Subgroups — C₂₃×#61171 #19208797

Order 5888.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3319	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3318	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3309	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3308	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3305	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3301	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3297	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3294	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#555	C₂²	1	2	yes	complemented
32	C₂₃×#553	C₂²	1	2	yes	complemented
33	C₂₃×#553	C₂²	1	2	yes	complemented
34	C₂₃×#551	—	2	2	no	—
35	C₂₃×#550	C₂²	1	2	yes	complemented
36	C₂₃×#548	C₂²	1	2	yes	complemented
37	C₂₃×#547	C₂²	1	2	yes	complemented
38	C₂₃×#546	—	2	2	no	—
39	C₂₃×#546	—	2	2	no	—
40	C₂₃×#546	C₂²	1	2	yes	complemented
41	D₄²×C₂₃	—	2	2	no	—
42	D₄²×C₂₃	C₂²	1	2	yes	complemented
43	C₂₃×#544	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#542	—	2	1	no	—
45	C₂₃×#540	—	2	1	no	—
46	C₂₃×#537	—	2	1	no	—
47	C₂₃×#537	C₂²	1	1	yes	characteristic
48	C₂₃×#535	—	2	1	no	—
49	C₂₃×#535	C₂²	1	1	yes	characteristic
50	C₂₃×#535	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#532	—	2	1	no	—
52	C₂₃×#529	—	2	1	no	—
53	C₂₃×#525	—	2	1	no	—
54	C₂₃×#525	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×#121	—	2	1	no	—
56	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
57	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#520	C₂²	1	1	yes	characteristic
59	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#518	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#490	C₂²	1	2	yes	complemented
63	C₂₃×#489	C₂²	1	2	yes	complemented
64	C₂₃×#488	C₂²	1	2	yes	complemented
65	C₂₃×#486	C₂²	1	2	yes	complemented
66	C₂₃×#485	C₂²	1	2	yes	complemented
67	C₂₃×#484	C₂²	1	2	yes	complemented
68	C₂₃×#482	C₂²	1	2	yes	complemented
69	C₂₃×#482	C₂²	1	2	yes	complemented
70	C₂₃×#482	C₂²	1	2	yes	complemented
71	C₂₃×#481	C₂²	1	2	yes	complemented
72	C₂₃×#480	C₂²	1	2	yes	complemented
73	C₂₃×#480	C₂²	1	2	yes	complemented
74	C₂₃×#479	C₂²	1	2	yes	complemented
75	C₂₃×#478	C₂²	1	2	yes	complemented
76	C₂₃×#477	C₂²	1	2	yes	complemented
77	C₂₃×#474	C₂²	1	2	yes	complemented
78	C₂₃×#469	C₂²	1	2	yes	complemented
79	C₂₃×#468	C₂²	1	2	yes	complemented
80	C₂₃×#466	C₂²	1	2	yes	complemented
81	C₂₃×#466	C₂²	1	2	yes	complemented
82	C₂₃×#466	C₂²	1	2	yes	complemented
83	C₂₃×#466	C₂²	1	2	yes	complemented
84	C₂₃×#466	C₂²	1	2	yes	complemented
85	C₂₃×#465	C₂²	1	2	yes	complemented
86	C₂₃×#463	C₂²	1	2	yes	complemented
87	C₂₃×#463	C₂²	1	2	yes	complemented
88	C₂₃×#459	C₂²	1	2	yes	complemented
89	C₂₃×#459	C₂²	1	2	yes	complemented
90	C₂₃×#449	C₂²	1	2	yes	complemented
91	C₂₃×#449	C₂²	1	2	yes	complemented
92	C₂₃×#449	C₂²	1	2	yes	complemented
93	C₂₃×#449	C₂²	1	2	yes	complemented
94	C₂₃×#448	C₂²	1	2	yes	complemented
95	C₂₃×#447	C₂²	1	2	yes	complemented
96	C₂₃×#447	C₂²	1	2	yes	complemented
97	C₂₃×#447	C₂²	1	2	yes	complemented
98	C₂₃×#442	C₂²	1	2	yes	complemented
99	C₂₃×#440	C₂²	1	2	yes	complemented
100	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
101	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
102	C₂₃×#435	C₂²	1	2	yes	complemented
103	C₂₃×#435	C₂²	1	2	yes	complemented
104	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
105	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
106	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#418	C₂²	1	2	yes	complemented
113	C₂₃×#417	C₂²	1	1	yes	characteristic
114	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#417	C₂²	1	2	yes	complemented
116	C₂₃×#416	C₂²	1	1	yes	characteristic
117	C₂₃×#416	C₂²	1	1	yes	characteristic
118	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
119	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
120	C₂₃×#416	C₂²	1	2	yes	complemented
121	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
122	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
123	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
124	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
130	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
132	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
133	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
134	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂₃×H(5,𝔽₂)	—	2	4	no	—
136	C₂₃×H(5,𝔽₂)	—	4	2	no	—
137	C₂×#41×C₂₃	—	2	1	no	—
138	C₂×#41×C₂₃	—	2	2	no	—
139	C₂×#41×C₂₃	—	2	1	no	—
140	C₂×#41×C₂₃	—	2	1	no	—
141	C₂×#41×C₂₃	—	2	4	no	—
142	C₂×#41×C₂₃	—	4	2	no	—
143	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×#41×C₂₃	C₂³	1	2	yes	—
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	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₂₃	—	2	1	no	—
151	C₂²×D₄×C₂₃	—	2	1	no	—
152	C₂²×D₄×C₂₃	—	2	1	no	—
153	C₂²×D₄×C₂₃	—	2	1	no	—
154	C₂²×D₄×C₂₃	—	2	2	no	—
155	C₂²×D₄×C₂₃	—	2	2	no	—
156	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
158	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
159	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
160	C₂³×C₄×C₂₃	—	2	1	no	—
161	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
162	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
163	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
164	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
166	C₂×D₈×C₂₃	—	4	2	no	—
167	C₂×D₈×C₂₃	C₂³	1	2	yes	—
168	C₂×D₈×C₂₃	C₂³	1	2	yes	—
169	C₂×D₈×C₂₃	C₂³	1	2	yes	—
170	C₂×D₈×C₂₃	C₂³	1	2	yes	—
171	C₂₃×#131	—	4	2	no	—
172	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
175	C₂²×C₈×C₂₃	—	4	2	no	—
176	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
179	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
181	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
