Subgroups — C₂₃×#60296 #19207922

Order 5888.

1684 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3455	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2995	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2994	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2993	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2992	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2985	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2977	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2976	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2969	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2968	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2967	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2966	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2925	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2924	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#542	C₄	1	2	yes	—
21	C₂₃×#542	C₄	1	2	yes	—
22	C₂₃×#541	C₄	1	2	yes	—
23	C₂₃×#540	C₄	1	2	yes	—
24	C₂₃×#539	C₄	1	2	yes	—
25	C₂₃×#539	C₄	1	2	yes	—
26	C₂₃×#538	C₄	1	2	yes	—
27	C₂₃×#538	C₄	1	2	yes	—
28	C₂₃×#533	C₂²	1	1	yes	characteristic
29	C₂₃×#532	C₂²	1	1	yes	characteristic
30	C₂₃×#529	C₂²	1	2	yes	—
31	C₂₃×#529	C₂²	1	2	yes	—
32	C₂₃×#529	C₂²	1	2	yes	—
33	C₂₃×#529	C₂²	1	2	yes	—
34	C₂₃×#525	C₂²	1	1	yes	characteristic
35	C₂₃×#525	C₂²	1	1	yes	characteristic
36	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
37	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
39	C₂₃×#446	C₂²	1	2	yes	complemented
40	C₂₃×#446	C₂²	1	2	yes	complemented
41	C₂₃×#446	C₂²	1	2	yes	complemented
42	C₂₃×#446	C₂²	1	2	yes	complemented
43	C₂₃×#446	C₂²	1	2	yes	complemented
44	C₂₃×#446	C₂²	1	2	yes	complemented
45	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
46	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
47	C₂₃×#436	C₂²	1	2	yes	—
48	C₂₃×#436	C₂²	1	2	yes	—
49	C₂₃×#436	C₂²	1	2	yes	—
50	C₂₃×#436	C₂²	1	2	yes	—
51	C₂₃×#436	C₂²	1	2	yes	complemented
52	C₂₃×#436	C₂²	1	2	yes	complemented
53	C₂₃×#435	C₂²	1	2	yes	—
54	C₂₃×#435	C₂²	1	2	yes	—
55	C₂₃×#435	C₂²	1	2	yes	—
56	C₂₃×#435	C₂²	1	2	yes	—
57	C₂₃×#435	C₂²	1	2	yes	—
58	C₂₃×#435	C₂²	1	2	yes	—
59	C₂₃×#435	C₂²	1	2	yes	—
60	C₂₃×#435	C₂²	1	2	yes	—
61	C₂₃×#435	C₂²	1	2	yes	complemented
62	C₂₃×#435	C₂²	1	2	yes	complemented
63	C₂₃×#435	C₂²	1	2	yes	complemented
64	C₂₃×#435	C₂²	1	2	yes	complemented
65	C₈×D₄×C₂₃	C₂²	1	2	yes	—
66	C₈×D₄×C₂₃	C₂²	1	2	yes	—
67	C₈×D₄×C₂₃	C₂²	1	2	yes	—
68	C₈×D₄×C₂₃	C₂²	1	2	yes	—
69	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
70	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
71	C₂₃×#433	C₂²	1	2	yes	—
72	C₂₃×#433	C₂²	1	2	yes	—
73	C₂₃×#433	C₂²	1	2	yes	—
74	C₂₃×#433	C₂²	1	2	yes	—
75	C₂₃×#433	C₂²	1	2	yes	—
76	C₂₃×#433	C₂²	1	2	yes	—
77	C₂₃×#433	C₂²	1	2	yes	—
78	C₂₃×#433	C₂²	1	2	yes	—
79	C₂₃×#433	C₂²	1	2	yes	complemented
80	C₂₃×#433	C₂²	1	2	yes	complemented
81	C₂₃×#433	C₂²	1	2	yes	complemented
82	C₂₃×#433	C₂²	1	2	yes	complemented
83	C₂₃×#432	C₂²	1	2	yes	—
84	C₂₃×#432	C₂²	1	2	yes	—
85	C₂₃×#432	C₂²	1	2	yes	complemented
86	C₂₃×#432	C₂²	1	2	yes	complemented
87	C₂₃×#431	C₂²	1	2	yes	—
88	C₂₃×#431	C₂²	1	2	yes	—
