Subgroups — C₂₃×#61058 #19208684

Order 5888.

2890 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3485	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3273	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3272	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3267	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3264	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3057	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
23	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#576	—	2	8	no	—
25	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
27	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
29	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
30	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
33	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
34	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
36	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
39	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²×D₈×C₂₃	C₂²	1	2	yes	complemented
41	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
42	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#547	—	2	2	no	—
44	C₂₃×#547	C₂²	1	4	yes	complemented
45	C₂₃×#546	—	2	2	no	—
46	C₂₃×#546	—	2	2	no	—
47	C₂₃×#546	C₂²	1	4	yes	complemented
48	C₂₃×#546	C₂²	1	4	yes	complemented
49	D₄²×C₂₃	—	2	2	no	—
50	D₄²×C₂₃	C₂²	1	4	yes	complemented
51	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#535	C₂²	1	1	yes	characteristic
54	C₂₃×#535	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#534	—	2	2	no	—
56	C₂₃×#534	—	2	2	no	—
57	C₂₃×#525	C₂²	1	1	yes	characteristic
58	C₂₃×#525	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#525	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂₃×#123	—	2	2	no	—
61	C₂×C₂₃×#120	—	2	2	no	—
62	C₂₃×#518	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#518	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#497	C₂²	1	2	yes	complemented
65	C₂₃×#496	C₂²	1	2	yes	complemented
66	C₂₃×#495	C₂²	1	2	yes	complemented
67	C₂₃×#492	C₂²	1	2	yes	complemented
68	C₂₃×#470	C₂²	1	2	yes	complemented
69	C₂₃×#469	C₂²	1	2	yes	complemented
70	C₂₃×#468	C₂²	1	4	yes	complemented
71	C₂₃×#468	C₂²	1	2	yes	complemented
72	C₂₃×#468	C₂²	1	2	yes	complemented
73	C₂₃×#465	C₂²	1	4	yes	complemented
74	C₂₃×#463	C₂²	1	4	yes	complemented
75	C₂₃×#463	C₂²	1	4	yes	complemented
76	C₂₃×#461	C₂²	1	4	yes	complemented
77	C₂₃×#459	C₂²	1	4	yes	complemented
78	C₂₃×#452	C₂²	1	4	yes	complemented
79	C₂₃×#452	C₂²	1	4	yes	complemented
80	C₂₃×#450	C₂²	1	4	yes	complemented
81	C₂₃×#450	C₂²	1	4	yes	complemented
82	C₂₃×#449	C₂²	1	4	yes	complemented
83	C₂₃×#449	C₂²	1	4	yes	complemented
84	C₂₃×#447	C₂²	1	4	yes	complemented
85	C₂₃×#447	C₂²	1	4	yes	complemented
86	C₂₃×#442	C₂²	1	4	yes	complemented
87	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
88	C₂₃×#436	C₂²	1	4	yes	complemented
89	C₂₃×#435	C₂²	1	4	yes	complemented
90	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
96	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
97	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
98	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵×C₂₃	—	2	1	no	—
102	C₂₃×H(5,𝔽₂)	—	2	4	no	—
103	C₂₃×H(5,𝔽₂)	—	2	4	no	—
104	C₂₃×H(5,𝔽₂)	—	4	2	no	—
105	C₂₃×H(5,𝔽₂)	—	4	2	no	—
106	C₂×#41×C₂₃	—	2	1	no	—
107	C₂×#41×C₂₃	—	2	1	no	—
108	C₂×#41×C₂₃	—	2	2	no	—
109	C₂×#41×C₂₃	—	2	4	no	—
110	C₂×#41×C₂₃	—	4	2	no	—
111	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
112	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×#41×C₂₃	C₂³	1	4	yes	—
114	C₂×#41×C₂₃	C₂³	1	2	yes	—
115	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×#41×C₂₃	C₂³	1	2	yes	complemented
117	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₂₃	—	2	4	no	—
119	C₂²×D₄×C₂₃	—	2	1	no	—
120	C₂²×D₄×C₂₃	—	2	2	no	—
121	C₂²×D₄×C₂₃	—	2	1	no	—
122	C₂²×D₄×C₂₃	—	2	2	no	—
123	C₂²×D₄×C₂₃	—	2	1	no	—
124	C₂²×D₄×C₂₃	—	2	4	no	—
125	C₂²×D₄×C₂₃	—	2	1	no	—
126	C₂²×D₄×C₂₃	—	2	2	no	—
127	C₂²×D₄×C₂₃	—	4	2	no	—
128	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
130	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
131	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₂₃	C₂³	1	2	yes	complemented
134	C₂³×C₄×C₂₃	—	2	1	no	—
135	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂₃×#137	—	4	2	no	—
137	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
138	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
139	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
140	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
141	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
142	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
143	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
144	C₂₃×#135	—	2	8	no	—
145	C₂₃×#135	—	2	4	no	—
146	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic, complemented
147	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	complemented
148	C₂×SD₁₆×C₂₃	—	2	4	no	—
149	C₂×SD₁₆×C₂₃	—	2	4	no	—
150	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
151	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	complemented