182	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
183	C₂₃×C₄⋊Q₈	—	2	1	no	—
184	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
185	C₂₃×#127	—	2	2	no	—
186	C₂₃×#127	—	2	1	no	—
187	C₂₃×#127	C₂³	1	2	yes	—
188	C₂₃×#126	—	2	2	no	—
189	C₂₃×#126	—	2	2	no	—
190	C₂₃×#125	—	2	1	no	—
191	C₂₃×#125	C₂³	1	2	yes	—
192	C₂₃×#124	—	2	1	no	—
193	C₂₃×#124	—	2	2	no	—
194	C₂₃×#124	—	2	2	no	—
195	C₂₃×#124	—	2	2	no	—
196	C₂₃×#124	C₂³	1	2	yes	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×#123	—	2	2	no	—
199	C₂₃×#123	—	2	2	no	—
200	C₂₃×#123	—	2	2	no	—
201	C₂₃×#123	—	2	2	no	—
202	C₂₃×#123	D₄	1	2	yes	—
203	C₂₃×C₂²⋊Q₈	—	2	1	no	—
204	C₂₃×C₂²⋊Q₈	—	2	2	no	—
205	C₂₃×C₂²⋊Q₈	—	2	2	no	—
206	C₂₃×C₂²⋊Q₈	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₂₃×#121	—	2	2	no	—
211	C₂₃×#121	—	2	2	no	—
212	C₂₃×#121	—	2	2	no	—
213	C₂₃×#121	—	2	2	no	—
214	C₂₃×#121	—	2	1	no	—
215	C₂₃×#121	—	2	2	no	—
216	C₂₃×#121	—	2	1	no	—
217	C₂₃×#121	—	2	1	no	—
218	C₂₃×#121	—	2	1	no	—
219	C₂₃×#121	—	2	1	no	—
220	C₂₃×#121	—	2	1	no	—
221	C₂₃×#121	—	2	1	no	—
222	C₂₃×#121	—	2	2	no	—
223	C₂₃×#121	—	2	2	no	—
224	C₂₃×#121	—	2	2	no	—
225	C₂₃×#121	—	2	2	no	—
226	C₂₃×#121	D₄	1	1	yes	characteristic
227	C₂₃×#121	D₄	1	1	yes	characteristic
228	C₂₃×#121	C₂³	1	2	yes	—
229	C₂₃×#121	C₂³	1	2	yes	—
230	C₂₃×#121	C₂³	1	2	yes	—
231	C₂₃×#121	C₂³	1	2	yes	—
232	C₂₃×#121	C₂³	1	2	yes	—
233	C₂₃×#121	C₂³	1	2	yes	—
234	C₂₃×#121	C₂³	1	2	yes	—
235	C₂₃×#120	—	2	2	no	—
236	C₂₃×#120	—	2	2	no	—
237	C₂₃×#120	—	2	2	no	—
238	C₂₃×#120	—	2	2	no	—
239	C₂₃×#120	—	2	2	no	—
240	C₂₃×#120	D₄	1	2	yes	—
241	C₄×Q₈×C₂₃	—	2	1	no	—
242	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
243	C₄×D₄×C₂₃	—	2	2	no	—
244	C₄×D₄×C₂₃	—	2	1	no	—
245	C₄×D₄×C₂₃	—	2	2	no	—
246	C₄×D₄×C₂₃	—	2	1	no	—
247	C₄×D₄×C₂₃	—	2	1	no	—
248	C₄×D₄×C₂₃	—	2	2	no	—
249	C₄×D₄×C₂₃	—	2	2	no	—
250	C₄×D₄×C₂₃	—	2	2	no	—
251	C₄×D₄×C₂₃	—	2	2	no	—
252	C₄×D₄×C₂₃	C₂³	1	2	yes	—
253	C₄×D₄×C₂₃	C₂³	1	2	yes	—
254	C₄×D₄×C₂₃	C₂³	1	2	yes	—
255	C₄×D₄×C₂₃	C₂³	1	2	yes	—
256	C₄×D₄×C₂₃	C₂³	1	2	yes	—
257	C₂₃×#117	—	2	1	no	—
258	C₂₃×#117	—	2	1	no	—
259	C₂₃×#117	—	2	2	no	—
260	C₂₃×#117	—	2	1	no	—
261	C₂₃×#117	C₂³	1	1	yes	characteristic
262	C₂₃×#117	C₂³	1	2	yes	—
263	C₂₃×#117	C₂³	1	1	yes	characteristic
264	C₂₃×#117	C₂³	1	1	yes	characteristic
265	C₂₃×#117	C₂³	1	1	yes	characteristic
266	C₂₃×#117	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
274	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
275	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
276	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
277	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
278	C₂×C₄²×C₂₃	—	2	1	no	—
279	C₂₃×#107	C₂³	1	2	yes	—
280	C₂₃×#107	C₂³	1	2	yes	—
281	C₂₃×#107	C₂³	1	2	yes	—
282	C₂₃×#107	C₂³	1	2	yes	—
283	C₂₃×#106	C₂³	1	2	yes	—
284	C₂₃×#106	C₂³	1	2	yes	—
285	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
286	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	1	yes	characteristic
289	C₂₃×#103	C₂³	1	1	yes	characteristic
290	C₂₃×#103	C₂³	1	1	yes	characteristic
291	C₂₃×#103	C₂³	1	1	yes	characteristic
292	C₂₃×#103	C₂³	1	1	yes	characteristic
293	C₂₃×#103	C₂³	1	1	yes	characteristic
294	C₂₃×#103	C₂³	1	1	yes	characteristic
295	C₂₃×#103	C₂³	1	2	yes	—
296	C₂₃×#103	C₂³	1	2	yes	—
297	C₂₃×#102	C₂³	1	1	yes	characteristic
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	1	yes	characteristic
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×#102	C₂³	1	1	yes	characteristic
303	C₂₃×#102	C₂³	1	1	yes	characteristic
304	C₂₃×#102	C₂³	1	1	yes	characteristic
305	C₂₃×#102	C₂³	1	1	yes	characteristic
306	C₂₃×#102	C₂³	1	2	yes	—
307	C₂₃×#102	C₂³	1	2	yes	—
308	C₂₃×#102	C₂³	1	2	yes	—
309	C₂₃×#102	C₂³	1	2	yes	—
310	C₂₃×#102	C₂³	1	2	yes	—
311	C₂₃×#102	C₂³	1	2	yes	—
312	C₂₃×#102	C₂³	1	2	yes	—
313	C₂₃×#102	C₂³	1	2	yes	—
314	C₂₃×#102	C₂³	1	2	yes	—
315	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₂₃×#97	C₂³	1	2	yes	—
320	C₄×C₈×C₂₃	C₂³	1	2	yes	—
321	C₂⁴×C₂₃	—	2	1	no	—
322	C₂⁴×C₂₃	—	2	1	no	—
323	C₂⁴×C₂₃	—	2	2	no	—
324	C₂⁴×C₂₃	—	2	1	no	—
325	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
326	#41×C₂₃	—	2	2	no	—
327	#41×C₂₃	—	2	2	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	2	no	—
334	#41×C₂₃	—	4	4	no	—
335	#41×C₂₃	—	4	1	no	—
336	#41×C₂₃	—	4	1	no	—
337	#41×C₂₃	—	4	2	no	—
338	#41×C₂₃	—	4	4	no	—
339	#41×C₂₃	—	4	4	no	—
340	#41×C₂₃	—	8	4	no	—
341	#41×C₂₃	#41	1	4	yes	complemented
342	C₂×Q₈×C₂₃	—	2	1	no	—
343	C₂×Q₈×C₂₃	—	2	2	no	—
344	C₂×Q₈×C₂₃	—	2	2	no	—
345	C₂×Q₈×C₂₃	—	4	1	no	—
346	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
347	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
348	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₂₃	—	2	1	no	—
350	C₂×D₄×C₂₃	—	2	2	no	—
351	C₂×D₄×C₂₃	—	2	4	no	—
352	C₂×D₄×C₂₃	—	2	2	no	—
353	C₂×D₄×C₂₃	—	2	2	no	—
354	C₂×D₄×C₂₃	—	2	1	no	—
355	C₂×D₄×C₂₃	—	2	1	no	—
356	C₂×D₄×C₂₃	—	2	2	no	—
357	C₂×D₄×C₂₃	—	2	1	no	—
358	C₂×D₄×C₂₃	—	2	2	no	—
359	C₂×D₄×C₂₃	—	2	2	no	—
360	C₂×D₄×C₂₃	—	2	2	no	—
361	C₂×D₄×C₂₃	—	2	2	no	—
362	C₂×D₄×C₂₃	—	2	2	no	—
363	C₂×D₄×C₂₃	—	2	1	no	—
364	C₂×D₄×C₂₃	—	2	1	no	—
365	C₂×D₄×C₂₃	—	2	2	no	—
366	C₂×D₄×C₂₃	—	2	1	no	—
367	C₂×D₄×C₂₃	—	2	2	no	—
368	C₂×D₄×C₂₃	—	2	2	no	—
369	C₂×D₄×C₂₃	—	2	2	no	—
370	C₂×D₄×C₂₃	—	2	2	no	—
371	C₂×D₄×C₂₃	—	2	2	no	—
372	C₂×D₄×C₂₃	—	2	2	no	—
373	C₂×D₄×C₂₃	—	4	1	no	—
374	C₂×D₄×C₂₃	—	4	2	no	—
375	C₂×D₄×C₂₃	—	4	4	no	—
376	C₂×D₄×C₂₃	—	4	8	no	—
377	C₂×D₄×C₂₃	—	4	4	no	—
378	C₂×D₄×C₂₃	—	8	4	no	—
379	C₂×D₄×C₂₃	—	8	2	no	—
380	C₂×D₄×C₂₃	—	8	2	no	—
381	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
382	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
384	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
385	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
