Subgroups — C₂₃×#61344 #19208970

Order 5888.

1748 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3510	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3377	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3377	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3375	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3371	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3371	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3369	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3365	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3364	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3136	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3043	C₂	1	1	yes	maximal, characteristic
19	C₂×C₂₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2949	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₂₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
25	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
26	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#559	C₂²	1	2	yes	—
28	C₂₃×#559	C₂²	1	2	yes	—
29	Q₈²×C₂₃	—	2	1	no	—
30	Q₈²×C₂₃	C₂²	1	2	yes	complemented
31	C₂₃×#557	—	2	1	no	—
32	C₂₃×#557	—	2	1	no	—
33	C₂₃×#557	—	2	1	no	—
34	C₂₃×#557	C₂²	1	2	yes	complemented
35	C₂₃×#557	C₂²	1	2	yes	complemented
36	C₂₃×#557	C₂²	1	2	yes	complemented
37	C₂₃×#556	C₂²	1	2	yes	—
38	C₂₃×#556	C₂²	1	2	yes	—
39	C₂₃×#551	—	2	2	no	—
40	C₂₃×#551	—	2	2	no	—
41	C₂₃×#544	—	2	2	no	—
42	C₂₃×#544	C₂²	1	1	yes	characteristic
43	C₂₃×#544	C₂²	1	1	yes	characteristic
44	C₂₃×#542	—	2	1	no	—
45	C₂₃×#542	—	2	1	no	—
46	C₂₃×#536	C₂²	1	1	yes	characteristic
47	C₂₃×#535	C₂²	1	1	yes	characteristic
48	C₂₃×#533	—	2	2	no	—
49	C₂₃×#533	C₂²	1	1	yes	characteristic
50	C₂₃×#533	C₂²	1	1	yes	characteristic
51	C₂₃×#529	—	2	1	no	—
52	C₂₃×#529	—	2	1	no	—
53	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
54	C₂₃×#519	C₂²	1	1	yes	characteristic
55	C₂₃×#519	C₂²	1	1	yes	characteristic
56	C₂₃×#519	C₂²	1	1	yes	characteristic
57	C₂₃×#518	C₂²	1	1	yes	characteristic
58	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
59	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
60	C₂₃×#491	C₂²	1	2	yes	complemented
61	C₂₃×#490	C₂²	1	2	yes	—
62	C₂₃×#489	C₂²	1	2	yes	—
63	C₂₃×#489	C₂²	1	2	yes	—
64	C₂₃×#489	C₂²	1	2	yes	—
65	C₂₃×#489	C₂²	1	2	yes	complemented
66	C₂₃×#488	C₂²	1	2	yes	—
67	C₂₃×#488	C₂²	1	2	yes	—
68	C₂₃×#488	C₂²	1	2	yes	—
69	C₂₃×#488	C₂²	1	2	yes	complemented
70	C₂₃×#487	C₂²	1	2	yes	complemented
71	C₂₃×#486	C₂²	1	2	yes	—
72	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#479	C₂²	1	2	yes	complemented
75	C₂₃×#479	C₂²	1	2	yes	complemented
76	C₂₃×#478	C₂²	1	2	yes	—
77	C₂₃×#478	C₂²	1	2	yes	—
78	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#477	C₂²	1	2	yes	complemented
82	C₂₃×#476	C₂²	1	2	yes	—
83	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#475	C₂²	1	2	yes	complemented
86	C₂₃×#474	C₂²	1	2	yes	—
87	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#464	C₂²	1	2	yes	—
89	C₂₃×#464	C₂²	1	2	yes	—
90	C₂₃×#464	C₂²	1	2	yes	—
91	C₂₃×#464	C₂²	1	2	yes	—
92	C₂₃×#464	C₂²	1	2	yes	—
93	C₂₃×#464	C₂²	1	2	yes	—
94	C₂₃×#464	C₂²	1	2	yes	complemented
95	C₂₃×#464	C₂²	1	2	yes	complemented
96	C₂₃×#462	C₂²	1	2	yes	complemented
97	C₂₃×#462	C₂²	1	2	yes	complemented
98	C₂₃×#460	C₂²	1	2	yes	—
99	C₂₃×#460	C₂²	1	2	yes	—
100	C₂₃×#446	C₂²	1	2	yes	complemented
101	C₂₃×#446	C₂²	1	2	yes	complemented
102	C₂₃×#446	C₂²	1	2	yes	complemented
103	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
104	C₂₃×#441	C₂²	1	2	yes	complemented
105	C₂₃×#441	C₂²	1	2	yes	complemented
106	C₂₃×#441	C₂²	1	2	yes	complemented
107	C₂₃×#440	C₂²	1	2	yes	—
108	C₂₃×#440	C₂²	1	2	yes	—
109	C₂₃×#440	C₂²	1	2	yes	complemented
110	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
112	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
116	C₂₃×#428	C₂²	1	1	yes	characteristic
117	C₂₃×#427	C₂²	1	1	yes	characteristic
118	C₂₃×#427	C₂²	1	1	yes	characteristic
119	C₂₃×#424	C₂²	1	1	yes	characteristic
120	C₂₃×#424	C₂²	1	1	yes	characteristic
121	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
122	C₂₃×#419	C₂²	1	1	yes	characteristic
