂×D₄	—	4	1	no	—
1126	C₂×D₄	—	4	1	no	—
1127	C₂×D₄	—	4	2	no	—
1128	C₂×D₄	—	4	2	no	—
1129	C₂×D₄	—	4	2	no	—
1130	C₂×D₄	—	4	2	no	—
1131	C₂×D₄	—	4	1	no	—
1132	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1133	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1134	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1135	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1136	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1137	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1138	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1139	C₂²×C₄	—	2	1	no	—
1140	C₂²×C₄	—	2	1	no	—
1141	C₂²×C₄	—	2	1	no	—
1142	C₂²×C₄	—	2	1	no	—
1143	C₂²×C₄	—	2	1	no	—
1144	C₂²×C₄	—	2	1	no	—
1145	C₂²×C₄	—	2	1	no	—
1146	C₂²×C₄	—	4	1	no	—
1147	C₂²×C₄	—	4	2	no	—
1148	C₂²×C₄	—	4	2	no	—
1149	C₂²×C₄	—	4	1	no	—
1150	C₂²×C₄	—	4	1	no	—
1151	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1152	Q₁₆	—	2	2	no	—
1153	Q₁₆	—	2	4	no	—
1154	Q₁₆	—	2	4	no	—
1155	Q₁₆	—	2	2	no	—
1156	Q₁₆	—	2	2	no	—
1157	Q₁₆	—	2	2	no	—
1158	Q₁₆	—	2	1	no	—
1159	Q₁₆	—	2	4	no	—
1160	Q₁₆	—	2	1	no	—
1161	Q₁₆	C₂×D₄×C₂₃	1	2	yes	—
1162	Q₁₆	C₂×D₄×C₂₃	1	4	yes	—
1163	Q₁₆	C₂×D₄×C₂₃	1	2	yes	—
1164	SD₁₆	—	2	4	no	—
1165	SD₁₆	—	2	4	no	—
1166	SD₁₆	—	2	2	no	—
1167	SD₁₆	—	2	2	no	—
1168	SD₁₆	—	2	2	no	—
1169	SD₁₆	—	2	2	no	—
1170	SD₁₆	—	2	4	no	—
1171	SD₁₆	—	2	2	no	—
1172	SD₁₆	—	2	4	no	—
1173	SD₁₆	—	2	2	no	—
1174	SD₁₆	—	2	2	no	—
1175	SD₁₆	—	2	2	no	—
1176	SD₁₆	—	2	2	no	—
1177	SD₁₆	—	2	2	no	—
1178	SD₁₆	—	2	2	no	—
1179	SD₁₆	—	2	2	no	—
1180	SD₁₆	—	2	1	no	—
1181	SD₁₆	—	2	1	no	—
1182	SD₁₆	—	2	4	no	—
1183	SD₁₆	—	2	4	no	—
1184	SD₁₆	—	2	1	no	—
1185	SD₁₆	—	2	1	no	—
1186	SD₁₆	C₂×D₄×C₂₃	1	2	yes	—
1187	SD₁₆	C₂×D₄×C₂₃	1	2	yes	—
1188	SD₁₆	C₂×D₄×C₂₃	1	2	yes	—
1189	SD₁₆	C₂×D₄×C₂₃	1	4	yes	—
1190	SD₁₆	C₂×D₄×C₂₃	1	4	yes	—
1191	SD₁₆	C₂×D₄×C₂₃	1	2	yes	—
1192	D₈	—	2	2	no	—
1193	D₈	—	2	4	no	—
1194	D₈	—	2	2	no	—
1195	D₈	—	2	4	no	—
1196	D₈	—	2	2	no	—
1197	D₈	—	2	2	no	—
1198	D₈	—	2	1	no	—
1199	D₈	—	2	4	no	—
1200	D₈	—	2	1	no	—
1201	D₈	C₂×D₄×C₂₃	1	2	yes	—
1202	D₈	C₂×D₄×C₂₃	1	4	yes	—
1203	D₈	C₂×D₄×C₂₃	1	2	yes	—
1204	M₁₆	—	2	1	no	—
1205	M₁₆	—	2	1	no	—
1206	M₁₆	—	2	1	no	—
1207	M₁₆	—	2	1	no	—
1208	M₁₆	—	2	4	no	—
1209	M₁₆	—	2	2	no	—
