Subgroups — C₂₃×#61733 #19209359

Order 5888.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3345	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3343	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3318	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3310	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3188	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3094	C₂	1	2	yes	maximal, complemented
22	C₂×C₂₃×#482	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×H(5,𝔽₂)	—	2	1	no	—
25	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
26	C₂₃×#555	C₂²	1	1	yes	characteristic, complemented
27	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#553	C₂²	1	2	yes	complemented
29	C₂₃×#552	—	2	1	no	—
30	C₂₃×#552	C₂²	1	2	yes	complemented
31	C₂₃×#551	—	2	2	no	—
32	C₂₃×#547	C₂²	1	1	yes	characteristic
33	C₂₃×#547	C₂²	1	2	yes	—
34	C₂₃×#547	C₂²	1	1	yes	characteristic
35	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#546	—	2	1	no	—
37	C₂₃×#546	—	2	1	no	—
38	C₂₃×#546	—	2	2	no	—
39	C₂₃×#546	—	2	1	no	—
40	D₄²×C₂₃	C₂²	1	1	yes	characteristic
41	D₄²×C₂₃	C₂²	1	2	yes	—
42	D₄²×C₂₃	C₂²	1	1	yes	characteristic
43	C₂₃×#537	—	2	1	no	—
44	C₂₃×#534	—	2	2	no	—
45	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#532	C₂²	1	1	yes	characteristic
48	C₂₃×#529	—	2	2	no	—
49	C₂₃×#529	—	2	1	no	—
50	C₂₃×#525	C₂²	1	2	yes	complemented
51	C₂×C₂₃×#121	C₂²	1	2	yes	—
52	C₂×C₂₃×#121	C₂²	1	2	yes	—
53	C₄×#41×C₂₃	—	2	1	no	—
54	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
57	C₂₃×#501	C₂²	1	2	yes	complemented
58	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#490	C₂²	1	2	yes	complemented
61	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#484	C₂²	1	2	yes	complemented
64	C₂₃×#483	C₂²	1	2	yes	complemented
65	C₂₃×#482	C₂²	1	2	yes	complemented
66	C₂₃×#482	C₂²	1	2	yes	complemented
67	C₂₃×#482	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×#482	C₂²	1	2	yes	complemented
72	C₂₃×#482	C₂²	1	2	yes	complemented
73	C₂₃×#482	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#482	C₂²	1	2	yes	complemented
75	C₂₃×#482	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#481	C₂²	1	2	yes	complemented
77	C₂₃×#481	C₂²	1	2	yes	complemented
78	C₂₃×#481	C₂²	1	2	yes	complemented
79	C₂₃×#480	C₂²	1	2	yes	complemented
80	C₂₃×#480	C₂²	1	2	yes	complemented
81	C₂₃×#480	C₂²	1	2	yes	complemented
82	C₂₃×#478	C₂²	1	2	yes	complemented
83	C₂₃×#478	C₂²	1	2	yes	complemented
84	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#469	C₂²	1	2	yes	complemented
93	C₂₃×#469	C₂²	1	2	yes	complemented
94	C₂₃×#468	C₂²	1	2	yes	complemented
95	C₂₃×#468	C₂²	1	2	yes	complemented
96	C₂₃×#466	C₂²	1	2	yes	complemented
97	C₂₃×#466	C₂²	1	2	yes	complemented
98	C₂₃×#465	C₂²	1	2	yes	complemented
99	C₂₃×#465	C₂²	1	2	yes	complemented
100	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#450	C₂²	1	2	yes	complemented
105	C₂₃×#450	C₂²	1	2	yes	complemented
106	C₂₃×#449	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#449	C₂²	1	2	yes	complemented
108	C₂₃×#449	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#447	C₂²	1	2	yes	complemented
110	C₂₃×#447	C₂²	1	2	yes	complemented
111	C₂₃×#442	C₂²	1	2	yes	complemented
112	C₂₃×#440	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
118	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
119	C₂₃×#435	C₂²	1	2	yes	complemented
120	C₂₃×#435	C₂²	1	2	yes	complemented
121	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
122	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
123	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
124	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
125	C₂₃×#428	C₂²	1	2	yes	complemented
126	C₂₃×#428	C₂²	1	2	yes	complemented
127	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
128	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
129	C₂₃×#418	C₂²	1	2	yes	complemented
130	C₂₃×#418	C₂²	1	2	yes	complemented
131	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
132	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
133	C₂₃×#407	C₂²	1	2	yes	complemented
134	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₂₃×H(5,𝔽₂)	—	4	8	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	—	2	1	no	—
142	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₂₃	—	2	2	no	—
144	C₂²×D₄×C₂₃	—	2	2	no	—
145	C₂²×D₄×C₂₃	—	2	2	no	—
146	C₂²×D₄×C₂₃	—	2	1	no	—
147	C₂²×D₄×C₂₃	—	2	1	no	—
148	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
149	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
150	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
151	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×D₈×C₂₃	C₂³	1	2	yes	—
158	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
159	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
160	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
161	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
162	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₂₃×#127	C₂³	1	1	yes	characteristic
167	C₂₃×#127	C₂³	1	1	yes	characteristic
