Subgroups — C₂₃×#61170 #19208796

Order 5888.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3321	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3317	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3313	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3309	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3305	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3304	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3301	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#556	—	2	1	no	—
32	C₂₃×#556	C₂²	1	2	yes	complemented
33	C₂₃×#555	—	2	1	no	—
34	C₂₃×#555	C₂²	1	2	yes	complemented
35	C₂₃×#553	—	2	1	no	—
36	C₂₃×#553	C₂²	1	2	yes	complemented
37	C₂₃×#552	—	2	1	no	—
38	C₂₃×#552	C₂²	1	2	yes	complemented
39	C₂₃×#550	—	2	1	no	—
40	C₂₃×#550	—	2	1	no	—
41	C₂₃×#550	C₂²	1	2	yes	—
42	C₂₃×#550	C₂²	1	2	yes	—
43	C₂₃×#548	—	2	1	no	—
44	C₂₃×#548	—	2	1	no	—
45	C₂₃×#548	C₂²	1	2	yes	—
46	C₂₃×#548	C₂²	1	2	yes	—
47	C₂₃×#544	C₂²	1	1	yes	characteristic
48	C₂₃×#538	—	2	2	no	—
49	C₂₃×#537	C₂²	1	1	yes	characteristic
50	C₂₃×#535	—	2	2	no	—
51	C₂₃×#535	C₂²	1	1	yes	characteristic
52	C₂₃×#535	C₂²	1	1	yes	characteristic
53	C₂₃×#529	—	2	2	no	—
54	C₂₃×#525	—	2	2	no	—
55	C₂₃×#525	C₂²	1	1	yes	characteristic
56	C₂₃×#525	C₂²	1	1	yes	characteristic
57	C₂₃×#525	C₂²	1	1	yes	characteristic
58	C₂₃×#520	C₂²	1	1	yes	characteristic
59	C₂₃×#520	C₂²	1	1	yes	characteristic
60	C₂₃×#519	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
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×#485	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×#481	C₂²	1	2	yes	complemented
73	C₂₃×#480	C₂²	1	2	yes	complemented
74	C₂₃×#479	C₂²	1	2	yes	complemented
75	C₂₃×#479	C₂²	1	2	yes	complemented
76	C₂₃×#477	C₂²	1	2	yes	complemented
77	C₂₃×#475	C₂²	1	2	yes	complemented
78	C₂₃×#469	C₂²	1	2	yes	complemented
79	C₂₃×#468	C₂²	1	2	yes	complemented
80	C₂₃×#467	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#467	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#466	C₂²	1	2	yes	complemented
83	C₂₃×#466	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#466	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#465	C₂²	1	2	yes	complemented
86	C₂₃×#465	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#465	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#465	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#465	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#464	C₂²	1	2	yes	complemented
91	C₂₃×#463	C₂²	1	2	yes	complemented
92	C₂₃×#460	C₂²	1	2	yes	complemented
93	C₂₃×#459	C₂²	1	2	yes	complemented
94	C₂₃×#452	C₂²	1	2	yes	—
95	C₂₃×#452	C₂²	1	2	yes	—
96	C₂₃×#452	C₂²	1	2	yes	complemented
97	C₂₃×#451	C₂²	1	2	yes	complemented
98	C₂₃×#449	C₂²	1	2	yes	—
99	C₂₃×#449	C₂²	1	2	yes	—
100	C₂₃×#449	C₂²	1	2	yes	complemented
101	C₂₃×#448	C₂²	1	2	yes	complemented
102	C₂₃×#441	C₂²	1	2	yes	complemented
103	C₂₃×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
106	C₂₃×#435	C₂²	1	2	yes	complemented
107	C₂₃×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
109	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
110	C₂₃×#428	C₂²	1	1	yes	characteristic
111	C₂₃×#428	C₂²	1	1	yes	characteristic
112	C₂₃×#427	C₂²	1	1	yes	characteristic
113	C₂₃×#424	C₂²	1	1	yes	characteristic
114	C₂₃×#419	C₂²	1	1	yes	characteristic
115	C₂₃×#419	C₂²	1	2	yes	complemented
116	C₂₃×#418	C₂²	1	1	yes	characteristic
117	C₂₃×#417	C₂²	1	1	yes	characteristic
118	C₂₃×#417	C₂²	1	1	yes	characteristic
119	C₂₃×#417	C₂²	1	2	yes	complemented
120	C₂₃×#416	C₂²	1	1	yes	characteristic
121	C₂₃×#416	C₂²	1	2	yes	—
122	C₂₃×#416	C₂²	1	2	yes	—
123	C₂₃×#416	C₂²	1	1	yes	characteristic
124	C₂₃×#416	C₂²	1	2	yes	—
125	C₂₃×#416	C₂²	1	2	yes	—
126	C₂₃×#416	C₂²	1	2	yes	complemented
127	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
128	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
129	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
130	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
131	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
132	C₂₃×#408	C₂²	1	1	yes	characteristic
133	C₂₃×#407	C₂²	1	1	yes	characteristic
134	C₂₃×#405	C₂²	1	1	yes	characteristic
135	C₂₃×2₋¹⁺⁴	—	2	4	no	—
136	C₂₃×2₋¹⁺⁴	—	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	1	yes	characteristic
145	C₂×#41×C₂₃	C₂³	1	2	yes	—
146	C₂×#41×C₂₃	C₂³	1	2	yes	—
147	C₂×#41×C₂₃	C₂³	1	2	yes	—
148	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₂₃	—	2	1	no	—
150	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
151	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
152	C₂²×D₄×C₂₃	—	2	1	no	—
153	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₂₃	—	2	1	no	—
155	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂₃×#137	—	2	4	no	—
157	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
158	C₂₃×#135	—	4	2	no	—
159	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
165	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₂×D₈×C₂₃	C₂³	1	2	yes	—