386	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
387	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
388	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₂₃	—	2	1	no	—
390	C₂²×C₄×C₂₃	—	2	2	no	—
391	C₂²×C₄×C₂₃	—	2	2	no	—
392	C₂²×C₄×C₂₃	—	2	1	no	—
393	C₂²×C₄×C₂₃	—	2	1	no	—
394	C₂²×C₄×C₂₃	—	2	1	no	—
395	C₂²×C₄×C₂₃	—	2	1	no	—
396	C₂²×C₄×C₂₃	—	2	1	no	—
397	C₂²×C₄×C₂₃	—	2	2	no	—
398	C₂²×C₄×C₂₃	—	2	1	no	—
399	C₂²×C₄×C₂₃	—	2	1	no	—
400	C₂²×C₄×C₂₃	—	2	2	no	—
401	C₂²×C₄×C₂₃	—	2	1	no	—
402	C₂²×C₄×C₂₃	—	2	2	no	—
403	C₂²×C₄×C₂₃	—	2	2	no	—
404	C₂²×C₄×C₂₃	—	2	2	no	—
405	C₂²×C₄×C₂₃	—	4	4	no	—
406	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
411	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
413	SD₁₆×C₂₃	—	2	4	no	—
414	SD₁₆×C₂₃	—	4	2	no	—
415	D₈×C₂₃	—	2	4	no	—
416	D₈×C₂₃	—	4	2	no	—
417	D₈×C₂₃	—	4	2	no	—
418	D₈×C₂₃	—	4	2	no	—
419	M₁₆×C₂₃	—	2	2	no	—
420	M₁₆×C₂₃	—	2	2	no	—
421	M₁₆×C₂₃	—	4	2	no	—
422	C₂×C₈×C₂₃	—	2	2	no	—
423	C₂×C₈×C₂₃	—	2	2	no	—
424	C₂×C₈×C₂₃	—	4	1	no	—
425	C₂×C₈×C₂₃	—	4	1	no	—
426	C₂×C₈×C₂₃	—	4	1	no	—
427	C₂×C₈×C₂₃	—	4	1	no	—
428	C₂×C₈×C₂₃	—	4	2	no	—
429	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
430	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
431	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
432	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
433	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
434	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₂₃	—	2	1	no	—
436	C₄⋊C₄×C₂₃	—	2	2	no	—
437	C₄⋊C₄×C₂₃	—	2	1	no	—
438	C₄⋊C₄×C₂₃	—	2	1	no	—
439	C₄⋊C₄×C₂₃	—	2	1	no	—
440	C₄⋊C₄×C₂₃	—	2	2	no	—
441	C₄⋊C₄×C₂₃	—	2	2	no	—
442	C₄⋊C₄×C₂₃	—	2	2	no	—
443	C₄⋊C₄×C₂₃	—	2	2	no	—
444	C₄⋊C₄×C₂₃	—	2	2	no	—
445	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
448	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
449	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
453	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
455	C₂²⋊C₄×C₂₃	—	2	1	no	—
456	C₂²⋊C₄×C₂₃	—	2	1	no	—
457	C₂²⋊C₄×C₂₃	—	2	1	no	—
458	C₂²⋊C₄×C₂₃	—	2	1	no	—
459	C₂²⋊C₄×C₂₃	—	2	2	no	—
460	C₂²⋊C₄×C₂₃	—	2	2	no	—
461	C₂²⋊C₄×C₂₃	—	2	2	no	—
462	C₂²⋊C₄×C₂₃	—	2	2	no	—
463	C₂²⋊C₄×C₂₃	—	2	2	no	—
464	C₂²⋊C₄×C₂₃	—	2	2	no	—
465	C₂²⋊C₄×C₂₃	—	2	2	no	—
466	C₂²⋊C₄×C₂₃	—	2	2	no	—
467	C₂²⋊C₄×C₂₃	—	2	2	no	—
468	C₂²⋊C₄×C₂₃	—	2	2	no	—
469	C₂²⋊C₄×C₂₃	—	2	2	no	—
470	C₂²⋊C₄×C₂₃	—	2	2	no	—
471	C₂²⋊C₄×C₂₃	—	2	2	no	—
472	C₂²⋊C₄×C₂₃	—	2	2	no	—
473	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
474	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
475	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
476	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
477	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
478	C₄²×C₂₃	—	2	1	no	—
479	C₄²×C₂₃	—	2	1	no	—
480	C₄²×C₂₃	—	2	1	no	—
481	C₄²×C₂₃	—	2	1	no	—
482	C₄²×C₂₃	—	2	2	no	—
483	C₄²×C₂₃	—	2	2	no	—
484	C₄²×C₂₃	C₂⁴	1	2	yes	—
485	#61171	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
486	C₂³×C₂₃	—	2	2	no	—
487	C₂³×C₂₃	—	2	2	no	—
488	C₂³×C₂₃	—	2	1	no	—
489	C₂³×C₂₃	—	2	2	no	—
490	C₂³×C₂₃	—	2	2	no	—
491	C₂³×C₂₃	—	2	1	no	—
492	C₂³×C₂₃	—	4	1	no	—
493	C₂³×C₂₃	—	4	2	no	—
494	C₂³×C₂₃	—	4	4	no	—
495	C₂³×C₂₃	—	4	2	no	—
496	C₂³×C₂₃	—	4	2	no	—
497	C₂³×C₂₃	—	4	2	no	—
498	C₂³×C₂₃	—	8	1	no	—
499	C₂³×C₂₃	—	8	1	no	—
500	C₂³×C₂₃	—	8	1	no	—
501	C₂³×C₂₃	—	8	2	no	—
502	C₂³×C₂₃	—	8	1	no	—
503	C₂³×C₂₃	—	8	1	no	—
504	C₂³×C₂₃	—	8	2	no	—
505	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
506	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
507	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
508	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
509	Q₈×C₂₃	—	2	2	no	—
510	Q₈×C₂₃	—	2	1	no	—
511	Q₈×C₂₃	—	2	1	no	—
512	Q₈×C₂₃	—	2	1	no	—
513	Q₈×C₂₃	—	4	2	no	—
514	Q₈×C₂₃	—	8	2	no	—
515	Q₈×C₂₃	C₂×#41	1	2	yes	—
516	D₄×C₂₃	—	2	4	no	—
517	D₄×C₂₃	—	2	4	no	—
518	D₄×C₂₃	—	2	4	no	—
519	D₄×C₂₃	—	2	2	no	—
520	D₄×C₂₃	—	2	2	no	—
521	D₄×C₂₃	—	2	2	no	—
522	D₄×C₂₃	—	2	1	no	—
523	D₄×C₂₃	—	2	1	no	—
524	D₄×C₂₃	—	2	2	no	—
525	D₄×C₂₃	—	2	2	no	—
526	D₄×C₂₃	—	2	1	no	—
527	D₄×C₂₃	—	4	2	no	—
528	D₄×C₂₃	—	4	4	no	—
529	D₄×C₂₃	—	4	2	no	—
530	D₄×C₂₃	—	4	4	no	—
531	D₄×C₂₃	—	4	2	no	—
532	D₄×C₂₃	—	4	2	no	—
533	D₄×C₂₃	—	4	2	no	—
534	D₄×C₂₃	—	4	4	no	—
535	D₄×C₂₃	—	4	4	no	—
536	D₄×C₂₃	—	4	2	no	—
537	D₄×C₂₃	—	4	2	no	—
538	D₄×C₂₃	—	8	2	no	—
539	D₄×C₂₃	—	8	2	no	—
540	D₄×C₂₃	—	8	2	no	—
541	D₄×C₂₃	—	8	2	no	—
542	D₄×C₂₃	—	8	2	no	—
543	D₄×C₂₃	—	8	2	no	—
544	D₄×C₂₃	—	8	2	no	—
545	D₄×C₂₃	C₂×#41	1	2	yes	—
546	C₂×C₄×C₂₃	—	2	2	no	—
547	C₂×C₄×C₂₃	—	2	1	no	—
548	C₂×C₄×C₂₃	—	2	2	no	—
549	C₂×C₄×C₂₃	—	2	2	no	—
550	C₂×C₄×C₂₃	—	2	4	no	—
551	C₂×C₄×C₂₃	—	2	1	no	—
552	C₂×C₄×C₂₃	—	2	1	no	—
553	C₂×C₄×C₂₃	—	2	2	no	—
554	C₂×C₄×C₂₃	—	2	1	no	—
555	C₂×C₄×C₂₃	—	2	1	no	—
556	C₂×C₄×C₂₃	—	2	2	no	—
557	C₂×C₄×C₂₃	—	2	1	no	—
558	C₂×C₄×C₂₃	—	2	1	no	—
559	C₂×C₄×C₂₃	—	2	1	no	—
560	C₂×C₄×C₂₃	—	2	1	no	—
561	C₂×C₄×C₂₃	—	2	2	no	—
562	C₂×C₄×C₂₃	—	2	2	no	—
563	C₂×C₄×C₂₃	—	2	1	no	—
564	C₂×C₄×C₂₃	—	4	2	no	—
565	C₂×C₄×C₂₃	—	4	4	no	—
566	C₂×C₄×C₂₃	—	4	2	no	—
567	C₂×C₄×C₂₃	—	4	2	no	—
568	C₂×C₄×C₂₃	—	4	2	no	—
569	C₂×C₄×C₂₃	—	4	2	no	—
570	C₂×C₄×C₂₃	—	8	2	no	—
571	C₂×C₄×C₂₃	—	8	2	no	—
572	C₂×C₄×C₂₃	—	8	2	no	—
573	C₂×C₄×C₂₃	—	8	1	no	—
574	C₂×C₄×C₂₃	—	8	1	no	—
575	C₂×C₄×C₂₃	—	8	1	no	—
576	C₂×C₄×C₂₃	—	8	2	no	—
577	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
579	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
580	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
581	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
584	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
585	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
586	C₈×C₂₃	—	2	2	no	—
587	C₈×C₂₃	—	2	1	no	—
588	C₈×C₂₃	—	2	1	no	—
589	C₈×C₂₃	—	2	1	no	—
590	C₈×C₂₃	—	2	1	no	—
591	C₈×C₂₃	—	2	2	no	—