123	C₂₃×#419	C₂²	1	1	yes	characteristic
124	C₂₃×#419	C₂²	1	1	yes	characteristic
125	C₂₃×#418	C₂²	1	1	yes	characteristic
126	C₂₃×#418	C₂²	1	1	yes	characteristic
127	C₂₃×#417	C₂²	1	1	yes	characteristic
128	C₂₃×#416	C₂²	1	1	yes	characteristic
129	C₂₃×#416	C₂²	1	1	yes	characteristic
130	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
131	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
132	C₂₃×#405	C₂²	1	1	yes	characteristic
133	C₂₃×#405	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂₃×#137	—	2	4	no	—
140	C₂×Q₁₆×C₂₃	—	2	4	no	—
141	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₂₃	—	2	4	no	—
145	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
152	C₂₃×C₄⋊Q₈	—	2	2	no	—
153	C₂₃×C₄⋊Q₈	—	2	2	no	—
154	C₂₃×C₄⋊Q₈	—	2	2	no	—
155	C₂₃×C₄⋊Q₈	—	2	1	no	—
156	C₂₃×C₄⋊Q₈	—	2	1	no	—
157	C₂₃×C₄⋊Q₈	—	2	2	no	—
158	C₂₃×C₄⋊Q₈	—	2	2	no	—
159	C₂₃×C₄⋊Q₈	—	2	2	no	—
160	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
161	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
162	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₂₃×#127	C₂³	1	2	yes	—
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#126	—	2	2	no	—
172	C₂₃×#125	—	2	1	no	—
173	C₂₃×#125	—	2	1	no	—
174	C₂₃×#125	—	2	2	no	—
175	C₂₃×#125	—	2	2	no	—
176	C₂₃×#125	—	2	2	no	—
177	C₂₃×#125	—	2	2	no	—
178	C₂₃×#125	—	2	2	no	—
179	C₂₃×#125	—	2	2	no	—
180	C₂₃×#125	D₄	1	1	yes	characteristic
181	C₂₃×#125	D₄	1	1	yes	characteristic
182	C₂₃×#125	C₂³	1	2	yes	—
183	C₂₃×#125	C₂³	1	1	yes	characteristic
184	C₂₃×#125	C₂³	1	1	yes	characteristic
185	C₂₃×#125	C₂³	1	2	yes	—
186	C₂₃×#124	—	2	2	no	—
187	C₂₃×#124	—	2	2	no	—
188	C₂₃×#124	—	2	1	no	—
189	C₂₃×#124	—	2	1	no	—
190	C₂₃×#124	C₂³	1	2	yes	—
191	C₂₃×#124	C₂³	1	2	yes	—
192	C₂₃×#124	C₂³	1	2	yes	—
193	C₂₃×#124	C₂³	1	2	yes	—
194	C₂₃×#123	—	2	2	no	—
195	C₂₃×#123	—	2	2	no	—
196	C₂₃×#123	—	2	2	no	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×#123	—	2	2	no	—
199	C₂₃×C₂²⋊Q₈	—	2	2	no	—
200	C₂₃×C₂²⋊Q₈	—	2	2	no	—
201	C₂₃×C₂²⋊Q₈	—	2	1	no	—
202	C₂₃×C₂²⋊Q₈	—	2	1	no	—
203	C₂₃×C₂²⋊Q₈	—	2	1	no	—
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	D₄	1	2	yes	—
208	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
209	C₂₃×#121	—	2	1	no	—
210	C₂₃×#121	—	2	1	no	—
211	C₂₃×#120	—	2	2	no	—
212	C₄×Q₈×C₂₃	—	2	2	no	—
213	C₄×Q₈×C₂₃	—	2	1	no	—
214	C₄×Q₈×C₂₃	—	2	1	no	—
215	C₄×Q₈×C₂₃	—	2	2	no	—
216	C₄×Q₈×C₂₃	—	2	2	no	—
217	C₄×Q₈×C₂₃	—	2	1	no	—
218	C₄×Q₈×C₂₃	—	2	1	no	—
219	C₄×Q₈×C₂₃	—	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	—	2	1	no	—
224	C₄×Q₈×C₂₃	—	2	1	no	—
225	C₄×Q₈×C₂₃	—	2	1	no	—
226	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
229	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
230	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
231	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
232	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
233	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
234	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
235	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
236	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
237	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
238	C₄×D₄×C₂₃	—	2	1	no	—
239	C₄×D₄×C₂₃	—	2	1	no	—
240	C₄×D₄×C₂₃	—	2	2	no	—
241	C₄×D₄×C₂₃	—	2	2	no	—
242	C₄×D₄×C₂₃	—	2	1	no	—
243	C₄×D₄×C₂₃	—	2	1	no	—
244	C₄×D₄×C₂₃	C₂³	1	2	yes	—
245	C₄×D₄×C₂₃	C₂³	1	2	yes	—
246	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
248	C₂₃×#117	—	2	2	no	—
249	C₂₃×#117	—	2	2	no	—
250	C₂₃×#117	—	2	2	no	—
251	C₂₃×#117	—	2	2	no	—
252	C₂₃×#117	—	2	2	no	—
253	C₂₃×#117	—	2	1	no	—
254	C₂₃×#117	C₂³	1	1	yes	characteristic
255	C₂₃×#117	C₂³	1	1	yes	characteristic
256	C₂₃×#117	C₂³	1	1	yes	characteristic
257	C₂₃×#117	C₂³	1	1	yes	characteristic
258	C₂₃×#117	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
262	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
264	C₂×C₄²×C₂₃	—	2	1	no	—
265	C₂×C₄²×C₂₃	—	2	1	no	—
266	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
267	C₂₃×#107	C₂³	1	1	yes	characteristic
268	C₂₃×#107	C₂³	1	1	yes	characteristic
269	C₂₃×#107	C₂³	1	1	yes	characteristic