167	C₂₃×#131	—	4	2	no	—
168	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
171	C₂²×C₈×C₂₃	—	4	2	no	—
172	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
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	—
179	C₂₃×C₄⋊Q₈	—	2	1	no	—
180	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
181	C₂₃×#127	—	2	1	no	—
182	C₂₃×#127	—	2	2	no	—
183	C₂₃×#127	—	2	2	no	—
184	C₂₃×#127	C₂³	1	2	yes	—
185	C₂₃×#126	—	2	2	no	—
186	C₂₃×#126	—	2	2	no	—
187	C₂₃×#126	—	2	2	no	—
188	C₂₃×#126	—	2	2	no	—
189	C₂₃×#125	—	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	—	2	2	no	—
197	C₂₃×#124	—	2	2	no	—
198	C₂₃×#124	C₂³	1	2	yes	—
199	C₂₃×#123	—	2	2	no	—
200	C₂₃×#123	—	2	1	no	—
201	C₂₃×#123	—	2	1	no	—
202	C₂₃×#123	—	2	2	no	—
203	C₂₃×#123	D₄	1	2	yes	—
204	C₂₃×C₂²⋊Q₈	—	2	1	no	—
205	C₂₃×C₂²⋊Q₈	—	2	2	no	—
206	C₂₃×C₂²⋊Q₈	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	—	2	2	no	—
208	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂₃×#121	—	2	2	no	—
216	C₂₃×#121	—	2	2	no	—
217	C₂₃×#121	—	2	1	no	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	2	no	—
221	C₂₃×#121	—	2	1	no	—
222	C₂₃×#121	—	2	1	no	—
223	C₂₃×#121	—	2	2	no	—
224	C₂₃×#121	—	2	2	no	—
225	C₂₃×#121	—	2	2	no	—
226	C₂₃×#121	—	2	2	no	—
227	C₂₃×#121	D₄	1	1	yes	characteristic
228	C₂₃×#121	D₄	1	1	yes	characteristic
229	C₂₃×#121	C₂³	1	2	yes	—
230	C₂₃×#121	C₂³	1	2	yes	—
231	C₂₃×#121	C₂³	1	1	yes	characteristic
232	C₂₃×#121	C₂³	1	1	yes	characteristic
233	C₂₃×#121	C₂³	1	1	yes	characteristic
234	C₂₃×#121	C₂³	1	2	yes	—
235	C₂₃×#121	C₂³	1	1	yes	characteristic
236	C₂₃×#120	—	2	1	no	—
237	C₂₃×#120	—	2	1	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	—	2	1	no	—
243	C₄×Q₈×C₂₃	—	2	1	no	—
244	C₄×Q₈×C₂₃	—	2	2	no	—
245	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
246	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
247	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
248	C₄×D₄×C₂₃	—	2	1	no	—
249	C₄×D₄×C₂₃	—	2	2	no	—
250	C₄×D₄×C₂₃	—	2	1	no	—
251	C₄×D₄×C₂₃	—	2	1	no	—
252	C₄×D₄×C₂₃	—	2	1	no	—
253	C₄×D₄×C₂₃	—	2	1	no	—
254	C₄×D₄×C₂₃	—	2	2	no	—
255	C₄×D₄×C₂₃	—	2	2	no	—
256	C₄×D₄×C₂₃	—	2	2	no	—
257	C₄×D₄×C₂₃	—	2	2	no	—
258	C₄×D₄×C₂₃	—	2	2	no	—
259	C₄×D₄×C₂₃	—	2	2	no	—
260	C₄×D₄×C₂₃	C₂³	1	2	yes	—
261	C₄×D₄×C₂₃	C₂³	1	2	yes	—
262	C₄×D₄×C₂₃	C₂³	1	2	yes	—
263	C₂₃×#117	—	2	1	no	—
264	C₂₃×#117	—	2	1	no	—
265	C₂₃×#117	—	2	2	no	—
266	C₂₃×#117	—	2	1	no	—
267	C₂₃×#117	—	2	2	no	—
268	C₂₃×#117	—	2	2	no	—
269	C₂₃×#117	C₂³	1	2	yes	—
270	C₂₃×#117	C₂³	1	2	yes	—
271	C₂₃×#117	C₂³	1	2	yes	—
272	C₂₃×#117	C₂³	1	1	yes	characteristic
273	C₂₃×#117	C₂³	1	1	yes	characteristic
274	C₂₃×#117	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
276	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
277	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
280	C₂×C₄²×C₂₃	—	2	1	no	—
281	C₂₃×#107	C₂³	1	1	yes	characteristic
282	C₂₃×#107	C₂³	1	1	yes	characteristic
283	C₂₃×#107	C₂³	1	2	yes	—
284	C₂₃×#107	C₂³	1	2	yes	—
285	C₂₃×#106	C₂³	1	1	yes	characteristic
286	C₂₃×#106	C₂³	1	1	yes	characteristic
287	C₂₃×#106	C₂³	1	2	yes	—
288	C₂₃×#106	C₂³	1	2	yes	—
289	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
290	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	2	yes	—
292	C₂₃×#103	C₂³	1	2	yes	—
293	C₂₃×#103	C₂³	1	2	yes	—
294	C₂₃×#103	C₂³	1	2	yes	—
295	C₂₃×#103	C₂³	1	1	yes	characteristic
296	C₂₃×#103	C₂³	1	2	yes	—
297	C₂₃×#103	C₂³	1	2	yes	—
298	C₂₃×#103	C₂³	1	1	yes	characteristic
299	C₂₃×#103	C₂³	1	1	yes	characteristic
300	C₂₃×#103	C₂³	1	1	yes	characteristic
301	C₂₃×#103	C₂³	1	2	yes	—
302	C₂₃×#103	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	2	yes	—
304	C₂₃×#102	C₂³	1	2	yes	—
305	C₂₃×#102	C₂³	1	2	yes	—
306	C₂₃×#102	C₂³	1	2	yes	—
307	C₂₃×#102	C₂³	1	1	yes	characteristic
308	C₂₃×#102	C₂³	1	1	yes	characteristic
309	C₂₃×#102	C₂³	1	1	yes	characteristic
310	C₂₃×#102	C₂³	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
323	#41×C₂₃	—	2	2	no	—
324	#41×C₂₃	—	2	2	no	—
325	#41×C₂₃	—	2	4	no	—
326	#41×C₂₃	—	2	4	no	—
327	#41×C₂₃	—	2	4	no	—
328	#41×C₂₃	—	2	2	no	—
329	#41×C₂₃	—	2	2	no	—
330	#41×C₂₃	—	2	2	no	—
331	#41×C₂₃	—	2	2	no	—
332	#41×C₂₃	—	4	2	no	—
333	#41×C₂₃	—	4	2	no	—
334	#41×C₂₃	—	4	2	no	—
335	#41×C₂₃	—	4	8	no	—
336	#41×C₂₃	—	4	4	no	—
337	#41×C₂₃	—	4	4	no	—
338	#41×C₂₃	—	4	4	no	—
339	C₂×Q₈×C₂₃	—	2	1	no	—
340	C₂×Q₈×C₂₃	—	2	2	no	—
341	C₂×Q₈×C₂₃	—	2	2	no	—
342	C₂×Q₈×C₂₃	—	2	2	no	—
343	C₂×Q₈×C₂₃	—	2	4	no	—
344	C₂×Q₈×C₂₃	—	4	2	no	—
345	C₂×Q₈×C₂₃	—	4	4	no	—
346	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
347	C₂×Q₈×C₂₃	#41	1	4	yes	—
348	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
350	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
351	C₂×D₄×C₂₃	—	2	1	no	—
352	C₂×D₄×C₂₃	—	2	1	no	—
353	C₂×D₄×C₂₃	—	2	2	no	—
354	C₂×D₄×C₂₃	—	2	2	no	—
355	C₂×D₄×C₂₃	—	2	2	no	—
356	C₂×D₄×C₂₃	—	2	1	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	1	no	—
361	C₂×D₄×C₂₃	—	2	1	no	—
362	C₂×D₄×C₂₃	—	2	2	no	—
363	C₂×D₄×C₂₃	—	2	1	no	—
364	C₂×D₄×C₂₃	—	2	2	no	—