1210	M₁₆	—	2	2	no	—
1211	M₁₆	—	2	2	no	—
1212	M₁₆	—	2	2	no	—
1213	M₁₆	—	2	4	no	—
1214	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
1215	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
1216	M₁₆	C₂⁴×C₂₃	1	2	yes	—
1217	M₁₆	C₂⁴×C₂₃	1	2	yes	—
1218	M₁₆	C₂⁴×C₂₃	1	2	yes	—
1219	M₁₆	C₂⁴×C₂₃	1	2	yes	—
1220	C₂×C₈	—	2	1	no	—
1221	C₂×C₈	—	2	1	no	—
1222	C₂×C₈	—	2	1	no	—
1223	C₂×C₈	—	2	1	no	—
1224	C₂×C₈	—	2	2	no	—
1225	C₂×C₈	—	2	2	no	—
1226	C₂×C₈	—	2	2	no	—
1227	C₂×C₈	—	2	2	no	—
1228	C₂×C₈	—	2	4	no	—
1229	C₂×C₈	—	2	4	no	—
1230	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1231	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1232	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1233	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1234	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1235	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1236	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1237	C₄⋊C₄	—	2	1	no	—
1238	C₄⋊C₄	—	4	2	no	—
1239	C₂²⋊C₄	—	2	1	no	—
1240	C₂²⋊C₄	—	4	2	no	—
1241	C₂²⋊C₄	—	4	2	no	—
1242	C₄²	C₂⁴×C₂₃	1	2	yes	—
1243	C₂³	—	2	1	no	—
1244	C₂³	—	2	1	no	—
1245	C₂³	—	2	1	no	—
1246	C₂³	—	2	1	no	—
1247	C₂³	—	2	1	no	—
1248	C₂³	—	2	2	no	—
1249	C₂³	—	2	1	no	—
1250	C₂³	—	4	2	no	—
1251	C₂³	—	4	2	no	—
1252	C₂³	—	4	4	no	—
1253	C₂³	—	4	1	no	—
1254	C₂³	—	4	1	no	—
1255	C₂³	—	16	1	no	—
1256	C₂³	—	16	2	no	—
1257	C₂³	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1258	Q₈	—	2	1	no	—
1259	Q₈	—	2	1	no	—
1260	Q₈	—	2	1	no	—
1261	Q₈	—	2	1	no	—
1262	Q₈	—	2	2	no	—
1263	Q₈	—	2	1	no	—
1264	Q₈	—	2	2	no	—
1265	Q₈	—	2	1	no	—
1266	Q₈	—	2	1	no	—
1267	Q₈	—	2	1	no	—
1268	Q₈	—	4	4	no	—
1269	Q₈	—	4	2	no	—
1270	Q₈	—	4	2	no	—
1271	Q₈	—	4	1	no	—
1272	Q₈	—	4	1	no	—
1273	Q₈	C₂²×D₄×C₂₃	1	2	yes	—
1274	Q₈	C₂²×D₄×C₂₃	1	2	yes	—
1275	Q₈	C₂²×D₄×C₂₃	1	2	yes	—
1276	Q₈	C₂²×D₄×C₂₃	1	2	yes	—
1277	D₄	—	2	2	no	—
1278	D₄	—	2	2	no	—
1279	D₄	—	2	2	no	—
1280	D₄	—	2	2	no	—
1281	D₄	—	2	2	no	—
1282	D₄	—	2	2	no	—
1283	D₄	—	2	2	no	—
1284	D₄	—	2	2	no	—
1285	D₄	—	2	1	no	—
1286	D₄	—	2	2	no	—
1287	D₄	—	2	1	no	—
1288	D₄	—	2	1	no	—
1289	D₄	—	2	2	no	—
1290	D₄	—	2	1	no	—
1291	D₄	—	2	1	no	—
1292	D₄	—	2	1	no	—
1293	D₄	—	2	1	no	—
1294	D₄	—	2	1	no	—
