Subgroups — C₂₃×#61222 #19208848

Order 5888.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3321	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3319	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3316	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3314	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3313	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3311	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3308	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3306	C₂	1	2	yes	maximal, complemented
11	C₂×C₂₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
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	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#556	C₂²	1	2	yes	complemented
32	C₂₃×#555	C₂²	1	2	yes	complemented
33	C₂₃×#554	C₂²	1	2	yes	complemented
34	C₂₃×#553	—	2	2	no	—
35	C₂₃×#548	—	2	2	no	—
36	C₂₃×#548	C₂²	1	2	yes	—
37	C₂₃×#548	C₂²	1	2	yes	—
38	C₂₃×#547	C₂²	1	2	yes	complemented
39	C₂₃×#546	—	2	2	no	—
40	C₂₃×#546	—	2	2	no	—
41	C₂₃×#546	C₂²	1	2	yes	—
42	C₂₃×#546	C₂²	1	2	yes	—
43	C₂₃×#542	—	2	1	no	—
44	C₂₃×#542	—	2	1	no	—
45	C₂₃×#537	C₂²	1	1	yes	characteristic
46	C₂₃×#537	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#536	—	2	1	no	—
48	C₂₃×#536	C₂²	1	1	yes	characteristic
49	C₂₃×#535	—	2	1	no	—
50	C₂₃×#535	C₂²	1	1	yes	characteristic
51	C₂₃×#533	—	2	1	no	—
52	C₂₃×#532	—	2	1	no	—
53	C₂₃×#532	—	2	1	no	—
54	C₂₃×#532	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₂₃×#124	—	2	1	no	—
57	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
58	C₂₃×#520	C₂²	1	1	yes	characteristic
59	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
61	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#489	C₂²	1	2	yes	complemented
63	C₂₃×#489	C₂²	1	2	yes	complemented
64	C₂₃×#489	C₂²	1	2	yes	complemented
65	C₂₃×#489	C₂²	1	2	yes	complemented
66	C₂₃×#485	C₂²	1	2	yes	complemented
67	C₂₃×#485	C₂²	1	2	yes	complemented
68	C₂₃×#484	C₂²	1	2	yes	complemented
69	C₂₃×#483	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×#477	C₂²	1	2	yes	complemented
75	C₂₃×#476	C₂²	1	2	yes	complemented
76	C₂₃×#475	C₂²	1	2	yes	complemented
77	C₂₃×#474	C₂²	1	2	yes	complemented
78	C₂₃×#470	C₂²	1	2	yes	complemented
79	C₂₃×#469	C₂²	1	2	yes	complemented
80	C₂₃×#468	C₂²	1	2	yes	complemented
81	C₂₃×#468	C₂²	1	2	yes	complemented
82	C₂₃×#467	C₂²	1	2	yes	complemented
83	C₂₃×#466	C₂²	1	2	yes	complemented
84	C₂₃×#465	C₂²	1	2	yes	complemented
85	C₂₃×#465	C₂²	1	2	yes	complemented
86	C₂₃×#464	C₂²	1	2	yes	complemented
87	C₂₃×#464	C₂²	1	2	yes	complemented
88	C₂₃×#463	C₂²	1	2	yes	complemented
89	C₂₃×#463	C₂²	1	2	yes	complemented
90	C₂₃×#452	C₂²	1	2	yes	—
91	C₂₃×#452	C₂²	1	2	yes	complemented
92	C₂₃×#451	C₂²	1	2	yes	complemented
93	C₂₃×#450	C₂²	1	2	yes	—
94	C₂₃×#449	C₂²	1	2	yes	—
95	C₂₃×#449	C₂²	1	2	yes	complemented
96	C₂₃×#448	C₂²	1	2	yes	complemented
97	C₂₃×#447	C₂²	1	2	yes	—
98	C₂₃×#442	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#442	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#441	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#441	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#440	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#440	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#440	C₂²	1	1	yes	characteristic, complemented
105	C₂₃×#440	C₂²	1	1	yes	characteristic, complemented
106	C₂₃×#435	C₂²	1	2	yes	complemented
107	C₂₃×#435	C₂²	1	2	yes	complemented
108	C₂₃×#435	C₂²	1	2	yes	complemented
109	C₂₃×#435	C₂²	1	2	yes	complemented
110	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
114	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#419	C₂²	1	2	yes	complemented
116	C₂₃×#418	C₂²	1	1	yes	characteristic
117	C₂₃×#418	C₂²	1	2	yes	—
118	C₂₃×#417	C₂²	1	1	yes	characteristic
119	C₂₃×#417	C₂²	1	1	yes	characteristic
120	C₂₃×#417	C₂²	1	2	yes	—
121	C₂₃×#417	C₂²	1	2	yes	complemented
122	C₂₃×#416	C₂²	1	1	yes	characteristic
123	C₂₃×#416	C₂²	1	2	yes	—
124	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂₃×#416	C₂²	1	2	yes	complemented
126	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
128	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
130	C₂×C₂₃×#102	C₂²	1	2	yes	—
131	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
132	C₂₃×#408	C₂²	1	1	yes	characteristic
133	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
135	C₂₃×2₋¹⁺⁴	—	2	4	no	—
136	C₂₃×2₋¹⁺⁴	—	4	2	no	—
137	C₂₃×H(5,𝔽₂)	—	2	4	no	—
138	C₂₃×H(5,𝔽₂)	—	4	2	no	—
139	C₂×#41×C₂₃	—	2	1	no	—
140	C₂×#41×C₂₃	—	2	1	no	—
141	C₂×#41×C₂₃	—	2	2	no	—
142	C₂×#41×C₂₃	—	2	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	2	yes	—
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	—	2	1	no	—
150	C₂²×Q₈×C₂₃	—	2	1	no	—
151	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
152	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
153	C₂²×D₄×C₂₃	—	2	1	no	—
154	C₂²×D₄×C₂₃	—	2	2	no	—
155	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
157	C₂₃×#137	—	4	2	no	—
158	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
159	C₂₃×#135	—	2	4	no	—
160	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
161	C₂×Q₁₆×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×SD₁₆×C₂₃	C₂³	1	2	yes	—