365	C₂×D₄×C₂₃	—	2	2	no	—
366	C₂×D₄×C₂₃	—	2	2	no	—
367	C₂×D₄×C₂₃	—	2	2	no	—
368	C₂×D₄×C₂₃	—	4	4	no	—
369	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
373	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
374	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₂₃	—	2	1	no	—
377	C₂²×C₄×C₂₃	—	2	2	no	—
378	C₂²×C₄×C₂₃	—	2	2	no	—
379	C₂²×C₄×C₂₃	—	2	2	no	—
380	C₂²×C₄×C₂₃	—	2	1	no	—
381	C₂²×C₄×C₂₃	—	2	1	no	—
382	C₂²×C₄×C₂₃	—	2	2	no	—
383	C₂²×C₄×C₂₃	—	2	1	no	—
384	C₂²×C₄×C₂₃	—	2	2	no	—
385	C₂²×C₄×C₂₃	—	2	1	no	—
386	C₂²×C₄×C₂₃	—	2	2	no	—
387	C₂²×C₄×C₂₃	—	2	2	no	—
388	C₂²×C₄×C₂₃	—	2	2	no	—
389	C₂²×C₄×C₂₃	—	4	4	no	—
390	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
394	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
397	Q₁₆×C₂₃	—	2	4	no	—
398	Q₁₆×C₂₃	—	4	1	no	—
399	SD₁₆×C₂₃	—	2	4	no	—
400	SD₁₆×C₂₃	—	4	1	no	—
401	SD₁₆×C₂₃	—	4	1	no	—
402	SD₁₆×C₂₃	—	4	2	no	—
403	D₈×C₂₃	—	4	1	no	—
404	D₈×C₂₃	—	4	2	no	—
405	M₁₆×C₂₃	—	2	2	no	—
406	M₁₆×C₂₃	—	2	2	no	—
407	M₁₆×C₂₃	—	4	2	no	—
408	C₂×C₈×C₂₃	—	2	2	no	—
409	C₂×C₈×C₂₃	—	2	2	no	—
410	C₂×C₈×C₂₃	—	4	1	no	—
411	C₂×C₈×C₂₃	—	4	1	no	—
412	C₂×C₈×C₂₃	—	4	1	no	—
413	C₂×C₈×C₂₃	—	4	1	no	—
414	C₂×C₈×C₂₃	—	4	2	no	—
415	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
418	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₂₃	—	2	1	no	—
422	C₄⋊C₄×C₂₃	—	2	2	no	—
423	C₄⋊C₄×C₂₃	—	2	1	no	—
424	C₄⋊C₄×C₂₃	—	2	2	no	—
425	C₄⋊C₄×C₂₃	—	2	1	no	—
426	C₄⋊C₄×C₂₃	—	2	2	no	—
427	C₄⋊C₄×C₂₃	—	2	2	no	—
428	C₄⋊C₄×C₂₃	—	2	2	no	—
429	C₄⋊C₄×C₂₃	—	2	2	no	—
430	C₄⋊C₄×C₂₃	—	2	1	no	—
431	C₄⋊C₄×C₂₃	—	2	1	no	—
432	C₄⋊C₄×C₂₃	—	2	1	no	—
433	C₄⋊C₄×C₂₃	—	2	2	no	—
434	C₄⋊C₄×C₂₃	—	2	2	no	—
435	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
438	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
439	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
440	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
442	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
443	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
445	C₂²⋊C₄×C₂₃	—	2	2	no	—
446	C₂²⋊C₄×C₂₃	—	2	2	no	—
447	C₂²⋊C₄×C₂₃	—	2	1	no	—
448	C₂²⋊C₄×C₂₃	—	2	2	no	—
449	C₂²⋊C₄×C₂₃	—	2	1	no	—
450	C₂²⋊C₄×C₂₃	—	2	2	no	—
451	C₂²⋊C₄×C₂₃	—	2	1	no	—
452	C₂²⋊C₄×C₂₃	—	2	1	no	—
453	C₂²⋊C₄×C₂₃	—	2	1	no	—
454	C₂²⋊C₄×C₂₃	—	2	1	no	—
455	C₂²⋊C₄×C₂₃	—	2	1	no	—
456	C₂²⋊C₄×C₂₃	—	2	2	no	—
457	C₂²⋊C₄×C₂₃	—	2	2	no	—
458	C₂²⋊C₄×C₂₃	—	2	1	no	—
459	C₂²⋊C₄×C₂₃	—	2	1	no	—
460	C₂²⋊C₄×C₂₃	—	2	1	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	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
467	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
468	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
469	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
470	C₄²×C₂₃	—	2	2	no	—
471	C₄²×C₂₃	—	2	2	no	—
472	C₄²×C₂₃	—	2	2	no	—
473	C₄²×C₂₃	—	2	2	no	—
474	C₄²×C₂₃	—	2	2	no	—
475	C₄²×C₂₃	—	2	2	no	—
476	C₄²×C₂₃	—	2	1	no	—
477	C₄²×C₂₃	—	2	1	no	—
478	C₄²×C₂₃	C₂⁴	1	2	yes	—
479	#61170	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
480	C₂³×C₂₃	—	2	2	no	—
481	C₂³×C₂₃	—	2	1	no	—
482	C₂³×C₂₃	—	2	2	no	—
483	C₂³×C₂₃	—	2	1	no	—
484	C₂³×C₂₃	—	4	1	no	—
485	C₂³×C₂₃	—	4	1	no	—
486	C₂³×C₂₃	—	4	2	no	—
487	C₂³×C₂₃	—	8	1	no	—
488	C₂³×C₂₃	—	8	1	no	—
489	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
490	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
491	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
492	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
493	Q₈×C₂₃	—	2	4	no	—
494	Q₈×C₂₃	—	2	2	no	—
495	Q₈×C₂₃	—	2	2	no	—
496	Q₈×C₂₃	—	2	1	no	—
497	Q₈×C₂₃	—	2	1	no	—
498	Q₈×C₂₃	—	2	1	no	—
499	Q₈×C₂₃	—	2	1	no	—
500	Q₈×C₂₃	—	4	4	no	—
501	Q₈×C₂₃	—	8	2	no	—
502	Q₈×C₂₃	C₂×#41	1	4	yes	—
503	D₄×C₂₃	—	2	4	no	—
504	D₄×C₂₃	—	2	2	no	—
505	D₄×C₂₃	—	2	1	no	—
506	D₄×C₂₃	—	2	2	no	—
507	D₄×C₂₃	—	2	1	no	—
508	D₄×C₂₃	—	2	1	no	—
509	D₄×C₂₃	—	2	2	no	—
510	D₄×C₂₃	—	2	1	no	—
511	D₄×C₂₃	—	4	2	no	—
512	D₄×C₂₃	—	4	2	no	—
513	D₄×C₂₃	—	4	4	no	—
514	D₄×C₂₃	—	4	4	no	—
515	D₄×C₂₃	—	4	4	no	—
516	D₄×C₂₃	—	4	2	no	—
517	D₄×C₂₃	—	4	2	no	—
518	D₄×C₂₃	—	4	2	no	—
519	D₄×C₂₃	—	8	2	no	—
520	D₄×C₂₃	—	8	2	no	—
521	D₄×C₂₃	—	8	1	no	—
522	D₄×C₂₃	—	8	2	no	—
523	D₄×C₂₃	—	8	2	no	—
524	D₄×C₂₃	—	8	2	no	—
525	D₄×C₂₃	—	8	1	no	—
526	D₄×C₂₃	—	8	1	no	—
527	D₄×C₂₃	—	8	1	no	—
528	C₂×C₄×C₂₃	—	2	2	no	—
529	C₂×C₄×C₂₃	—	2	4	no	—
530	C₂×C₄×C₂₃	—	2	2	no	—
531	C₂×C₄×C₂₃	—	2	2	no	—
532	C₂×C₄×C₂₃	—	2	2	no	—
533	C₂×C₄×C₂₃	—	2	1	no	—
534	C₂×C₄×C₂₃	—	2	1	no	—
535	C₂×C₄×C₂₃	—	2	2	no	—
536	C₂×C₄×C₂₃	—	2	1	no	—
537	C₂×C₄×C₂₃	—	2	1	no	—
538	C₂×C₄×C₂₃	—	2	2	no	—
539	C₂×C₄×C₂₃	—	2	2	no	—
540	C₂×C₄×C₂₃	—	2	1	no	—
541	C₂×C₄×C₂₃	—	2	1	no	—
542	C₂×C₄×C₂₃	—	2	1	no	—
543	C₂×C₄×C₂₃	—	2	1	no	—
544	C₂×C₄×C₂₃	—	2	2	no	—
545	C₂×C₄×C₂₃	—	2	1	no	—
546	C₂×C₄×C₂₃	—	2	1	no	—
547	C₂×C₄×C₂₃	—	4	4	no	—
548	C₂×C₄×C₂₃	—	4	4	no	—
549	C₂×C₄×C₂₃	—	4	4	no	—
550	C₂×C₄×C₂₃	—	4	4	no	—
551	C₂×C₄×C₂₃	—	4	2	no	—
552	C₂×C₄×C₂₃	—	4	2	no	—
553	C₂×C₄×C₂₃	—	8	2	no	—
554	C₂×C₄×C₂₃	—	8	1	no	—
555	C₂×C₄×C₂₃	—	8	2	no	—