270	C₂₃×#107	C₂³	1	1	yes	characteristic
271	C₂₃×#107	C₂³	1	2	yes	—
272	C₂₃×#106	C₂³	1	1	yes	characteristic
273	C₂₃×#106	C₂³	1	1	yes	characteristic
274	C₂₃×#106	C₂³	1	1	yes	characteristic
275	C₂₃×#106	C₂³	1	1	yes	characteristic
276	C₂₃×#106	C₂³	1	2	yes	—
277	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
284	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
285	C₂₃×#103	C₂³	1	2	yes	—
286	C₂₃×#103	C₂³	1	2	yes	—
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	1	yes	characteristic
289	C₂₃×#103	C₂³	1	1	yes	characteristic
290	C₂₃×#103	C₂³	1	1	yes	characteristic
291	C₂₃×#103	C₂³	1	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	2	yes	—
297	C₂₃×#103	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	1	yes	characteristic
303	C₂₃×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
309	C₂₃×#97	C₂³	1	2	yes	—
310	C₂₃×#97	C₂³	1	2	yes	—
311	C₂₃×#97	C₂³	1	2	yes	—
312	C₄×C₈×C₂₃	C₂³	1	2	yes	—
313	C₄×C₈×C₂₃	C₂³	1	2	yes	—
314	C₄×C₈×C₂₃	C₂³	1	2	yes	—
315	C₂⁴×C₂₃	—	2	1	no	—
316	#41×C₂₃	—	2	2	no	—
317	#41×C₂₃	—	2	2	no	—
318	C₂×Q₈×C₂₃	—	2	1	no	—
319	C₂×Q₈×C₂₃	—	2	1	no	—
320	C₂×Q₈×C₂₃	—	2	1	no	—
321	C₂×Q₈×C₂₃	—	2	1	no	—
322	C₂×Q₈×C₂₃	—	2	2	no	—
323	C₂×Q₈×C₂₃	—	2	2	no	—
324	C₂×Q₈×C₂₃	—	2	2	no	—
325	C₂×Q₈×C₂₃	—	2	2	no	—
326	C₂×Q₈×C₂₃	—	2	2	no	—
327	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
328	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
329	C₂×Q₈×C₂₃	#41	1	4	yes	—
330	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
333	C₂×D₄×C₂₃	—	2	1	no	—
334	C₂×D₄×C₂₃	—	2	1	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	2	no	—
337	C₂×D₄×C₂₃	—	2	2	no	—
338	C₂×D₄×C₂₃	—	2	2	no	—
339	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
340	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₂₃	—	2	1	no	—
342	C₂²×C₄×C₂₃	—	2	1	no	—
343	C₂²×C₄×C₂₃	—	2	1	no	—
344	C₂²×C₄×C₂₃	—	2	1	no	—
345	C₂²×C₄×C₂₃	—	2	1	no	—
346	C₂²×C₄×C₂₃	—	2	1	no	—
347	C₂²×C₄×C₂₃	—	2	2	no	—
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
352	Q₁₆×C₂₃	—	2	4	no	—
353	Q₁₆×C₂₃	—	2	4	no	—
354	Q₁₆×C₂₃	—	2	4	no	—
355	SD₁₆×C₂₃	—	2	4	no	—
356	SD₁₆×C₂₃	—	2	4	no	—
357	SD₁₆×C₂₃	—	2	4	no	—
358	M₁₆×C₂₃	—	2	2	no	—
359	M₁₆×C₂₃	—	2	2	no	—
360	C₂×C₈×C₂₃	—	2	2	no	—
361	C₂×C₈×C₂₃	—	2	2	no	—
362	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
363	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
366	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₂₃	—	2	2	no	—
369	C₄⋊C₄×C₂₃	—	2	2	no	—
370	C₄⋊C₄×C₂₃	—	2	1	no	—
371	C₄⋊C₄×C₂₃	—	2	1	no	—
372	C₄⋊C₄×C₂₃	—	2	1	no	—
373	C₄⋊C₄×C₂₃	—	2	2	no	—
374	C₄⋊C₄×C₂₃	—	2	2	no	—
375	C₄⋊C₄×C₂₃	—	2	2	no	—
376	C₄⋊C₄×C₂₃	—	2	2	no	—
377	C₄⋊C₄×C₂₃	—	2	2	no	—
378	C₄⋊C₄×C₂₃	—	2	2	no	—
379	C₄⋊C₄×C₂₃	—	2	2	no	—
380	C₄⋊C₄×C₂₃	—	2	2	no	—
381	C₄⋊C₄×C₂₃	—	2	1	no	—
382	C₄⋊C₄×C₂₃	—	2	1	no	—
383	C₄⋊C₄×C₂₃	—	2	1	no	—
384	C₄⋊C₄×C₂₃	—	2	1	no	—
385	C₄⋊C₄×C₂₃	—	2	2	no	—
386	C₄⋊C₄×C₂₃	—	2	2	no	—
387	C₄⋊C₄×C₂₃	—	2	2	no	—
388	C₄⋊C₄×C₂₃	—	2	2	no	—
389	C₄⋊C₄×C₂₃	—	2	1	no	—
390	C₄⋊C₄×C₂₃	—	2	1	no	—
391	C₄⋊C₄×C₂₃	—	2	2	no	—
392	C₄⋊C₄×C₂₃	—	2	2	no	—
393	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
410	C₂²⋊C₄×C₂₃	—	2	1	no	—
411	C₂²⋊C₄×C₂₃	—	2	1	no	—
412	C₂²⋊C₄×C₂₃	—	2	1	no	—
413	C₂²⋊C₄×C₂₃	—	2	2	no	—
414	C₂²⋊C₄×C₂₃	—	2	2	no	—
415	C₂²⋊C₄×C₂₃	—	2	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	2	no	—
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	1	no	—
420	C₂²⋊C₄×C₂₃	—	2	1	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₂²⋊C₄×C₂₃	—	2	2	no	—
423	C₂²⋊C₄×C₂₃	—	2	2	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
427	C₄²×C₂₃	—	2	1	no	—
428	C₄²×C₂₃	—	2	1	no	—
429	C₄²×C₂₃	—	2	1	no	—
430	C₄²×C₂₃	—	2	2	no	—
431	C₄²×C₂₃	—	2	2	no	—
432	C₄²×C₂₃	—	2	2	no	—
433	C₄²×C₂₃	—	2	2	no	—
434	C₄²×C₂₃	—	2	2	no	—
435	C₄²×C₂₃	—	2	2	no	—
436	C₄²×C₂₃	—	2	2	no	—
437	C₄²×C₂₃	—	2	2	no	—
438	C₄²×C₂₃	—	2	1	no	—
439	C₄²×C₂₃	—	2	1	no	—
440	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
443	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
444	C₄²×C₂₃	C₂⁴	1	2	yes	—
445	C₄²×C₂₃	C₂⁴	1	2	yes	—
446	#61344	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₂₃	—	2	2	no	—