156	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic, complemented
157	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic, complemented
158	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	complemented
159	C₂×D₈×C₂₃	—	2	4	no	—
160	C₂×D₈×C₂₃	—	2	8	no	—
161	C₂×D₈×C₂₃	D₄	1	8	yes	complemented
162	C₂×D₈×C₂₃	C₂³	1	2	yes	—
163	C₂×D₈×C₂₃	C₂³	1	4	yes	—
164	C₂×D₈×C₂₃	C₂³	1	2	yes	—
165	C₂×D₈×C₂₃	C₂³	1	2	yes	—
166	C₂×D₈×C₂₃	C₂³	1	2	yes	—
167	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic, complemented
168	C₂×D₈×C₂₃	C₂³	1	2	yes	complemented
169	C₂₃×#131	—	2	4	no	—
170	C₂×M₁₆×C₂₃	—	2	4	no	—
171	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
172	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
173	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×M₁₆×C₂₃	C₂³	1	2	yes	complemented
176	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₂₃	C₂³	1	2	yes	complemented
179	C₂₃×C₄⋊Q₈	—	2	1	no	—
180	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
181	C₂₃×#127	—	2	1	no	—
182	C₂₃×#127	C₂³	1	2	yes	—
183	C₂₃×#124	—	2	1	no	—
184	C₂₃×#124	—	2	1	no	—
185	C₂₃×#124	C₂³	1	2	yes	—
186	C₂₃×#124	C₂³	1	2	yes	complemented
187	C₂₃×#123	—	2	2	no	—
188	C₂₃×#123	—	2	1	no	—
189	C₂₃×#123	—	2	1	no	—
190	C₂₃×#123	—	2	4	no	—
191	C₂₃×#123	—	2	4	no	—
192	C₂₃×#123	—	2	4	no	—
193	C₂₃×#123	—	2	4	no	—
194	C₂₃×#123	—	2	2	no	—
195	C₂₃×#123	D₄	1	2	yes	—
196	C₂₃×C₂²⋊Q₈	—	2	2	no	—
197	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
198	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
201	C₂₃×#121	—	2	4	no	—
202	C₂₃×#121	—	2	4	no	—
203	C₂₃×#121	—	2	2	no	—
204	C₂₃×#121	—	2	4	no	—
205	C₂₃×#121	—	2	4	no	—
206	C₂₃×#121	D₄	1	2	yes	—
207	C₂₃×#121	C₂³	1	2	yes	—
208	C₂₃×#121	C₂³	1	4	yes	—
209	C₂₃×#121	C₂³	1	2	yes	—
210	C₂₃×#120	—	2	1	no	—
211	C₂₃×#120	—	2	1	no	—
212	C₂₃×#120	—	2	2	no	—
213	C₂₃×#120	—	2	4	no	—
214	C₂₃×#120	—	2	4	no	—
215	C₂₃×#120	—	2	2	no	—
216	C₂₃×#120	—	2	4	no	—
217	C₂₃×#120	—	2	4	no	—
218	C₂₃×#120	D₄	1	2	yes	—
219	C₄×D₄×C₂₃	—	2	2	no	—
220	C₄×D₄×C₂₃	—	2	2	no	—
221	C₄×D₄×C₂₃	—	2	2	no	—
222	C₄×D₄×C₂₃	—	2	2	no	—
223	C₄×D₄×C₂₃	C₂³	1	4	yes	—
224	C₄×D₄×C₂₃	C₂³	1	4	yes	—
225	C₄×D₄×C₂₃	C₂³	1	4	yes	complemented
226	C₂₃×#117	C₂³	1	1	yes	characteristic
227	C₂₃×#117	C₂³	1	1	yes	characteristic
228	C₂₃×#117	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
230	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
231	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
232	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
233	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
234	C₂₃×#107	C₂³	1	2	yes	complemented
235	C₂₃×#106	C₂³	1	2	yes	complemented
236	C₂₃×C₄⋊C₈	C₂³	1	4	yes	complemented
237	C₂₃×#103	C₂³	1	2	yes	complemented
238	C₂₃×#103	C₂³	1	2	yes	complemented
239	C₂₃×#103	C₂³	1	4	yes	complemented
240	C₂₃×#102	C₂³	1	4	yes	—
241	C₂₃×#102	C₂³	1	4	yes	—
242	C₂₃×#102	C₂³	1	2	yes	complemented
243	C₂₃×#102	C₂³	1	2	yes	complemented
244	C₂₃×#102	C₂³	1	4	yes	complemented
245	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
246	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
247	C₂₃×#97	C₂³	1	2	yes	complemented
248	C₄×C₈×C₂₃	C₂³	1	2	yes	complemented
249	C₂⁴×C₂₃	—	2	1	no	—
250	C₂⁴×C₂₃	—	2	1	no	—
251	C₂⁴×C₂₃	—	2	4	no	—
252	C₂⁴×C₂₃	—	2	2	no	—
253	C₂⁴×C₂₃	—	2	1	no	—
254	C₂⁴×C₂₃	—	2	2	no	—
255	C₂⁴×C₂₃	—	4	4	no	—
256	C₂⁴×C₂₃	—	8	4	no	—
257	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
258	#41×C₂₃	—	2	2	no	—
259	#41×C₂₃	—	2	2	no	—
260	#41×C₂₃	—	2	4	no	—
261	#41×C₂₃	—	2	4	no	—
262	#41×C₂₃	—	2	8	no	—
263	#41×C₂₃	—	2	2	no	—
264	#41×C₂₃	—	2	2	no	—
265	#41×C₂₃	—	2	2	no	—
266	#41×C₂₃	—	2	2	no	—
267	#41×C₂₃	—	4	4	no	—
268	#41×C₂₃	—	4	2	no	—
269	#41×C₂₃	—	4	2	no	—
270	#41×C₂₃	—	4	8	no	—
271	#41×C₂₃	—	4	4	no	—
272	#41×C₂₃	—	4	4	no	—
273	C₂×Q₈×C₂₃	—	2	1	no	—
274	C₂×Q₈×C₂₃	—	2	2	no	—
275	C₂×Q₈×C₂₃	—	2	2	no	—
276	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
277	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
278	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
279	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
280	C₂×D₄×C₂₃	—	2	4	no	—
281	C₂×D₄×C₂₃	—	2	4	no	—
282	C₂×D₄×C₂₃	—	2	8	no	—
283	C₂×D₄×C₂₃	—	2	2	no	—
284	C₂×D₄×C₂₃	—	2	1	no	—
285	C₂×D₄×C₂₃	—	2	2	no	—
286	C₂×D₄×C₂₃	—	2	4	no	—
287	C₂×D₄×C₂₃	—	2	1	no	—
288	C₂×D₄×C₂₃	—	2	2	no	—
289	C₂×D₄×C₂₃	—	2	2	no	—
290	C₂×D₄×C₂₃	—	2	4	no	—
291	C₂×D₄×C₂₃	—	2	1	no	—
292	C₂×D₄×C₂₃	—	2	1	no	—
293	C₂×D₄×C₂₃	—	2	2	no	—
294	C₂×D₄×C₂₃	—	2	2	no	—
295	C₂×D₄×C₂₃	—	2	4	no	—
296	C₂×D₄×C₂₃	—	2	2	no	—
297	C₂×D₄×C₂₃	—	2	1	no	—
298	C₂×D₄×C₂₃	—	2	4	no	—
299	C₂×D₄×C₂₃	—	2	2	no	—
300	C₂×D₄×C₂₃	—	2	2	no	—
301	C₂×D₄×C₂₃	—	2	2	no	—
302	C₂×D₄×C₂₃	—	4	4	no	—
303	C₂×D₄×C₂₃	—	4	2	no	—
304	C₂×D₄×C₂₃	—	4	2	no	—
305	C₂×D₄×C₂₃	—	4	8	no	—
306	C₂×D₄×C₂₃	—	4	4	no	—
307	C₂×D₄×C₂₃	—	4	4	no	—
308	C₂×D₄×C₂₃	—	4	4	no	—
309	C₂×D₄×C₂₃	—	4	8	no	—
310	C₂×D₄×C₂₃	—	4	8	no	—
311	C₂×D₄×C₂₃	—	4	4	no	—
312	C₂×D₄×C₂₃	—	8	8	no	—
313	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
314	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
315	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