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#125	—	2	2	no	—
172	C₂₃×#125	—	2	1	no	—
173	C₂₃×#125	C₂³	1	2	yes	—
174	C₂₃×#124	—	2	1	no	—
175	C₂₃×#124	—	2	2	no	—
176	C₂₃×#124	—	2	1	no	—
177	C₂₃×#124	—	2	1	no	—
178	C₂₃×#123	—	2	2	no	—
179	C₂₃×#123	—	2	2	no	—
180	C₂₃×#123	—	2	2	no	—
181	C₂₃×#123	—	2	2	no	—
182	C₂₃×#123	—	2	2	no	—
183	C₂₃×#123	—	2	2	no	—
184	C₂₃×#123	—	2	2	no	—
185	C₂₃×#123	—	2	2	no	—
186	C₂₃×C₂²⋊Q₈	—	2	1	no	—
187	C₂₃×C₂²⋊Q₈	—	2	1	no	—
188	C₂₃×C₂²⋊Q₈	—	2	1	no	—
189	C₂₃×C₂²⋊Q₈	—	2	1	no	—
190	C₂₃×C₂²⋊Q₈	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	—	2	1	no	—
192	C₂₃×C₂²⋊Q₈	—	2	2	no	—
193	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₂₃×#121	—	2	2	no	—
196	C₂₃×#121	—	2	1	no	—
197	C₂₃×#121	—	2	2	no	—
198	C₂₃×#121	—	2	2	no	—
199	C₂₃×#121	—	2	2	no	—
200	C₂₃×#121	—	2	2	no	—
201	C₂₃×#121	—	2	1	no	—
202	C₂₃×#121	—	2	1	no	—
203	C₂₃×#121	—	2	1	no	—
204	C₂₃×#121	—	2	1	no	—
205	C₂₃×#121	—	2	2	no	—
206	C₂₃×#121	C₂³	1	2	yes	—
207	C₂₃×#121	C₂³	1	2	yes	—
208	C₂₃×#121	C₂³	1	2	yes	—
209	C₂₃×#121	C₂³	1	2	yes	—
210	C₂₃×#121	C₂³	1	2	yes	—
211	C₂₃×#121	C₂³	1	2	yes	—
212	C₂₃×#121	C₂³	1	1	yes	characteristic
213	C₂₃×#121	C₂³	1	2	yes	—
214	C₂₃×#121	C₂³	1	1	yes	characteristic
215	C₂₃×#120	—	2	2	no	—
216	C₂₃×#120	—	2	2	no	—
217	C₂₃×#120	—	2	2	no	—
218	C₂₃×#120	—	2	2	no	—
219	C₂₃×#120	—	2	2	no	—
220	C₄×Q₈×C₂₃	—	2	1	no	—
221	C₄×Q₈×C₂₃	—	2	1	no	—
222	C₄×Q₈×C₂₃	—	2	1	no	—
223	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₂₃	—	2	1	no	—
226	C₄×D₄×C₂₃	—	2	1	no	—
227	C₄×D₄×C₂₃	—	2	1	no	—
228	C₄×D₄×C₂₃	—	2	2	no	—
229	C₄×D₄×C₂₃	—	2	2	no	—
230	C₄×D₄×C₂₃	—	2	2	no	—
231	C₄×D₄×C₂₃	—	2	1	no	—
232	C₄×D₄×C₂₃	—	2	1	no	—
233	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
234	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
235	C₄×D₄×C₂₃	D₄	1	2	yes	—
236	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₂₃	C₂³	1	2	yes	—
239	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₂₃	C₂³	1	2	yes	—
243	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
244	C₂₃×#117	—	2	2	no	—
245	C₂₃×#117	—	2	2	no	—
246	C₂₃×#117	—	2	1	no	—
247	C₂₃×#117	—	2	2	no	—
248	C₂₃×#117	—	2	1	no	—
249	C₂₃×#117	C₂³	1	2	yes	—
250	C₂₃×#117	C₂³	1	2	yes	—
251	C₂₃×#117	C₂³	1	1	yes	characteristic
252	C₂₃×#117	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
262	C₂×C₄²×C₂₃	—	2	2	no	—
263	C₂×C₄²×C₂₃	—	2	1	no	—
264	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
265	C₂₃×#107	C₂³	1	1	yes	characteristic
266	C₂₃×#107	C₂³	1	2	yes	—
267	C₂₃×#107	C₂³	1	2	yes	—
268	C₂₃×#107	C₂³	1	2	yes	—
269	C₂₃×#107	C₂³	1	1	yes	characteristic
270	C₂₃×#107	C₂³	1	2	yes	—
271	C₂₃×#107	C₂³	1	2	yes	—
272	C₂₃×#106	C₂³	1	1	yes	characteristic
273	C₂₃×#106	C₂³	1	2	yes	—
274	C₂₃×#106	C₂³	1	2	yes	—
275	C₂₃×#106	C₂³	1	2	yes	—
276	C₂₃×#106	C₂³	1	1	yes	characteristic
277	C₂₃×#106	C₂³	1	2	yes	—
278	C₂₃×#106	C₂³	1	2	yes	—
279	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₂₃×#103	C₂³	1	1	yes	characteristic
284	C₂₃×#103	C₂³	1	1	yes	characteristic
285	C₂₃×#103	C₂³	1	2	yes	—
286	C₂₃×#102	C₂³	1	1	yes	characteristic
287	C₂₃×#102	C₂³	1	1	yes	characteristic
288	C₂₃×#102	C₂³	1	2	yes	—
289	C₂₃×#102	C₂³	1	2	yes	—
290	C₂₃×#102	C₂³	1	2	yes	—
291	C₂₃×#102	C₂³	1	2	yes	—
292	C₂₃×#102	C₂³	1	2	yes	—
293	C₂₃×#102	C₂³	1	2	yes	—
294	C₂₃×#102	C₂³	1	1	yes	characteristic
295	C₂₃×#102	C₂³	1	1	yes	characteristic
296	C₂₃×#102	C₂³	1	2	yes	—
297	C₂₃×#102	C₂³	1	2	yes	—
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×#102	C₂³	1	2	yes	—
303	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂₃×#97	C₂³	1	2	yes	—
311	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
313	C₂⁴×C₂₃	—	2	2	no	—
314	C₂⁴×C₂₃	—	2	2	no	—
315	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
316	#41×C₂₃	—	4	1	no	—
317	#41×C₂₃	—	4	1	no	—
318	#41×C₂₃	—	4	4	no	—
319	#41×C₂₃	—	4	4	no	—
320	#41×C₂₃	—	4	8	no	—
321	#41×C₂₃	—	4	4	no	—
322	#41×C₂₃	—	4	4	no	—
323	#41×C₂₃	—	4	4	no	—
324	C₂×Q₈×C₂₃	—	2	1	no	—
325	C₂×Q₈×C₂₃	—	2	1	no	—
326	C₂×Q₈×C₂₃	—	2	1	no	—
327	C₂×Q₈×C₂₃	—	2	1	no	—
328	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₂₃	—	2	4	no	—
330	C₂×D₄×C₂₃	—	2	1	no	—
331	C₂×D₄×C₂₃	—	2	2	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	2	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	1	no	—
337	C₂×D₄×C₂₃	—	2	2	no	—
338	C₂×D₄×C₂₃	—	2	1	no	—
339	C₂×D₄×C₂₃	—	2	2	no	—
340	C₂×D₄×C₂₃	—	2	1	no	—
341	C₂×D₄×C₂₃	—	2	1	no	—
342	C₂×D₄×C₂₃	—	2	1	no	—
343	C₂×D₄×C₂₃	—	2	1	no	—
344	C₂×D₄×C₂₃	—	2	2	no	—
345	C₂×D₄×C₂₃	—	2	2	no	—
346	C₂×D₄×C₂₃	—	4	2	no	—
347	C₂×D₄×C₂₃	—	4	2	no	—
348	C₂×D₄×C₂₃	—	4	2	no	—
349	C₂×D₄×C₂₃	—	4	2	no	—
350	C₂×D₄×C₂₃	—	4	8	no	—
351	C₂×D₄×C₂₃	—	4	4	no	—
352	C₂×D₄×C₂₃	—	4	8	no	—
353	C₂×D₄×C₂₃	—	4	8	no	—
354	C₂×D₄×C₂₃	—	4	4	no	—
355	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
356	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
357	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
358	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