166	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
167	C₂×D₈×C₂₃	C₂³	1	2	yes	—
168	C₂₃×#131	—	4	2	no	—
169	C₂₃×#131	—	4	2	no	—
170	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
173	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
174	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
177	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
178	C₂₃×C₄⋊Q₈	—	2	1	no	—
179	C₂₃×C₄⋊Q₈	—	2	1	no	—
180	C₂₃×C₄⋊Q₈	—	2	1	no	—
181	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
182	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
183	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
184	C₂₃×#127	—	2	1	no	—
185	C₂₃×#127	D₄	1	1	yes	characteristic
186	C₂₃×#126	—	2	2	no	—
187	C₂₃×#126	—	2	2	no	—
188	C₂₃×#125	—	2	2	no	—
189	C₂₃×#124	—	2	1	no	—
190	C₂₃×#124	—	2	2	no	—
191	C₂₃×#124	—	2	1	no	—
192	C₂₃×#124	—	2	2	no	—
193	C₂₃×#124	—	2	2	no	—
194	C₂₃×#124	—	2	2	no	—
195	C₂₃×#124	—	2	2	no	—
196	C₂₃×#124	—	2	1	no	—
197	C₂₃×#124	—	2	1	no	—
198	C₂₃×#124	D₄	1	1	yes	characteristic
199	C₂₃×#124	D₄	1	1	yes	characteristic
200	C₂₃×#124	C₂³	1	2	yes	—
201	C₂₃×#124	C₂³	1	2	yes	—
202	C₂₃×#123	—	2	2	no	—
203	C₂₃×#123	—	2	2	no	—
204	C₂₃×#123	—	2	2	no	—
205	C₂₃×#123	—	2	2	no	—
206	C₂₃×#123	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	—	2	1	no	—
208	C₂₃×C₂²⋊Q₈	—	2	1	no	—
209	C₂₃×C₂²⋊Q₈	—	2	2	no	—
210	C₂₃×C₂²⋊Q₈	—	2	2	no	—
211	C₂₃×C₂²⋊Q₈	—	2	2	no	—
212	C₂₃×C₂²⋊Q₈	—	2	2	no	—
213	C₂₃×C₂²⋊Q₈	—	2	2	no	—
214	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	2	no	—
221	C₂₃×#121	—	2	2	no	—
222	C₂₃×#121	—	2	2	no	—
223	C₂₃×#121	—	2	1	no	—
224	C₂₃×#121	—	2	1	no	—
225	C₂₃×#121	—	2	2	no	—
226	C₂₃×#121	—	2	2	no	—
227	C₂₃×#121	D₄	1	2	yes	—
228	C₂₃×#121	D₄	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×#120	—	2	2	no	—
234	C₂₃×#120	—	2	2	no	—
235	C₂₃×#120	—	2	2	no	—
236	C₄×Q₈×C₂₃	—	2	1	no	—
237	C₄×Q₈×C₂₃	—	2	1	no	—
238	C₄×Q₈×C₂₃	—	2	2	no	—
239	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₂₃	—	2	2	no	—
244	C₄×D₄×C₂₃	—	2	2	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	1	no	—
249	C₄×D₄×C₂₃	—	2	1	no	—
250	C₄×D₄×C₂₃	—	2	1	no	—
251	C₄×D₄×C₂₃	—	2	1	no	—
252	C₄×D₄×C₂₃	—	2	2	no	—
253	C₄×D₄×C₂₃	—	2	2	no	—
254	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₂₃	C₂³	1	2	yes	—
259	C₄×D₄×C₂₃	C₂³	1	2	yes	—
260	C₂₃×#117	—	2	2	no	—
261	C₂₃×#117	—	2	1	no	—
262	C₂₃×#117	—	2	1	no	—
263	C₂₃×#117	C₂³	1	2	yes	—
264	C₂₃×#117	C₂³	1	2	yes	—
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	2	yes	—
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×C₂²⋊C₄×C₂₃	—	2	1	no	—
273	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
274	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
276	C₂×C₄²×C₂₃	—	2	1	no	—
277	C₂×C₄²×C₂₃	—	2	1	no	—
278	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
279	C₂₃×#107	C₂³	1	1	yes	characteristic
280	C₂₃×#107	C₂³	1	1	yes	characteristic
281	C₂₃×#107	C₂³	1	2	yes	—
282	C₂₃×#107	C₂³	1	2	yes	—
283	C₂₃×#106	C₂³	1	1	yes	characteristic
284	C₂₃×#106	C₂³	1	1	yes	characteristic
285	C₂₃×#106	C₂³	1	2	yes	—
286	C₂₃×#106	C₂³	1	2	yes	—
287	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
288	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
289	C₂₃×#103	C₂³	1	1	yes	characteristic
290	C₂₃×#103	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	2	yes	—
296	C₂₃×#103	C₂³	1	1	yes	characteristic
297	C₂₃×#103	C₂³	1	2	yes	—
298	C₂₃×#103	C₂³	1	2	yes	—
299	C₂₃×#103	C₂³	1	1	yes	characteristic
300	C₂₃×#103	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×#102	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	2	yes	—
308	C₂₃×#102	C₂³	1	1	yes	characteristic
309	C₂₃×#102	C₂³	1	2	yes	—
310	C₂₃×#102	C₂³	1	2	yes	—
311	C₂₃×#102	C₂³	1	1	yes	characteristic
312	C₂₃×#102	C₂³	1	1	yes	characteristic
313	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₂₃×#97	C₂³	1	1	yes	characteristic
318	C₂₃×#97	C₂³	1	1	yes	characteristic
319	C₂₃×#97	C₂³	1	1	yes	characteristic
320	C₂₃×#97	C₂³	1	1	yes	characteristic
321	C₂⁴×C₂₃	—	2	2	no	—
322	C₂⁴×C₂₃	—	2	1	no	—
323	#41×C₂₃	—	2	2	no	—
324	#41×C₂₃	—	2	2	no	—
325	#41×C₂₃	—	2	2	no	—
326	#41×C₂₃	—	2	2	no	—
327	#41×C₂₃	—	2	2	no	—
328	#41×C₂₃	—	2	4	no	—
329	#41×C₂₃	—	2	4	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	4	no	—
335	#41×C₂₃	—	4	4	no	—
336	#41×C₂₃	—	4	8	no	—
337	#41×C₂₃	—	8	4	no	—
338	#41×C₂₃	#41	1	4	yes	complemented
339	C₂×Q₈×C₂₃	—	2	2	no	—
340	C₂×Q₈×C₂₃	—	2	2	no	—
341	C₂×Q₈×C₂₃	—	2	1	no	—
342	C₂×Q₈×C₂₃	—	2	2	no	—
343	C₂×Q₈×C₂₃	—	2	4	no	—
344	C₂×Q₈×C₂₃	—	2	2	no	—
345	C₂×Q₈×C₂₃	—	2	2	no	—
346	C₂×Q₈×C₂₃	—	4	2	no	—
347	C₂×Q₈×C₂₃	—	4	4	no	—
348	C₂×Q₈×C₂₃	—	8	2	no	—
349	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
350	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
351	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
352	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
353	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₂₃	—	2	1	no	—
355	C₂×D₄×C₂₃	—	2	4	no	—
356	C₂×D₄×C₂₃	—	2	1	no	—
357	C₂×D₄×C₂₃	—	2	2	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	2	no	—
364	C₂×D₄×C₂₃	—	2	1	no	—
365	C₂×D₄×C₂₃	—	2	2	no	—