316	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
317	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	complemented
318	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
319	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
321	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
322	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₂₃	—	2	2	no	—
324	C₂²×C₄×C₂₃	—	2	2	no	—
325	C₂²×C₄×C₂₃	—	2	1	no	—
326	C₂²×C₄×C₂₃	—	2	2	no	—
327	C₂²×C₄×C₂₃	—	2	4	no	—
328	C₂²×C₄×C₂₃	—	2	2	no	—
329	C₂²×C₄×C₂₃	—	2	1	no	—
330	C₂²×C₄×C₂₃	—	2	1	no	—
331	C₂²×C₄×C₂₃	—	2	4	no	—
332	C₂²×C₄×C₂₃	—	2	4	no	—
333	C₂²×C₄×C₂₃	—	4	4	no	—
334	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
335	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
339	Q₁₆×C₂₃	—	2	2	no	—
340	Q₁₆×C₂₃	—	4	2	no	—
341	SD₁₆×C₂₃	—	2	8	no	—
342	SD₁₆×C₂₃	—	2	4	no	—
343	SD₁₆×C₂₃	—	2	4	no	—
344	SD₁₆×C₂₃	—	2	4	no	—
345	SD₁₆×C₂₃	—	2	4	no	—
346	SD₁₆×C₂₃	—	2	2	no	—
347	SD₁₆×C₂₃	—	2	2	no	—
348	SD₁₆×C₂₃	—	4	2	no	—
349	SD₁₆×C₂₃	—	4	2	no	—
350	D₈×C₂₃	—	2	4	no	—
351	D₈×C₂₃	—	2	8	no	—
352	D₈×C₂₃	—	2	4	no	—
353	D₈×C₂₃	—	2	2	no	—
354	D₈×C₂₃	—	4	2	no	—
355	D₈×C₂₃	C₂×D₄	1	8	yes	complemented
356	D₈×C₂₃	C₂×D₄	1	8	yes	complemented
357	M₁₆×C₂₃	—	2	2	no	—
358	M₁₆×C₂₃	—	2	2	no	—
359	M₁₆×C₂₃	—	2	4	no	—
360	M₁₆×C₂₃	—	2	4	no	—
361	M₁₆×C₂₃	—	2	4	no	—
362	C₂×C₈×C₂₃	—	2	2	no	—
363	C₂×C₈×C₂₃	—	2	4	no	—
364	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	complemented
365	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
366	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
367	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
368	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₂₃	—	2	2	no	—
371	C₄⋊C₄×C₂₃	—	2	4	no	—
372	C₄⋊C₄×C₂₃	—	2	4	no	—
373	C₄⋊C₄×C₂₃	—	2	2	no	—
374	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
375	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
378	C₂²⋊C₄×C₂₃	—	2	1	no	—
379	C₂²⋊C₄×C₂₃	—	2	1	no	—
380	C₂²⋊C₄×C₂₃	—	2	2	no	—
381	C₂²⋊C₄×C₂₃	—	2	4	no	—
382	C₂²⋊C₄×C₂₃	—	2	2	no	—
383	C₂²⋊C₄×C₂₃	—	2	2	no	—
384	C₂²⋊C₄×C₂₃	—	2	4	no	—
385	C₂²⋊C₄×C₂₃	—	2	4	no	—
386	C₂²⋊C₄×C₂₃	—	2	4	no	—
387	C₂²⋊C₄×C₂₃	—	2	4	no	—
388	C₂²⋊C₄×C₂₃	—	2	4	no	—
389	C₂²⋊C₄×C₂₃	—	2	2	no	—
390	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
392	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
393	C₄²×C₂₃	—	2	1	no	—
394	C₄²×C₂₃	—	2	1	no	—
395	C₄²×C₂₃	C₂⁴	1	2	yes	—
396	#61058	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
397	C₂³×C₂₃	—	2	2	no	—
398	C₂³×C₂₃	—	2	2	no	—
399	C₂³×C₂₃	—	2	2	no	—
400	C₂³×C₂₃	—	2	4	no	—
401	C₂³×C₂₃	—	2	4	no	—
402	C₂³×C₂₃	—	2	1	no	—
403	C₂³×C₂₃	—	2	2	no	—
404	C₂³×C₂₃	—	2	1	no	—
405	C₂³×C₂₃	—	4	2	no	—
406	C₂³×C₂₃	—	4	8	no	—
407	C₂³×C₂₃	—	4	4	no	—
408	C₂³×C₂₃	—	4	4	no	—
409	C₂³×C₂₃	—	4	8	no	—
410	C₂³×C₂₃	—	4	2	no	—
411	C₂³×C₂₃	—	8	2	no	—
412	C₂³×C₂₃	—	8	2	no	—
413	C₂³×C₂₃	—	8	2	no	—
414	C₂³×C₂₃	—	8	4	no	—
415	C₂³×C₂₃	—	8	4	no	—
416	C₂³×C₂₃	—	8	4	no	—
417	C₂³×C₂₃	—	8	16	no	—
418	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
419	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
420	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
421	Q₈×C₂₃	—	2	2	no	—
422	Q₈×C₂₃	—	2	2	no	—
423	Q₈×C₂₃	—	2	1	no	—
424	Q₈×C₂₃	—	2	1	no	—
425	Q₈×C₂₃	—	2	1	no	—
426	Q₈×C₂₃	—	2	2	no	—
427	Q₈×C₂₃	—	2	1	no	—
428	Q₈×C₂₃	—	4	2	no	—
429	D₄×C₂₃	—	2	4	no	—
430	D₄×C₂₃	—	2	4	no	—
431	D₄×C₂₃	—	2	4	no	—
432	D₄×C₂₃	—	2	2	no	—
433	D₄×C₂₃	—	2	1	no	—
434	D₄×C₂₃	—	2	1	no	—
435	D₄×C₂₃	—	2	2	no	—
436	D₄×C₂₃	—	2	2	no	—
437	D₄×C₂₃	—	2	2	no	—
438	D₄×C₂₃	—	2	1	no	—
439	D₄×C₂₃	—	2	2	no	—
440	D₄×C₂₃	—	2	1	no	—
441	D₄×C₂₃	—	4	4	no	—
442	D₄×C₂₃	—	4	8	no	—
443	D₄×C₂₃	—	4	4	no	—
444	D₄×C₂₃	—	4	4	no	—
445	D₄×C₂₃	—	4	4	no	—
446	D₄×C₂₃	—	4	4	no	—
447	D₄×C₂₃	—	4	8	no	—
448	D₄×C₂₃	—	4	4	no	—
449	D₄×C₂₃	—	4	2	no	—
450	D₄×C₂₃	—	4	2	no	—
451	D₄×C₂₃	—	4	2	no	—
452	D₄×C₂₃	—	8	4	no	—
453	D₄×C₂₃	—	8	2	no	—
454	D₄×C₂₃	—	8	4	no	—
455	D₄×C₂₃	C₂²×D₄	1	4	yes	—
456	D₄×C₂₃	C₂²×D₄	1	4	yes	—
457	C₂×C₄×C₂₃	—	2	2	no	—
458	C₂×C₄×C₂₃	—	2	4	no	—
459	C₂×C₄×C₂₃	—	2	2	no	—
460	C₂×C₄×C₂₃	—	2	2	no	—
461	C₂×C₄×C₂₃	—	2	2	no	—
462	C₂×C₄×C₂₃	—	2	2	no	—
463	C₂×C₄×C₂₃	—	2	2	no	—
464	C₂×C₄×C₂₃	—	2	2	no	—
465	C₂×C₄×C₂₃	—	2	1	no	—
466	C₂×C₄×C₂₃	—	2	2	no	—
467	C₂×C₄×C₂₃	—	2	1	no	—
468	C₂×C₄×C₂₃	—	4	8	no	—
469	C₂×C₄×C₂₃	—	4	4	no	—
470	C₂×C₄×C₂₃	—	4	4	no	—
471	C₂×C₄×C₂₃	—	4	2	no	—
472	C₂×C₄×C₂₃	—	4	2	no	—
473	C₂×C₄×C₂₃	—	4	2	no	—
474	C₂×C₄×C₂₃	—	8	4	no	—
475	C₂×C₄×C₂₃	—	8	4	no	—
476	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
477	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
482	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
483	C₈×C₂₃	—	2	2	no	—
484	C₈×C₂₃	—	2	2	no	—
485	C₈×C₂₃	—	2	2	no	—
486	C₈×C₂₃	C₂²×D₄	1	2	yes	—
487	C₈×C₂₃	C₂²×D₄	1	2	yes	—
488	C₂×#576	C₂×C₂₃	1	1	yes	characteristic, complemented
489	C₂²×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
490	#3485	C₂×C₂₃	1	1	yes	characteristic, complemented
491	#3484	C₂×C₂₃	1	1	yes	characteristic, complemented
492	#3273	C₂×C₂₃	1	4	yes	complemented
493	#3272	C₂×C₂₃	1	4	yes	complemented
494	#3267	C₂×C₂₃	1	4	yes	complemented