1295	D₄	—	4	4	no	—
1296	D₄	—	4	4	no	—
1297	D₄	—	4	2	no	—
1298	D₄	—	4	2	no	—
1299	D₄	—	4	2	no	—
1300	D₄	—	4	2	no	—
1301	D₄	—	4	2	no	—
1302	D₄	—	4	2	no	—
1303	D₄	—	4	4	no	—
1304	D₄	—	4	1	no	—
1305	D₄	—	4	1	no	—
1306	D₄	—	4	1	no	—
1307	D₄	—	4	1	no	—
1308	D₄	—	4	1	no	—
1309	D₄	—	4	1	no	—
1310	D₄	—	16	2	no	—
1311	D₄	C₂²×D₄×C₂₃	1	2	yes	—
1312	D₄	C₂²×D₄×C₂₃	1	2	yes	—
1313	D₄	C₂²×D₄×C₂₃	1	2	yes	—
1314	D₄	C₂²×D₄×C₂₃	1	2	yes	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	2	no	—
1320	C₂×C₄	—	2	2	no	—
1321	C₂×C₄	—	2	2	no	—
1322	C₂×C₄	—	2	2	no	—
1323	C₂×C₄	—	2	2	no	—
1324	C₂×C₄	—	2	2	no	—
1325	C₂×C₄	—	2	2	no	—
1326	C₂×C₄	—	2	2	no	—
1327	C₂×C₄	—	2	2	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	2	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	4	4	no	—
1332	C₂×C₄	—	4	2	no	—
1333	C₂×C₄	—	4	2	no	—
1334	C₂×C₄	—	4	2	no	—
1335	C₂×C₄	—	4	2	no	—
1336	C₂×C₄	—	4	2	no	—
1337	C₂×C₄	—	4	2	no	—
1338	C₂×C₄	—	4	4	no	—
1339	C₂×C₄	—	4	4	no	—
1340	C₂×C₄	—	4	1	no	—
1341	C₂×C₄	—	4	1	no	—
1342	C₂×C₄	—	4	1	no	—
1343	C₂×C₄	—	4	1	no	—
1344	C₂×C₄	—	4	1	no	—
1345	C₂×C₄	—	4	1	no	—
1346	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1347	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1348	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1349	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1350	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1351	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1352	C₈	—	2	2	no	—
1353	C₈	—	2	2	no	—
1354	C₈	—	2	2	no	—
1355	C₈	—	2	2	no	—
1356	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
1357	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
1358	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
1359	C₈	C₂²×D₄×C₂₃	1	4	yes	—
1360	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
1361	C₂²	—	2	2	no	—
1362	C₂²	—	2	2	no	—
1363	C₂²	—	2	2	no	—
1364	C₂²	—	2	2	no	—
1365	C₂²	—	4	1	no	—
1366	C₂²	—	4	2	no	—
1367	C₂²	—	4	1	no	—
1368	C₂²	—	4	1	no	—
1369	C₂²	—	4	2	no	—
1370	C₂²	—	8	1	no	—
1371	C₂²	—	8	1	no	—
1372	C₂²	—	8	1	no	—
1373	C₂²	—	8	1	no	—
1374	C₂²	—	8	2	no	—
1375	C₂²	—	8	1	no	—
1376	C₂²	—	8	2	no	—
1377	C₂²	—	16	1	no	—
1378	C₂²	—	16	4	no	—
1379	C₂²	—	16	2	no	—
1380	C₂²	—	16	2	no	—