556	C₂×C₄×C₂₃	—	8	1	no	—
557	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
558	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
561	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
562	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
564	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
565	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
566	C₈×C₂₃	—	2	2	no	—
567	C₈×C₂₃	—	2	1	no	—
568	C₈×C₂₃	—	2	1	no	—
569	C₈×C₂₃	—	2	1	no	—
570	C₈×C₂₃	—	2	1	no	—
571	C₈×C₂₃	—	2	2	no	—
572	#3493	C₂×C₂₃	1	1	yes	characteristic, complemented
573	#3487	C₂×C₂₃	1	1	yes	characteristic, complemented
574	#3321	C₂×C₂₃	1	2	yes	complemented
575	#3317	C₂×C₂₃	1	2	yes	complemented
576	#3313	C₂×C₂₃	1	2	yes	complemented
577	#3309	C₂×C₂₃	1	2	yes	complemented
578	#3305	C₂×C₂₃	1	2	yes	complemented
579	#3304	C₂×C₂₃	1	2	yes	complemented
580	#3301	C₂×C₂₃	1	2	yes	complemented
581	#3300	C₂×C₂₃	1	2	yes	complemented
582	#3136	C₂×C₂₃	1	1	yes	characteristic, complemented
583	#3096	C₂×C₂₃	1	1	yes	characteristic, complemented
584	#3093	C₂×C₂₃	1	1	yes	characteristic, complemented
585	#3082	C₂×C₂₃	1	1	yes	characteristic, complemented
586	#3062	C₂×C₂₃	1	1	yes	characteristic, complemented
587	#3050	C₂×C₂₃	1	1	yes	characteristic, complemented
588	#3045	C₂×C₂₃	1	1	yes	characteristic, complemented
589	#3013	C₂×C₂₃	1	1	yes	characteristic, complemented
590	#3005	C₂×C₂₃	1	1	yes	characteristic, complemented
591	#2947	C₂×C₂₃	1	1	yes	characteristic, complemented
592	#2929	C₂×C₂₃	1	1	yes	characteristic, complemented
593	#2898	C₂×C₂₃	1	1	yes	characteristic, complemented
594	C₂×#416	C₂×C₂₃	1	1	yes	characteristic, complemented
595	C₂²×C₂₃	—	2	1	no	—
596	C₂²×C₂₃	—	2	1	no	—
597	C₂²×C₂₃	—	2	2	no	—
598	C₂²×C₂₃	—	2	1	no	—
599	C₂²×C₂₃	—	2	1	no	—
600	C₂²×C₂₃	—	2	2	no	—
601	C₂²×C₂₃	—	2	1	no	—
602	C₂²×C₂₃	—	2	1	no	—
603	C₂²×C₂₃	—	2	1	no	—
604	C₂²×C₂₃	—	2	1	no	—
605	C₂²×C₂₃	—	2	2	no	—
606	C₂²×C₂₃	—	4	4	no	—
607	C₂²×C₂₃	—	4	1	no	—
608	C₂²×C₂₃	—	4	1	no	—
609	C₂²×C₂₃	—	4	1	no	—
610	C₂²×C₂₃	—	4	1	no	—
611	C₂²×C₂₃	—	4	2	no	—
612	C₂²×C₂₃	—	4	2	no	—
613	C₂²×C₂₃	—	4	1	no	—
614	C₂²×C₂₃	—	4	2	no	—
615	C₂²×C₂₃	—	4	1	no	—
616	C₂²×C₂₃	—	8	4	no	—
617	C₂²×C₂₃	#546	1	2	yes	—
618	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
619	C₄×C₂₃	—	2	2	no	—
620	C₄×C₂₃	—	2	2	no	—
621	C₄×C₂₃	—	2	1	no	—
622	C₄×C₂₃	—	2	1	no	—
623	C₄×C₂₃	—	2	4	no	—
624	C₄×C₂₃	—	2	2	no	—
625	C₄×C₂₃	—	4	2	no	—
626	C₄×C₂₃	—	4	1	no	—
627	C₄×C₂₃	—	4	2	no	—
628	C₄×C₂₃	—	4	1	no	—
629	C₄×C₂₃	—	4	1	no	—
630	C₄×C₂₃	—	4	1	no	—
631	C₄×C₂₃	—	4	1	no	—
632	C₄×C₂₃	—	4	1	no	—
633	C₄×C₂₃	#546	1	2	yes	—
634	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
635	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
636	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
637	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
638	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
639	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
640	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
641	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
642	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
643	#556	—	2	1	no	—
644	#556	C₂²×C₂₃	1	2	yes	complemented
645	#555	—	2	1	no	—
646	#555	C₂²×C₂₃	1	2	yes	complemented
647	#553	—	2	1	no	—
648	#553	C₂²×C₂₃	1	2	yes	complemented
649	#552	—	2	1	no	—
650	#552	C₂²×C₂₃	1	2	yes	complemented
651	#550	—	2	1	no	—
652	#550	—	2	1	no	—
653	#550	C₂²×C₂₃	1	2	yes	—
654	#550	C₂²×C₂₃	1	2	yes	—
655	#548	—	2	1	no	—
656	#548	—	2	1	no	—
657	#548	C₂²×C₂₃	1	2	yes	—
658	#548	C₂²×C₂₃	1	2	yes	—
659	#544	C₂²×C₂₃	1	1	yes	characteristic
660	#538	—	2	2	no	—
661	#537	C₂²×C₂₃	1	1	yes	characteristic
662	#535	—	2	2	no	—
663	#535	C₂²×C₂₃	1	1	yes	characteristic
664	#535	C₂²×C₂₃	1	1	yes	characteristic
665	#529	—	2	2	no	—
666	#525	—	2	2	no	—
667	#525	C₂²×C₂₃	1	1	yes	characteristic
668	#525	C₂²×C₂₃	1	1	yes	characteristic
669	#525	C₂²×C₂₃	1	1	yes	characteristic
670	#520	C₂²×C₂₃	1	1	yes	characteristic
671	#520	C₂²×C₂₃	1	1	yes	characteristic
672	#519	C₂²×C₂₃	1	1	yes	characteristic
673	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
674	#490	C₂²×C₂₃	1	2	yes	complemented
675	#489	C₂²×C₂₃	1	2	yes	complemented
676	#488	C₂²×C₂₃	1	2	yes	complemented
677	#486	C₂²×C₂₃	1	2	yes	complemented
678	#485	C₂²×C₂₃	1	2	yes	complemented
679	#485	C₂²×C₂₃	1	2	yes	complemented
680	#482	C₂²×C₂₃	1	2	yes	complemented
681	#482	C₂²×C₂₃	1	2	yes	complemented
682	#482	C₂²×C₂₃	1	2	yes	complemented
683	#482	C₂²×C₂₃	1	2	yes	complemented
684	#481	C₂²×C₂₃	1	2	yes	complemented
685	#480	C₂²×C₂₃	1	2	yes	complemented
686	#479	C₂²×C₂₃	1	2	yes	complemented
687	#479	C₂²×C₂₃	1	2	yes	complemented
688	#477	C₂²×C₂₃	1	2	yes	complemented
689	#475	C₂²×C₂₃	1	2	yes	complemented
690	#469	C₂²×C₂₃	1	2	yes	complemented
691	#468	C₂²×C₂₃	1	2	yes	complemented
692	#467	C₂²×C₂₃	1	1	yes	characteristic, complemented
693	#467	C₂²×C₂₃	1	1	yes	characteristic, complemented
694	#466	C₂²×C₂₃	1	2	yes	complemented