495	#3264	C₂×C₂₃	1	4	yes	complemented
496	#3154	C₂×C₂₃	1	1	yes	characteristic, complemented
497	#3057	C₂×C₂₃	1	1	yes	characteristic, complemented
498	#3054	C₂×C₂₃	1	1	yes	characteristic, complemented
499	#3042	C₂×C₂₃	1	1	yes	characteristic, complemented
500	#3041	C₂×C₂₃	1	1	yes	characteristic, complemented
501	#3009	C₂×C₂₃	1	1	yes	characteristic, complemented
502	#3008	C₂×C₂₃	1	1	yes	characteristic, complemented
503	#3005	C₂×C₂₃	1	1	yes	characteristic, complemented
504	#3003	C₂×C₂₃	1	1	yes	characteristic, complemented
505	#2948	C₂×C₂₃	1	1	yes	characteristic, complemented
506	#2930	C₂×C₂₃	1	1	yes	characteristic, complemented
507	C₂²×C₂₃	—	2	2	no	—
508	C₂²×C₂₃	—	2	2	no	—
509	C₂²×C₂₃	—	2	4	no	—
510	C₂²×C₂₃	—	2	2	no	—
511	C₂²×C₂₃	—	2	2	no	—
512	C₂²×C₂₃	—	2	2	no	—
513	C₂²×C₂₃	—	2	4	no	—
514	C₂²×C₂₃	—	2	4	no	—
515	C₂²×C₂₃	—	4	4	no	—
516	C₂²×C₂₃	—	4	4	no	—
517	C₂²×C₂₃	—	4	4	no	—
518	C₂²×C₂₃	—	4	2	no	—
519	C₂²×C₂₃	—	4	4	no	—
520	C₂²×C₂₃	—	4	2	no	—
521	C₂²×C₂₃	—	4	1	no	—
522	C₂²×C₂₃	—	4	1	no	—
523	C₂²×C₂₃	—	4	2	no	—
524	C₂²×C₂₃	—	8	4	no	—
525	C₂²×C₂₃	—	8	4	no	—
526	C₂²×C₂₃	—	8	4	no	—
527	C₂²×C₂₃	—	8	16	no	—
528	C₂²×C₂₃	—	16	4	no	—
529	C₂²×C₂₃	—	16	4	no	—
530	C₂²×C₂₃	D₄²	1	2	yes	—
531	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
532	C₄×C₂₃	—	2	4	no	—
533	C₄×C₂₃	—	2	2	no	—
534	C₄×C₂₃	—	2	2	no	—
535	C₄×C₂₃	—	4	2	no	—
536	C₄×C₂₃	—	4	2	no	—
537	C₄×C₂₃	—	4	1	no	—
538	C₄×C₂₃	—	4	1	no	—
539	C₄×C₂₃	—	4	2	no	—
540	C₄×C₂₃	D₄²	1	2	yes	—
541	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
542	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
543	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
544	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic, complemented
545	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
546	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
547	#576	—	2	8	no	—
548	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
549	C₂×AGL(1,ℤ/8)	—	2	8	no	—
550	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
551	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
552	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
553	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
554	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
555	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
556	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
557	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic, complemented
558	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
559	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
560	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
561	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
562	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
563	C₂²×D₈	C₂²×C₂₃	1	2	yes	complemented
564	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
565	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
566	#547	—	2	2	no	—
567	#547	C₂²×C₂₃	1	4	yes	complemented
568	#546	—	2	2	no	—
569	#546	—	2	2	no	—
570	#546	C₂²×C₂₃	1	4	yes	complemented
571	#546	C₂²×C₂₃	1	4	yes	complemented
572	D₄²	—	2	2	no	—
573	D₄²	C₂²×C₂₃	1	4	yes	complemented
574	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
575	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
576	#535	C₂²×C₂₃	1	1	yes	characteristic
577	#535	C₂²×C₂₃	1	1	yes	characteristic, complemented
578	#534	—	2	2	no	—
579	#534	—	2	2	no	—
580	#525	C₂²×C₂₃	1	1	yes	characteristic
581	#525	C₂²×C₂₃	1	1	yes	characteristic, complemented
582	#525	C₂²×C₂₃	1	1	yes	characteristic, complemented
583	C₂×#123	—	2	2	no	—
584	C₂×#120	—	2	2	no	—
585	#518	C₂²×C₂₃	1	1	yes	characteristic, complemented
586	#518	C₂²×C₂₃	1	1	yes	characteristic, complemented
587	#497	C₂²×C₂₃	1	2	yes	complemented
588	#496	C₂²×C₂₃	1	2	yes	complemented
589	#495	C₂²×C₂₃	1	2	yes	complemented
590	#492	C₂²×C₂₃	1	2	yes	complemented
591	#470	C₂²×C₂₃	1	2	yes	complemented
592	#469	C₂²×C₂₃	1	2	yes	complemented
593	#468	C₂²×C₂₃	1	4	yes	complemented
594	#468	C₂²×C₂₃	1	2	yes	complemented
595	#468	C₂²×C₂₃	1	2	yes	complemented
596	#465	C₂²×C₂₃	1	4	yes	complemented
597	#463	C₂²×C₂₃	1	4	yes	complemented
598	#463	C₂²×C₂₃	1	4	yes	complemented
599	#461	C₂²×C₂₃	1	4	yes	complemented
600	#459	C₂²×C₂₃	1	4	yes	complemented
601	#452	C₂²×C₂₃	1	4	yes	complemented
602	#452	C₂²×C₂₃	1	4	yes	complemented
603	#450	C₂²×C₂₃	1	4	yes	complemented
604	#450	C₂²×C₂₃	1	4	yes	complemented
605	#449	C₂²×C₂₃	1	4	yes	complemented
606	#449	C₂²×C₂₃	1	4	yes	complemented
607	#447	C₂²×C₂₃	1	4	yes	complemented
608	#447	C₂²×C₂₃	1	4	yes	complemented
609	#442	C₂²×C₂₃	1	4	yes	complemented
610	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
611	#436	C₂²×C₂₃	1	4	yes	complemented
612	#435	C₂²×C₂₃	1	4	yes	complemented
613	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
614	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
615	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
616	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
617	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
618	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