1381	C₂²	D₄²×C₂₃	1	1	yes	characteristic
1382	C₂²	D₄²×C₂₃	1	1	yes	characteristic
1383	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1384	C₄	—	2	2	no	—
1385	C₄	—	2	2	no	—
1386	C₄	—	2	2	no	—
1387	C₄	—	2	2	no	—
1388	C₄	—	4	2	no	—
1389	C₄	—	4	1	no	—
1390	C₄	—	4	1	no	—
1391	C₄	—	4	2	no	—
1392	C₄	D₄²×C₂₃	1	1	yes	characteristic
1393	C₄	D₄²×C₂₃	1	1	yes	characteristic
1394	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
1395	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
1396	C₂	—	2	1	no	—
1397	C₂	—	2	1	no	—
1398	C₂	—	2	1	no	—
1399	C₂	—	4	2	no	—
1400	C₂	—	4	2	no	—
1401	C₂	—	4	2	no	—
1402	C₂	—	4	2	no	—
1403	C₂	—	8	2	no	—
1404	C₂	—	8	1	no	—
1405	C₂	—	8	1	no	—
1406	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₃	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#3586	C₂	semidirect
2. C₂₃×#3585	C₂	semidirect
3. C₂₃×#3584	C₂	semidirect
4. C₂×C₂₃×#577	C₂	semidirect
5. C₂₃×#3291	C₂	semidirect
6. C₂₃×#3290	C₂	semidirect
7. C₂₃×#3289	C₂	semidirect
8. C₂₃×#3288	C₂	semidirect
9. C₂₃×#3154	C₂	semidirect
10. C₂₃×#3069	C₂	semidirect
11. C₂₃×#3068	C₂	semidirect
12. C₂₃×#3067	C₂	semidirect
13. C₂×C₂₃×#471	C₂	semidirect
14. C₂₃×#3022	C₂	semidirect
15. C₂₃×#3021	C₂	semidirect
16. C₂₃×#3020	C₂	semidirect
17. C₂₃×#3019	C₂	semidirect
18. C₂₃×#2957	C₂	semidirect
19. C₂₃×#2955	C₂	semidirect
21. C₂₃×#585	C₂²	semidirect
22. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
23. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
26. C₂₃×#578	C₂²	semidirect
27. C₂₃×#578	C₂²	semidirect
34. C₂₃×#577	C₂²	semidirect
35. C₂₃×#577	C₂²	semidirect
36. C₂₃×#577	C₂²	semidirect
37. C₂₃×#577	C₂²	semidirect
38. C₂₃×#577	C₂²	semidirect
39. C₂₃×#577	C₂²	semidirect
42. C₂₃×#576	C₂²	semidirect
43. C₂₃×#576	C₂²	semidirect
49. C₂₃×#575	C₂²	semidirect
50. C₂₃×#575	C₂²	semidirect
51. C₂₃×#575	C₂²	semidirect
54. C₂×C₂₃×#137	C₂²	semidirect
55. C₂×C₂₃×#137	C₂²	semidirect
56. C₂×C₂₃×#137	C₂²	semidirect
60. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
61. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
65. C₂×C₂₃×#135	C₂²	semidirect
67. C₂²×SD₁₆×C₂₃	C₂²	semidirect
68. C₂₃×#568	C₂²	semidirect
69. C₂₃×#568	C₂²	semidirect
70. C₂×C₂₃×#131	C₂²	semidirect