695	#466	C₂²×C₂₃	1	1	yes	characteristic, complemented
696	#466	C₂²×C₂₃	1	1	yes	characteristic, complemented
697	#465	C₂²×C₂₃	1	2	yes	complemented
698	#465	C₂²×C₂₃	1	1	yes	characteristic, complemented
699	#465	C₂²×C₂₃	1	1	yes	characteristic, complemented
700	#465	C₂²×C₂₃	1	1	yes	characteristic, complemented
701	#465	C₂²×C₂₃	1	1	yes	characteristic, complemented
702	#464	C₂²×C₂₃	1	2	yes	complemented
703	#463	C₂²×C₂₃	1	2	yes	complemented
704	#460	C₂²×C₂₃	1	2	yes	complemented
705	#459	C₂²×C₂₃	1	2	yes	complemented
706	#452	C₂²×C₂₃	1	2	yes	—
707	#452	C₂²×C₂₃	1	2	yes	—
708	#452	C₂²×C₂₃	1	2	yes	complemented
709	#451	C₂²×C₂₃	1	2	yes	complemented
710	#449	C₂²×C₂₃	1	2	yes	—
711	#449	C₂²×C₂₃	1	2	yes	—
712	#449	C₂²×C₂₃	1	2	yes	complemented
713	#448	C₂²×C₂₃	1	2	yes	complemented
714	#441	C₂²×C₂₃	1	2	yes	complemented
715	#440	C₂²×C₂₃	1	2	yes	complemented
716	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
717	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
718	#435	C₂²×C₂₃	1	2	yes	complemented
719	#435	C₂²×C₂₃	1	2	yes	complemented
720	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
721	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
722	#428	C₂²×C₂₃	1	1	yes	characteristic
723	#428	C₂²×C₂₃	1	1	yes	characteristic
724	#427	C₂²×C₂₃	1	1	yes	characteristic
725	#424	C₂²×C₂₃	1	1	yes	characteristic
726	#419	C₂²×C₂₃	1	1	yes	characteristic
727	#419	C₂²×C₂₃	1	2	yes	complemented
728	#418	C₂²×C₂₃	1	1	yes	characteristic
729	#417	C₂²×C₂₃	1	1	yes	characteristic
730	#417	C₂²×C₂₃	1	1	yes	characteristic
731	#417	C₂²×C₂₃	1	2	yes	complemented
732	#416	C₂²×C₂₃	1	1	yes	characteristic
733	#416	C₂²×C₂₃	1	2	yes	—
734	#416	C₂²×C₂₃	1	2	yes	—
735	#416	C₂²×C₂₃	1	2	yes	—
736	#416	C₂²×C₂₃	1	2	yes	—
737	#416	C₂²×C₂₃	1	1	yes	characteristic
738	#416	C₂²×C₂₃	1	2	yes	complemented
739	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
740	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
741	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
742	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
743	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
744	#408	C₂²×C₂₃	1	1	yes	characteristic
745	#407	C₂²×C₂₃	1	1	yes	characteristic
746	#405	C₂²×C₂₃	1	1	yes	characteristic
747	C₂×C₂₃	—	2	2	no	—
748	C₂×C₂₃	—	4	2	no	—
749	C₂×C₂₃	—	4	1	no	—
750	C₂×C₂₃	—	4	1	no	—
751	C₂×C₂₃	—	8	1	no	—
752	C₂×C₂₃	—	8	1	no	—
753	C₂×C₂₃	—	8	2	no	—
754	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
755	C₂×C₂₃	#3584	1	1	yes	characteristic
756	C₂×C₂₃	#3584	1	1	yes	characteristic
757	2₋¹⁺⁴	—	2	4	no	—
758	2₋¹⁺⁴	—	4	2	no	—
759	C₂×#41	—	2	2	no	—
760	C₂×#41	—	2	1	no	—
761	C₂×#41	—	2	1	no	—
762	C₂×#41	—	2	1	no	—
763	C₂×#41	—	2	4	no	—
764	C₂×#41	—	4	2	no	—
765	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
766	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
767	C₂×#41	C₂³×C₂₃	1	2	yes	—
768	C₂×#41	C₂³×C₂₃	1	2	yes	—
769	C₂×#41	C₂³×C₂₃	1	2	yes	—
770	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
771	C₂²×Q₈	—	2	1	no	—
772	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
773	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
774	C₂²×D₄	—	2	1	no	—
775	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
776	C₂³×C₄	—	2	1	no	—
777	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
778	#137	—	2	4	no	—
779	AGL(1,ℤ/8)	—	4	2	no	—
780	#135	—	4	2	no	—
781	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
782	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
783	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
785	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
786	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
787	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
788	C₂×D₈	C₂³×C₂₃	1	2	yes	—
789	#131	—	4	2	no	—
790	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
791	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
792	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
793	C₂²×C₈	—	4	2	no	—
794	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
795	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
796	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
797	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
798	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
799	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
800	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
801	C₄⋊Q₈	—	2	1	no	—
802	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
803	#127	—	2	2	no	—
804	#127	—	2	2	no	—
805	#127	—	2	1	no	—
806	#127	C₂³×C₂₃	1	2	yes	—
807	#126	—	2	2	no	—
808	#126	—	2	2	no	—
809	#126	—	2	2	no	—
810	#126	—	2	2	no	—
811	#125	—	2	2	no	—
812	#125	—	2	1	no	—
813	#125	C₂³×C₂₃	1	2	yes	—
814	#124	—	2	1	no	—
815	#124	—	2	2	no	—
816	#124	—	2	2	no	—
817	#124	—	2	2	no	—
818	#124	—	2	2	no	—
819	#124	—	2	2	no	—
820	#124	C₂³×C₂₃	1	2	yes	—
821	#123	—	2	2	no	—
822	#123	—	2	1	no	—
823	#123	—	2	1	no	—
824	#123	—	2	2	no	—
825	#123	D₄×C₂₃	1	2	yes	—
826	C₂²⋊Q₈	—	2	1	no	—