592	#3494	C₂×C₂₃	1	1	yes	characteristic, complemented
593	#3488	C₂×C₂₃	1	1	yes	characteristic, complemented
594	#3319	C₂×C₂₃	1	2	yes	complemented
595	#3318	C₂×C₂₃	1	2	yes	complemented
596	#3309	C₂×C₂₃	1	2	yes	complemented
597	#3308	C₂×C₂₃	1	2	yes	complemented
598	#3305	C₂×C₂₃	1	2	yes	complemented
599	#3301	C₂×C₂₃	1	2	yes	complemented
600	#3297	C₂×C₂₃	1	2	yes	complemented
601	#3294	C₂×C₂₃	1	2	yes	complemented
602	#3136	C₂×C₂₃	1	1	yes	characteristic, complemented
603	#3098	C₂×C₂₃	1	1	yes	characteristic, complemented
604	#3094	C₂×C₂₃	1	1	yes	characteristic, complemented
605	#3083	C₂×C₂₃	1	1	yes	characteristic, complemented
606	#3062	C₂×C₂₃	1	1	yes	characteristic, complemented
607	C₂×#466	C₂×C₂₃	1	1	yes	characteristic, complemented
608	#3041	C₂×C₂₃	1	1	yes	characteristic, complemented
609	#3008	C₂×C₂₃	1	1	yes	characteristic, complemented
610	#3006	C₂×C₂₃	1	1	yes	characteristic, complemented
611	#2946	C₂×C₂₃	1	1	yes	characteristic, complemented
612	#2929	C₂×C₂₃	1	1	yes	characteristic, complemented
613	#2897	C₂×C₂₃	1	1	yes	characteristic, complemented
614	C₂×#416	C₂×C₂₃	1	1	yes	characteristic, complemented
615	C₂²×C₂₃	—	2	1	no	—
616	C₂²×C₂₃	—	2	1	no	—
617	C₂²×C₂₃	—	2	1	no	—
618	C₂²×C₂₃	—	2	1	no	—
619	C₂²×C₂₃	—	2	1	no	—
620	C₂²×C₂₃	—	2	2	no	—
621	C₂²×C₂₃	—	2	1	no	—
622	C₂²×C₂₃	—	2	2	no	—
623	C₂²×C₂₃	—	2	2	no	—
624	C₂²×C₂₃	—	2	2	no	—
625	C₂²×C₂₃	—	2	1	no	—
626	C₂²×C₂₃	—	4	4	no	—
627	C₂²×C₂₃	—	4	1	no	—
628	C₂²×C₂₃	—	4	1	no	—
629	C₂²×C₂₃	—	4	2	no	—
630	C₂²×C₂₃	—	4	1	no	—
631	C₂²×C₂₃	—	4	2	no	—
632	C₂²×C₂₃	—	4	1	no	—
633	C₂²×C₂₃	—	4	2	no	—
634	C₂²×C₂₃	—	4	2	no	—
635	C₂²×C₂₃	—	4	2	no	—
636	C₂²×C₂₃	—	4	2	no	—
637	C₂²×C₂₃	—	4	1	no	—
638	C₂²×C₂₃	—	8	4	no	—
639	C₂²×C₂₃	—	16	2	no	—
640	C₂²×C₂₃	—	16	2	no	—
641	C₂²×C₂₃	—	16	4	no	—
642	C₂²×C₂₃	#546	1	2	yes	—
643	C₂²×C₂₃	#576	1	2	yes	—
644	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
645	C₄×C₂₃	—	2	2	no	—
646	C₄×C₂₃	—	2	1	no	—
647	C₄×C₂₃	—	2	1	no	—
648	C₄×C₂₃	—	2	2	no	—
649	C₄×C₂₃	—	2	2	no	—
650	C₄×C₂₃	—	2	2	no	—
651	C₄×C₂₃	—	4	1	no	—
652	C₄×C₂₃	—	4	1	no	—
653	C₄×C₂₃	—	4	1	no	—
654	C₄×C₂₃	—	4	1	no	—
655	C₄×C₂₃	—	4	1	no	—
656	C₄×C₂₃	—	4	2	no	—
657	C₄×C₂₃	—	4	2	no	—
658	C₄×C₂₃	#546	1	2	yes	—
659	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
660	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
661	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
662	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
663	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
664	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
665	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
666	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
667	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
668	#555	C₂²×C₂₃	1	2	yes	complemented
669	#553	C₂²×C₂₃	1	2	yes	complemented
670	#553	C₂²×C₂₃	1	2	yes	complemented
671	#551	—	2	2	no	—
672	#550	C₂²×C₂₃	1	2	yes	complemented
673	#548	C₂²×C₂₃	1	2	yes	complemented
674	#547	C₂²×C₂₃	1	2	yes	complemented
675	#546	—	2	2	no	—
676	#546	—	2	2	no	—
677	#546	C₂²×C₂₃	1	2	yes	complemented
678	D₄²	—	2	2	no	—
679	D₄²	C₂²×C₂₃	1	2	yes	complemented
680	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
681	#542	—	2	1	no	—
682	#540	—	2	1	no	—
683	#537	—	2	1	no	—
684	#537	C₂²×C₂₃	1	1	yes	characteristic
685	#535	—	2	1	no	—
686	#535	C₂²×C₂₃	1	1	yes	characteristic
687	#535	C₂²×C₂₃	1	1	yes	characteristic, complemented
688	#532	—	2	1	no	—
689	#529	—	2	1	no	—
690	#525	—	2	1	no	—
691	#525	C₂²×C₂₃	1	1	yes	characteristic
692	C₂×#121	—	2	1	no	—
693	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
694	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
695	#520	C₂²×C₂₃	1	1	yes	characteristic
696	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
697	#518	C₂²×C₂₃	1	1	yes	characteristic, complemented
698	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
699	#490	C₂²×C₂₃	1	2	yes	complemented
700	#489	C₂²×C₂₃	1	2	yes	complemented
701	#488	C₂²×C₂₃	1	2	yes	complemented
702	#486	C₂²×C₂₃	1	2	yes	complemented
703	#485	C₂²×C₂₃	1	2	yes	complemented
704	#484	C₂²×C₂₃	1	2	yes	complemented
705	#482	C₂²×C₂₃	1	2	yes	complemented
706	#482	C₂²×C₂₃	1	2	yes	complemented
707	#482	C₂²×C₂₃	1	2	yes	complemented
708	#481	C₂²×C₂₃	1	2	yes	complemented
709	#480	C₂²×C₂₃	1	2	yes	complemented
710	#480	C₂²×C₂₃	1	2	yes	complemented
711	#479	C₂²×C₂₃	1	2	yes	complemented
712	#478	C₂²×C₂₃	1	2	yes	complemented
713	#477	C₂²×C₂₃	1	2	yes	complemented
714	#474	C₂²×C₂₃	1	2	yes	complemented
715	#469	C₂²×C₂₃	1	2	yes	complemented
716	#468	C₂²×C₂₃	1	2	yes	complemented
717	#466	C₂²×C₂₃	1	2	yes	complemented
718	#466	C₂²×C₂₃	1	2	yes	complemented
719	#466	C₂²×C₂₃	1	2	yes	complemented
720	#466	C₂²×C₂₃	1	2	yes	complemented
721	#466	C₂²×C₂₃	1	2	yes	complemented
722	#465	C₂²×C₂₃	1	2	yes	complemented
723	#463	C₂²×C₂₃	1	2	yes	complemented
724	#463	C₂²×C₂₃	1	2	yes	complemented
725	#459	C₂²×C₂₃	1	2	yes	complemented
726	#459	C₂²×C₂₃	1	2	yes	complemented
727	#449	C₂²×C₂₃	1	2	yes	complemented
728	#449	C₂²×C₂₃	1	2	yes	complemented
729	#449	C₂²×C₂₃	1	2	yes	complemented
730	#449	C₂²×C₂₃	1	2	yes	complemented
731	#448	C₂²×C₂₃	1	2	yes	complemented
732	#447	C₂²×C₂₃	1	2	yes	complemented
733	#447	C₂²×C₂₃	1	2	yes	complemented
734	#447	C₂²×C₂₃	1	2	yes	complemented
735	#442	C₂²×C₂₃	1	2	yes	complemented
736	#440	C₂²×C₂₃	1	2	yes	complemented
737	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
738	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
739	#435	C₂²×C₂₃	1	2	yes	complemented
740	#435	C₂²×C₂₃	1	2	yes	complemented
741	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
742	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
743	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
744	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