366	C₂×D₄×C₂₃	—	2	2	no	—
367	C₂×D₄×C₂₃	—	4	2	no	—
368	C₂×D₄×C₂₃	—	4	4	no	—
369	C₂×D₄×C₂₃	—	4	8	no	—
370	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
375	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
376	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
377	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
378	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₂₃	—	2	1	no	—
380	C₂²×C₄×C₂₃	—	2	1	no	—
381	C₂²×C₄×C₂₃	—	2	2	no	—
382	C₂²×C₄×C₂₃	—	2	1	no	—
383	C₂²×C₄×C₂₃	—	2	1	no	—
384	C₂²×C₄×C₂₃	—	2	2	no	—
385	C₂²×C₄×C₂₃	—	2	2	no	—
386	C₂²×C₄×C₂₃	—	2	1	no	—
387	C₂²×C₄×C₂₃	—	2	1	no	—
388	C₂²×C₄×C₂₃	—	2	1	no	—
389	C₂²×C₄×C₂₃	—	2	2	no	—
390	C₂²×C₄×C₂₃	—	2	2	no	—
391	C₂²×C₄×C₂₃	—	2	1	no	—
392	C₂²×C₄×C₂₃	—	2	1	no	—
393	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
396	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
398	Q₁₆×C₂₃	—	2	2	no	—
399	Q₁₆×C₂₃	—	4	2	no	—
400	SD₁₆×C₂₃	—	2	2	no	—
401	SD₁₆×C₂₃	—	2	2	no	—
402	SD₁₆×C₂₃	—	4	2	no	—
403	SD₁₆×C₂₃	—	4	2	no	—
404	D₈×C₂₃	—	2	2	no	—
405	D₈×C₂₃	—	4	2	no	—
406	M₁₆×C₂₃	—	2	2	no	—
407	M₁₆×C₂₃	—	2	2	no	—
408	M₁₆×C₂₃	—	4	2	no	—
409	M₁₆×C₂₃	—	4	2	no	—
410	C₂×C₈×C₂₃	—	2	2	no	—
411	C₂×C₈×C₂₃	—	2	2	no	—
412	C₂×C₈×C₂₃	—	4	2	no	—
413	C₂×C₈×C₂₃	—	4	2	no	—
414	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
417	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₂₃	—	2	2	no	—
421	C₄⋊C₄×C₂₃	—	2	2	no	—
422	C₄⋊C₄×C₂₃	—	2	1	no	—
423	C₄⋊C₄×C₂₃	—	2	1	no	—
424	C₄⋊C₄×C₂₃	—	2	2	no	—
425	C₄⋊C₄×C₂₃	—	2	2	no	—
426	C₄⋊C₄×C₂₃	—	2	1	no	—
427	C₄⋊C₄×C₂₃	—	2	1	no	—
428	C₄⋊C₄×C₂₃	—	2	1	no	—
429	C₄⋊C₄×C₂₃	—	2	1	no	—
430	C₄⋊C₄×C₂₃	—	2	2	no	—
431	C₄⋊C₄×C₂₃	—	2	2	no	—
432	C₄⋊C₄×C₂₃	—	2	2	no	—
433	C₄⋊C₄×C₂₃	—	2	2	no	—
434	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
435	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
436	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
439	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
442	C₂²⋊C₄×C₂₃	—	2	2	no	—
443	C₂²⋊C₄×C₂₃	—	2	2	no	—
444	C₂²⋊C₄×C₂₃	—	2	1	no	—
445	C₂²⋊C₄×C₂₃	—	2	1	no	—
446	C₂²⋊C₄×C₂₃	—	2	2	no	—
447	C₂²⋊C₄×C₂₃	—	2	2	no	—
448	C₂²⋊C₄×C₂₃	—	2	2	no	—
449	C₂²⋊C₄×C₂₃	—	2	2	no	—
450	C₂²⋊C₄×C₂₃	—	2	2	no	—
451	C₂²⋊C₄×C₂₃	—	2	2	no	—
452	C₂²⋊C₄×C₂₃	—	2	2	no	—
453	C₂²⋊C₄×C₂₃	—	2	2	no	—
454	C₂²⋊C₄×C₂₃	—	2	2	no	—
455	C₂²⋊C₄×C₂₃	—	2	2	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	1	no	—
460	C₂²⋊C₄×C₂₃	—	2	2	no	—
461	C₂²⋊C₄×C₂₃	—	2	2	no	—
462	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
466	C₄²×C₂₃	—	2	1	no	—
467	C₄²×C₂₃	—	2	1	no	—
468	C₄²×C₂₃	—	2	1	no	—
469	C₄²×C₂₃	—	2	1	no	—
470	C₄²×C₂₃	—	2	1	no	—
471	C₄²×C₂₃	—	2	1	no	—
472	C₄²×C₂₃	—	2	2	no	—
473	C₄²×C₂₃	—	2	2	no	—
474	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
475	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
476	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
477	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
478	#61222	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
479	C₂³×C₂₃	—	2	1	no	—
480	C₂³×C₂₃	—	2	1	no	—
481	C₂³×C₂₃	—	2	2	no	—
482	C₂³×C₂₃	—	4	4	no	—
483	C₂³×C₂₃	—	4	2	no	—
484	C₂³×C₂₃	—	8	1	no	—
485	C₂³×C₂₃	—	8	1	no	—
486	C₂³×C₂₃	—	8	2	no	—
487	C₂³×C₂₃	—	8	2	no	—
488	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
489	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
490	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
491	Q₈×C₂₃	—	2	2	no	—
492	Q₈×C₂₃	—	2	2	no	—
493	Q₈×C₂₃	—	2	1	no	—
494	Q₈×C₂₃	—	2	1	no	—
495	Q₈×C₂₃	—	2	2	no	—
496	Q₈×C₂₃	—	2	1	no	—
497	Q₈×C₂₃	—	2	2	no	—
498	Q₈×C₂₃	—	4	4	no	—
499	Q₈×C₂₃	—	4	4	no	—
500	Q₈×C₂₃	—	4	2	no	—
501	Q₈×C₂₃	—	8	2	no	—
502	Q₈×C₂₃	C₂×#41	1	2	yes	—
503	D₄×C₂₃	—	2	4	no	—
504	D₄×C₂₃	—	2	4	no	—
505	D₄×C₂₃	—	2	4	no	—
506	D₄×C₂₃	—	2	2	no	—
507	D₄×C₂₃	—	2	2	no	—
508	D₄×C₂₃	—	2	1	no	—
509	D₄×C₂₃	—	2	2	no	—
510	D₄×C₂₃	—	2	1	no	—
511	D₄×C₂₃	—	2	1	no	—
512	D₄×C₂₃	—	2	2	no	—
513	D₄×C₂₃	—	4	2	no	—
514	D₄×C₂₃	—	4	2	no	—
515	D₄×C₂₃	—	4	4	no	—
516	D₄×C₂₃	—	4	4	no	—
517	D₄×C₂₃	—	4	4	no	—
518	D₄×C₂₃	—	4	2	no	—
519	D₄×C₂₃	—	4	2	no	—
520	D₄×C₂₃	—	8	2	no	—
521	D₄×C₂₃	—	8	2	no	—
522	D₄×C₂₃	—	8	2	no	—
523	D₄×C₂₃	—	8	2	no	—
524	D₄×C₂₃	C₂×#41	1	2	yes	—
525	C₂×C₄×C₂₃	—	2	1	no	—
526	C₂×C₄×C₂₃	—	2	4	no	—
527	C₂×C₄×C₂₃	—	2	2	no	—
528	C₂×C₄×C₂₃	—	2	2	no	—
529	C₂×C₄×C₂₃	—	2	2	no	—
530	C₂×C₄×C₂₃	—	2	2	no	—
531	C₂×C₄×C₂₃	—	2	1	no	—
532	C₂×C₄×C₂₃	—	2	1	no	—
533	C₂×C₄×C₂₃	—	2	1	no	—
534	C₂×C₄×C₂₃	—	2	1	no	—
535	C₂×C₄×C₂₃	—	2	1	no	—
536	C₂×C₄×C₂₃	—	2	2	no	—
537	C₂×C₄×C₂₃	—	2	2	no	—
538	C₂×C₄×C₂₃	—	2	2	no	—
539	C₂×C₄×C₂₃	—	4	1	no	—
540	C₂×C₄×C₂₃	—	4	1	no	—
541	C₂×C₄×C₂₃	—	4	4	no	—
542	C₂×C₄×C₂₃	—	4	4	no	—
543	C₂×C₄×C₂₃	—	4	4	no	—
544	C₂×C₄×C₂₃	—	4	2	no	—
545	C₂×C₄×C₂₃	—	4	2	no	—
546	C₂×C₄×C₂₃	—	4	2	no	—
547	C₂×C₄×C₂₃	—	4	2	no	—
548	C₂×C₄×C₂₃	—	8	1	no	—
549	C₂×C₄×C₂₃	—	8	1	no	—
550	C₂×C₄×C₂₃	—	8	1	no	—
551	C₂×C₄×C₂₃	—	8	1	no	—
552	C₂×C₄×C₂₃	—	8	2	no	—
553	C₂×C₄×C₂₃	—	8	2	no	—
554	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
562	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
563	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
564	C₈×C₂₃	—	2	1	no	—
565	C₈×C₂₃	—	2	1	no	—
566	C₈×C₂₃	—	2	1	no	—
567	C₈×C₂₃	—	2	1	no	—