827	C₂²⋊Q₈	—	2	2	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	—	2	2	no	—
830	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
831	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
832	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
833	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
834	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
835	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
836	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	1	no	—
841	#121	—	2	2	no	—
842	#121	—	2	2	no	—
843	#121	—	2	1	no	—
844	#121	—	2	1	no	—
845	#121	—	2	2	no	—
846	#121	—	2	2	no	—
847	#121	—	2	2	no	—
848	#121	—	2	2	no	—
849	#121	D₄×C₂₃	1	1	yes	characteristic
850	#121	D₄×C₂₃	1	1	yes	characteristic
851	#121	C₂³×C₂₃	1	1	yes	characteristic
852	#121	C₂³×C₂₃	1	1	yes	characteristic
853	#121	C₂³×C₂₃	1	1	yes	characteristic
854	#121	C₂³×C₂₃	1	1	yes	characteristic
855	#121	C₂³×C₂₃	1	2	yes	—
856	#121	C₂³×C₂₃	1	2	yes	—
857	#121	C₂³×C₂₃	1	2	yes	—
858	#120	—	2	1	no	—
859	#120	—	2	1	no	—
860	#120	—	2	2	no	—
861	#120	—	2	2	no	—
862	#120	D₄×C₂₃	1	2	yes	—
863	C₄×Q₈	—	2	1	no	—
864	C₄×Q₈	—	2	1	no	—
865	C₄×Q₈	—	2	1	no	—
866	C₄×Q₈	—	2	2	no	—
867	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
868	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
869	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
870	C₄×D₄	—	2	2	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	2	no	—
877	C₄×D₄	—	2	2	no	—
878	C₄×D₄	—	2	2	no	—
879	C₄×D₄	—	2	2	no	—
880	C₄×D₄	—	2	2	no	—
881	C₄×D₄	—	2	2	no	—
882	C₄×D₄	C₂³×C₂₃	1	2	yes	—
883	C₄×D₄	C₂³×C₂₃	1	2	yes	—
884	C₄×D₄	C₂³×C₂₃	1	2	yes	—
885	#117	—	2	1	no	—
886	#117	—	2	1	no	—
887	#117	—	2	1	no	—
888	#117	—	2	2	no	—
889	#117	—	2	2	no	—
890	#117	—	2	2	no	—
891	#117	C₂³×C₂₃	1	2	yes	—
892	#117	C₂³×C₂₃	1	2	yes	—
893	#117	C₂³×C₂₃	1	1	yes	characteristic
894	#117	C₂³×C₂₃	1	1	yes	characteristic
895	#117	C₂³×C₂₃	1	2	yes	—
896	#117	C₂³×C₂₃	1	1	yes	characteristic
897	C₂×C₄⋊C₄	—	2	1	no	—
898	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
899	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
900	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
901	C₂×C₂²⋊C₄	—	2	1	no	—
902	C₂×C₄²	—	2	1	no	—
903	#107	C₂³×C₂₃	1	1	yes	characteristic
904	#107	C₂³×C₂₃	1	1	yes	characteristic
905	#107	C₂³×C₂₃	1	2	yes	—
906	#107	C₂³×C₂₃	1	2	yes	—
907	#106	C₂³×C₂₃	1	1	yes	characteristic
908	#106	C₂³×C₂₃	1	1	yes	characteristic
909	#106	C₂³×C₂₃	1	2	yes	—
910	#106	C₂³×C₂₃	1	2	yes	—
911	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
912	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
913	#103	C₂³×C₂₃	1	2	yes	—
914	#103	C₂³×C₂₃	1	2	yes	—
915	#103	C₂³×C₂₃	1	2	yes	—
916	#103	C₂³×C₂₃	1	2	yes	—
917	#103	C₂³×C₂₃	1	1	yes	characteristic
918	#103	C₂³×C₂₃	1	2	yes	—
919	#103	C₂³×C₂₃	1	2	yes	—
920	#103	C₂³×C₂₃	1	1	yes	characteristic
921	#103	C₂³×C₂₃	1	1	yes	characteristic
922	#103	C₂³×C₂₃	1	1	yes	characteristic
923	#103	C₂³×C₂₃	1	2	yes	—
924	#103	C₂³×C₂₃	1	2	yes	—
925	#102	C₂³×C₂₃	1	2	yes	—
926	#102	C₂³×C₂₃	1	2	yes	—
927	#102	C₂³×C₂₃	1	2	yes	—
928	#102	C₂³×C₂₃	1	2	yes	—
929	#102	C₂³×C₂₃	1	1	yes	characteristic
930	#102	C₂³×C₂₃	1	1	yes	characteristic
931	#102	C₂³×C₂₃	1	1	yes	characteristic
932	#102	C₂³×C₂₃	1	1	yes	characteristic
933	#102	C₂³×C₂₃	1	2	yes	—
934	#102	C₂³×C₂₃	1	2	yes	—
935	#102	C₂³×C₂₃	1	2	yes	—
936	#102	C₂³×C₂₃	1	2	yes	—
937	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
938	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
939	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
940	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
941	#97	C₂³×C₂₃	1	2	yes	—
942	C₄×C₈	C₂³×C₂₃	1	2	yes	—
943	C₂₃	#61170	1	1	yes	characteristic, direct product factor, Sylow
944	C₂⁴	—	2	1	no	—
945	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
946	#41	—	2	2	no	—
947	#41	—	2	2	no	—
948	#41	—	2	4	no	—
949	#41	—	2	4	no	—
950	#41	—	2	4	no	—
951	#41	—	2	2	no	—
952	#41	—	2	2	no	—
953	#41	—	2	2	no	—
954	#41	—	2	2	no	—
955	#41	—	4	2	no	—
956	#41	—	4	2	no	—
957	#41	—	4	2	no	—
958	#41	—	4	8	no	—
959	#41	—	4	4	no	—
960	#41	—	4	4	no	—
961	#41	—	4	4	no	—
962	C₂×Q₈	—	2	1	no	—
963	C₂×Q₈	—	2	2	no	—
964	C₂×Q₈	—	2	2	no	—
965	C₂×Q₈	—	2	2	no	—
966	C₂×Q₈	—	2	4	no	—
967	C₂×Q₈	—	4	2	no	—
968	C₂×Q₈	—	4	4	no	—
969	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
970	C₂×Q₈	#41×C₂₃	1	4	yes	—
971	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
972	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
973	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	2	no	—
991	C₂×D₄	—	4	4	no	—
992	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
993	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
994	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
995	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
996	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
997	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
998	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	4	4	no	—