71. C₂×C₂₃×#131	C₂²	semidirect
72. C₂₃×#536	C₂²	semidirect
73. C₂₃×#535	C₂²	semidirect
74. C₂₃×#497	C₂²	semidirect
75. C₂₃×#496	C₂²	semidirect
76. C₂₃×#495	C₂²	semidirect
77. C₂₃×#492	C₂²	semidirect
78. C₂₃×#473	C₂²	semidirect
79. C₂₃×#473	C₂²	semidirect
80. C₂₃×#472	C₂²	semidirect
81. C₂₃×#472	C₂²	semidirect
82. C₂₃×#471	C₂²	semidirect
83. C₂₃×#471	C₂²	semidirect
84. C₂₃×#471	C₂²	semidirect
85. C₂₃×#471	C₂²	semidirect
86. C₂₃×#471	C₂²	semidirect
87. C₂₃×#471	C₂²	semidirect
88. C₂₃×#456	C₂²	semidirect
89. C₂₃×#456	C₂²	semidirect
90. C₂₃×#455	C₂²	semidirect
91. C₂₃×#455	C₂²	semidirect
92. C₂₃×#454	C₂²	semidirect
93. C₂₃×#454	C₂²	semidirect
94. C₂₃×#453	C₂²	semidirect
95. C₂₃×#453	C₂²	semidirect
96. C₂₃×#444	C₂²	semidirect
97. C₂₃×#444	C₂²	semidirect
98. C₂₃×#443	C₂²	semidirect
99. C₂₃×#443	C₂²	semidirect
100. C₂₃×#430	C₂²	semidirect
101. C₂×C₂₃×#108	C₂²	semidirect
102. C₂₃×#421	C₂²	semidirect
103. C₂₃×#421	C₂²	semidirect
104. C₂₃×#421	C₂²	semidirect
105. C₂₃×#421	C₂²	semidirect
106. C₂₃×#413	C₂²	semidirect
107. C₂₃×#413	C₂²	semidirect
108. C₂×C₂₃×#101	C₂²	semidirect
109. C₂×C₂₃×#100	C₂²	semidirect
110. C₂₃×#405	C₂²	semidirect
120. C₂₃×2₋¹⁺⁴	C₂³	semidirect
132. C₂₃×H(5,𝔽₂)	C₂³	semidirect
175. C₂₃×#137	D₄	semidirect
176. C₂₃×#137	D₄	semidirect
181. C₂₃×#137	C₂³	semidirect
182. C₂₃×#137	C₂³	semidirect
201. C₂₃×AGL(1,ℤ/8)	D₄	semidirect
202. C₂₃×AGL(1,ℤ/8)	D₄	semidirect
208. C₂₃×AGL(1,ℤ/8)	C₂³	semidirect
227. C₂₃×#135	D₄	semidirect
228. C₂₃×#135	D₄	semidirect
236. C₂×Q₁₆×C₂₃	D₄	semidirect
237. C₂×Q₁₆×C₂₃	C₂³	semidirect
238. C₂×Q₁₆×C₂₃	C₂³	semidirect
253. C₂×SD₁₆×C₂₃	D₄	semidirect
254. C₂×SD₁₆×C₂₃	D₄	semidirect
258. C₂×SD₁₆×C₂₃	C₂³	semidirect
259. C₂×SD₁₆×C₂₃	C₂³	semidirect
260. C₂×SD₁₆×C₂₃	C₂³	semidirect
265. C₂×D₈×C₂₃	D₄	semidirect
267. C₂×D₈×C₂₃	C₂³	semidirect
277. C₂₃×#131	C₂³	semidirect
278. C₂₃×#131	C₂³	semidirect
279. C₂₃×#131	C₂³	semidirect
292. C₂₃×C₄⋊Q₈	C₂³	semidirect
295. C₂₃×#124	C₂³	semidirect
301. C₂₃×#108	C₂³	semidirect
302. C₂₃×#108	C₂³	semidirect
303. C₂₃×#108	C₂³	semidirect
306. C₂₃×#104	C₂³	semidirect
307. C₂₃×#104	C₂³	semidirect
308. C₂₃×#101	C₂³	semidirect
309. C₂₃×#101	C₂³	semidirect
310. C₂₃×#101	C₂³	semidirect