745	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
746	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
747	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
748	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
749	#418	C₂²×C₂₃	1	2	yes	complemented
750	#417	C₂²×C₂₃	1	1	yes	characteristic
751	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
752	#417	C₂²×C₂₃	1	2	yes	complemented
753	#416	C₂²×C₂₃	1	1	yes	characteristic
754	#416	C₂²×C₂₃	1	1	yes	characteristic
755	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
756	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
757	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
758	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
759	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
760	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
761	#416	C₂²×C₂₃	1	2	yes	complemented
762	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
763	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
764	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
765	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
766	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
767	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
768	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
769	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
770	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
771	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
772	C₂×C₂₃	—	2	2	no	—
773	C₂×C₂₃	—	2	2	no	—
774	C₂×C₂₃	—	4	1	no	—
775	C₂×C₂₃	—	4	2	no	—
776	C₂×C₂₃	—	4	2	no	—
777	C₂×C₂₃	—	8	1	no	—
778	C₂×C₂₃	—	8	2	no	—
779	C₂×C₂₃	—	8	2	no	—
780	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
781	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
782	C₂×C₂₃	#3584	1	1	yes	characteristic
783	H(5,𝔽₂)	—	2	4	no	—
784	H(5,𝔽₂)	—	4	2	no	—
785	C₂×#41	—	2	1	no	—
786	C₂×#41	—	2	2	no	—
787	C₂×#41	—	2	1	no	—
788	C₂×#41	—	2	1	no	—
789	C₂×#41	—	2	4	no	—
790	C₂×#41	—	4	2	no	—
791	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
792	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
793	C₂×#41	C₂³×C₂₃	1	2	yes	—
794	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
795	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
796	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
797	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
798	C₂²×D₄	—	2	1	no	—
799	C₂²×D₄	—	2	1	no	—
800	C₂²×D₄	—	2	1	no	—
801	C₂²×D₄	—	2	1	no	—
802	C₂²×D₄	—	2	2	no	—
803	C₂²×D₄	—	2	2	no	—
804	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
805	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
806	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
807	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
808	C₂³×C₄	—	2	1	no	—
809	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
810	AGL(1,ℤ/8)	—	2	4	no	—
811	AGL(1,ℤ/8)	—	4	2	no	—
812	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
813	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
814	C₂×D₈	—	4	2	no	—
815	C₂×D₈	C₂³×C₂₃	1	2	yes	—
816	C₂×D₈	C₂³×C₂₃	1	2	yes	—
817	C₂×D₈	C₂³×C₂₃	1	2	yes	—
818	C₂×D₈	C₂³×C₂₃	1	2	yes	—
819	#131	—	4	2	no	—
820	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
821	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
822	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
823	C₂²×C₈	—	4	2	no	—
824	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
825	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
826	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
827	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
828	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
829	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
830	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
831	C₄⋊Q₈	—	2	1	no	—
832	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
833	#127	—	2	1	no	—
834	#127	—	2	2	no	—
835	#127	C₂³×C₂₃	1	2	yes	—
836	#126	—	2	2	no	—
837	#126	—	2	2	no	—
838	#125	—	2	1	no	—
839	#125	C₂³×C₂₃	1	2	yes	—
840	#124	—	2	1	no	—
841	#124	—	2	2	no	—
842	#124	—	2	2	no	—
843	#124	—	2	2	no	—
844	#124	C₂³×C₂₃	1	2	yes	—
845	#123	—	2	2	no	—
846	#123	—	2	2	no	—
847	#123	—	2	2	no	—
848	#123	—	2	2	no	—
849	#123	—	2	2	no	—
850	#123	D₄×C₂₃	1	2	yes	—
851	C₂²⋊Q₈	—	2	1	no	—
852	C₂²⋊Q₈	—	2	2	no	—
853	C₂²⋊Q₈	—	2	2	no	—
854	C₂²⋊Q₈	—	2	2	no	—
855	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
856	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
858	#121	—	2	1	no	—
859	#121	—	2	2	no	—
860	#121	—	2	2	no	—
861	#121	—	2	2	no	—
862	#121	—	2	2	no	—
863	#121	—	2	2	no	—
864	#121	—	2	1	no	—
865	#121	—	2	1	no	—
866	#121	—	2	1	no	—
867	#121	—	2	1	no	—
868	#121	—	2	1	no	—
869	#121	—	2	1	no	—
870	#121	—	2	2	no	—
871	#121	—	2	2	no	—
872	#121	—	2	2	no	—
873	#121	—	2	2	no	—
874	#121	D₄×C₂₃	1	1	yes	characteristic
875	#121	D₄×C₂₃	1	1	yes	characteristic
876	#121	C₂³×C₂₃	1	2	yes	—
877	#121	C₂³×C₂₃	1	2	yes	—
878	#121	C₂³×C₂₃	1	2	yes	—
879	#121	C₂³×C₂₃	1	2	yes	—
880	#121	C₂³×C₂₃	1	2	yes	—
881	#121	C₂³×C₂₃	1	2	yes	—
882	#121	C₂³×C₂₃	1	2	yes	—
883	#120	—	2	2	no	—
884	#120	—	2	2	no	—
885	#120	—	2	2	no	—
886	#120	—	2	2	no	—
887	#120	—	2	2	no	—
888	#120	D₄×C₂₃	1	2	yes	—
889	C₄×Q₈	—	2	1	no	—
890	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	2	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	2	no	—
896	C₄×D₄	—	2	2	no	—
897	C₄×D₄	—	2	2	no	—
898	C₄×D₄	—	2	2	no	—
899	C₄×D₄	—	2	2	no	—
900	C₄×D₄	C₂³×C₂₃	1	2	yes	—
901	C₄×D₄	C₂³×C₂₃	1	2	yes	—
902	C₄×D₄	C₂³×C₂₃	1	2	yes	—
903	C₄×D₄	C₂³×C₂₃	1	2	yes	—
904	C₄×D₄	C₂³×C₂₃	1	2	yes	—
905	#117	—	2	1	no	—
906	#117	—	2	1	no	—
907	#117	—	2	1	no	—
908	#117	—	2	2	no	—
909	#117	C₂³×C₂₃	1	1	yes	characteristic
910	#117	C₂³×C₂₃	1	1	yes	characteristic