1013	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1014	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1015	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1016	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1017	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1020	Q₁₆	—	2	4	no	—
1021	Q₁₆	—	4	1	no	—
1022	SD₁₆	—	2	4	no	—
1023	SD₁₆	—	4	1	no	—
1024	SD₁₆	—	4	1	no	—
1025	SD₁₆	—	4	2	no	—
1026	D₈	—	4	1	no	—
1027	D₈	—	4	2	no	—
1028	M₁₆	—	2	2	no	—
1029	M₁₆	—	2	2	no	—
1030	M₁₆	—	4	2	no	—
1031	C₂×C₈	—	2	2	no	—
1032	C₂×C₈	—	2	2	no	—
1033	C₂×C₈	—	4	1	no	—
1034	C₂×C₈	—	4	1	no	—
1035	C₂×C₈	—	4	1	no	—
1036	C₂×C₈	—	4	1	no	—
1037	C₂×C₈	—	4	2	no	—
1038	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1039	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1040	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1041	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1042	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1043	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1059	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1060	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1061	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1062	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1063	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1064	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1065	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1089	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1091	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1092	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1093	C₄²	—	2	2	no	—
1094	C₄²	—	2	2	no	—
1095	C₄²	—	2	2	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	2	no	—
1099	C₄²	—	2	1	no	—
1100	C₄²	—	2	1	no	—
1101	C₄²	C₂⁴×C₂₃	1	2	yes	—
1102	C₂³	—	2	2	no	—
1103	C₂³	—	2	1	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	1	no	—
1106	C₂³	—	4	1	no	—
1107	C₂³	—	4	1	no	—
1108	C₂³	—	4	2	no	—
1109	C₂³	—	8	1	no	—
1110	C₂³	—	8	1	no	—
1111	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1112	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1113	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1114	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1115	Q₈	—	2	2	no	—
1116	Q₈	—	2	4	no	—
1117	Q₈	—	2	2	no	—
1118	Q₈	—	2	1	no	—
1119	Q₈	—	2	1	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	2	1	no	—
1122	Q₈	—	4	4	no	—
1123	Q₈	—	8	2	no	—
1124	Q₈	C₂×#41×C₂₃	1	4	yes	—
1125	D₄	—	2	4	no	—
1126	D₄	—	2	1	no	—
1127	D₄	—	2	2	no	—
1128	D₄	—	2	1	no	—
1129	D₄	—	2	1	no	—
1130	D₄	—	2	2	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	2	no	—
1133	D₄	—	4	2	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	4	no	—
1136	D₄	—	4	4	no	—
1137	D₄	—	4	4	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	4	2	no	—
1141	D₄	—	8	2	no	—
1142	D₄	—	8	2	no	—
1143	D₄	—	8	1	no	—
1144	D₄	—	8	2	no	—
1145	D₄	—	8	2	no	—
1146	D₄	—	8	2	no	—
1147	D₄	—	8	1	no	—
1148	D₄	—	8	1	no	—
1149	D₄	—	8	1	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	4	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	4	4	no	—
1170	C₂×C₄	—	4	4	no	—
1171	C₂×C₄	—	4	4	no	—
1172	C₂×C₄	—	4	4	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	4	2	no	—
1175	C₂×C₄	—	8	2	no	—
1176	C₂×C₄	—	8	1	no	—
1177	C₂×C₄	—	8	2	no	—
1178	C₂×C₄	—	8	1	no	—
1179	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1180	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1181	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1182	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1183	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1184	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1185	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1186	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1187	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1188	C₈	—	2	2	no	—
1189	C₈	—	2	1	no	—
1190	C₈	—	2	1	no	—
1191	C₈	—	2	1	no	—
1192	C₈	—	2	1	no	—
1193	C₈	—	2	2	no	—
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	1	no	—
1198	C₂²	—	2	2	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	4	4	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	2	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	1	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	2	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	8	4	no	—
1216	C₂²	C₂₃×#546	1	2	yes	—
1217	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1218	C₄	—	2	1	no	—
1219	C₄	—	2	1	no	—
1220	C₄	—	2	4	no	—
1221	C₄	—	2	2	no	—
1222	C₄	—	2	2	no	—
1223	C₄	—	2	2	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	2	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	2	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	C₂₃×#546	1	2	yes	—
1233	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1234	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1235	C₂	—	2	2	no	—
1236	C₂	—	4	1	no	—
1237	C₂	—	4	1	no	—
1238	C₂	—	4	2	no	—
1239	C₂	—	8	2	no	—