448	C₂³×C₂₃	—	2	1	no	—
449	C₂³×C₂₃	—	4	2	no	—
450	C₂³×C₂₃	—	8	1	no	—
451	C₂³×C₂₃	—	8	1	no	—
452	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
453	Q₈×C₂₃	—	2	4	no	—
454	Q₈×C₂₃	—	2	2	no	—
455	Q₈×C₂₃	—	2	2	no	—
456	Q₈×C₂₃	—	2	1	no	—
457	Q₈×C₂₃	—	2	2	no	—
458	Q₈×C₂₃	—	2	1	no	—
459	Q₈×C₂₃	—	4	2	no	—
460	Q₈×C₂₃	—	4	2	no	—
461	Q₈×C₂₃	—	4	2	no	—
462	Q₈×C₂₃	—	4	2	no	—
463	Q₈×C₂₃	—	8	1	no	—
464	Q₈×C₂₃	—	8	2	no	—
465	Q₈×C₂₃	—	8	2	no	—
466	Q₈×C₂₃	C₂×#41	1	4	yes	—
467	D₄×C₂₃	—	2	2	no	—
468	D₄×C₂₃	—	2	1	no	—
469	D₄×C₂₃	—	2	2	no	—
470	D₄×C₂₃	—	2	1	no	—
471	D₄×C₂₃	—	4	2	no	—
472	D₄×C₂₃	—	4	2	no	—
473	D₄×C₂₃	—	8	2	no	—
474	D₄×C₂₃	—	8	2	no	—
475	C₂×C₄×C₂₃	—	2	4	no	—
476	C₂×C₄×C₂₃	—	2	2	no	—
477	C₂×C₄×C₂₃	—	2	1	no	—
478	C₂×C₄×C₂₃	—	2	1	no	—
479	C₂×C₄×C₂₃	—	2	1	no	—
480	C₂×C₄×C₂₃	—	2	1	no	—
481	C₂×C₄×C₂₃	—	2	1	no	—
482	C₂×C₄×C₂₃	—	2	1	no	—
483	C₂×C₄×C₂₃	—	2	2	no	—
484	C₂×C₄×C₂₃	—	2	1	no	—
485	C₂×C₄×C₂₃	—	2	2	no	—
486	C₂×C₄×C₂₃	—	4	1	no	—
487	C₂×C₄×C₂₃	—	4	1	no	—
488	C₂×C₄×C₂₃	—	4	2	no	—
489	C₂×C₄×C₂₃	—	4	2	no	—
490	C₂×C₄×C₂₃	—	8	1	no	—
491	C₂×C₄×C₂₃	—	8	2	no	—
492	C₂×C₄×C₂₃	—	8	1	no	—
493	C₂×C₄×C₂₃	—	8	2	no	—
494	C₂×C₄×C₂₃	—	8	1	no	—
495	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
505	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
506	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
507	C₈×C₂₃	—	2	1	no	—
508	C₈×C₂₃	—	2	1	no	—
509	C₈×C₂₃	—	2	1	no	—
510	C₈×C₂₃	—	2	1	no	—
511	C₈×C₂₃	—	2	2	no	—
512	C₈×C₂₃	—	2	2	no	—
513	#3510	C₂×C₂₃	1	1	yes	characteristic
514	#3502	C₂×C₂₃	1	1	yes	characteristic, complemented
515	#3377	C₂×C₂₃	1	2	yes	complemented
516	#3377	C₂×C₂₃	1	2	yes	complemented
517	#3375	C₂×C₂₃	1	2	yes	complemented
518	#3371	C₂×C₂₃	1	2	yes	complemented
519	#3371	C₂×C₂₃	1	2	yes	complemented
520	#3369	C₂×C₂₃	1	2	yes	complemented
521	#3365	C₂×C₂₃	1	2	yes	complemented
522	#3364	C₂×C₂₃	1	2	yes	complemented
523	#3140	C₂×C₂₃	1	1	yes	characteristic, complemented
524	#3137	C₂×C₂₃	1	1	yes	characteristic, complemented
525	#3136	C₂×C₂₃	1	1	yes	characteristic
526	#3082	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#3081	C₂×C₂₃	1	1	yes	characteristic, complemented
528	#3076	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#3044	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#3043	C₂×C₂₃	1	1	yes	characteristic
531	C₂×#464	C₂×C₂₃	1	1	yes	characteristic, complemented
532	#2962	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#2950	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#2949	C₂×C₂₃	1	1	yes	characteristic, complemented
535	C₄×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
536	C₂²×C₂₃	—	2	1	no	—
537	C₂²×C₂₃	—	2	1	no	—
538	C₂²×C₂₃	—	4	1	no	—
539	C₂²×C₂₃	—	4	2	no	—
540	C₂²×C₂₃	—	4	1	no	—
541	C₂²×C₂₃	—	4	2	no	—
542	C₂²×C₂₃	—	4	1	no	—
543	C₂²×C₂₃	—	4	2	no	—
544	C₂²×C₂₃	—	16	2	no	—
545	C₂²×C₂₃	#548	1	2	yes	—
546	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
547	C₄×C₂₃	—	2	1	no	—
548	C₄×C₂₃	—	2	1	no	—
549	C₄×C₂₃	—	2	2	no	—
550	C₄×C₂₃	—	2	2	no	—
551	C₄×C₂₃	—	2	1	no	—
552	C₄×C₂₃	—	2	1	no	—
553	C₄×C₂₃	—	2	2	no	—
554	C₄×C₂₃	—	2	2	no	—
555	C₄×C₂₃	—	2	4	no	—
556	C₄×C₂₃	—	4	1	no	—
557	C₄×C₂₃	—	4	2	no	—
558	C₄×C₂₃	—	4	1	no	—
559	C₄×C₂₃	—	4	1	no	—
560	C₄×C₂₃	—	4	1	no	—
561	C₄×C₂₃	—	4	1	no	—
562	C₄×C₂₃	—	4	1	no	—
563	C₄×C₂₃	—	4	1	no	—
564	C₄×C₂₃	—	4	2	no	—
565	C₄×C₂₃	#548	1	2	yes	—
566	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
567	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
568	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
569	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
570	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
571	#559	C₂²×C₂₃	1	2	yes	—
572	#559	C₂²×C₂₃	1	2	yes	—
573	Q₈²	—	2	1	no	—
574	Q₈²	C₂²×C₂₃	1	2	yes	complemented
575	#557	—	2	1	no	—
576	#557	—	2	1	no	—
577	#557	—	2	1	no	—
578	#557	C₂²×C₂₃	1	2	yes	complemented
579	#557	C₂²×C₂₃	1	2	yes	complemented
580	#557	C₂²×C₂₃	1	2	yes	complemented
581	#556	C₂²×C₂₃	1	2	yes	—
582	#556	C₂²×C₂₃	1	2	yes	—
583	#551	—	2	2	no	—
584	#551	—	2	2	no	—
585	#544	—	2	2	no	—
586	#544	C₂²×C₂₃	1	1	yes	characteristic
587	#544	C₂²×C₂₃	1	1	yes	characteristic