911	#117	C₂³×C₂₃	1	1	yes	characteristic
912	#117	C₂³×C₂₃	1	1	yes	characteristic
913	#117	C₂³×C₂₃	1	2	yes	—
914	#117	C₂³×C₂₃	1	1	yes	characteristic
915	C₂×C₄⋊C₄	—	2	1	no	—
916	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
917	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
918	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
919	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
920	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
921	C₂×C₂²⋊C₄	—	2	1	no	—
922	C₂×C₂²⋊C₄	—	2	1	no	—
923	C₂×C₂²⋊C₄	—	2	1	no	—
924	C₂×C₂²⋊C₄	—	2	2	no	—
925	C₂×C₂²⋊C₄	—	2	2	no	—
926	C₂×C₄²	—	2	1	no	—
927	#107	C₂³×C₂₃	1	2	yes	—
928	#107	C₂³×C₂₃	1	2	yes	—
929	#107	C₂³×C₂₃	1	2	yes	—
930	#107	C₂³×C₂₃	1	2	yes	—
931	#106	C₂³×C₂₃	1	2	yes	—
932	#106	C₂³×C₂₃	1	2	yes	—
933	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
934	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
935	#103	C₂³×C₂₃	1	1	yes	characteristic
936	#103	C₂³×C₂₃	1	1	yes	characteristic
937	#103	C₂³×C₂₃	1	1	yes	characteristic
938	#103	C₂³×C₂₃	1	1	yes	characteristic
939	#103	C₂³×C₂₃	1	1	yes	characteristic
940	#103	C₂³×C₂₃	1	1	yes	characteristic
941	#103	C₂³×C₂₃	1	1	yes	characteristic
942	#103	C₂³×C₂₃	1	1	yes	characteristic
943	#103	C₂³×C₂₃	1	2	yes	—
944	#103	C₂³×C₂₃	1	2	yes	—
945	#102	C₂³×C₂₃	1	1	yes	characteristic
946	#102	C₂³×C₂₃	1	2	yes	—
947	#102	C₂³×C₂₃	1	1	yes	characteristic
948	#102	C₂³×C₂₃	1	1	yes	characteristic
949	#102	C₂³×C₂₃	1	1	yes	characteristic
950	#102	C₂³×C₂₃	1	1	yes	characteristic
951	#102	C₂³×C₂₃	1	1	yes	characteristic
952	#102	C₂³×C₂₃	1	1	yes	characteristic
953	#102	C₂³×C₂₃	1	1	yes	characteristic
954	#102	C₂³×C₂₃	1	2	yes	—
955	#102	C₂³×C₂₃	1	2	yes	—
956	#102	C₂³×C₂₃	1	2	yes	—
957	#102	C₂³×C₂₃	1	2	yes	—
958	#102	C₂³×C₂₃	1	2	yes	—
959	#102	C₂³×C₂₃	1	2	yes	—
960	#102	C₂³×C₂₃	1	2	yes	—
961	#102	C₂³×C₂₃	1	2	yes	—
962	#102	C₂³×C₂₃	1	2	yes	—
963	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
964	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
965	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
966	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
967	#97	C₂³×C₂₃	1	2	yes	—
968	C₄×C₈	C₂³×C₂₃	1	2	yes	—
969	C₂₃	#61171	1	1	yes	characteristic, direct product factor, Sylow
970	C₂⁴	—	2	1	no	—
971	C₂⁴	—	2	1	no	—
972	C₂⁴	—	2	2	no	—
973	C₂⁴	—	2	1	no	—
974	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
975	#41	—	2	2	no	—
976	#41	—	2	2	no	—
977	#41	—	2	2	no	—
978	#41	—	2	2	no	—
979	#41	—	2	4	no	—
980	#41	—	2	2	no	—
981	#41	—	2	2	no	—
982	#41	—	2	2	no	—
983	#41	—	4	4	no	—
984	#41	—	4	1	no	—
985	#41	—	4	1	no	—
986	#41	—	4	2	no	—
987	#41	—	4	4	no	—
988	#41	—	4	4	no	—
989	#41	—	8	4	no	—
990	#41	#41×C₂₃	1	4	yes	complemented
991	C₂×Q₈	—	2	1	no	—
992	C₂×Q₈	—	2	2	no	—
993	C₂×Q₈	—	2	2	no	—
994	C₂×Q₈	—	4	1	no	—
995	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
996	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
997	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	4	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	2	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	2	no	—
1010	C₂×D₄	—	2	2	no	—
1011	C₂×D₄	—	2	2	no	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	1	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	2	no	—
1019	C₂×D₄	—	2	2	no	—
1020	C₂×D₄	—	2	2	no	—
1021	C₂×D₄	—	2	2	no	—
1022	C₂×D₄	—	4	1	no	—
1023	C₂×D₄	—	4	2	no	—
1024	C₂×D₄	—	4	4	no	—
1025	C₂×D₄	—	4	8	no	—
1026	C₂×D₄	—	4	4	no	—
1027	C₂×D₄	—	8	4	no	—
1028	C₂×D₄	—	8	2	no	—
1029	C₂×D₄	—	8	2	no	—
1030	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1031	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1032	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1033	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1034	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1035	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1036	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1037	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	2	no	—
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	1	no	—
1046	C₂²×C₄	—	2	2	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	1	no	—
1049	C₂²×C₄	—	2	2	no	—
1050	C₂²×C₄	—	2	1	no	—
1051	C₂²×C₄	—	2	2	no	—
1052	C₂²×C₄	—	2	2	no	—
1053	C₂²×C₄	—	2	2	no	—
1054	C₂²×C₄	—	4	4	no	—
1055	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1056	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1057	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1058	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1059	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1060	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1062	SD₁₆	—	2	4	no	—
1063	SD₁₆	—	4	2	no	—
1064	D₈	—	2	4	no	—
1065	D₈	—	4	2	no	—
1066	D₈	—	4	2	no	—
1067	D₈	—	4	2	no	—
1068	M₁₆	—	2	2	no	—
1069	M₁₆	—	2	2	no	—
1070	M₁₆	—	4	2	no	—
1071	C₂×C₈	—	2	2	no	—
1072	C₂×C₈	—	2	2	no	—
1073	C₂×C₈	—	4	1	no	—
1074	C₂×C₈	—	4	1	no	—
1075	C₂×C₈	—	4	1	no	—
1076	C₂×C₈	—	4	1	no	—
1077	C₂×C₈	—	4	2	no	—
1078	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1079	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1080	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1081	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1082	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1083	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1084	C₄⋊C₄	—	2	1	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	—	2	2	no	—
1092	C₄⋊C₄	—	2	2	no	—
1093	C₄⋊C₄	—	2	2	no	—