360	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
361	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₂₃	—	2	2	no	—
363	C₂²×C₄×C₂₃	—	2	2	no	—
364	C₂²×C₄×C₂₃	—	2	2	no	—
365	C₂²×C₄×C₂₃	—	2	2	no	—
366	C₂²×C₄×C₂₃	—	2	1	no	—
367	C₂²×C₄×C₂₃	—	2	1	no	—
368	C₂²×C₄×C₂₃	—	2	2	no	—
369	C₂²×C₄×C₂₃	—	2	1	no	—
370	C₂²×C₄×C₂₃	—	2	1	no	—
371	C₂²×C₄×C₂₃	—	2	1	no	—
372	C₂²×C₄×C₂₃	—	4	2	no	—
373	C₂²×C₄×C₂₃	—	4	2	no	—
374	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
376	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
378	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
379	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
382	SD₁₆×C₂₃	—	4	1	no	—
383	SD₁₆×C₂₃	—	4	2	no	—
384	SD₁₆×C₂₃	—	4	1	no	—
385	D₈×C₂₃	—	4	1	no	—
386	D₈×C₂₃	—	4	2	no	—
387	D₈×C₂₃	—	4	1	no	—
388	M₁₆×C₂₃	—	4	2	no	—
389	M₁₆×C₂₃	—	4	2	no	—
390	C₂×C₈×C₂₃	—	4	2	no	—
391	C₂×C₈×C₂₃	—	4	2	no	—
392	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
394	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
396	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₂₃	—	2	2	no	—
399	C₄⋊C₄×C₂₃	—	2	2	no	—
400	C₄⋊C₄×C₂₃	—	2	2	no	—
401	C₄⋊C₄×C₂₃	—	2	2	no	—
402	C₄⋊C₄×C₂₃	—	2	1	no	—
403	C₄⋊C₄×C₂₃	—	2	2	no	—
404	C₄⋊C₄×C₂₃	—	2	2	no	—
405	C₄⋊C₄×C₂₃	—	2	1	no	—
406	C₄⋊C₄×C₂₃	—	2	1	no	—
407	C₄⋊C₄×C₂₃	—	2	1	no	—
408	C₄⋊C₄×C₂₃	—	2	1	no	—
409	C₄⋊C₄×C₂₃	—	2	2	no	—
410	C₄⋊C₄×C₂₃	—	2	2	no	—
411	C₄⋊C₄×C₂₃	—	2	1	no	—
412	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
422	C₂²⋊C₄×C₂₃	—	2	1	no	—
423	C₂²⋊C₄×C₂₃	—	2	2	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	2	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	2	no	—
428	C₂²⋊C₄×C₂₃	—	2	1	no	—
429	C₂²⋊C₄×C₂₃	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	1	no	—
431	C₂²⋊C₄×C₂₃	—	2	2	no	—
432	C₂²⋊C₄×C₂₃	—	2	2	no	—
433	C₂²⋊C₄×C₂₃	—	2	2	no	—
434	C₂²⋊C₄×C₂₃	—	2	2	no	—
435	C₂²⋊C₄×C₂₃	—	2	2	no	—
436	C₂²⋊C₄×C₂₃	—	2	1	no	—
437	C₂²⋊C₄×C₂₃	—	2	1	no	—
438	C₂²⋊C₄×C₂₃	—	2	2	no	—
439	C₂²⋊C₄×C₂₃	—	2	2	no	—
440	C₂²⋊C₄×C₂₃	—	2	1	no	—
441	C₂²⋊C₄×C₂₃	—	2	1	no	—
442	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
446	C₄²×C₂₃	—	2	1	no	—
447	C₄²×C₂₃	—	2	2	no	—
448	C₄²×C₂₃	—	2	1	no	—
449	C₄²×C₂₃	—	2	2	no	—
450	C₄²×C₂₃	—	2	2	no	—
451	C₄²×C₂₃	—	2	1	no	—
452	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
455	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
456	#61733	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
457	C₂³×C₂₃	—	2	4	no	—
458	C₂³×C₂₃	—	2	1	no	—
459	C₂³×C₂₃	—	2	2	no	—
460	C₂³×C₂₃	—	2	1	no	—
461	C₂³×C₂₃	—	2	1	no	—
462	C₂³×C₂₃	—	4	2	no	—
463	C₂³×C₂₃	—	4	2	no	—
464	C₂³×C₂₃	—	4	4	no	—
465	C₂³×C₂₃	—	4	4	no	—
466	C₂³×C₂₃	—	8	2	no	—
467	C₂³×C₂₃	—	8	2	no	—
468	C₂³×C₂₃	—	8	2	no	—
469	C₂³×C₂₃	—	8	2	no	—
470	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
471	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
472	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
473	Q₈×C₂₃	—	2	1	no	—
474	Q₈×C₂₃	—	2	1	no	—
475	Q₈×C₂₃	—	4	2	no	—
476	Q₈×C₂₃	—	4	2	no	—
477	Q₈×C₂₃	—	4	2	no	—
478	Q₈×C₂₃	—	8	1	no	—
479	D₄×C₂₃	—	2	4	no	—
480	D₄×C₂₃	—	2	2	no	—
481	D₄×C₂₃	—	2	1	no	—
482	D₄×C₂₃	—	2	1	no	—
483	D₄×C₂₃	—	2	1	no	—
484	D₄×C₂₃	—	2	1	no	—
485	D₄×C₂₃	—	2	2	no	—
486	D₄×C₂₃	—	2	2	no	—
487	D₄×C₂₃	—	2	1	no	—
488	D₄×C₂₃	—	2	1	no	—
489	D₄×C₂₃	—	4	2	no	—
490	D₄×C₂₃	—	4	4	no	—
491	D₄×C₂₃	—	4	2	no	—
492	D₄×C₂₃	—	4	2	no	—
493	D₄×C₂₃	—	4	4	no	—
494	D₄×C₂₃	—	4	4	no	—
495	D₄×C₂₃	—	4	2	no	—
496	D₄×C₂₃	—	4	4	no	—
497	D₄×C₂₃	—	4	4	no	—
498	D₄×C₂₃	—	4	4	no	—
499	D₄×C₂₃	—	4	2	no	—
500	D₄×C₂₃	—	8	1	no	—
501	D₄×C₂₃	—	8	1	no	—
502	D₄×C₂₃	—	8	2	no	—
503	D₄×C₂₃	—	8	2	no	—
504	D₄×C₂₃	—	8	2	no	—
505	D₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
506	C₂×C₄×C₂₃	—	2	2	no	—
507	C₂×C₄×C₂₃	—	2	2	no	—
508	C₂×C₄×C₂₃	—	2	2	no	—
509	C₂×C₄×C₂₃	—	2	2	no	—
510	C₂×C₄×C₂₃	—	2	2	no	—
511	C₂×C₄×C₂₃	—	2	1	no	—
512	C₂×C₄×C₂₃	—	2	1	no	—
513	C₂×C₄×C₂₃	—	2	1	no	—
514	C₂×C₄×C₂₃	—	2	1	no	—
515	C₂×C₄×C₂₃	—	2	1	no	—
516	C₂×C₄×C₂₃	—	2	2	no	—
517	C₂×C₄×C₂₃	—	2	2	no	—
518	C₂×C₄×C₂₃	—	2	2	no	—
519	C₂×C₄×C₂₃	—	2	1	no	—
520	C₂×C₄×C₂₃	—	2	1	no	—
521	C₂×C₄×C₂₃	—	4	2	no	—
522	C₂×C₄×C₂₃	—	4	2	no	—
523	C₂×C₄×C₂₃	—	4	2	no	—
524	C₂×C₄×C₂₃	—	4	1	no	—
525	C₂×C₄×C₂₃	—	4	4	no	—
526	C₂×C₄×C₂₃	—	4	2	no	—
527	C₂×C₄×C₂₃	—	4	4	no	—
528	C₂×C₄×C₂₃	—	4	4	no	—
529	C₂×C₄×C₂₃	—	4	4	no	—
530	C₂×C₄×C₂₃	—	4	2	no	—
531	C₂×C₄×C₂₃	—	4	2	no	—
532	C₂×C₄×C₂₃	—	4	2	no	—
533	C₂×C₄×C₂₃	—	8	1	no	—
534	C₂×C₄×C₂₃	—	8	2	no	—
535	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
543	C₈×C₂₃	—	2	1	no	—
544	C₈×C₂₃	—	2	1	no	—
545	C₈×C₂₃	—	2	2	no	—
546	C₈×C₂₃	—	2	2	no	—
547	C₈×C₂₃	—	2	1	no	—
548	C₈×C₂₃	—	2	1	no	—
549	#3496	C₂×C₂₃	1	1	yes	characteristic, complemented
550	#3475	C₂×C₂₃	1	1	yes	characteristic, complemented
551	#3354	C₂×C₂₃	1	1	yes	characteristic, complemented
552	#3353	C₂×C₂₃	1	1	yes	characteristic, complemented
553	#3345	C₂×C₂₃	1	2	yes	complemented
554	#3343	C₂×C₂₃	1	2	yes	complemented
555	#3335	C₂×C₂₃	1	1	yes	characteristic, complemented
556	#3334	C₂×C₂₃	1	1	yes	characteristic, complemented