1240	C₂	—	8	1	no	—
1241	C₂	—	8	1	no	—
1242	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
1243	C₂	C₂₃×#3584	1	1	yes	characteristic
1244	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×#3493	C₂	semidirect
2. C₂₃×#3487	C₂	semidirect
3. C₂₃×#3321	C₂	semidirect
4. C₂₃×#3317	C₂	semidirect
5. C₂₃×#3313	C₂	semidirect
6. C₂₃×#3309	C₂	semidirect
7. C₂₃×#3305	C₂	semidirect
8. C₂₃×#3304	C₂	semidirect
9. C₂₃×#3301	C₂	semidirect
10. C₂₃×#3300	C₂	semidirect
11. C₂₃×#3136	C₂	semidirect
12. C₂₃×#3096	C₂	semidirect
13. C₂₃×#3093	C₂	semidirect
14. C₂₃×#3082	C₂	semidirect
15. C₂₃×#3062	C₂	semidirect
16. C₂₃×#3050	C₂	semidirect
17. C₂₃×#3045	C₂	semidirect
18. C₂₃×#3013	C₂	semidirect
19. C₂₃×#3005	C₂	semidirect
20. C₂₃×#2947	C₂	semidirect
21. C₂₃×#2929	C₂	semidirect
22. C₂₃×#2898	C₂	semidirect
23. C₂×C₂₃×#416	C₂	semidirect
32. C₂₃×#556	C₂²	semidirect
34. C₂₃×#555	C₂²	semidirect
36. C₂₃×#553	C₂²	semidirect
38. C₂₃×#552	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×#485	C₂²	semidirect
68. C₂₃×#482	C₂²	semidirect
69. C₂₃×#482	C₂²	semidirect
70. C₂₃×#482	C₂²	semidirect
71. C₂₃×#482	C₂²	semidirect
72. C₂₃×#481	C₂²	semidirect
73. C₂₃×#480	C₂²	semidirect
74. C₂₃×#479	C₂²	semidirect
75. C₂₃×#479	C₂²	semidirect
76. C₂₃×#477	C₂²	semidirect
77. C₂₃×#475	C₂²	semidirect
78. C₂₃×#469	C₂²	semidirect
79. C₂₃×#468	C₂²	semidirect
80. C₂₃×#467	C₂²	semidirect
81. C₂₃×#467	C₂²	semidirect
82. C₂₃×#466	C₂²	semidirect
83. C₂₃×#466	C₂²	semidirect
84. C₂₃×#466	C₂²	semidirect
85. C₂₃×#465	C₂²	semidirect
86. C₂₃×#465	C₂²	semidirect
87. C₂₃×#465	C₂²	semidirect
88. C₂₃×#465	C₂²	semidirect
89. C₂₃×#465	C₂²	semidirect
90. C₂₃×#464	C₂²	semidirect
91. C₂₃×#463	C₂²	semidirect
92. C₂₃×#460	C₂²	semidirect
93. C₂₃×#459	C₂²	semidirect
96. C₂₃×#452	C₂²	semidirect
97. C₂₃×#451	C₂²	semidirect
100. C₂₃×#449	C₂²	semidirect
101. C₂₃×#448	C₂²	semidirect
102. C₂₃×#441	C₂²	semidirect
103. C₂₃×#440	C₂²	semidirect
104. C₄×Q₁₆×C₂₃	C₂²	semidirect
105. C₄×SD₁₆×C₂₃	C₂²	semidirect
106. C₂₃×#435	C₂²	semidirect
107. C₂₃×#435	C₂²	semidirect
108. C₈×D₄×C₂₃	C₂²	semidirect
109. C₈×D₄×C₂₃	C₂²	semidirect
115. C₂₃×#419	C₂²	semidirect
119. C₂₃×#417	C₂²	semidirect
126. C₂₃×#416	C₂²	semidirect
129. C₂×C₂₃×#103	C₂²	semidirect
479. #61170	C₂₃	direct (N × H)
572. #3493	C₂×C₂₃	semidirect
573. #3487	C₂×C₂₃	semidirect
574. #3321	C₂×C₂₃	semidirect
575. #3317	C₂×C₂₃	semidirect
576. #3313	C₂×C₂₃	semidirect
577. #3309	C₂×C₂₃	semidirect
578. #3305	C₂×C₂₃	semidirect
579. #3304	C₂×C₂₃	semidirect
580. #3301	C₂×C₂₃	semidirect
581. #3300	C₂×C₂₃	semidirect
582. #3136	C₂×C₂₃	semidirect
583. #3096	C₂×C₂₃	semidirect
584. #3093	C₂×C₂₃	semidirect
585. #3082	C₂×C₂₃	semidirect
586. #3062	C₂×C₂₃	semidirect
587. #3050	C₂×C₂₃	semidirect
588. #3045	C₂×C₂₃	semidirect
589. #3013	C₂×C₂₃	semidirect
590. #3005	C₂×C₂₃	semidirect
591. #2947	C₂×C₂₃	semidirect
592. #2929	C₂×C₂₃	semidirect
593. #2898	C₂×C₂₃	semidirect
594. C₂×#416	C₂×C₂₃	semidirect
644. #556	C₂²×C₂₃	semidirect
646. #555	C₂²×C₂₃	semidirect
648. #553	C₂²×C₂₃	semidirect
650. #552	C₂²×C₂₃	semidirect
674. #490	C₂²×C₂₃	semidirect
675. #489	C₂²×C₂₃	semidirect
676. #488	C₂²×C₂₃	semidirect
677. #486	C₂²×C₂₃	semidirect
678. #485	C₂²×C₂₃	semidirect
679. #485	C₂²×C₂₃	semidirect
680. #482	C₂²×C₂₃	semidirect
681. #482	C₂²×C₂₃	semidirect
682. #482	C₂²×C₂₃	semidirect
683. #482	C₂²×C₂₃	semidirect
684. #481	C₂²×C₂₃	semidirect
685. #480	C₂²×C₂₃	semidirect
686. #479	C₂²×C₂₃	semidirect
687. #479	C₂²×C₂₃	semidirect
688. #477	C₂²×C₂₃	semidirect
689. #475	C₂²×C₂₃	semidirect
690. #469	C₂²×C₂₃	semidirect
691. #468	C₂²×C₂₃	semidirect
692. #467	C₂²×C₂₃	semidirect
693. #467	C₂²×C₂₃	semidirect
694. #466	C₂²×C₂₃	semidirect
695. #466	C₂²×C₂₃	semidirect
696. #466	C₂²×C₂₃	semidirect
697. #465	C₂²×C₂₃	semidirect
698. #465	C₂²×C₂₃	semidirect
699. #465	C₂²×C₂₃	semidirect
700. #465	C₂²×C₂₃	semidirect
701. #465	C₂²×C₂₃	semidirect
702. #464	C₂²×C₂₃	semidirect
703. #463	C₂²×C₂₃	semidirect
704. #460	C₂²×C₂₃	semidirect
705. #459	C₂²×C₂₃	semidirect
708. #452	C₂²×C₂₃	semidirect
709. #451	C₂²×C₂₃	semidirect
712. #449	C₂²×C₂₃	semidirect
713. #448	C₂²×C₂₃	semidirect
714. #441	C₂²×C₂₃	semidirect
715. #440	C₂²×C₂₃	semidirect
716. C₄×Q₁₆	C₂²×C₂₃	semidirect
717. C₄×SD₁₆	C₂²×C₂₃	semidirect
718. #435	C₂²×C₂₃	semidirect
719. #435	C₂²×C₂₃	semidirect
720. C₈×D₄	C₂²×C₂₃	semidirect
721. C₈×D₄	C₂²×C₂₃	semidirect
727. #419	C₂²×C₂₃	semidirect
731. #417	C₂²×C₂₃	semidirect
738. #416	C₂²×C₂₃	semidirect
741. C₂×#103	C₂²×C₂₃	semidirect
943. C₂₃	#61170	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×#3493	2
C₂₃×#3487	2
C₂₃×#3321	2
C₂₃×#3317	2
C₂₃×#3313	2
C₂₃×#3309	2
C₂₃×#3305	2
C₂₃×#3304	2
C₂₃×#3301	2
C₂₃×#3300	2
C₂₃×#3136	2
C₂₃×#3096	2
C₂₃×#3093	2
C₂₃×#3082	2
C₂₃×#3062	2
C₂₃×#3050	2
C₂₃×#3045	2
C₂₃×#3013	2
C₂₃×#3005	2
C₂₃×#2947	2
C₂₃×#2929	2
C₂₃×#2898	2
C₂×C₂₃×#416	2
#61170	23

Subgroups — C23×#61170 #19208796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61170 #19208796