619	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
620	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
621	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
622	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
623	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
624	C₂×C₂₃	—	2	2	no	—
625	C₂×C₂₃	—	4	2	no	—
626	C₂×C₂₃	—	4	2	no	—
627	C₂×C₂₃	—	4	4	no	—
628	C₂×C₂₃	—	4	4	no	—
629	C₂×C₂₃	—	8	2	no	—
630	C₂×C₂₃	—	8	1	no	—
631	C₂×C₂₃	—	8	1	no	—
632	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
633	C₂×C₂₃	#3585	1	2	yes	—
634	C₂⁵	—	2	1	no	—
635	H(5,𝔽₂)	—	2	4	no	—
636	H(5,𝔽₂)	—	2	4	no	—
637	H(5,𝔽₂)	—	4	2	no	—
638	H(5,𝔽₂)	—	4	2	no	—
639	C₂×#41	—	2	1	no	—
640	C₂×#41	—	2	1	no	—
641	C₂×#41	—	2	2	no	—
642	C₂×#41	—	2	4	no	—
643	C₂×#41	—	4	2	no	—
644	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
645	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
646	C₂×#41	C₂³×C₂₃	1	2	yes	—
647	C₂×#41	C₂³×C₂₃	1	4	yes	—
648	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
649	C₂×#41	C₂³×C₂₃	1	2	yes	complemented
650	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
651	C₂²×D₄	—	2	4	no	—
652	C₂²×D₄	—	2	1	no	—
653	C₂²×D₄	—	2	2	no	—
654	C₂²×D₄	—	2	2	no	—
655	C₂²×D₄	—	2	1	no	—
656	C₂²×D₄	—	2	1	no	—
657	C₂²×D₄	—	2	4	no	—
658	C₂²×D₄	—	2	1	no	—
659	C₂²×D₄	—	2	2	no	—
660	C₂²×D₄	—	4	2	no	—
661	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
662	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
663	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
664	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
665	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
666	C₂²×D₄	C₂³×C₂₃	1	2	yes	complemented
667	C₂³×C₄	—	2	1	no	—
668	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
669	#137	—	4	2	no	—
670	AGL(1,ℤ/8)	—	2	4	no	—
671	AGL(1,ℤ/8)	—	2	4	no	—
672	AGL(1,ℤ/8)	—	2	16	no	—
673	AGL(1,ℤ/8)	—	2	16	no	—
674	AGL(1,ℤ/8)	—	2	8	no	—
675	AGL(1,ℤ/8)	—	2	8	no	—
676	AGL(1,ℤ/8)	—	4	2	no	—
677	#135	—	2	8	no	—
678	#135	—	2	4	no	—
679	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic, complemented
680	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	complemented
681	C₂×SD₁₆	—	2	4	no	—
682	C₂×SD₁₆	—	2	4	no	—
683	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
684	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
685	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	complemented
689	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic, complemented
690	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic, complemented
691	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	complemented
692	C₂×D₈	—	2	4	no	—
693	C₂×D₈	—	2	8	no	—
694	C₂×D₈	D₄×C₂₃	1	8	yes	complemented
695	C₂×D₈	C₂³×C₂₃	1	2	yes	—
696	C₂×D₈	C₂³×C₂₃	1	4	yes	—
697	C₂×D₈	C₂³×C₂₃	1	2	yes	—
698	C₂×D₈	C₂³×C₂₃	1	2	yes	—
699	C₂×D₈	C₂³×C₂₃	1	2	yes	—
700	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
701	C₂×D₈	C₂³×C₂₃	1	2	yes	complemented
702	#131	—	2	4	no	—
703	C₂×M₁₆	—	2	4	no	—
704	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
705	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
706	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
707	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
708	C₂×M₁₆	C₂³×C₂₃	1	2	yes	complemented
709	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
710	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
711	C₂²×C₈	C₂³×C₂₃	1	2	yes	complemented
712	C₄⋊Q₈	—	2	1	no	—
713	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
714	#127	—	2	1	no	—
715	#127	C₂³×C₂₃	1	2	yes	—
716	#124	—	2	1	no	—
717	#124	—	2	1	no	—
718	#124	C₂³×C₂₃	1	2	yes	—
719	#124	C₂³×C₂₃	1	2	yes	complemented
720	#123	—	2	2	no	—
721	#123	—	2	1	no	—
722	#123	—	2	1	no	—
723	#123	—	2	4	no	—
724	#123	—	2	4	no	—
725	#123	—	2	2	no	—
726	#123	—	2	4	no	—
727	#123	—	2	4	no	—
728	#123	D₄×C₂₃	1	2	yes	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
731	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
732	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
733	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
734	#121	—	2	4	no	—
735	#121	—	2	4	no	—
736	#121	—	2	2	no	—
737	#121	—	2	4	no	—
738	#121	—	2	4	no	—
739	#121	D₄×C₂₃	1	2	yes	—
740	#121	C₂³×C₂₃	1	2	yes	—
741	#121	C₂³×C₂₃	1	2	yes	—
742	#121	C₂³×C₂₃	1	4	yes	—
743	#120	—	2	1	no	—
744	#120	—	2	1	no	—
745	#120	—	2	2	no	—
746	#120	—	2	4	no	—
747	#120	—	2	4	no	—
748	#120	—	2	2	no	—
749	#120	—	2	4	no	—
750	#120	—	2	4	no	—
751	#120	D₄×C₂₃	1	2	yes	—
752	C₄×D₄	—	2	2	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	C₂³×C₂₃	1	4	yes	—
757	C₄×D₄	C₂³×C₂₃	1	4	yes	—
758	C₄×D₄	C₂³×C₂₃	1	4	yes	complemented
759	#117	C₂³×C₂₃	1	1	yes	characteristic
760	#117	C₂³×C₂₃	1	1	yes	characteristic
761	#117	C₂³×C₂₃	1	1	yes	characteristic
762	C₂×C₄⋊C₄	—	2	4	no	—
763	C₂×C₂²⋊C₄	—	2	2	no	—
764	C₂×C₂²⋊C₄	—	2	2	no	—
765	C₂×C₂²⋊C₄	—	2	4	no	—
766	C₂×C₂²⋊C₄	—	2	4	no	—
767	#107	C₂³×C₂₃	1	2	yes	complemented
768	#106	C₂³×C₂₃	1	2	yes	complemented
769	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
770	#103	C₂³×C₂₃	1	2	yes	complemented
771	#103	C₂³×C₂₃	1	2	yes	complemented