1094	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1095	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1096	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1097	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1098	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1099	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1100	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1101	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1102	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1103	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1123	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1124	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1125	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1126	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1127	C₄²	—	2	1	no	—
1128	C₄²	—	2	1	no	—
1129	C₄²	—	2	1	no	—
1130	C₄²	—	2	1	no	—
1131	C₄²	—	2	2	no	—
1132	C₄²	—	2	2	no	—
1133	C₄²	C₂⁴×C₂₃	1	2	yes	—
1134	C₂³	—	2	2	no	—
1135	C₂³	—	2	1	no	—
1136	C₂³	—	2	2	no	—
1137	C₂³	—	2	2	no	—
1138	C₂³	—	2	2	no	—
1139	C₂³	—	2	1	no	—
1140	C₂³	—	4	1	no	—
1141	C₂³	—	4	2	no	—
1142	C₂³	—	4	4	no	—
1143	C₂³	—	4	2	no	—
1144	C₂³	—	4	2	no	—
1145	C₂³	—	4	2	no	—
1146	C₂³	—	8	1	no	—
1147	C₂³	—	8	1	no	—
1148	C₂³	—	8	1	no	—
1149	C₂³	—	8	2	no	—
1150	C₂³	—	8	1	no	—
1151	C₂³	—	8	1	no	—
1152	C₂³	—	8	2	no	—
1153	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1154	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1155	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1156	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1157	Q₈	—	2	1	no	—
1158	Q₈	—	2	2	no	—
1159	Q₈	—	2	1	no	—
1160	Q₈	—	2	1	no	—
1161	Q₈	—	4	2	no	—
1162	Q₈	—	8	2	no	—
1163	Q₈	C₂×#41×C₂₃	1	2	yes	—
1164	D₄	—	2	4	no	—
1165	D₄	—	2	4	no	—
1166	D₄	—	2	4	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	2	2	no	—
1172	D₄	—	2	2	no	—
1173	D₄	—	2	1	no	—
1174	D₄	—	2	2	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	4	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	4	4	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	4	no	—
1182	D₄	—	4	4	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	2	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	D₄	—	8	2	no	—
1192	D₄	—	8	2	no	—
1193	D₄	C₂×#41×C₂₃	1	2	yes	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	2	4	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	4	2	no	—
1213	C₂×C₄	—	4	4	no	—
1214	C₂×C₄	—	4	2	no	—
1215	C₂×C₄	—	4	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	8	2	no	—
1219	C₂×C₄	—	8	2	no	—
1220	C₂×C₄	—	8	2	no	—
1221	C₂×C₄	—	8	1	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	—	8	2	no	—
1224	C₂×C₄	—	8	1	no	—
1225	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1226	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1227	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1228	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1229	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1230	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1231	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1232	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1233	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1234	C₈	—	2	2	no	—
1235	C₈	—	2	1	no	—
1236	C₈	—	2	1	no	—
1237	C₈	—	2	1	no	—
1238	C₈	—	2	1	no	—
1239	C₈	—	2	2	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	2	no	—
1246	C₂²	—	2	2	no	—
1247	C₂²	—	2	2	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	1	no	—
1250	C₂²	—	2	2	no	—
1251	C₂²	—	4	4	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	4	2	no	—
1258	C₂²	—	4	2	no	—
1259	C₂²	—	4	1	no	—
1260	C₂²	—	4	2	no	—
1261	C₂²	—	4	1	no	—
1262	C₂²	—	4	2	no	—
1263	C₂²	—	8	4	no	—
1264	C₂²	—	16	2	no	—
1265	C₂²	—	16	2	no	—
1266	C₂²	—	16	4	no	—
1267	C₂²	C₂₃×#546	1	2	yes	—
1268	C₂²	C₂₃×#576	1	2	yes	—
1269	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	2	2	no	—
1273	C₄	—	2	2	no	—
1274	C₄	—	2	2	no	—
1275	C₄	—	2	2	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	1	no	—
1279	C₄	—	4	2	no	—
1280	C₄	—	4	2	no	—
1281	C₄	—	4	1	no	—
1282	C₄	—	4	1	no	—
1283	C₄	C₂₃×#546	1	2	yes	—
1284	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1285	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1286	C₂	—	2	2	no	—
1287	C₂	—	2	2	no	—
1288	C₂	—	4	1	no	—
1289	C₂	—	4	2	no	—
1290	C₂	—	4	2	no	—
1291	C₂	—	8	1	no	—
1292	C₂	—	8	2	no	—
1293	C₂	—	8	2	no	—
1294	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
1295	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
1296	C₂	C₂₃×#3584	1	1	yes	characteristic

	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. C₂₃×#3494	C₂	semidirect
2. C₂₃×#3488	C₂	semidirect
3. C₂₃×#3319	C₂	semidirect
4. C₂₃×#3318	C₂	semidirect
5. C₂₃×#3309	C₂	semidirect
6. C₂₃×#3308	C₂	semidirect
7. C₂₃×#3305	C₂	semidirect
8. C₂₃×#3301	C₂	semidirect
9. C₂₃×#3297	C₂	semidirect
10. C₂₃×#3294	C₂	semidirect
11. C₂₃×#3136	C₂	semidirect
12. C₂₃×#3098	C₂	semidirect
13. C₂₃×#3094	C₂	semidirect
14. C₂₃×#3083	C₂	semidirect
15. C₂₃×#3062	C₂	semidirect
16. C₂×C₂₃×#466	C₂	semidirect
17. C₂₃×#3041	C₂	semidirect
18. C₂₃×#3008	C₂	semidirect
19. C₂₃×#3006	C₂	semidirect
20. C₂₃×#2946	C₂	semidirect
21. C₂₃×#2929	C₂	semidirect
22. C₂₃×#2897	C₂	semidirect
23. C₂×C₂₃×#416	C₂	semidirect
27. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂²×D₈×C₂₃	C₂²	semidirect
29. C₂×C₂₃×#131	C₂²	semidirect
30. C₂³×C₈×C₂₃	C₂²	semidirect
31. C₂₃×#555	C₂²	semidirect
32. C₂₃×#553	C₂²	semidirect
33. C₂₃×#553	C₂²	semidirect
35. C₂₃×#550	C₂²	semidirect
36. C₂₃×#548	C₂²	semidirect
37. C₂₃×#547	C₂²	semidirect
40. C₂₃×#546	C₂²	semidirect
42. D₄²×C₂₃	C₂²	semidirect
43. C₂₃×#544	C₂²	semidirect
50. C₂₃×#535	C₂²	semidirect
57. C₂×C₂₃×#121	C₂²	semidirect
59. C₂₃×#520	C₂²	semidirect
60. C₂₃×#518	C₂²	semidirect
61. C₂×C₂₃×#117	C₂²	semidirect
62. C₂₃×#490	C₂²	semidirect
63. C₂₃×#489	C₂²	semidirect
64. C₂₃×#488	C₂²	semidirect
65. C₂₃×#486	C₂²	semidirect
66. C₂₃×#485	C₂²	semidirect
67. C₂₃×#484	C₂²	semidirect
68. C₂₃×#482	C₂²	semidirect
69. C₂₃×#482	C₂²	semidirect