557	#3325	C₂×C₂₃	1	1	yes	characteristic, complemented
558	#3324	C₂×C₂₃	1	1	yes	characteristic, complemented
559	#3318	C₂×C₂₃	1	2	yes	complemented
560	#3310	C₂×C₂₃	1	2	yes	complemented
561	#3295	C₂×C₂₃	1	1	yes	characteristic, complemented
562	#3294	C₂×C₂₃	1	1	yes	characteristic, complemented
563	#3235	C₂×C₂₃	1	1	yes	characteristic, complemented
564	#3228	C₂×C₂₃	1	1	yes	characteristic, complemented
565	#3194	C₂×C₂₃	1	2	yes	complemented
566	#3188	C₂×C₂₃	1	2	yes	complemented
567	#3115	C₂×C₂₃	1	1	yes	characteristic, complemented
568	#3106	C₂×C₂₃	1	1	yes	characteristic, complemented
569	#3094	C₂×C₂₃	1	2	yes	complemented
570	C₂×#482	C₂×C₂₃	1	2	yes	complemented
571	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
572	C₂²×C₂₃	—	2	2	no	—
573	C₂²×C₂₃	—	2	2	no	—
574	C₂²×C₂₃	—	2	1	no	—
575	C₂²×C₂₃	—	2	2	no	—
576	C₂²×C₂₃	—	2	1	no	—
577	C₂²×C₂₃	—	2	2	no	—
578	C₂²×C₂₃	—	2	1	no	—
579	C₂²×C₂₃	—	2	2	no	—
580	C₂²×C₂₃	—	4	1	no	—
581	C₂²×C₂₃	—	4	1	no	—
582	C₂²×C₂₃	—	4	2	no	—
583	C₂²×C₂₃	—	4	1	no	—
584	C₂²×C₂₃	—	4	1	no	—
585	C₂²×C₂₃	—	4	1	no	—
586	C₂²×C₂₃	—	4	2	no	—
587	C₂²×C₂₃	—	4	1	no	—
588	C₂²×C₂₃	—	4	2	no	—
589	C₂²×C₂₃	—	4	1	no	—
590	C₂²×C₂₃	—	4	1	no	—
591	C₂²×C₂₃	—	4	1	no	—
592	C₂²×C₂₃	—	8	4	no	—
593	C₂²×C₂₃	—	16	4	no	—
594	C₂²×C₂₃	—	16	4	no	—
595	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
596	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
597	C₄×C₂₃	—	2	1	no	—
598	C₄×C₂₃	—	2	1	no	—
599	C₄×C₂₃	—	2	1	no	—
600	C₄×C₂₃	—	2	2	no	—
601	C₄×C₂₃	—	2	2	no	—
602	C₄×C₂₃	—	2	1	no	—
603	C₄×C₂₃	—	4	1	no	—
604	C₄×C₂₃	—	4	2	no	—
605	C₄×C₂₃	—	4	1	no	—
606	C₄×C₂₃	—	4	1	no	—
607	C₄×C₂₃	—	4	2	no	—
608	C₄×C₂₃	—	4	1	no	—
609	C₄×C₂₃	—	4	1	no	—
610	C₄×C₂₃	—	4	2	no	—
611	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
612	C₄×C₂₃	#585	1	1	yes	characteristic
613	C₄×C₂₃	#585	1	1	yes	characteristic
614	C₂×H(5,𝔽₂)	—	2	1	no	—
615	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
616	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
617	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
618	#553	C₂²×C₂₃	1	2	yes	complemented
619	#552	—	2	1	no	—
620	#552	C₂²×C₂₃	1	2	yes	complemented
621	#551	—	2	2	no	—
622	#547	C₂²×C₂₃	1	1	yes	characteristic
623	#547	C₂²×C₂₃	1	2	yes	—
624	#547	C₂²×C₂₃	1	1	yes	characteristic
625	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
626	#546	—	2	1	no	—
627	#546	—	2	1	no	—
628	#546	—	2	2	no	—
629	#546	—	2	1	no	—
630	D₄²	C₂²×C₂₃	1	1	yes	characteristic
631	D₄²	C₂²×C₂₃	1	2	yes	—
632	D₄²	C₂²×C₂₃	1	1	yes	characteristic
633	#537	—	2	1	no	—
634	#534	—	2	2	no	—
635	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
636	#532	C₂²×C₂₃	1	1	yes	characteristic
637	#532	C₂²×C₂₃	1	1	yes	characteristic
638	#529	—	2	2	no	—
639	#529	—	2	1	no	—
640	#525	C₂²×C₂₃	1	2	yes	complemented
641	C₂×#121	C₂²×C₂₃	1	2	yes	—
642	C₂×#121	C₂²×C₂₃	1	2	yes	—
643	C₄×#41	—	2	1	no	—
644	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
645	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
646	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
647	#501	C₂²×C₂₃	1	2	yes	complemented
648	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
649	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
650	#490	C₂²×C₂₃	1	2	yes	complemented
651	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
652	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
653	#484	C₂²×C₂₃	1	2	yes	complemented
654	#483	C₂²×C₂₃	1	2	yes	complemented
655	#482	C₂²×C₂₃	1	1	yes	characteristic, complemented
656	#482	C₂²×C₂₃	1	2	yes	complemented
657	#482	C₂²×C₂₃	1	2	yes	complemented
658	#482	C₂²×C₂₃	1	2	yes	complemented
659	#482	C₂²×C₂₃	1	2	yes	complemented
660	#482	C₂²×C₂₃	1	2	yes	complemented
661	#482	C₂²×C₂₃	1	2	yes	complemented
662	#482	C₂²×C₂₃	1	2	yes	complemented
663	#482	C₂²×C₂₃	1	1	yes	characteristic, complemented
664	#482	C₂²×C₂₃	1	2	yes	complemented
665	#482	C₂²×C₂₃	1	2	yes	complemented
666	#481	C₂²×C₂₃	1	2	yes	complemented
667	#481	C₂²×C₂₃	1	2	yes	complemented
668	#481	C₂²×C₂₃	1	2	yes	complemented
669	#480	C₂²×C₂₃	1	2	yes	complemented
670	#480	C₂²×C₂₃	1	2	yes	complemented
671	#480	C₂²×C₂₃	1	2	yes	complemented
672	#478	C₂²×C₂₃	1	2	yes	complemented
673	#478	C₂²×C₂₃	1	2	yes	complemented
674	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
675	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
678	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
679	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
680	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
681	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	#469	C₂²×C₂₃	1	2	yes	complemented
683	#469	C₂²×C₂₃	1	2	yes	complemented
684	#468	C₂²×C₂₃	1	2	yes	complemented
685	#468	C₂²×C₂₃	1	2	yes	complemented
686	#466	C₂²×C₂₃	1	2	yes	complemented
687	#466	C₂²×C₂₃	1	2	yes	complemented
688	#465	C₂²×C₂₃	1	2	yes	complemented
689	#465	C₂²×C₂₃	1	2	yes	complemented
690	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
692	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