772	#103	C₂³×C₂₃	1	4	yes	complemented
773	#102	C₂³×C₂₃	1	4	yes	—
774	#102	C₂³×C₂₃	1	4	yes	—
775	#102	C₂³×C₂₃	1	2	yes	complemented
776	#102	C₂³×C₂₃	1	2	yes	complemented
777	#102	C₂³×C₂₃	1	4	yes	complemented
778	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
779	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
780	#97	C₂³×C₂₃	1	2	yes	complemented
781	C₄×C₈	C₂³×C₂₃	1	2	yes	complemented
782	C₂₃	#61058	1	1	yes	characteristic, direct product factor, Sylow
783	C₂⁴	—	2	1	no	—
784	C₂⁴	—	2	1	no	—
785	C₂⁴	—	2	4	no	—
786	C₂⁴	—	2	2	no	—
787	C₂⁴	—	2	1	no	—
788	C₂⁴	—	2	2	no	—
789	C₂⁴	—	4	4	no	—
790	C₂⁴	—	8	4	no	—
791	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
792	#41	—	2	2	no	—
793	#41	—	2	2	no	—
794	#41	—	2	4	no	—
795	#41	—	2	4	no	—
796	#41	—	2	8	no	—
797	#41	—	2	2	no	—
798	#41	—	2	2	no	—
799	#41	—	2	2	no	—
800	#41	—	2	2	no	—
801	#41	—	4	4	no	—
802	#41	—	4	2	no	—
803	#41	—	4	2	no	—
804	#41	—	4	8	no	—
805	#41	—	4	4	no	—
806	#41	—	4	4	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	2	no	—
809	C₂×Q₈	—	2	2	no	—
810	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
811	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
812	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
813	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	8	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	1	no	—
826	C₂×D₄	—	2	1	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	4	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	4	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	4	4	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	4	2	no	—
839	C₂×D₄	—	4	8	no	—
840	C₂×D₄	—	4	4	no	—
841	C₂×D₄	—	4	4	no	—
842	C₂×D₄	—	4	4	no	—
843	C₂×D₄	—	4	8	no	—
844	C₂×D₄	—	4	8	no	—
845	C₂×D₄	—	4	4	no	—
846	C₂×D₄	—	8	8	no	—
847	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
848	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
849	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
850	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
851	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	complemented
852	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
853	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
854	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
855	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
856	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	4	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	4	no	—
866	C₂²×C₄	—	2	4	no	—
867	C₂²×C₄	—	4	4	no	—
868	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
869	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
871	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
873	Q₁₆	—	2	2	no	—
874	Q₁₆	—	4	2	no	—
875	SD₁₆	—	2	8	no	—
876	SD₁₆	—	2	4	no	—
877	SD₁₆	—	2	4	no	—
878	SD₁₆	—	2	4	no	—
879	SD₁₆	—	2	4	no	—
880	SD₁₆	—	2	2	no	—
881	SD₁₆	—	2	2	no	—
882	SD₁₆	—	4	2	no	—
883	SD₁₆	—	4	2	no	—
884	D₈	—	2	4	no	—
885	D₈	—	2	8	no	—
886	D₈	—	2	4	no	—
887	D₈	—	2	2	no	—
888	D₈	—	4	2	no	—
889	D₈	C₂×D₄×C₂₃	1	8	yes	complemented
890	D₈	C₂×D₄×C₂₃	1	8	yes	complemented
891	M₁₆	—	2	2	no	—
892	M₁₆	—	2	2	no	—
893	M₁₆	—	2	4	no	—
894	M₁₆	—	2	4	no	—
895	M₁₆	—	2	4	no	—
896	C₂×C₈	—	2	2	no	—
897	C₂×C₈	—	2	4	no	—
898	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	complemented
899	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
900	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
901	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
902	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	2	4	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
909	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
910	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
911	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
912	C₂²⋊C₄	—	2	1	no	—
913	C₂²⋊C₄	—	2	1	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	4	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
925	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
926	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
927	C₄²	—	2	1	no	—
928	C₄²	—	2	1	no	—
929	C₄²	C₂⁴×C₂₃	1	2	yes	—
930	C₂³	—	2	2	no	—
931	C₂³	—	2	2	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	4	no	—
934	C₂³	—	2	4	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	4	2	no	—
939	C₂³	—	4	8	no	—
940	C₂³	—	4	4	no	—
941	C₂³	—	4	4	no	—
942	C₂³	—	4	8	no	—
943	C₂³	—	4	2	no	—
944	C₂³	—	8	2	no	—
945	C₂³	—	8	2	no	—
946	C₂³	—	8	4	no	—
947	C₂³	—	8	2	no	—
948	C₂³	—	8	4	no	—
949	C₂³	—	8	4	no	—
950	C₂³	—	8	16	no	—
951	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
952	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
953	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
954	Q₈	—	2	2	no	—
955	Q₈	—	2	2	no	—
956	Q₈	—	2	1	no	—
957	Q₈	—	2	1	no	—
958	Q₈	—	2	1	no	—
959	Q₈	—	2	2	no	—
960	Q₈	—	2	1	no	—
961	Q₈	—	4	2	no	—
962	D₄	—	2	4	no	—
963	D₄	—	2	1	no	—
964	D₄	—	2	1	no	—
965	D₄	—	2	2	no	—
966	D₄	—	2	2	no	—
967	D₄	—	2	2	no	—
968	D₄	—	2	1	no	—
969	D₄	—	2	2	no	—
970	D₄	—	2	1	no	—
971	D₄	—	2	4	no	—
972	D₄	—	2	4	no	—
973	D₄	—	2	2	no	—
974	D₄	—	4	4	no	—
975	D₄	—	4	8	no	—
976	D₄	—	4	4	no	—
977	D₄	—	4	4	no	—