70. C₂₃×#482	C₂²	semidirect
71. C₂₃×#481	C₂²	semidirect
72. C₂₃×#480	C₂²	semidirect
73. C₂₃×#480	C₂²	semidirect
74. C₂₃×#479	C₂²	semidirect
75. C₂₃×#478	C₂²	semidirect
76. C₂₃×#477	C₂²	semidirect
77. C₂₃×#474	C₂²	semidirect
78. C₂₃×#469	C₂²	semidirect
79. C₂₃×#468	C₂²	semidirect
80. C₂₃×#466	C₂²	semidirect
81. C₂₃×#466	C₂²	semidirect
82. C₂₃×#466	C₂²	semidirect
83. C₂₃×#466	C₂²	semidirect
84. C₂₃×#466	C₂²	semidirect
85. C₂₃×#465	C₂²	semidirect
86. C₂₃×#463	C₂²	semidirect
87. C₂₃×#463	C₂²	semidirect
88. C₂₃×#459	C₂²	semidirect
89. C₂₃×#459	C₂²	semidirect
90. C₂₃×#449	C₂²	semidirect
91. C₂₃×#449	C₂²	semidirect
92. C₂₃×#449	C₂²	semidirect
93. C₂₃×#449	C₂²	semidirect
94. C₂₃×#448	C₂²	semidirect
95. C₂₃×#447	C₂²	semidirect
96. C₂₃×#447	C₂²	semidirect
97. C₂₃×#447	C₂²	semidirect
98. C₂₃×#442	C₂²	semidirect
99. C₂₃×#440	C₂²	semidirect
100. C₄×SD₁₆×C₂₃	C₂²	semidirect
101. C₄×D₈×C₂₃	C₂²	semidirect
102. C₂₃×#435	C₂²	semidirect
103. C₂₃×#435	C₂²	semidirect
104. C₈×D₄×C₂₃	C₂²	semidirect
105. C₈×D₄×C₂₃	C₂²	semidirect
106. C₂₃×#428	C₂²	semidirect
107. C₂₃×#428	C₂²	semidirect
108. C₂×C₂₃×#107	C₂²	semidirect
109. C₂₃×#424	C₂²	semidirect
110. C₂₃×#418	C₂²	semidirect
111. C₂₃×#418	C₂²	semidirect
112. C₂₃×#418	C₂²	semidirect
114. C₂₃×#417	C₂²	semidirect
115. C₂₃×#417	C₂²	semidirect
118. C₂₃×#416	C₂²	semidirect
119. C₂₃×#416	C₂²	semidirect
120. C₂₃×#416	C₂²	semidirect
121. C₂₃×#416	C₂²	semidirect
122. C₂₃×#416	C₂²	semidirect
123. C₂₃×#416	C₂²	semidirect
124. C₂₃×#416	C₂²	semidirect
125. C₂×C₂₃×#103	C₂²	semidirect
126. C₂×C₂₃×#103	C₂²	semidirect
127. C₂×C₂₃×#102	C₂²	semidirect
128. C₂×C₂₃×#102	C₂²	semidirect
129. C₂×C₂₃×#102	C₂²	semidirect
130. C₂×C₂₃×#102	C₂²	semidirect
131. C₂×C₂₃×#102	C₂²	semidirect
132. C₂₃×#408	C₂²	semidirect
133. C₂₃×#407	C₂²	semidirect
134. C₂₃×#405	C₂²	semidirect
341. #41×C₂₃	#41	semidirect
485. #61171	C₂₃	direct (N × H)
592. #3494	C₂×C₂₃	semidirect
593. #3488	C₂×C₂₃	semidirect
594. #3319	C₂×C₂₃	semidirect
595. #3318	C₂×C₂₃	semidirect
596. #3309	C₂×C₂₃	semidirect
597. #3308	C₂×C₂₃	semidirect
598. #3305	C₂×C₂₃	semidirect
599. #3301	C₂×C₂₃	semidirect
600. #3297	C₂×C₂₃	semidirect
601. #3294	C₂×C₂₃	semidirect
602. #3136	C₂×C₂₃	semidirect
603. #3098	C₂×C₂₃	semidirect
604. #3094	C₂×C₂₃	semidirect
605. #3083	C₂×C₂₃	semidirect
606. #3062	C₂×C₂₃	semidirect
607. C₂×#466	C₂×C₂₃	semidirect
608. #3041	C₂×C₂₃	semidirect
609. #3008	C₂×C₂₃	semidirect
610. #3006	C₂×C₂₃	semidirect
611. #2946	C₂×C₂₃	semidirect
612. #2929	C₂×C₂₃	semidirect
613. #2897	C₂×C₂₃	semidirect
614. C₂×#416	C₂×C₂₃	semidirect
664. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
665. C₂²×D₈	C₂²×C₂₃	semidirect
666. C₂×#131	C₂²×C₂₃	semidirect
667. C₂³×C₈	C₂²×C₂₃	semidirect
668. #555	C₂²×C₂₃	semidirect
669. #553	C₂²×C₂₃	semidirect
670. #553	C₂²×C₂₃	semidirect
672. #550	C₂²×C₂₃	semidirect
673. #548	C₂²×C₂₃	semidirect
674. #547	C₂²×C₂₃	semidirect
677. #546	C₂²×C₂₃	semidirect
679. D₄²	C₂²×C₂₃	semidirect
680. #544	C₂²×C₂₃	semidirect
687. #535	C₂²×C₂₃	semidirect
694. C₂×#121	C₂²×C₂₃	semidirect
696. #520	C₂²×C₂₃	semidirect
697. #518	C₂²×C₂₃	semidirect
698. C₂×#117	C₂²×C₂₃	semidirect
699. #490	C₂²×C₂₃	semidirect
700. #489	C₂²×C₂₃	semidirect
701. #488	C₂²×C₂₃	semidirect
702. #486	C₂²×C₂₃	semidirect
703. #485	C₂²×C₂₃	semidirect
704. #484	C₂²×C₂₃	semidirect
705. #482	C₂²×C₂₃	semidirect
706. #482	C₂²×C₂₃	semidirect
707. #482	C₂²×C₂₃	semidirect
708. #481	C₂²×C₂₃	semidirect
709. #480	C₂²×C₂₃	semidirect
710. #480	C₂²×C₂₃	semidirect
711. #479	C₂²×C₂₃	semidirect
712. #478	C₂²×C₂₃	semidirect
713. #477	C₂²×C₂₃	semidirect
714. #474	C₂²×C₂₃	semidirect
715. #469	C₂²×C₂₃	semidirect
716. #468	C₂²×C₂₃	semidirect
717. #466	C₂²×C₂₃	semidirect
718. #466	C₂²×C₂₃	semidirect
719. #466	C₂²×C₂₃	semidirect
720. #466	C₂²×C₂₃	semidirect
721. #466	C₂²×C₂₃	semidirect
722. #465	C₂²×C₂₃	semidirect
723. #463	C₂²×C₂₃	semidirect
724. #463	C₂²×C₂₃	semidirect
725. #459	C₂²×C₂₃	semidirect
726. #459	C₂²×C₂₃	semidirect
727. #449	C₂²×C₂₃	semidirect
728. #449	C₂²×C₂₃	semidirect
729. #449	C₂²×C₂₃	semidirect
730. #449	C₂²×C₂₃	semidirect
731. #448	C₂²×C₂₃	semidirect
732. #447	C₂²×C₂₃	semidirect
733. #447	C₂²×C₂₃	semidirect
734. #447	C₂²×C₂₃	semidirect
735. #442	C₂²×C₂₃	semidirect
736. #440	C₂²×C₂₃	semidirect
737. C₄×SD₁₆	C₂²×C₂₃	semidirect
738. C₄×D₈	C₂²×C₂₃	semidirect
739. #435	C₂²×C₂₃	semidirect
740. #435	C₂²×C₂₃	semidirect
741. C₈×D₄	C₂²×C₂₃	semidirect
742. C₈×D₄	C₂²×C₂₃	semidirect
743. #428	C₂²×C₂₃	semidirect
744. #428	C₂²×C₂₃	semidirect
745. C₂×#107	C₂²×C₂₃	semidirect
746. #424	C₂²×C₂₃	semidirect
747. #418	C₂²×C₂₃	semidirect
748. #418	C₂²×C₂₃	semidirect
749. #418	C₂²×C₂₃	semidirect
751. #417	C₂²×C₂₃	semidirect
752. #417	C₂²×C₂₃	semidirect
755. #416	C₂²×C₂₃	semidirect
756. #416	C₂²×C₂₃	semidirect
757. #416	C₂²×C₂₃	semidirect
758. #416	C₂²×C₂₃	semidirect
759. #416	C₂²×C₂₃	semidirect
760. #416	C₂²×C₂₃	semidirect
761. #416	C₂²×C₂₃	semidirect
762. C₂×#103	C₂²×C₂₃	semidirect
763. C₂×#103	C₂²×C₂₃	semidirect
764. C₂×#102	C₂²×C₂₃	semidirect
765. C₂×#102	C₂²×C₂₃	semidirect
766. C₂×#102	C₂²×C₂₃	semidirect
767. C₂×#102	C₂²×C₂₃	semidirect
768. C₂×#102	C₂²×C₂₃	semidirect
769. #408	C₂²×C₂₃	semidirect
770. #407	C₂²×C₂₃	semidirect
771. #405	C₂²×C₂₃	semidirect
969. C₂₃	#61171	direct (N × H)
990. #41	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3494	2
C₂₃×#3488	2
C₂₃×#3319	2
C₂₃×#3318	2
C₂₃×#3309	2
C₂₃×#3308	2
C₂₃×#3305	2
C₂₃×#3301	2
C₂₃×#3297	2
C₂₃×#3294	2
C₂₃×#3136	2
C₂₃×#3098	2
C₂₃×#3094	2
C₂₃×#3083	2
C₂₃×#3062	2
C₂×C₂₃×#466	2
C₂₃×#3041	2
C₂₃×#3008	2
C₂₃×#3006	2
C₂₃×#2946	2
C₂₃×#2929	2
C₂₃×#2897	2
C₂×C₂₃×#416	2
#61171	23

Subgroups — C23×#61171 #19208797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61171 #19208797