693	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
694	#450	C₂²×C₂₃	1	2	yes	complemented
695	#450	C₂²×C₂₃	1	2	yes	complemented
696	#449	C₂²×C₂₃	1	1	yes	characteristic, complemented
697	#449	C₂²×C₂₃	1	1	yes	characteristic, complemented
698	#449	C₂²×C₂₃	1	2	yes	complemented
699	#447	C₂²×C₂₃	1	2	yes	complemented
700	#447	C₂²×C₂₃	1	2	yes	complemented
701	#442	C₂²×C₂₃	1	2	yes	complemented
702	#440	C₂²×C₂₃	1	2	yes	complemented
703	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
704	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
705	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
706	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
707	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
708	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
709	#435	C₂²×C₂₃	1	2	yes	complemented
710	#435	C₂²×C₂₃	1	2	yes	complemented
711	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
712	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
713	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
714	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
715	#428	C₂²×C₂₃	1	2	yes	complemented
716	#428	C₂²×C₂₃	1	2	yes	complemented
717	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
718	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
719	#418	C₂²×C₂₃	1	2	yes	complemented
720	#418	C₂²×C₂₃	1	2	yes	complemented
721	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
722	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
723	#407	C₂²×C₂₃	1	2	yes	complemented
724	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
725	C₂×C₂₃	—	2	4	no	—
726	C₂×C₂₃	—	4	1	no	—
727	C₂×C₂₃	—	4	2	no	—
728	C₂×C₂₃	—	8	1	no	—
729	C₂×C₂₃	—	8	1	no	—
730	C₂×C₂₃	—	8	2	no	—
731	C₂×C₂₃	—	8	1	no	—
732	C₂×C₂₃	#3485	1	1	yes	characteristic
733	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
734	C₂×C₂₃	#3584	1	1	yes	characteristic
735	H(5,𝔽₂)	—	4	8	no	—
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	2	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	—	2	1	no	—
740	C₂×#41	—	2	1	no	—
741	C₂×#41	—	2	1	no	—
742	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
743	C₂²×D₄	—	2	2	no	—
744	C₂²×D₄	—	2	2	no	—
745	C₂²×D₄	—	2	2	no	—
746	C₂²×D₄	—	2	1	no	—
747	C₂²×D₄	—	2	1	no	—
748	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
749	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
750	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
751	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
752	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
753	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
754	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
755	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
756	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
757	C₂×D₈	C₂³×C₂₃	1	2	yes	—
758	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
759	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
760	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
761	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
762	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
763	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
764	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
765	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
766	#127	C₂³×C₂₃	1	1	yes	characteristic
767	#127	C₂³×C₂₃	1	1	yes	characteristic
768	#126	—	2	2	no	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#125	—	2	2	no	—
772	#125	—	2	1	no	—
773	#125	C₂³×C₂₃	1	2	yes	—
774	#124	—	2	1	no	—
775	#124	—	2	2	no	—
776	#124	—	2	1	no	—
777	#124	—	2	1	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
795	#121	—	2	2	no	—
796	#121	—	2	1	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	1	no	—
802	#121	—	2	1	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	2	no	—
806	#121	C₂³×C₂₃	1	1	yes	characteristic
807	#121	C₂³×C₂₃	1	2	yes	—
808	#121	C₂³×C₂₃	1	1	yes	characteristic
809	#121	C₂³×C₂₃	1	2	yes	—
810	#121	C₂³×C₂₃	1	2	yes	—
811	#121	C₂³×C₂₃	1	2	yes	—
812	#121	C₂³×C₂₃	1	2	yes	—
813	#121	C₂³×C₂₃	1	2	yes	—
814	#121	C₂³×C₂₃	1	2	yes	—
815	#120	—	2	2	no	—
816	#120	—	2	2	no	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	C₄×Q₈	—	2	1	no	—
821	C₄×Q₈	—	2	1	no	—
822	C₄×Q₈	—	2	1	no	—
823	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
824	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
834	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
835	C₄×D₄	D₄×C₂₃	1	2	yes	—
836	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₂₃	1	2	yes	—
841	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₂₃	1	2	yes	—
843	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
844	#117	—	2	2	no	—
845	#117	—	2	2	no	—
846	#117	—	2	1	no	—
847	#117	—	2	2	no	—
848	#117	—	2	1	no	—
849	#117	C₂³×C₂₃	1	1	yes	characteristic
850	#117	C₂³×C₂₃	1	2	yes	—
851	#117	C₂³×C₂₃	1	2	yes	—
852	#117	C₂³×C₂₃	1	2	yes	—
853	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
854	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