978	D₄	—	4	4	no	—
979	D₄	—	4	4	no	—
980	D₄	—	4	8	no	—
981	D₄	—	4	4	no	—
982	D₄	—	4	2	no	—
983	D₄	—	4	2	no	—
984	D₄	—	4	2	no	—
985	D₄	—	8	4	no	—
986	D₄	—	8	4	no	—
987	D₄	—	8	2	no	—
988	D₄	C₂²×D₄×C₂₃	1	4	yes	—
989	D₄	C₂²×D₄×C₂₃	1	4	yes	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	4	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	4	8	no	—
1002	C₂×C₄	—	4	4	no	—
1003	C₂×C₄	—	4	4	no	—
1004	C₂×C₄	—	4	2	no	—
1005	C₂×C₄	—	4	2	no	—
1006	C₂×C₄	—	4	2	no	—
1007	C₂×C₄	—	8	4	no	—
1008	C₂×C₄	—	8	4	no	—
1009	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1010	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1011	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1012	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1013	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1014	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1015	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1016	C₈	—	2	2	no	—
1017	C₈	—	2	2	no	—
1018	C₈	—	2	2	no	—
1019	C₈	C₂²×D₄×C₂₃	1	2	yes	—
1020	C₈	C₂²×D₄×C₂₃	1	2	yes	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	2	no	—
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	4	no	—
1025	C₂²	—	2	4	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	4	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	4	4	no	—
1030	C₂²	—	4	4	no	—
1031	C₂²	—	4	4	no	—
1032	C₂²	—	4	1	no	—
1033	C₂²	—	4	1	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	4	4	no	—
1037	C₂²	—	4	2	no	—
1038	C₂²	—	8	4	no	—
1039	C₂²	—	8	4	no	—
1040	C₂²	—	8	4	no	—
1041	C₂²	—	8	16	no	—
1042	C₂²	—	16	4	no	—
1043	C₂²	—	16	4	no	—
1044	C₂²	D₄²×C₂₃	1	2	yes	—
1045	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1046	C₄	—	2	2	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	4	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	2	no	—
1054	C₄	D₄²×C₂₃	1	2	yes	—
1055	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
1056	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1057	C₂	—	2	2	no	—
1058	C₂	—	4	2	no	—
1059	C₂	—	4	2	no	—
1060	C₂	—	4	4	no	—
1061	C₂	—	4	4	no	—
1062	C₂	—	8	2	no	—
1063	C₂	—	8	1	no	—
1064	C₂	—	8	1	no	—
1065	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
1066	C₂	C₂₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#576	C₂	semidirect
2. C₂²×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
3. C₂₃×#3485	C₂	semidirect
4. C₂₃×#3484	C₂	semidirect
5. C₂₃×#3273	C₂	semidirect
6. C₂₃×#3272	C₂	semidirect
7. C₂₃×#3267	C₂	semidirect
8. C₂₃×#3264	C₂	semidirect
9. C₂₃×#3154	C₂	semidirect
10. C₂₃×#3057	C₂	semidirect
11. C₂₃×#3054	C₂	semidirect
12. C₂₃×#3042	C₂	semidirect
13. C₂₃×#3041	C₂	semidirect
14. C₂₃×#3009	C₂	semidirect
15. C₂₃×#3008	C₂	semidirect
16. C₂₃×#3005	C₂	semidirect
17. C₂₃×#3003	C₂	semidirect
18. C₂₃×#2948	C₂	semidirect
19. C₂₃×#2930	C₂	semidirect
21. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
22. C₂²×#41×C₂₃	C₂²	semidirect
23. C₂³×D₄×C₂₃	C₂²	semidirect
25. C₂×C₂₃×#137	C₂²	semidirect
28. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
29. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
30. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
31. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
32. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
33. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
34. C₂×C₂₃×#135	C₂²	semidirect
35. C₂×C₂₃×#135	C₂²	semidirect
36. C₂²×SD₁₆×C₂₃	C₂²	semidirect
37. C₂²×SD₁₆×C₂₃	C₂²	semidirect
39. C₂²×D₈×C₂₃	C₂²	semidirect
40. C₂²×D₈×C₂₃	C₂²	semidirect
41. C₂×C₂₃×#131	C₂²	semidirect
42. C₂²×M₁₆×C₂₃	C₂²	semidirect
44. C₂₃×#547	C₂²	semidirect
47. C₂₃×#546	C₂²	semidirect
48. C₂₃×#546	C₂²	semidirect
50. D₄²×C₂₃	C₂²	semidirect
51. C₂₃×#536	C₂²	semidirect
52. C₂₃×#536	C₂²	semidirect
54. C₂₃×#535	C₂²	semidirect
58. C₂₃×#525	C₂²	semidirect
59. C₂₃×#525	C₂²	semidirect
62. C₂₃×#518	C₂²	semidirect
63. C₂₃×#518	C₂²	semidirect
64. C₂₃×#497	C₂²	semidirect
65. C₂₃×#496	C₂²	semidirect
66. C₂₃×#495	C₂²	semidirect
67. C₂₃×#492	C₂²	semidirect
68. C₂₃×#470	C₂²	semidirect
69. C₂₃×#469	C₂²	semidirect
70. C₂₃×#468	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#468	C₂²	semidirect
73. C₂₃×#465	C₂²	semidirect
74. C₂₃×#463	C₂²	semidirect
75. C₂₃×#463	C₂²	semidirect
76. C₂₃×#461	C₂²	semidirect
77. C₂₃×#459	C₂²	semidirect
78. C₂₃×#452	C₂²	semidirect
79. C₂₃×#452	C₂²	semidirect
80. C₂₃×#450	C₂²	semidirect
81. C₂₃×#450	C₂²	semidirect
82. C₂₃×#449	C₂²	semidirect
83. C₂₃×#449	C₂²	semidirect
84. C₂₃×#447	C₂²	semidirect
85. C₂₃×#447	C₂²	semidirect
86. C₂₃×#442	C₂²	semidirect
87. C₄×D₈×C₂₃	C₂²	semidirect
88. C₂₃×#436	C₂²	semidirect
89. C₂₃×#435	C₂²	semidirect
90. C₂₃×#427	C₂²	semidirect
91. C₂₃×#424	C₂²	semidirect
92. C₂₃×#419	C₂²	semidirect
93. C₂₃×#418	C₂²	semidirect
94. C₂₃×#418	C₂²	semidirect
95. C₂₃×#418	C₂²	semidirect
96. C₂₃×#416	C₂²	semidirect
97. C₂₃×#416	C₂²	semidirect
98. C₂₃×#408	C₂²	semidirect
99. C₂₃×#407	C₂²	semidirect
100. C₂₃×#405	C₂²	semidirect
116. C₂×#41×C₂₃	C₂³	semidirect
133. C₂²×D₄×C₂₃	C₂³	semidirect
146. C₂×Q₁₆×C₂₃	C₂³	semidirect
147. C₂×Q₁₆×C₂₃	C₂³	semidirect
155. C₂×SD₁₆×C₂₃	C₂³	semidirect