588	#542	—	2	1	no	—
589	#542	—	2	1	no	—
590	#536	C₂²×C₂₃	1	1	yes	characteristic
591	#535	C₂²×C₂₃	1	1	yes	characteristic
592	#533	—	2	2	no	—
593	#533	C₂²×C₂₃	1	1	yes	characteristic
594	#533	C₂²×C₂₃	1	1	yes	characteristic
595	#529	—	2	1	no	—
596	#529	—	2	1	no	—
597	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
598	#519	C₂²×C₂₃	1	1	yes	characteristic
599	#519	C₂²×C₂₃	1	1	yes	characteristic
600	#519	C₂²×C₂₃	1	1	yes	characteristic
601	#518	C₂²×C₂₃	1	1	yes	characteristic
602	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
603	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
604	#491	C₂²×C₂₃	1	2	yes	complemented
605	#490	C₂²×C₂₃	1	2	yes	—
606	#489	C₂²×C₂₃	1	2	yes	—
607	#489	C₂²×C₂₃	1	2	yes	—
608	#489	C₂²×C₂₃	1	2	yes	—
609	#489	C₂²×C₂₃	1	2	yes	complemented
610	#488	C₂²×C₂₃	1	2	yes	—
611	#488	C₂²×C₂₃	1	2	yes	—
612	#488	C₂²×C₂₃	1	2	yes	—
613	#488	C₂²×C₂₃	1	2	yes	complemented
614	#487	C₂²×C₂₃	1	2	yes	complemented
615	#486	C₂²×C₂₃	1	2	yes	—
616	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
617	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
618	#479	C₂²×C₂₃	1	2	yes	complemented
619	#479	C₂²×C₂₃	1	2	yes	complemented
620	#478	C₂²×C₂₃	1	2	yes	—
621	#478	C₂²×C₂₃	1	2	yes	—
622	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
623	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
624	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
625	#477	C₂²×C₂₃	1	2	yes	complemented
626	#476	C₂²×C₂₃	1	2	yes	—
627	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
628	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
629	#475	C₂²×C₂₃	1	2	yes	complemented
630	#474	C₂²×C₂₃	1	2	yes	—
631	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
632	#464	C₂²×C₂₃	1	2	yes	—
633	#464	C₂²×C₂₃	1	2	yes	—
634	#464	C₂²×C₂₃	1	2	yes	—
635	#464	C₂²×C₂₃	1	2	yes	—
636	#464	C₂²×C₂₃	1	2	yes	—
637	#464	C₂²×C₂₃	1	2	yes	—
638	#464	C₂²×C₂₃	1	2	yes	complemented
639	#464	C₂²×C₂₃	1	2	yes	complemented
640	#462	C₂²×C₂₃	1	2	yes	complemented
641	#462	C₂²×C₂₃	1	2	yes	complemented
642	#460	C₂²×C₂₃	1	2	yes	—
643	#460	C₂²×C₂₃	1	2	yes	—
644	#446	C₂²×C₂₃	1	2	yes	complemented
645	#446	C₂²×C₂₃	1	2	yes	complemented
646	#446	C₂²×C₂₃	1	2	yes	complemented
647	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
648	#441	C₂²×C₂₃	1	2	yes	complemented
649	#441	C₂²×C₂₃	1	2	yes	complemented
650	#441	C₂²×C₂₃	1	2	yes	complemented
651	#440	C₂²×C₂₃	1	2	yes	—
652	#440	C₂²×C₂₃	1	2	yes	—
653	#440	C₂²×C₂₃	1	2	yes	complemented
654	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
655	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
656	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
657	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
658	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
659	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
660	#428	C₂²×C₂₃	1	1	yes	characteristic
661	#427	C₂²×C₂₃	1	1	yes	characteristic
662	#427	C₂²×C₂₃	1	1	yes	characteristic
663	#424	C₂²×C₂₃	1	1	yes	characteristic
664	#424	C₂²×C₂₃	1	1	yes	characteristic
665	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
666	#419	C₂²×C₂₃	1	1	yes	characteristic
667	#419	C₂²×C₂₃	1	1	yes	characteristic
668	#419	C₂²×C₂₃	1	1	yes	characteristic
669	#418	C₂²×C₂₃	1	1	yes	characteristic
670	#418	C₂²×C₂₃	1	1	yes	characteristic
671	#417	C₂²×C₂₃	1	1	yes	characteristic
672	#416	C₂²×C₂₃	1	1	yes	characteristic
673	#416	C₂²×C₂₃	1	1	yes	characteristic
674	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
675	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
676	#405	C₂²×C₂₃	1	1	yes	characteristic
677	#405	C₂²×C₂₃	1	1	yes	characteristic
678	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
679	C₂×C₂₃	—	2	2	no	—
680	C₂×C₂₃	—	8	1	no	—
681	C₂×C₂₃	—	8	2	no	—
682	C₂×C₂₃	C₂×#548	1	1	yes	characteristic
683	C₂×C₂₃	#3584	1	1	yes	characteristic
684	C₂×C₂₃	#3586	1	1	yes	characteristic
685	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
686	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
687	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
688	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