568	C₈×C₂₃	—	2	2	no	—
569	C₈×C₂₃	—	2	2	no	—
570	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
571	#3500	C₂×C₂₃	1	1	yes	characteristic, complemented
572	#3321	C₂×C₂₃	1	2	yes	complemented
573	#3319	C₂×C₂₃	1	2	yes	complemented
574	#3316	C₂×C₂₃	1	2	yes	complemented
575	#3314	C₂×C₂₃	1	2	yes	complemented
576	#3313	C₂×C₂₃	1	2	yes	complemented
577	#3311	C₂×C₂₃	1	2	yes	complemented
578	#3308	C₂×C₂₃	1	2	yes	complemented
579	#3306	C₂×C₂₃	1	2	yes	complemented
580	C₂×#489	C₂×C₂₃	1	1	yes	characteristic, complemented
581	#3097	C₂×C₂₃	1	1	yes	characteristic, complemented
582	#3096	C₂×C₂₃	1	1	yes	characteristic, complemented
583	#3079	C₂×C₂₃	1	1	yes	characteristic, complemented
584	#3063	C₂×C₂₃	1	1	yes	characteristic, complemented
585	#3062	C₂×C₂₃	1	1	yes	characteristic, complemented
586	#3040	C₂×C₂₃	1	1	yes	characteristic, complemented
587	#3013	C₂×C₂₃	1	1	yes	characteristic, complemented
588	#3012	C₂×C₂₃	1	1	yes	characteristic, complemented
589	#2943	C₂×C₂₃	1	1	yes	characteristic, complemented
590	#2932	C₂×C₂₃	1	1	yes	characteristic, complemented
591	#2898	C₂×C₂₃	1	1	yes	characteristic, complemented
592	#2897	C₂×C₂₃	1	1	yes	characteristic, complemented
593	C₂²×C₂₃	—	2	1	no	—
594	C₂²×C₂₃	—	2	1	no	—
595	C₂²×C₂₃	—	2	2	no	—
596	C₂²×C₂₃	—	2	2	no	—
597	C₂²×C₂₃	—	2	2	no	—
598	C₂²×C₂₃	—	2	2	no	—
599	C₂²×C₂₃	—	2	2	no	—
600	C₂²×C₂₃	—	2	2	no	—
601	C₂²×C₂₃	—	2	2	no	—
602	C₂²×C₂₃	—	4	1	no	—
603	C₂²×C₂₃	—	4	1	no	—
604	C₂²×C₂₃	—	4	1	no	—
605	C₂²×C₂₃	—	4	2	no	—
606	C₂²×C₂₃	—	4	1	no	—
607	C₂²×C₂₃	—	4	2	no	—
608	C₂²×C₂₃	—	4	2	no	—
609	C₂²×C₂₃	—	4	1	no	—
610	C₂²×C₂₃	—	16	2	no	—
611	C₂²×C₂₃	—	16	4	no	—
612	C₂²×C₂₃	#546	1	2	yes	—
613	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
614	C₄×C₂₃	—	2	1	no	—
615	C₄×C₂₃	—	2	1	no	—
616	C₄×C₂₃	—	2	1	no	—
617	C₄×C₂₃	—	2	1	no	—
618	C₄×C₂₃	—	2	2	no	—
619	C₄×C₂₃	—	2	2	no	—
620	C₄×C₂₃	—	2	2	no	—
621	C₄×C₂₃	—	4	1	no	—
622	C₄×C₂₃	—	4	2	no	—
623	C₄×C₂₃	—	4	2	no	—
624	C₄×C₂₃	—	4	1	no	—
625	C₄×C₂₃	—	4	1	no	—
626	C₄×C₂₃	—	4	1	no	—
627	C₄×C₂₃	—	4	2	no	—
628	C₄×C₂₃	—	4	1	no	—
629	C₄×C₂₃	#546	1	2	yes	—
630	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
631	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
632	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
633	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
634	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
635	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
636	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
637	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
638	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
639	#556	C₂²×C₂₃	1	2	yes	complemented
640	#555	C₂²×C₂₃	1	2	yes	complemented
641	#554	C₂²×C₂₃	1	2	yes	complemented
642	#553	—	2	2	no	—
643	#548	—	2	2	no	—
644	#548	C₂²×C₂₃	1	2	yes	—
645	#548	C₂²×C₂₃	1	2	yes	—
646	#547	C₂²×C₂₃	1	2	yes	complemented
647	#546	—	2	2	no	—
648	#546	—	2	2	no	—
649	#546	C₂²×C₂₃	1	2	yes	—
650	#546	C₂²×C₂₃	1	2	yes	—
651	#542	—	2	1	no	—
652	#542	—	2	1	no	—
653	#537	C₂²×C₂₃	1	1	yes	characteristic
654	#537	C₂²×C₂₃	1	1	yes	characteristic, complemented
655	#536	—	2	1	no	—
656	#536	C₂²×C₂₃	1	1	yes	characteristic
657	#535	—	2	1	no	—
658	#535	C₂²×C₂₃	1	1	yes	characteristic
659	#533	—	2	1	no	—
660	#532	—	2	1	no	—
661	#532	—	2	1	no	—
662	#532	C₂²×C₂₃	1	1	yes	characteristic
663	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
664	C₂×#124	—	2	1	no	—
665	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
666	#520	C₂²×C₂₃	1	1	yes	characteristic
667	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
668	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
669	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
670	#489	C₂²×C₂₃	1	2	yes	complemented
671	#489	C₂²×C₂₃	1	2	yes	complemented
672	#489	C₂²×C₂₃	1	2	yes	complemented
673	#489	C₂²×C₂₃	1	2	yes	complemented
674	#485	C₂²×C₂₃	1	2	yes	complemented
675	#485	C₂²×C₂₃	1	2	yes	complemented
676	#484	C₂²×C₂₃	1	2	yes	complemented
677	#483	C₂²×C₂₃	1	2	yes	complemented
678	#482	C₂²×C₂₃	1	2	yes	complemented
679	#482	C₂²×C₂₃	1	2	yes	complemented
680	#481	C₂²×C₂₃	1	2	yes	complemented
681	#480	C₂²×C₂₃	1	2	yes	complemented
682	#477	C₂²×C₂₃	1	2	yes	complemented
683	#476	C₂²×C₂₃	1	2	yes	complemented
684	#475	C₂²×C₂₃	1	2	yes	complemented
685	#474	C₂²×C₂₃	1	2	yes	complemented
686	#470	C₂²×C₂₃	1	2	yes	complemented
687	#469	C₂²×C₂₃	1	2	yes	complemented
688	#468	C₂²×C₂₃	1	2	yes	complemented
689	#468	C₂²×C₂₃	1	2	yes	complemented
690	#467	C₂²×C₂₃	1	2	yes	complemented
691	#466	C₂²×C₂₃	1	2	yes	complemented
692	#465	C₂²×C₂₃	1	2	yes	complemented
693	#465	C₂²×C₂₃	1	2	yes	complemented
694	#464	C₂²×C₂₃	1	2	yes	complemented
695	#464	C₂²×C₂₃	1	2	yes	complemented
696	#463	C₂²×C₂₃	1	2	yes	complemented
697	#463	C₂²×C₂₃	1	2	yes	complemented
698	#452	C₂²×C₂₃	1	2	yes	—
699	#452	C₂²×C₂₃	1	2	yes	complemented
700	#451	C₂²×C₂₃	1	2	yes	complemented
701	#450	C₂²×C₂₃	1	2	yes	—
702	#449	C₂²×C₂₃	1	2	yes	—
703	#449	C₂²×C₂₃	1	2	yes	complemented
704	#448	C₂²×C₂₃	1	2	yes	complemented
705	#447	C₂²×C₂₃	1	2	yes	—
706	#442	C₂²×C₂₃	1	1	yes	characteristic, complemented
707	#442	C₂²×C₂₃	1	1	yes	characteristic, complemented