855	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
856	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
857	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
858	C₂×C₂²⋊C₄	—	2	2	no	—
859	C₂×C₂²⋊C₄	—	2	2	no	—
860	C₂×C₂²⋊C₄	—	2	2	no	—
861	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
862	C₂×C₄²	—	2	2	no	—
863	C₂×C₄²	—	2	1	no	—
864	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
865	#107	C₂³×C₂₃	1	1	yes	characteristic
866	#107	C₂³×C₂₃	1	2	yes	—
867	#107	C₂³×C₂₃	1	2	yes	—
868	#107	C₂³×C₂₃	1	2	yes	—
869	#107	C₂³×C₂₃	1	1	yes	characteristic
870	#107	C₂³×C₂₃	1	2	yes	—
871	#107	C₂³×C₂₃	1	2	yes	—
872	#106	C₂³×C₂₃	1	1	yes	characteristic
873	#106	C₂³×C₂₃	1	2	yes	—
874	#106	C₂³×C₂₃	1	2	yes	—
875	#106	C₂³×C₂₃	1	2	yes	—
876	#106	C₂³×C₂₃	1	1	yes	characteristic
877	#106	C₂³×C₂₃	1	2	yes	—
878	#106	C₂³×C₂₃	1	2	yes	—
879	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
880	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
881	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
883	#103	C₂³×C₂₃	1	1	yes	characteristic
884	#103	C₂³×C₂₃	1	1	yes	characteristic
885	#103	C₂³×C₂₃	1	2	yes	—
886	#102	C₂³×C₂₃	1	1	yes	characteristic
887	#102	C₂³×C₂₃	1	1	yes	characteristic
888	#102	C₂³×C₂₃	1	2	yes	—
889	#102	C₂³×C₂₃	1	2	yes	—
890	#102	C₂³×C₂₃	1	2	yes	—
891	#102	C₂³×C₂₃	1	2	yes	—
892	#102	C₂³×C₂₃	1	2	yes	—
893	#102	C₂³×C₂₃	1	2	yes	—
894	#102	C₂³×C₂₃	1	1	yes	characteristic
895	#102	C₂³×C₂₃	1	1	yes	characteristic
896	#102	C₂³×C₂₃	1	2	yes	—
897	#102	C₂³×C₂₃	1	2	yes	—
898	#102	C₂³×C₂₃	1	2	yes	—
899	#102	C₂³×C₂₃	1	2	yes	—
900	#102	C₂³×C₂₃	1	1	yes	characteristic
901	#102	C₂³×C₂₃	1	1	yes	characteristic
902	#102	C₂³×C₂₃	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
904	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
905	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
908	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
909	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
910	#97	C₂³×C₂₃	1	2	yes	—
911	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
912	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
913	C₂₃	#61733	1	1	yes	characteristic, direct product factor, Sylow
914	C₂⁴	—	2	2	no	—
915	C₂⁴	—	2	2	no	—
916	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
917	#41	—	4	1	no	—
918	#41	—	4	1	no	—
919	#41	—	4	4	no	—
920	#41	—	4	4	no	—
921	#41	—	4	8	no	—
922	#41	—	4	4	no	—
923	#41	—	4	4	no	—
924	#41	—	4	4	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	—	2	1	no	—
927	C₂×Q₈	—	2	1	no	—
928	C₂×Q₈	—	2	1	no	—
929	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	4	2	no	—
948	C₂×D₄	—	4	2	no	—
949	C₂×D₄	—	4	2	no	—
950	C₂×D₄	—	4	2	no	—
951	C₂×D₄	—	4	8	no	—
952	C₂×D₄	—	4	4	no	—
953	C₂×D₄	—	4	8	no	—
954	C₂×D₄	—	4	8	no	—
955	C₂×D₄	—	4	4	no	—
956	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
957	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
958	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
959	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
960	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
961	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
962	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	4	2	no	—
974	C₂²×C₄	—	4	2	no	—
975	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
976	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
977	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
978	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
979	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
980	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
981	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
982	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
983	SD₁₆	—	4	1	no	—
984	SD₁₆	—	4	2	no	—
985	SD₁₆	—	4	1	no	—
986	D₈	—	4	1	no	—
987	D₈	—	4	2	no	—
988	D₈	—	4	1	no	—
989	M₁₆	—	4	2	no	—
990	M₁₆	—	4	2	no	—
991	C₂×C₈	—	4	2	no	—
992	C₂×C₈	—	4	2	no	—
993	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
994	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
995	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
996	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
997	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
998	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1014	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1015	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1018	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1020	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1021	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1022	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₂₃	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	2	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	2	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	—	2	1	no	—
1053	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1054	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1056	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1057	C₂³	—	2	4	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	2	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	4	2	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	4	no	—