689	#137	—	2	4	no	—
690	C₂×Q₁₆	—	2	4	no	—
691	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
692	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
693	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
694	C₂×SD₁₆	—	2	4	no	—
695	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
696	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
697	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
698	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
699	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
700	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
701	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
702	C₄⋊Q₈	—	2	2	no	—
703	C₄⋊Q₈	—	2	2	no	—
704	C₄⋊Q₈	—	2	2	no	—
705	C₄⋊Q₈	—	2	2	no	—
706	C₄⋊Q₈	—	2	2	no	—
707	C₄⋊Q₈	—	2	2	no	—
708	C₄⋊Q₈	—	2	1	no	—
709	C₄⋊Q₈	—	2	1	no	—
710	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
711	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
712	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
713	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
714	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
716	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
717	#127	C₂³×C₂₃	1	2	yes	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	1	no	—
729	#125	—	2	1	no	—
730	#125	D₄×C₂₃	1	1	yes	characteristic
731	#125	D₄×C₂₃	1	1	yes	characteristic
732	#125	C₂³×C₂₃	1	1	yes	characteristic
733	#125	C₂³×C₂₃	1	1	yes	characteristic
734	#125	C₂³×C₂₃	1	2	yes	—
735	#125	C₂³×C₂₃	1	2	yes	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	—	2	1	no	—
739	#124	—	2	1	no	—
740	#124	C₂³×C₂₃	1	2	yes	—
741	#124	C₂³×C₂₃	1	2	yes	—
742	#124	C₂³×C₂₃	1	2	yes	—
743	#124	C₂³×C₂₃	1	2	yes	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
758	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
759	#121	—	2	1	no	—
760	#121	—	2	1	no	—
761	#120	—	2	2	no	—
762	C₄×Q₈	—	2	2	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	—	2	2	no	—
771	C₄×Q₈	—	2	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
777	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
778	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
781	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
782	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
783	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
784	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
785	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
786	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
787	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₂₃	1	2	yes	—
797	C₄×D₄	C₂³×C₂₃	1	2	yes	—
798	#117	—	2	2	no	—
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	2	2	no	—
803	#117	—	2	1	no	—
804	#117	C₂³×C₂₃	1	1	yes	characteristic
805	#117	C₂³×C₂₃	1	1	yes	characteristic
806	#117	C₂³×C₂₃	1	1	yes	characteristic
807	#117	C₂³×C₂₃	1	1	yes	characteristic
808	#117	C₂³×C₂₃	1	1	yes	characteristic
809	C₂×C₄⋊C₄	—	2	1	no	—
810	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
811	C₂×C₂²⋊C₄	—	2	1	no	—
812	C₂×C₂²⋊C₄	—	2	1	no	—
813	C₂×C₂²⋊C₄	—	2	2	no	—
814	C₂×C₄²	—	2	1	no	—
815	C₂×C₄²	—	2	1	no	—
816	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
817	#107	C₂³×C₂₃	1	1	yes	characteristic
818	#107	C₂³×C₂₃	1	1	yes	characteristic
819	#107	C₂³×C₂₃	1	1	yes	characteristic
820	#107	C₂³×C₂₃	1	1	yes	characteristic
821	#107	C₂³×C₂₃	1	2	yes	—
822	#106	C₂³×C₂₃	1	1	yes	characteristic
823	#106	C₂³×C₂₃	1	1	yes	characteristic
824	#106	C₂³×C₂₃	1	1	yes	characteristic
825	#106	C₂³×C₂₃	1	1	yes	characteristic
826	#106	C₂³×C₂₃	1	2	yes	—
827	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
832	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
833	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
834	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
835	#103	C₂³×C₂₃	1	2	yes	—
836	#103	C₂³×C₂₃	1	2	yes	—
837	#103	C₂³×C₂₃	1	1	yes	characteristic
838	#103	C₂³×C₂₃	1	1	yes	characteristic
839	#103	C₂³×C₂₃	1	1	yes	characteristic
840	#103	C₂³×C₂₃	1	1	yes	characteristic
841	#103	C₂³×C₂₃	1	2	yes	—
842	#103	C₂³×C₂₃	1	2	yes	—
843	#103	C₂³×C₂₃	1	2	yes	—
844	#103	C₂³×C₂₃	1	2	yes	—