708	#441	C₂²×C₂₃	1	1	yes	characteristic, complemented
709	#441	C₂²×C₂₃	1	1	yes	characteristic, complemented
710	#440	C₂²×C₂₃	1	1	yes	characteristic, complemented
711	#440	C₂²×C₂₃	1	1	yes	characteristic, complemented
712	#440	C₂²×C₂₃	1	1	yes	characteristic, complemented
713	#440	C₂²×C₂₃	1	1	yes	characteristic, complemented
714	#435	C₂²×C₂₃	1	2	yes	complemented
715	#435	C₂²×C₂₃	1	2	yes	complemented
716	#435	C₂²×C₂₃	1	2	yes	complemented
717	#435	C₂²×C₂₃	1	2	yes	complemented
718	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
719	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
720	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
721	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
722	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
723	#419	C₂²×C₂₃	1	2	yes	complemented
724	#418	C₂²×C₂₃	1	1	yes	characteristic
725	#418	C₂²×C₂₃	1	2	yes	—
726	#417	C₂²×C₂₃	1	1	yes	characteristic
727	#417	C₂²×C₂₃	1	1	yes	characteristic
728	#417	C₂²×C₂₃	1	2	yes	—
729	#417	C₂²×C₂₃	1	2	yes	complemented
730	#416	C₂²×C₂₃	1	1	yes	characteristic
731	#416	C₂²×C₂₃	1	2	yes	—
732	#416	C₂²×C₂₃	1	2	yes	complemented
733	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
734	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
735	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
736	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
737	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
738	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
739	C₂×#102	C₂²×C₂₃	1	2	yes	—
740	#408	C₂²×C₂₃	1	1	yes	characteristic
741	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
742	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
743	C₂×C₂₃	—	2	2	no	—
744	C₂×C₂₃	—	4	2	no	—
745	C₂×C₂₃	—	4	2	no	—
746	C₂×C₂₃	—	4	2	no	—
747	C₂×C₂₃	—	8	1	no	—
748	C₂×C₂₃	—	8	2	no	—
749	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
750	C₂×C₂₃	#3585	1	1	yes	characteristic
751	C₂×C₂₃	#3586	1	1	yes	characteristic
752	2₋¹⁺⁴	—	2	4	no	—
753	2₋¹⁺⁴	—	4	2	no	—
754	H(5,𝔽₂)	—	2	4	no	—
755	H(5,𝔽₂)	—	4	2	no	—
756	C₂×#41	—	2	1	no	—
757	C₂×#41	—	2	1	no	—
758	C₂×#41	—	2	2	no	—
759	C₂×#41	—	2	2	no	—
760	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
761	C₂×#41	C₂³×C₂₃	1	2	yes	—
762	C₂×#41	C₂³×C₂₃	1	2	yes	—
763	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
764	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
765	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
766	C₂²×Q₈	—	2	1	no	—
767	C₂²×Q₈	—	2	1	no	—
768	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
769	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
770	C₂²×D₄	—	2	1	no	—
771	C₂²×D₄	—	2	2	no	—
772	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
773	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
774	#137	—	4	2	no	—
775	AGL(1,ℤ/8)	—	4	2	no	—
776	#135	—	2	4	no	—
777	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
778	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
780	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
781	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
783	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
784	C₂×D₈	C₂³×C₂₃	1	2	yes	—
785	#131	—	4	2	no	—
786	#131	—	4	2	no	—
787	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
788	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
789	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
790	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
791	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
792	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
793	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
794	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
795	C₄⋊Q₈	—	2	1	no	—
796	C₄⋊Q₈	—	2	1	no	—
797	C₄⋊Q₈	—	2	1	no	—
798	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
799	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
800	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
801	#127	—	2	1	no	—
802	#127	D₄×C₂₃	1	1	yes	characteristic
803	#126	—	2	2	no	—
804	#126	—	2	2	no	—
805	#125	—	2	2	no	—
806	#124	—	2	1	no	—
807	#124	—	2	1	no	—
808	#124	—	2	2	no	—
809	#124	—	2	2	no	—
810	#124	—	2	2	no	—
811	#124	—	2	2	no	—
812	#124	—	2	2	no	—
813	#124	—	2	1	no	—
814	#124	—	2	1	no	—
815	#124	D₄×C₂₃	1	1	yes	characteristic
816	#124	D₄×C₂₃	1	1	yes	characteristic
817	#124	C₂³×C₂₃	1	2	yes	—
818	#124	C₂³×C₂₃	1	2	yes	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	C₂²⋊Q₈	—	2	1	no	—
825	C₂²⋊Q₈	—	2	1	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	—	2	2	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	—	2	2	no	—
830	C₂²⋊Q₈	—	2	2	no	—
831	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
832	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
833	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
834	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
835	#121	—	2	1	no	—
836	#121	—	2	1	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	2	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	D₄×C₂₃	1	2	yes	—
845	#121	D₄×C₂₃	1	2	yes	—
846	#121	C₂³×C₂₃	1	2	yes	—
847	#121	C₂³×C₂₃	1	2	yes	—
848	#121	C₂³×C₂₃	1	2	yes	—
849	#121	C₂³×C₂₃	1	2	yes	—