312. C₂₃×#100	C₂³	semidirect
313. C₂₃×#100	C₂³	semidirect
314. C₂₃×#97	C₂³	semidirect
315. C₄×C₈×C₂₃	C₂³	semidirect
539. #61107	C₂₃	direct (N × H)
658. #3586	C₂×C₂₃	semidirect
659. #3585	C₂×C₂₃	semidirect
660. #3584	C₂×C₂₃	semidirect
661. C₂×#577	C₂×C₂₃	semidirect
662. #3291	C₂×C₂₃	semidirect
663. #3290	C₂×C₂₃	semidirect
664. #3289	C₂×C₂₃	semidirect
665. #3288	C₂×C₂₃	semidirect
666. #3154	C₂×C₂₃	semidirect
667. #3069	C₂×C₂₃	semidirect
668. #3068	C₂×C₂₃	semidirect
669. #3067	C₂×C₂₃	semidirect
670. C₂×#471	C₂×C₂₃	semidirect
671. #3022	C₂×C₂₃	semidirect
672. #3021	C₂×C₂₃	semidirect
673. #3020	C₂×C₂₃	semidirect
674. #3019	C₂×C₂₃	semidirect
675. #2957	C₂×C₂₃	semidirect
676. #2955	C₂×C₂₃	semidirect
713. #585	C₂²×C₂₃	semidirect
714. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
715. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
718. #578	C₂²×C₂₃	semidirect
719. #578	C₂²×C₂₃	semidirect
726. #577	C₂²×C₂₃	semidirect
727. #577	C₂²×C₂₃	semidirect
728. #577	C₂²×C₂₃	semidirect
729. #577	C₂²×C₂₃	semidirect
730. #577	C₂²×C₂₃	semidirect
731. #577	C₂²×C₂₃	semidirect
734. #576	C₂²×C₂₃	semidirect
735. #576	C₂²×C₂₃	semidirect
741. #575	C₂²×C₂₃	semidirect
742. #575	C₂²×C₂₃	semidirect
743. #575	C₂²×C₂₃	semidirect
746. C₂×#137	C₂²×C₂₃	semidirect
747. C₂×#137	C₂²×C₂₃	semidirect
748. C₂×#137	C₂²×C₂₃	semidirect
752. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
753. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
757. C₂×#135	C₂²×C₂₃	semidirect
759. C₂²×SD₁₆	C₂²×C₂₃	semidirect
760. #568	C₂²×C₂₃	semidirect
761. #568	C₂²×C₂₃	semidirect
762. C₂×#131	C₂²×C₂₃	semidirect
763. C₂×#131	C₂²×C₂₃	semidirect
764. #536	C₂²×C₂₃	semidirect
765. #535	C₂²×C₂₃	semidirect
766. #497	C₂²×C₂₃	semidirect
767. #496	C₂²×C₂₃	semidirect
768. #495	C₂²×C₂₃	semidirect
769. #492	C₂²×C₂₃	semidirect
770. #473	C₂²×C₂₃	semidirect
771. #473	C₂²×C₂₃	semidirect
772. #472	C₂²×C₂₃	semidirect
773. #472	C₂²×C₂₃	semidirect
774. #471	C₂²×C₂₃	semidirect
775. #471	C₂²×C₂₃	semidirect
776. #471	C₂²×C₂₃	semidirect
777. #471	C₂²×C₂₃	semidirect
778. #471	C₂²×C₂₃	semidirect
779. #471	C₂²×C₂₃	semidirect
780. #456	C₂²×C₂₃	semidirect
781. #456	C₂²×C₂₃	semidirect