845	#103	C₂³×C₂₃	1	2	yes	—
846	#103	C₂³×C₂₃	1	2	yes	—
847	#103	C₂³×C₂₃	1	2	yes	—
848	#102	C₂³×C₂₃	1	2	yes	—
849	#102	C₂³×C₂₃	1	2	yes	—
850	#102	C₂³×C₂₃	1	1	yes	characteristic
851	#102	C₂³×C₂₃	1	1	yes	characteristic
852	#102	C₂³×C₂₃	1	1	yes	characteristic
853	#102	C₂³×C₂₃	1	1	yes	characteristic
854	#102	C₂³×C₂₃	1	2	yes	—
855	#102	C₂³×C₂₃	1	2	yes	—
856	#102	C₂³×C₂₃	1	2	yes	—
857	#102	C₂³×C₂₃	1	2	yes	—
858	#102	C₂³×C₂₃	1	2	yes	—
859	#97	C₂³×C₂₃	1	2	yes	—
860	#97	C₂³×C₂₃	1	2	yes	—
861	#97	C₂³×C₂₃	1	2	yes	—
862	C₄×C₈	C₂³×C₂₃	1	2	yes	—
863	C₄×C₈	C₂³×C₂₃	1	2	yes	—
864	C₄×C₈	C₂³×C₂₃	1	2	yes	—
865	C₂₃	#61344	1	1	yes	characteristic, direct product factor, Sylow
866	C₂⁴	—	2	1	no	—
867	#41	—	2	2	no	—
868	#41	—	2	2	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	2	2	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
879	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
880	C₂×Q₈	#41×C₂₃	1	4	yes	—
881	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
882	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
891	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
901	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
903	Q₁₆	—	2	4	no	—
904	Q₁₆	—	2	4	no	—
905	Q₁₆	—	2	4	no	—
906	SD₁₆	—	2	4	no	—
907	SD₁₆	—	2	4	no	—
908	SD₁₆	—	2	4	no	—
909	M₁₆	—	2	2	no	—
910	M₁₆	—	2	2	no	—
911	C₂×C₈	—	2	2	no	—
912	C₂×C₈	—	2	2	no	—
913	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
914	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
917	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
918	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
949	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
951	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
952	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
953	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
955	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
956	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
960	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
977	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	1	no	—
991	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
992	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
993	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
994	C₄²	C₂⁴×C₂₃	1	2	yes	—
995	C₄²	C₂⁴×C₂₃	1	2	yes	—
996	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
997	C₂³	—	2	2	no	—
998	C₂³	—	2	1	no	—
999	C₂³	—	4	2	no	—
1000	C₂³	—	8	1	no	—
1001	C₂³	—	8	1	no	—
1002	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1003	Q₈	—	2	4	no	—
1004	Q₈	—	2	2	no	—
1005	Q₈	—	2	2	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	4	2	no	—
1010	Q₈	—	4	2	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	4	2	no	—
1013	Q₈	—	8	1	no	—
1014	Q₈	—	8	2	no	—
1015	Q₈	—	8	2	no	—
1016	Q₈	C₂×#41×C₂₃	1	4	yes	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	1	no	—
1019	D₄	—	2	2	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	4	2	no	—
1023	D₄	—	8	2	no	—
1024	D₄	—	8	2	no	—
1025	C₂×C₄	—	2	4	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	4	1	no	—
1037	C₂×C₄	—	4	1	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	8	1	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	—	8	1	no	—
1043	C₂×C₄	—	8	2	no	—
1044	C₂×C₄	—	8	1	no	—
1045	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1049	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1051	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1052	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1054	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1055	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1056	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	1	no	—
1061	C₈	—	2	2	no	—
1062	C₈	—	2	2	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	16	2	no	—
1072	C₂²	C₂₃×#548	1	2	yes	—
1073	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1074	C₄	—	2	4	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	2	1	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	2	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	1	no	—
1092	C₄	C₂₃×#548	1	2	yes	—