850	#120	—	2	2	no	—
851	#120	—	2	2	no	—
852	#120	—	2	2	no	—
853	C₄×Q₈	—	2	1	no	—
854	C₄×Q₈	—	2	1	no	—
855	C₄×Q₈	—	2	2	no	—
856	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
857	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
858	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
859	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	2	no	—
871	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
872	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
873	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₂₃	1	2	yes	—
876	C₄×D₄	C₂³×C₂₃	1	2	yes	—
877	#117	—	2	2	no	—
878	#117	—	2	1	no	—
879	#117	—	2	1	no	—
880	#117	C₂³×C₂₃	1	1	yes	characteristic
881	#117	C₂³×C₂₃	1	1	yes	characteristic
882	#117	C₂³×C₂₃	1	2	yes	—
883	#117	C₂³×C₂₃	1	2	yes	—
884	C₂×C₄⋊C₄	—	2	1	no	—
885	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
887	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
888	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
889	C₂×C₂²⋊C₄	—	2	1	no	—
890	C₂×C₂²⋊C₄	—	2	1	no	—
891	C₂×C₂²⋊C₄	—	2	2	no	—
892	C₂×C₂²⋊C₄	—	2	2	no	—
893	C₂×C₄²	—	2	1	no	—
894	C₂×C₄²	—	2	1	no	—
895	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
896	#107	C₂³×C₂₃	1	1	yes	characteristic
897	#107	C₂³×C₂₃	1	1	yes	characteristic
898	#107	C₂³×C₂₃	1	2	yes	—
899	#107	C₂³×C₂₃	1	2	yes	—
900	#106	C₂³×C₂₃	1	1	yes	characteristic
901	#106	C₂³×C₂₃	1	1	yes	characteristic
902	#106	C₂³×C₂₃	1	2	yes	—
903	#106	C₂³×C₂₃	1	2	yes	—
904	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
905	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
906	#103	C₂³×C₂₃	1	1	yes	characteristic
907	#103	C₂³×C₂₃	1	2	yes	—
908	#103	C₂³×C₂₃	1	2	yes	—
909	#103	C₂³×C₂₃	1	2	yes	—
910	#103	C₂³×C₂₃	1	2	yes	—
911	#103	C₂³×C₂₃	1	2	yes	—
912	#103	C₂³×C₂₃	1	2	yes	—
913	#103	C₂³×C₂₃	1	1	yes	characteristic
914	#103	C₂³×C₂₃	1	2	yes	—
915	#103	C₂³×C₂₃	1	2	yes	—
916	#103	C₂³×C₂₃	1	1	yes	characteristic
917	#103	C₂³×C₂₃	1	1	yes	characteristic
918	#102	C₂³×C₂₃	1	1	yes	characteristic
919	#102	C₂³×C₂₃	1	2	yes	—
920	#102	C₂³×C₂₃	1	2	yes	—
921	#102	C₂³×C₂₃	1	2	yes	—
922	#102	C₂³×C₂₃	1	2	yes	—
923	#102	C₂³×C₂₃	1	2	yes	—
924	#102	C₂³×C₂₃	1	2	yes	—
925	#102	C₂³×C₂₃	1	1	yes	characteristic
926	#102	C₂³×C₂₃	1	2	yes	—
927	#102	C₂³×C₂₃	1	2	yes	—
928	#102	C₂³×C₂₃	1	1	yes	characteristic
929	#102	C₂³×C₂₃	1	1	yes	characteristic
930	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
931	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
932	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
933	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
934	#97	C₂³×C₂₃	1	1	yes	characteristic
935	#97	C₂³×C₂₃	1	1	yes	characteristic
936	#97	C₂³×C₂₃	1	1	yes	characteristic
937	#97	C₂³×C₂₃	1	1	yes	characteristic
938	C₂₃	#61222	1	1	yes	characteristic, direct product factor, Sylow
939	C₂⁴	—	2	2	no	—
940	C₂⁴	—	2	1	no	—
941	#41	—	2	2	no	—
942	#41	—	2	2	no	—
943	#41	—	2	2	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	2	4	no	—
947	#41	—	2	4	no	—
948	#41	—	2	2	no	—
949	#41	—	2	2	no	—
950	#41	—	4	2	no	—
951	#41	—	4	2	no	—
952	#41	—	4	4	no	—
953	#41	—	4	4	no	—
954	#41	—	4	8	no	—
955	#41	—	8	4	no	—
956	#41	#41×C₂₃	1	4	yes	complemented
957	C₂×Q₈	—	2	2	no	—
958	C₂×Q₈	—	2	2	no	—
959	C₂×Q₈	—	2	1	no	—
960	C₂×Q₈	—	2	2	no	—
961	C₂×Q₈	—	2	4	no	—
962	C₂×Q₈	—	2	2	no	—
963	C₂×Q₈	—	2	2	no	—
964	C₂×Q₈	—	4	2	no	—
965	C₂×Q₈	—	4	4	no	—
966	C₂×Q₈	—	8	2	no	—
967	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
968	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
969	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
970	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
971	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	4	no	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	4	2	no	—
986	C₂×D₄	—	4	4	no	—
987	C₂×D₄	—	4	8	no	—
988	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
989	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
990	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
991	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
992	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
993	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
994	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
995	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
996	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1012	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1014	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1015	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1016	Q₁₆	—	2	2	no	—
1017	Q₁₆	—	4	2	no	—
1018	SD₁₆	—	2	2	no	—
1019	SD₁₆	—	2	2	no	—
1020	SD₁₆	—	4	2	no	—
1021	SD₁₆	—	4	2	no	—
1022	D₈	—	2	2	no	—
1023	D₈	—	4	2	no	—
1024	M₁₆	—	2	2	no	—
1025	M₁₆	—	2	2	no	—
1026	M₁₆	—	4	2	no	—
1027	M₁₆	—	4	2	no	—
1028	C₂×C₈	—	2	2	no	—
1029	C₂×C₈	—	2	2	no	—
1030	C₂×C₈	—	4	2	no	—
1031	C₂×C₈	—	4	2	no	—