1066	C₂³	—	8	2	no	—
1067	C₂³	—	8	2	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1071	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1072	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1073	Q₈	—	2	1	no	—
1074	Q₈	—	2	1	no	—
1075	Q₈	—	4	2	no	—
1076	Q₈	—	4	2	no	—
1077	Q₈	—	4	2	no	—
1078	Q₈	—	8	1	no	—
1079	D₄	—	2	4	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	2	no	—
1086	D₄	—	2	2	no	—
1087	D₄	—	2	1	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	4	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	4	4	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	4	no	—
1097	D₄	—	4	4	no	—
1098	D₄	—	4	4	no	—
1099	D₄	—	4	2	no	—
1100	D₄	—	8	2	no	—
1101	D₄	—	8	2	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	1	no	—
1104	D₄	—	8	2	no	—
1105	D₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	2	no	—
1123	C₂×C₄	—	4	2	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	4	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	4	4	no	—
1128	C₂×C₄	—	4	4	no	—
1129	C₂×C₄	—	4	4	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	4	2	no	—
1132	C₂×C₄	—	4	2	no	—
1133	C₂×C₄	—	8	1	no	—
1134	C₂×C₄	—	8	2	no	—
1135	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1136	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1137	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1139	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1140	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1141	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1142	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1143	C₈	—	2	1	no	—
1144	C₈	—	2	1	no	—
1145	C₈	—	2	2	no	—
1146	C₈	—	2	2	no	—
1147	C₈	—	2	1	no	—
1148	C₈	—	2	1	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	1	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	2	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	8	4	no	—
1170	C₂²	—	16	4	no	—
1171	C₂²	—	16	4	no	—
1172	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	4	yes	—
1173	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1174	C₄	—	2	1	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	2	1	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	1	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	2	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	2	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
1189	C₄	C₂₃×#585	1	1	yes	characteristic
1190	C₄	C₂₃×#585	1	1	yes	characteristic
1191	C₂	—	2	4	no	—
1192	C₂	—	4	1	no	—
1193	C₂	—	4	2	no	—
1194	C₂	—	8	1	no	—
1195	C₂	—	8	2	no	—
1196	C₂	—	8	1	no	—
1197	C₂	—	8	1	no	—
1198	C₂	C₂₃×#3485	1	1	yes	characteristic
1199	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
1200	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 ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3496	C₂	semidirect
2. C₂₃×#3475	C₂	semidirect
3. C₂₃×#3354	C₂	semidirect
4. C₂₃×#3353	C₂	semidirect
5. C₂₃×#3345	C₂	semidirect
6. C₂₃×#3343	C₂	semidirect
7. C₂₃×#3335	C₂	semidirect
8. C₂₃×#3334	C₂	semidirect
9. C₂₃×#3325	C₂	semidirect
10. C₂₃×#3324	C₂	semidirect
11. C₂₃×#3318	C₂	semidirect
12. C₂₃×#3310	C₂	semidirect
13. C₂₃×#3295	C₂	semidirect
14. C₂₃×#3294	C₂	semidirect
15. C₂₃×#3235	C₂	semidirect
16. C₂₃×#3228	C₂	semidirect
17. C₂₃×#3194	C₂	semidirect
18. C₂₃×#3188	C₂	semidirect
19. C₂₃×#3115	C₂	semidirect
20. C₂₃×#3106	C₂	semidirect
21. C₂₃×#3094	C₂	semidirect
22. C₂×C₂₃×#482	C₂	semidirect
23. C₂₃×#2974	C₂	semidirect
25. C₂₃×#556	C₂²	semidirect
26. C₂₃×#555	C₂²	semidirect
27. C₂₃×#554	C₂²	semidirect
28. C₂₃×#553	C₂²	semidirect
30. C₂₃×#552	C₂²	semidirect
35. C₂₃×#547	C₂²	semidirect
45. C₂₃×#533	C₂²	semidirect
50. C₂₃×#525	C₂²	semidirect
54. C₄×#41×C₂₃	C₂²	semidirect
56. C₂×C₂₃×#117	C₂²	semidirect
57. C₂₃×#501	C₂²	semidirect
58. C₂₃×#500	C₂²	semidirect
59. C₂₃×#498	C₂²	semidirect
60. C₂₃×#490	C₂²	semidirect
61. C₂₃×#486	C₂²	semidirect
62. C₂₃×#486	C₂²	semidirect
63. C₂₃×#484	C₂²	semidirect
64. C₂₃×#483	C₂²	semidirect
65. C₂₃×#482	C₂²	semidirect
66. C₂₃×#482	C₂²	semidirect
67. C₂₃×#482	C₂²	semidirect
68. C₂₃×#482	C₂²	semidirect
69. C₂₃×#482	C₂²	semidirect
70. C₂₃×#482	C₂²	semidirect
71. C₂₃×#482	C₂²	semidirect
72. C₂₃×#482	C₂²	semidirect
73. C₂₃×#482	C₂²	semidirect
74. C₂₃×#482	C₂²	semidirect
75. C₂₃×#482	C₂²	semidirect
76. C₂₃×#481	C₂²	semidirect
77. C₂₃×#481	C₂²	semidirect
78. C₂₃×#481	C₂²	semidirect
79. C₂₃×#480	C₂²	semidirect
80. C₂₃×#480	C₂²	semidirect
81. C₂₃×#480	C₂²	semidirect
82. C₂₃×#478	C₂²	semidirect
83. C₂₃×#478	C₂²	semidirect
84. C₂₃×#477	C₂²	semidirect
85. C₂₃×#476	C₂²	semidirect
86. C₂₃×#476	C₂²	semidirect
87. C₂₃×#476	C₂²	semidirect
88. C₂₃×#475	C₂²	semidirect
89. C₂₃×#474	C₂²	semidirect
90. C₂₃×#474	C₂²	semidirect
91. C₂₃×#474	C₂²	semidirect
92. C₂₃×#469	C₂²	semidirect
93. C₂₃×#469	C₂²	semidirect
94. C₂₃×#468	C₂²	semidirect
95. C₂₃×#468	C₂²	semidirect
96. C₂₃×#466	C₂²	semidirect