156. C₂×SD₁₆×C₂₃	C₂³	semidirect
157. C₂×SD₁₆×C₂₃	C₂³	semidirect
158. C₂×SD₁₆×C₂₃	C₂³	semidirect
161. C₂×D₈×C₂₃	D₄	semidirect
167. C₂×D₈×C₂₃	C₂³	semidirect
168. C₂×D₈×C₂₃	C₂³	semidirect
175. C₂×M₁₆×C₂₃	C₂³	semidirect
178. C₂²×C₈×C₂₃	C₂³	semidirect
180. C₂₃×C₄⋊Q₈	C₂³	semidirect
186. C₂₃×#124	C₂³	semidirect
200. C₂₃×C₂²⋊Q₈	C₂³	semidirect
225. C₄×D₄×C₂₃	C₂³	semidirect
234. C₂₃×#107	C₂³	semidirect
235. C₂₃×#106	C₂³	semidirect
236. C₂₃×C₄⋊C₈	C₂³	semidirect
237. C₂₃×#103	C₂³	semidirect
238. C₂₃×#103	C₂³	semidirect
239. C₂₃×#103	C₂³	semidirect
242. C₂₃×#102	C₂³	semidirect
243. C₂₃×#102	C₂³	semidirect
244. C₂₃×#102	C₂³	semidirect
246. C₂₃×C₂²⋊C₈	C₂³	semidirect
247. C₂₃×#97	C₂³	semidirect
248. C₄×C₈×C₂₃	C₂³	semidirect
317. C₂×D₄×C₂₃	C₂×D₄	semidirect
355. D₈×C₂₃	C₂×D₄	semidirect
356. D₈×C₂₃	C₂×D₄	semidirect
364. C₂×C₈×C₂₃	C₂×D₄	semidirect
396. #61058	C₂₃	direct (N × H)
488. C₂×#576	C₂×C₂₃	semidirect
489. C₂²×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
490. #3485	C₂×C₂₃	semidirect
491. #3484	C₂×C₂₃	semidirect
492. #3273	C₂×C₂₃	semidirect
493. #3272	C₂×C₂₃	semidirect
494. #3267	C₂×C₂₃	semidirect
495. #3264	C₂×C₂₃	semidirect
496. #3154	C₂×C₂₃	semidirect
497. #3057	C₂×C₂₃	semidirect
498. #3054	C₂×C₂₃	semidirect
499. #3042	C₂×C₂₃	semidirect
500. #3041	C₂×C₂₃	semidirect
501. #3009	C₂×C₂₃	semidirect
502. #3008	C₂×C₂₃	semidirect
503. #3005	C₂×C₂₃	semidirect
504. #3003	C₂×C₂₃	semidirect
505. #2948	C₂×C₂₃	semidirect
506. #2930	C₂×C₂₃	semidirect
544. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
545. C₂²×#41	C₂²×C₂₃	semidirect
546. C₂³×D₄	C₂²×C₂₃	semidirect
548. C₂×#137	C₂²×C₂₃	semidirect
551. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
552. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
553. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
554. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
555. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
556. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
557. C₂×#135	C₂²×C₂₃	semidirect
558. C₂×#135	C₂²×C₂₃	semidirect
559. C₂²×SD₁₆	C₂²×C₂₃	semidirect
560. C₂²×SD₁₆	C₂²×C₂₃	semidirect
562. C₂²×D₈	C₂²×C₂₃	semidirect
563. C₂²×D₈	C₂²×C₂₃	semidirect
564. C₂×#131	C₂²×C₂₃	semidirect
565. C₂²×M₁₆	C₂²×C₂₃	semidirect
567. #547	C₂²×C₂₃	semidirect
570. #546	C₂²×C₂₃	semidirect
571. #546	C₂²×C₂₃	semidirect
573. D₄²	C₂²×C₂₃	semidirect
574. #536	C₂²×C₂₃	semidirect
575. #536	C₂²×C₂₃	semidirect
577. #535	C₂²×C₂₃	semidirect
581. #525	C₂²×C₂₃	semidirect
582. #525	C₂²×C₂₃	semidirect
585. #518	C₂²×C₂₃	semidirect
586. #518	C₂²×C₂₃	semidirect
587. #497	C₂²×C₂₃	semidirect
588. #496	C₂²×C₂₃	semidirect
589. #495	C₂²×C₂₃	semidirect
590. #492	C₂²×C₂₃	semidirect
591. #470	C₂²×C₂₃	semidirect
592. #469	C₂²×C₂₃	semidirect
593. #468	C₂²×C₂₃	semidirect
594. #468	C₂²×C₂₃	semidirect
595. #468	C₂²×C₂₃	semidirect
596. #465	C₂²×C₂₃	semidirect
597. #463	C₂²×C₂₃	semidirect
598. #463	C₂²×C₂₃	semidirect
599. #461	C₂²×C₂₃	semidirect
600. #459	C₂²×C₂₃	semidirect
601. #452	C₂²×C₂₃	semidirect
602. #452	C₂²×C₂₃	semidirect
603. #450	C₂²×C₂₃	semidirect
604. #450	C₂²×C₂₃	semidirect
605. #449	C₂²×C₂₃	semidirect
606. #449	C₂²×C₂₃	semidirect
607. #447	C₂²×C₂₃	semidirect
608. #447	C₂²×C₂₃	semidirect
609. #442	C₂²×C₂₃	semidirect
610. C₄×D₈	C₂²×C₂₃	semidirect
611. #436	C₂²×C₂₃	semidirect
612. #435	C₂²×C₂₃	semidirect
613. #427	C₂²×C₂₃	semidirect
614. #424	C₂²×C₂₃	semidirect
615. #419	C₂²×C₂₃	semidirect
616. #418	C₂²×C₂₃	semidirect
617. #418	C₂²×C₂₃	semidirect
618. #418	C₂²×C₂₃	semidirect
619. #416	C₂²×C₂₃	semidirect
620. #416	C₂²×C₂₃	semidirect
621. #408	C₂²×C₂₃	semidirect
622. #407	C₂²×C₂₃	semidirect
623. #405	C₂²×C₂₃	semidirect
649. C₂×#41	C₂³×C₂₃	semidirect
666. C₂²×D₄	C₂³×C₂₃	semidirect
679. C₂×Q₁₆	C₂³×C₂₃	semidirect
680. C₂×Q₁₆	C₂³×C₂₃	semidirect
688. C₂×SD₁₆	C₂³×C₂₃	semidirect
689. C₂×SD₁₆	C₂³×C₂₃	semidirect
690. C₂×SD₁₆	C₂³×C₂₃	semidirect
691. C₂×SD₁₆	C₂³×C₂₃	semidirect
694. C₂×D₈	D₄×C₂₃	semidirect
700. C₂×D₈	C₂³×C₂₃	semidirect
701. C₂×D₈	C₂³×C₂₃	semidirect
708. C₂×M₁₆	C₂³×C₂₃	semidirect
711. C₂²×C₈	C₂³×C₂₃	semidirect
713. C₄⋊Q₈	C₂³×C₂₃	semidirect
719. #124	C₂³×C₂₃	semidirect
733. C₂²⋊Q₈	C₂³×C₂₃	semidirect
758. C₄×D₄	C₂³×C₂₃	semidirect
767. #107	C₂³×C₂₃	semidirect
768. #106	C₂³×C₂₃	semidirect
769. C₄⋊C₈	C₂³×C₂₃	semidirect
770. #103	C₂³×C₂₃	semidirect
771. #103	C₂³×C₂₃	semidirect
772. #103	C₂³×C₂₃	semidirect
775. #102	C₂³×C₂₃	semidirect
776. #102	C₂³×C₂₃	semidirect
777. #102	C₂³×C₂₃	semidirect
779. C₂²⋊C₈	C₂³×C₂₃	semidirect
780. #97	C₂³×C₂₃	semidirect
781. C₄×C₈	C₂³×C₂₃	semidirect
782. C₂₃	#61058	direct (N × H)
851. C₂×D₄	C₂×D₄×C₂₃	semidirect
889. D₈	C₂×D₄×C₂₃	semidirect
890. D₈	C₂×D₄×C₂₃	semidirect
898. C₂×C₈	C₂×D₄×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#576	2
C₂²×C₂₃×AGL(1,ℤ/8)	2
C₂₃×#3485	2
C₂₃×#3484	2
C₂₃×#3273	2
C₂₃×#3272	2
C₂₃×#3267	2
C₂₃×#3264	2
C₂₃×#3154	2
C₂₃×#3057	2
C₂₃×#3054	2
C₂₃×#3042	2
C₂₃×#3041	2
C₂₃×#3009	2
C₂₃×#3008	2
C₂₃×#3005	2
C₂₃×#3003	2
C₂₃×#2948	2
C₂₃×#2930	2
#61058	23

Subgroups — C23×#61058 #19208684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61058 #19208684