1093	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1094	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1095	C₂	—	2	2	no	—
1096	C₂	—	8	2	no	—
1097	C₂	—	8	1	no	—
1098	C₂	C₂×C₂₃×#548	1	1	yes	characteristic
1099	C₂	C₂₃×#3584	1	1	yes	characteristic
1100	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#535	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3502	C₂	semidirect
3. C₂₃×#3377	C₂	semidirect
4. C₂₃×#3377	C₂	semidirect
5. C₂₃×#3375	C₂	semidirect
6. C₂₃×#3371	C₂	semidirect
7. C₂₃×#3371	C₂	semidirect
8. C₂₃×#3369	C₂	semidirect
9. C₂₃×#3365	C₂	semidirect
10. C₂₃×#3364	C₂	semidirect
11. C₂₃×#3140	C₂	semidirect
12. C₂₃×#3137	C₂	semidirect
14. C₂₃×#3082	C₂	semidirect
15. C₂₃×#3081	C₂	semidirect
16. C₂₃×#3076	C₂	semidirect
17. C₂₃×#3044	C₂	semidirect
19. C₂×C₂₃×#464	C₂	semidirect
20. C₂₃×#2962	C₂	semidirect
21. C₂₃×#2950	C₂	semidirect
22. C₂₃×#2949	C₂	semidirect
23. C₄×C₂₃×#137	C₂	semidirect
30. Q₈²×C₂₃	C₂²	semidirect
34. C₂₃×#557	C₂²	semidirect
35. C₂₃×#557	C₂²	semidirect
36. C₂₃×#557	C₂²	semidirect
60. C₂₃×#491	C₂²	semidirect
65. C₂₃×#489	C₂²	semidirect
69. C₂₃×#488	C₂²	semidirect
70. C₂₃×#487	C₂²	semidirect
72. C₂₃×#479	C₂²	semidirect
73. C₂₃×#479	C₂²	semidirect
74. C₂₃×#479	C₂²	semidirect
75. C₂₃×#479	C₂²	semidirect
78. C₂₃×#478	C₂²	semidirect
79. C₂₃×#478	C₂²	semidirect
80. C₂₃×#477	C₂²	semidirect
81. C₂₃×#477	C₂²	semidirect
83. C₂₃×#476	C₂²	semidirect
84. C₂₃×#475	C₂²	semidirect
85. C₂₃×#475	C₂²	semidirect
87. C₂₃×#474	C₂²	semidirect
94. C₂₃×#464	C₂²	semidirect
95. C₂₃×#464	C₂²	semidirect
96. C₂₃×#462	C₂²	semidirect
97. C₂₃×#462	C₂²	semidirect
100. C₂₃×#446	C₂²	semidirect
101. C₂₃×#446	C₂²	semidirect
102. C₂₃×#446	C₂²	semidirect
103. C₈×Q₈×C₂₃	C₂²	semidirect
104. C₂₃×#441	C₂²	semidirect
105. C₂₃×#441	C₂²	semidirect
106. C₂₃×#441	C₂²	semidirect
109. C₂₃×#440	C₂²	semidirect
110. C₄×Q₁₆×C₂₃	C₂²	semidirect
111. C₄×Q₁₆×C₂₃	C₂²	semidirect
112. C₄×Q₁₆×C₂₃	C₂²	semidirect
115. C₄×SD₁₆×C₂₃	C₂²	semidirect
446. #61344	C₂₃	direct (N × H)
514. #3502	C₂×C₂₃	semidirect
515. #3377	C₂×C₂₃	semidirect
516. #3377	C₂×C₂₃	semidirect
517. #3375	C₂×C₂₃	semidirect
518. #3371	C₂×C₂₃	semidirect
519. #3371	C₂×C₂₃	semidirect
520. #3369	C₂×C₂₃	semidirect
521. #3365	C₂×C₂₃	semidirect
522. #3364	C₂×C₂₃	semidirect
523. #3140	C₂×C₂₃	semidirect
524. #3137	C₂×C₂₃	semidirect
526. #3082	C₂×C₂₃	semidirect
527. #3081	C₂×C₂₃	semidirect
528. #3076	C₂×C₂₃	semidirect
529. #3044	C₂×C₂₃	semidirect
531. C₂×#464	C₂×C₂₃	semidirect
532. #2962	C₂×C₂₃	semidirect
533. #2950	C₂×C₂₃	semidirect
534. #2949	C₂×C₂₃	semidirect
535. C₄×#137	C₂×C₂₃	semidirect
574. Q₈²	C₂²×C₂₃	semidirect
578. #557	C₂²×C₂₃	semidirect
579. #557	C₂²×C₂₃	semidirect
580. #557	C₂²×C₂₃	semidirect
604. #491	C₂²×C₂₃	semidirect
609. #489	C₂²×C₂₃	semidirect
613. #488	C₂²×C₂₃	semidirect
614. #487	C₂²×C₂₃	semidirect
616. #479	C₂²×C₂₃	semidirect
617. #479	C₂²×C₂₃	semidirect
618. #479	C₂²×C₂₃	semidirect
619. #479	C₂²×C₂₃	semidirect
622. #478	C₂²×C₂₃	semidirect
623. #478	C₂²×C₂₃	semidirect
624. #477	C₂²×C₂₃	semidirect
625. #477	C₂²×C₂₃	semidirect
627. #476	C₂²×C₂₃	semidirect
628. #475	C₂²×C₂₃	semidirect
629. #475	C₂²×C₂₃	semidirect
631. #474	C₂²×C₂₃	semidirect
638. #464	C₂²×C₂₃	semidirect
639. #464	C₂²×C₂₃	semidirect
640. #462	C₂²×C₂₃	semidirect
641. #462	C₂²×C₂₃	semidirect
644. #446	C₂²×C₂₃	semidirect
645. #446	C₂²×C₂₃	semidirect
646. #446	C₂²×C₂₃	semidirect
647. C₈×Q₈	C₂²×C₂₃	semidirect
648. #441	C₂²×C₂₃	semidirect
649. #441	C₂²×C₂₃	semidirect
650. #441	C₂²×C₂₃	semidirect
653. #440	C₂²×C₂₃	semidirect
654. C₄×Q₁₆	C₂²×C₂₃	semidirect
655. C₄×Q₁₆	C₂²×C₂₃	semidirect
656. C₄×Q₁₆	C₂²×C₂₃	semidirect
659. C₄×SD₁₆	C₂²×C₂₃	semidirect
865. C₂₃	#61344	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×#3510	2
C₂₃×#3502	2
C₂₃×#3377	2
C₂₃×#3375	2
C₂₃×#3371	2
C₂₃×#3369	2
C₂₃×#3365	2
C₂₃×#3364	2
C₂₃×#3140	2
C₂₃×#3137	2
C₂₃×#3136	2
C₂₃×#3082	2
C₂₃×#3081	2
C₂₃×#3076	2
C₂₃×#3044	2
C₂₃×#3043	2
C₂×C₂₃×#464	2
C₂₃×#2962	2
C₂₃×#2950	2
C₂₃×#2949	2
C₄×C₂₃×#137	2
#61344	23

Subgroups — C23×#61344 #19208970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61344 #19208970