1032	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1033	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1034	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1035	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1036	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1037	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1053	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1054	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1055	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1056	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1057	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1058	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1059	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	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	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1081	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1082	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1083	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1084	C₄²	—	2	1	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	1	no	—
1087	C₄²	—	2	1	no	—
1088	C₄²	—	2	1	no	—
1089	C₄²	—	2	1	no	—
1090	C₄²	—	2	2	no	—
1091	C₄²	—	2	2	no	—
1092	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1093	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1094	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1095	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1096	C₂³	—	2	1	no	—
1097	C₂³	—	2	1	no	—
1098	C₂³	—	2	2	no	—
1099	C₂³	—	4	4	no	—
1100	C₂³	—	4	2	no	—
1101	C₂³	—	8	1	no	—
1102	C₂³	—	8	1	no	—
1103	C₂³	—	8	2	no	—
1104	C₂³	—	8	2	no	—
1105	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1106	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1107	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1108	Q₈	—	2	1	no	—
1109	Q₈	—	2	2	no	—
1110	Q₈	—	2	2	no	—
1111	Q₈	—	2	1	no	—
1112	Q₈	—	2	2	no	—
1113	Q₈	—	2	1	no	—
1114	Q₈	—	2	2	no	—
1115	Q₈	—	4	4	no	—
1116	Q₈	—	4	4	no	—
1117	Q₈	—	4	2	no	—
1118	Q₈	—	8	2	no	—
1119	Q₈	C₂×#41×C₂₃	1	2	yes	—
1120	D₄	—	2	4	no	—
1121	D₄	—	2	4	no	—
1122	D₄	—	2	4	no	—
1123	D₄	—	2	1	no	—
1124	D₄	—	2	2	no	—
1125	D₄	—	2	1	no	—
1126	D₄	—	2	1	no	—
1127	D₄	—	2	2	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	2	2	no	—
1130	D₄	—	4	2	no	—
1131	D₄	—	4	2	no	—
1132	D₄	—	4	4	no	—
1133	D₄	—	4	4	no	—
1134	D₄	—	4	4	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	8	2	no	—
1138	D₄	—	8	2	no	—
1139	D₄	—	8	2	no	—
1140	D₄	—	8	2	no	—
1141	D₄	C₂×#41×C₂₃	1	2	yes	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	4	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	4	no	—
1159	C₂×C₄	—	4	4	no	—
1160	C₂×C₄	—	4	4	no	—
1161	C₂×C₄	—	4	2	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	4	2	no	—
1164	C₂×C₄	—	4	2	no	—
1165	C₂×C₄	—	8	1	no	—
1166	C₂×C₄	—	8	1	no	—
1167	C₂×C₄	—	8	1	no	—
1168	C₂×C₄	—	8	1	no	—
1169	C₂×C₄	—	8	2	no	—
1170	C₂×C₄	—	8	2	no	—
1171	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1172	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1173	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1174	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1175	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1176	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1177	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1178	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1179	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1180	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1181	C₈	—	2	1	no	—
1182	C₈	—	2	1	no	—
1183	C₈	—	2	1	no	—
1184	C₈	—	2	1	no	—
1185	C₈	—	2	2	no	—
1186	C₈	—	2	2	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	2	2	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	2	no	—
1202	C₂²	—	4	1	no	—
1203	C₂²	—	4	2	no	—
1204	C₂²	—	16	2	no	—
1205	C₂²	—	16	4	no	—
1206	C₂²	C₂₃×#546	1	2	yes	—
1207	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1208	C₄	—	2	2	no	—
1209	C₄	—	2	2	no	—
1210	C₄	—	2	2	no	—
1211	C₄	—	2	1	no	—
1212	C₄	—	2	1	no	—
1213	C₄	—	2	1	no	—
1214	C₄	—	2	1	no	—
1215	C₄	—	4	2	no	—
1216	C₄	—	4	1	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	4	2	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	C₂₃×#546	1	2	yes	—
1224	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1225	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1226	C₂	—	2	2	no	—
1227	C₂	—	4	2	no	—
1228	C₂	—	4	2	no	—
1229	C₂	—	4	2	no	—
1230	C₂	—	8	2	no	—
1231	C₂	—	8	1	no	—
1232	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
1233	C₂	C₂₃×#3585	1	1	yes	characteristic
1234	C₂	C₂₃×#3586	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3511	C₂	semidirect
2. C₂₃×#3500	C₂	semidirect
3. C₂₃×#3321	C₂	semidirect
4. C₂₃×#3319	C₂	semidirect
5. C₂₃×#3316	C₂	semidirect
6. C₂₃×#3314	C₂	semidirect
7. C₂₃×#3313	C₂	semidirect
8. C₂₃×#3311	C₂	semidirect
9. C₂₃×#3308	C₂	semidirect
10. C₂₃×#3306	C₂	semidirect
11. C₂×C₂₃×#489	C₂	semidirect
12. C₂₃×#3097	C₂	semidirect
13. C₂₃×#3096	C₂	semidirect
14. C₂₃×#3079	C₂	semidirect
15. C₂₃×#3063	C₂	semidirect
16. C₂₃×#3062	C₂	semidirect
17. C₂₃×#3040	C₂	semidirect
18. C₂₃×#3013	C₂	semidirect
19. C₂₃×#3012	C₂	semidirect
20. C₂₃×#2943	C₂	semidirect
21. C₂₃×#2932	C₂	semidirect
22. C₂₃×#2898	C₂	semidirect
23. C₂₃×#2897	C₂	semidirect
26. C₂×C₂₃×#137	C₂²	semidirect
30. C₂×C₂₃×#131	C₂²	semidirect
31. C₂₃×#556	C₂²	semidirect
32. C₂₃×#555	C₂²	semidirect
33. C₂₃×#554	C₂²	semidirect