97. C₂₃×#466	C₂²	semidirect
98. C₂₃×#465	C₂²	semidirect
99. C₂₃×#465	C₂²	semidirect
100. C₂₃×#460	C₂²	semidirect
101. C₂₃×#460	C₂²	semidirect
102. C₂₃×#459	C₂²	semidirect
103. C₂₃×#459	C₂²	semidirect
104. C₂₃×#450	C₂²	semidirect
105. C₂₃×#450	C₂²	semidirect
106. C₂₃×#449	C₂²	semidirect
107. C₂₃×#449	C₂²	semidirect
108. C₂₃×#449	C₂²	semidirect
109. C₂₃×#447	C₂²	semidirect
110. C₂₃×#447	C₂²	semidirect
111. C₂₃×#442	C₂²	semidirect
112. C₂₃×#440	C₂²	semidirect
113. C₄×SD₁₆×C₂₃	C₂²	semidirect
114. C₄×SD₁₆×C₂₃	C₂²	semidirect
115. C₄×D₈×C₂₃	C₂²	semidirect
116. C₄×D₈×C₂₃	C₂²	semidirect
117. C₂₃×#436	C₂²	semidirect
118. C₂₃×#436	C₂²	semidirect
119. C₂₃×#435	C₂²	semidirect
120. C₂₃×#435	C₂²	semidirect
121. C₈×D₄×C₂₃	C₂²	semidirect
122. C₈×D₄×C₂₃	C₂²	semidirect
123. C₂₃×#432	C₂²	semidirect
124. C₂₃×#431	C₂²	semidirect
125. C₂₃×#428	C₂²	semidirect
126. C₂₃×#428	C₂²	semidirect
127. C₂×C₂₃×#107	C₂²	semidirect
128. C₂×C₂₃×#106	C₂²	semidirect
129. C₂₃×#418	C₂²	semidirect
130. C₂₃×#418	C₂²	semidirect
131. C₂×C₂₃×#102	C₂²	semidirect
132. C₂×C₂₃×#102	C₂²	semidirect
133. C₂₃×#407	C₂²	semidirect
134. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
456. #61733	C₂₃	direct (N × H)
549. #3496	C₂×C₂₃	semidirect
550. #3475	C₂×C₂₃	semidirect
551. #3354	C₂×C₂₃	semidirect
552. #3353	C₂×C₂₃	semidirect
553. #3345	C₂×C₂₃	semidirect
554. #3343	C₂×C₂₃	semidirect
555. #3335	C₂×C₂₃	semidirect
556. #3334	C₂×C₂₃	semidirect
557. #3325	C₂×C₂₃	semidirect
558. #3324	C₂×C₂₃	semidirect
559. #3318	C₂×C₂₃	semidirect
560. #3310	C₂×C₂₃	semidirect
561. #3295	C₂×C₂₃	semidirect
562. #3294	C₂×C₂₃	semidirect
563. #3235	C₂×C₂₃	semidirect
564. #3228	C₂×C₂₃	semidirect
565. #3194	C₂×C₂₃	semidirect
566. #3188	C₂×C₂₃	semidirect
567. #3115	C₂×C₂₃	semidirect
568. #3106	C₂×C₂₃	semidirect
569. #3094	C₂×C₂₃	semidirect
570. C₂×#482	C₂×C₂₃	semidirect
571. #2974	C₂×C₂₃	semidirect
615. #556	C₂²×C₂₃	semidirect
616. #555	C₂²×C₂₃	semidirect
617. #554	C₂²×C₂₃	semidirect
618. #553	C₂²×C₂₃	semidirect
620. #552	C₂²×C₂₃	semidirect
625. #547	C₂²×C₂₃	semidirect
635. #533	C₂²×C₂₃	semidirect
640. #525	C₂²×C₂₃	semidirect
644. C₄×#41	C₂²×C₂₃	semidirect
646. C₂×#117	C₂²×C₂₃	semidirect
647. #501	C₂²×C₂₃	semidirect
648. #500	C₂²×C₂₃	semidirect
649. #498	C₂²×C₂₃	semidirect
650. #490	C₂²×C₂₃	semidirect
651. #486	C₂²×C₂₃	semidirect
652. #486	C₂²×C₂₃	semidirect
653. #484	C₂²×C₂₃	semidirect
654. #483	C₂²×C₂₃	semidirect
655. #482	C₂²×C₂₃	semidirect
656. #482	C₂²×C₂₃	semidirect
657. #482	C₂²×C₂₃	semidirect
658. #482	C₂²×C₂₃	semidirect
659. #482	C₂²×C₂₃	semidirect
660. #482	C₂²×C₂₃	semidirect
661. #482	C₂²×C₂₃	semidirect
662. #482	C₂²×C₂₃	semidirect
663. #482	C₂²×C₂₃	semidirect
664. #482	C₂²×C₂₃	semidirect
665. #482	C₂²×C₂₃	semidirect
666. #481	C₂²×C₂₃	semidirect
667. #481	C₂²×C₂₃	semidirect
668. #481	C₂²×C₂₃	semidirect
669. #480	C₂²×C₂₃	semidirect
670. #480	C₂²×C₂₃	semidirect
671. #480	C₂²×C₂₃	semidirect
672. #478	C₂²×C₂₃	semidirect
673. #478	C₂²×C₂₃	semidirect
674. #477	C₂²×C₂₃	semidirect
675. #476	C₂²×C₂₃	semidirect
676. #476	C₂²×C₂₃	semidirect
677. #476	C₂²×C₂₃	semidirect
678. #475	C₂²×C₂₃	semidirect
679. #474	C₂²×C₂₃	semidirect
680. #474	C₂²×C₂₃	semidirect
681. #474	C₂²×C₂₃	semidirect
682. #469	C₂²×C₂₃	semidirect
683. #469	C₂²×C₂₃	semidirect
684. #468	C₂²×C₂₃	semidirect
685. #468	C₂²×C₂₃	semidirect
686. #466	C₂²×C₂₃	semidirect
687. #466	C₂²×C₂₃	semidirect
688. #465	C₂²×C₂₃	semidirect
689. #465	C₂²×C₂₃	semidirect
690. #460	C₂²×C₂₃	semidirect
691. #460	C₂²×C₂₃	semidirect
692. #459	C₂²×C₂₃	semidirect
693. #459	C₂²×C₂₃	semidirect
694. #450	C₂²×C₂₃	semidirect
695. #450	C₂²×C₂₃	semidirect
696. #449	C₂²×C₂₃	semidirect
697. #449	C₂²×C₂₃	semidirect
698. #449	C₂²×C₂₃	semidirect
699. #447	C₂²×C₂₃	semidirect
700. #447	C₂²×C₂₃	semidirect
701. #442	C₂²×C₂₃	semidirect
702. #440	C₂²×C₂₃	semidirect
703. C₄×SD₁₆	C₂²×C₂₃	semidirect
704. C₄×SD₁₆	C₂²×C₂₃	semidirect
705. C₄×D₈	C₂²×C₂₃	semidirect
706. C₄×D₈	C₂²×C₂₃	semidirect
707. #436	C₂²×C₂₃	semidirect
708. #436	C₂²×C₂₃	semidirect
709. #435	C₂²×C₂₃	semidirect
710. #435	C₂²×C₂₃	semidirect
711. C₈×D₄	C₂²×C₂₃	semidirect
712. C₈×D₄	C₂²×C₂₃	semidirect
713. #432	C₂²×C₂₃	semidirect
714. #431	C₂²×C₂₃	semidirect
715. #428	C₂²×C₂₃	semidirect
716. #428	C₂²×C₂₃	semidirect
717. C₂×#107	C₂²×C₂₃	semidirect
718. C₂×#106	C₂²×C₂₃	semidirect
719. #418	C₂²×C₂₃	semidirect
720. #418	C₂²×C₂₃	semidirect
721. C₂×#102	C₂²×C₂₃	semidirect
722. C₂×#102	C₂²×C₂₃	semidirect
723. #407	C₂²×C₂₃	semidirect
724. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
913. C₂₃	#61733	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×#3496	2
C₂₃×#3475	2
C₂₃×#3354	2
C₂₃×#3353	2
C₂₃×#3345	2
C₂₃×#3343	2
C₂₃×#3335	2
C₂₃×#3334	2
C₂₃×#3325	2
C₂₃×#3324	2
C₂₃×#3318	2
C₂₃×#3310	2
C₂₃×#3295	2
C₂₃×#3294	2
C₂₃×#3235	2
C₂₃×#3228	2
C₂₃×#3194	2
C₂₃×#3188	2
C₂₃×#3115	2
C₂₃×#3106	2
C₂₃×#3094	2
C₂×C₂₃×#482	2
C₂₃×#2974	2
#61733	23

Subgroups — C23×#61733 #19209359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61733 #19209359