782. #455	C₂²×C₂₃	semidirect
783. #455	C₂²×C₂₃	semidirect
784. #454	C₂²×C₂₃	semidirect
785. #454	C₂²×C₂₃	semidirect
786. #453	C₂²×C₂₃	semidirect
787. #453	C₂²×C₂₃	semidirect
788. #444	C₂²×C₂₃	semidirect
789. #444	C₂²×C₂₃	semidirect
790. #443	C₂²×C₂₃	semidirect
791. #443	C₂²×C₂₃	semidirect
792. #430	C₂²×C₂₃	semidirect
793. C₂×#108	C₂²×C₂₃	semidirect
794. #421	C₂²×C₂₃	semidirect
795. #421	C₂²×C₂₃	semidirect
796. #421	C₂²×C₂₃	semidirect
797. #421	C₂²×C₂₃	semidirect
798. #413	C₂²×C₂₃	semidirect
799. #413	C₂²×C₂₃	semidirect
800. C₂×#101	C₂²×C₂₃	semidirect
801. C₂×#100	C₂²×C₂₃	semidirect
802. #405	C₂²×C₂₃	semidirect
823. 2₋¹⁺⁴	C₂³×C₂₃	semidirect
835. H(5,𝔽₂)	C₂³×C₂₃	semidirect
878. #137	D₄×C₂₃	semidirect
879. #137	D₄×C₂₃	semidirect
884. #137	C₂³×C₂₃	semidirect
885. #137	C₂³×C₂₃	semidirect
904. AGL(1,ℤ/8)	D₄×C₂₃	semidirect
905. AGL(1,ℤ/8)	D₄×C₂₃	semidirect
911. AGL(1,ℤ/8)	C₂³×C₂₃	semidirect
930. #135	D₄×C₂₃	semidirect
931. #135	D₄×C₂₃	semidirect
939. C₂×Q₁₆	D₄×C₂₃	semidirect
940. C₂×Q₁₆	C₂³×C₂₃	semidirect
941. C₂×Q₁₆	C₂³×C₂₃	semidirect
956. C₂×SD₁₆	D₄×C₂₃	semidirect
957. C₂×SD₁₆	D₄×C₂₃	semidirect
961. C₂×SD₁₆	C₂³×C₂₃	semidirect
962. C₂×SD₁₆	C₂³×C₂₃	semidirect
963. C₂×SD₁₆	C₂³×C₂₃	semidirect
968. C₂×D₈	D₄×C₂₃	semidirect
970. C₂×D₈	C₂³×C₂₃	semidirect
980. #131	C₂³×C₂₃	semidirect
981. #131	C₂³×C₂₃	semidirect
982. #131	C₂³×C₂₃	semidirect
995. C₄⋊Q₈	C₂³×C₂₃	semidirect
998. #124	C₂³×C₂₃	semidirect
1004. #108	C₂³×C₂₃	semidirect
1005. #108	C₂³×C₂₃	semidirect
1006. #108	C₂³×C₂₃	semidirect
1009. #104	C₂³×C₂₃	semidirect
1010. #104	C₂³×C₂₃	semidirect
1011. #101	C₂³×C₂₃	semidirect
1012. #101	C₂³×C₂₃	semidirect
1013. #101	C₂³×C₂₃	semidirect
1015. #100	C₂³×C₂₃	semidirect
1016. #100	C₂³×C₂₃	semidirect
1017. #97	C₂³×C₂₃	semidirect
1018. C₄×C₈	C₂³×C₂₃	semidirect
1019. C₂₃	#61107	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3586	2
C₂₃×#3585	2
C₂₃×#3584	2
C₂×C₂₃×#577	2
C₂₃×#3291	2
C₂₃×#3290	2
C₂₃×#3289	2
C₂₃×#3288	2
C₂₃×#3154	2
C₂₃×#3069	2
C₂₃×#3068	2
C₂₃×#3067	2
C₂×C₂₃×#471	2
C₂₃×#3022	2
C₂₃×#3021	2
C₂₃×#3020	2
C₂₃×#3019	2
C₂₃×#2957	2
C₂₃×#2955	2
#61107	23

Subgroups — C23×#61107 #19208733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61107 #19208733