38. C₂₃×#547	C₂²	semidirect
46. C₂₃×#537	C₂²	semidirect
55. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
59. C₂₃×#520	C₂²	semidirect
61. C₄×#41×C₂₃	C₂²	semidirect
62. C₂₃×#489	C₂²	semidirect
63. C₂₃×#489	C₂²	semidirect
64. C₂₃×#489	C₂²	semidirect
65. C₂₃×#489	C₂²	semidirect
66. C₂₃×#485	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#484	C₂²	semidirect
69. C₂₃×#483	C₂²	semidirect
70. C₂₃×#482	C₂²	semidirect
71. C₂₃×#482	C₂²	semidirect
72. C₂₃×#481	C₂²	semidirect
73. C₂₃×#480	C₂²	semidirect
74. C₂₃×#477	C₂²	semidirect
75. C₂₃×#476	C₂²	semidirect
76. C₂₃×#475	C₂²	semidirect
77. C₂₃×#474	C₂²	semidirect
78. C₂₃×#470	C₂²	semidirect
79. C₂₃×#469	C₂²	semidirect
80. C₂₃×#468	C₂²	semidirect
81. C₂₃×#468	C₂²	semidirect
82. C₂₃×#467	C₂²	semidirect
83. C₂₃×#466	C₂²	semidirect
84. C₂₃×#465	C₂²	semidirect
85. C₂₃×#465	C₂²	semidirect
86. C₂₃×#464	C₂²	semidirect
87. C₂₃×#464	C₂²	semidirect
88. C₂₃×#463	C₂²	semidirect
89. C₂₃×#463	C₂²	semidirect
91. C₂₃×#452	C₂²	semidirect
92. C₂₃×#451	C₂²	semidirect
95. C₂₃×#449	C₂²	semidirect
96. C₂₃×#448	C₂²	semidirect
98. C₂₃×#442	C₂²	semidirect
99. C₂₃×#442	C₂²	semidirect
100. C₂₃×#441	C₂²	semidirect
101. C₂₃×#441	C₂²	semidirect
102. C₂₃×#440	C₂²	semidirect
103. C₂₃×#440	C₂²	semidirect
104. C₂₃×#440	C₂²	semidirect
105. C₂₃×#440	C₂²	semidirect
106. C₂₃×#435	C₂²	semidirect
107. C₂₃×#435	C₂²	semidirect
108. C₂₃×#435	C₂²	semidirect
109. C₂₃×#435	C₂²	semidirect
110. C₂₃×#428	C₂²	semidirect
111. C₂₃×#428	C₂²	semidirect
112. C₂₃×#427	C₂²	semidirect
113. C₂₃×#423	C₂²	semidirect
114. C₂₃×#419	C₂²	semidirect
115. C₂₃×#419	C₂²	semidirect
121. C₂₃×#417	C₂²	semidirect
124. C₂₃×#416	C₂²	semidirect
125. C₂₃×#416	C₂²	semidirect
126. C₂×C₂₃×#103	C₂²	semidirect
127. C₂×C₂₃×#103	C₂²	semidirect
128. C₂×C₂₃×#103	C₂²	semidirect
133. C₂₃×#408	C₂²	semidirect
134. C₂×C₂₃×#97	C₂²	semidirect
338. #41×C₂₃	#41	semidirect
478. #61222	C₂₃	direct (N × H)
570. #3511	C₂×C₂₃	semidirect
571. #3500	C₂×C₂₃	semidirect
572. #3321	C₂×C₂₃	semidirect
573. #3319	C₂×C₂₃	semidirect
574. #3316	C₂×C₂₃	semidirect
575. #3314	C₂×C₂₃	semidirect
576. #3313	C₂×C₂₃	semidirect
577. #3311	C₂×C₂₃	semidirect
578. #3308	C₂×C₂₃	semidirect
579. #3306	C₂×C₂₃	semidirect
580. C₂×#489	C₂×C₂₃	semidirect
581. #3097	C₂×C₂₃	semidirect
582. #3096	C₂×C₂₃	semidirect
583. #3079	C₂×C₂₃	semidirect
584. #3063	C₂×C₂₃	semidirect
585. #3062	C₂×C₂₃	semidirect
586. #3040	C₂×C₂₃	semidirect
587. #3013	C₂×C₂₃	semidirect
588. #3012	C₂×C₂₃	semidirect
589. #2943	C₂×C₂₃	semidirect
590. #2932	C₂×C₂₃	semidirect
591. #2898	C₂×C₂₃	semidirect
592. #2897	C₂×C₂₃	semidirect
634. C₂×#137	C₂²×C₂₃	semidirect
638. C₂×#131	C₂²×C₂₃	semidirect
639. #556	C₂²×C₂₃	semidirect
640. #555	C₂²×C₂₃	semidirect
641. #554	C₂²×C₂₃	semidirect
646. #547	C₂²×C₂₃	semidirect
654. #537	C₂²×C₂₃	semidirect
663. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
667. #520	C₂²×C₂₃	semidirect
669. C₄×#41	C₂²×C₂₃	semidirect
670. #489	C₂²×C₂₃	semidirect
671. #489	C₂²×C₂₃	semidirect
672. #489	C₂²×C₂₃	semidirect
673. #489	C₂²×C₂₃	semidirect
674. #485	C₂²×C₂₃	semidirect
675. #485	C₂²×C₂₃	semidirect
676. #484	C₂²×C₂₃	semidirect
677. #483	C₂²×C₂₃	semidirect
678. #482	C₂²×C₂₃	semidirect
679. #482	C₂²×C₂₃	semidirect
680. #481	C₂²×C₂₃	semidirect
681. #480	C₂²×C₂₃	semidirect
682. #477	C₂²×C₂₃	semidirect
683. #476	C₂²×C₂₃	semidirect
684. #475	C₂²×C₂₃	semidirect
685. #474	C₂²×C₂₃	semidirect
686. #470	C₂²×C₂₃	semidirect
687. #469	C₂²×C₂₃	semidirect
688. #468	C₂²×C₂₃	semidirect
689. #468	C₂²×C₂₃	semidirect
690. #467	C₂²×C₂₃	semidirect
691. #466	C₂²×C₂₃	semidirect
692. #465	C₂²×C₂₃	semidirect
693. #465	C₂²×C₂₃	semidirect
694. #464	C₂²×C₂₃	semidirect
695. #464	C₂²×C₂₃	semidirect
696. #463	C₂²×C₂₃	semidirect
697. #463	C₂²×C₂₃	semidirect
699. #452	C₂²×C₂₃	semidirect
700. #451	C₂²×C₂₃	semidirect
703. #449	C₂²×C₂₃	semidirect
704. #448	C₂²×C₂₃	semidirect
706. #442	C₂²×C₂₃	semidirect
707. #442	C₂²×C₂₃	semidirect
708. #441	C₂²×C₂₃	semidirect
709. #441	C₂²×C₂₃	semidirect
710. #440	C₂²×C₂₃	semidirect
711. #440	C₂²×C₂₃	semidirect
712. #440	C₂²×C₂₃	semidirect
713. #440	C₂²×C₂₃	semidirect
714. #435	C₂²×C₂₃	semidirect
715. #435	C₂²×C₂₃	semidirect
716. #435	C₂²×C₂₃	semidirect
717. #435	C₂²×C₂₃	semidirect
718. #428	C₂²×C₂₃	semidirect
719. #428	C₂²×C₂₃	semidirect
720. #427	C₂²×C₂₃	semidirect
721. #423	C₂²×C₂₃	semidirect
722. #419	C₂²×C₂₃	semidirect
723. #419	C₂²×C₂₃	semidirect
729. #417	C₂²×C₂₃	semidirect
732. #416	C₂²×C₂₃	semidirect
733. #416	C₂²×C₂₃	semidirect
734. C₂×#103	C₂²×C₂₃	semidirect
735. C₂×#103	C₂²×C₂₃	semidirect
736. C₂×#103	C₂²×C₂₃	semidirect
741. #408	C₂²×C₂₃	semidirect
742. C₂×#97	C₂²×C₂₃	semidirect
938. C₂₃	#61222	direct (N × H)
956. #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×#3511	2
C₂₃×#3500	2
C₂₃×#3321	2
C₂₃×#3319	2
C₂₃×#3316	2
C₂₃×#3314	2
C₂₃×#3313	2
C₂₃×#3311	2
C₂₃×#3308	2
C₂₃×#3306	2
C₂×C₂₃×#489	2
C₂₃×#3097	2
C₂₃×#3096	2
C₂₃×#3079	2
C₂₃×#3063	2
C₂₃×#3062	2
C₂₃×#3040	2
C₂₃×#3013	2
C₂₃×#3012	2
C₂₃×#2943	2
C₂₃×#2932	2
C₂₃×#2898	2
C₂₃×#2897	2
#61222	23

Subgroups — C23×#61222 #19208848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61222 #19208848