89	C₂₃×#431	C₂²	1	2	yes	complemented
90	C₂₃×#431	C₂²	1	2	yes	complemented
91	C₂₃×#424	C₂²	1	2	yes	—
92	C₂₃×#424	C₂²	1	2	yes	—
93	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
96	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
97	C₂₃×#423	C₂²	1	2	yes	complemented
98	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
99	C₂₃×#408	C₂²	1	1	yes	characteristic
100	C₂₃×#408	C₂²	1	1	yes	characteristic
101	C₂₃×#408	C₂²	1	1	yes	characteristic
102	C₂₃×#408	C₂²	1	1	yes	characteristic
103	C₂₃×#408	C₂²	1	2	yes	—
104	C₂₃×#408	C₂²	1	2	yes	—
105	C₂₃×#407	C₂²	1	2	yes	—
106	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
107	C₂₃×#405	C₂²	1	2	yes	—
108	C₂₃×#405	C₂²	1	2	yes	—
109	C₂₃×#405	C₂²	1	2	yes	complemented
110	C₂₃×#405	C₂²	1	2	yes	complemented
111	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
121	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
122	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
124	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
125	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
126	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
131	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
132	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
133	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
134	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
135	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
136	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
137	C₂₃×#126	C₂×C₄	1	2	yes	—
138	C₂₃×#126	C₂×C₄	1	2	yes	—
139	C₂₃×#126	C₂×C₄	1	2	yes	—
140	C₂₃×#126	C₂×C₄	1	2	yes	—
141	C₂₃×#126	C₂×C₄	1	2	yes	—
142	C₂₃×#126	C₂×C₄	1	2	yes	—
143	C₂₃×#126	C₂×C₄	1	2	yes	—
144	C₂₃×#126	C₂×C₄	1	2	yes	—
145	C₂₃×#125	C₂×C₄	1	2	yes	—
146	C₂₃×#125	C₂×C₄	1	2	yes	—
147	C₂₃×#125	C₂×C₄	1	2	yes	—
148	C₂₃×#125	C₂×C₄	1	2	yes	—
149	C₂₃×#125	C₂×C₄	1	2	yes	—
150	C₂₃×#124	C₂×C₄	1	2	yes	—
151	C₂₃×#124	C₂×C₄	1	2	yes	—
152	C₂₃×#124	C₂×C₄	1	2	yes	—
153	C₂₃×#124	C₂×C₄	1	2	yes	—
154	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
155	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
156	C₂₃×#123	C₂×C₄	1	2	yes	—
157	C₂₃×#123	C₂×C₄	1	1	yes	characteristic
158	C₂₃×#123	C₂×C₄	1	1	yes	characteristic
159	C₂₃×#123	C₂×C₄	1	2	yes	—
160	C₂₃×#123	C₂×C₄	1	2	yes	—
161	C₂₃×#123	C₂×C₄	1	2	yes	—
162	C₂₃×#123	C₂×C₄	1	2	yes	—
163	C₂₃×#123	C₂×C₄	1	2	yes	—
164	C₂₃×#123	C₂×C₄	1	2	yes	—
165	C₂₃×#123	C₂×C₄	1	2	yes	—
166	C₂₃×#123	C₂×C₄	1	2	yes	—
167	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
168	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
169	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
170	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
171	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
172	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
173	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
174	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
175	C₂₃×#121	C₂×C₄	1	2	yes	—
176	C₂₃×#121	C₂×C₄	1	2	yes	—
177	C₂₃×#121	C₂×C₄	1	2	yes	—
178	C₂₃×#121	C₂×C₄	1	2	yes	—
179	C₂₃×#121	C₂×C₄	1	2	yes	—
180	C₂₃×#121	C₂×C₄	1	2	yes	—
181	C₂₃×#121	C₂×C₄	1	2	yes	—
182	C₂₃×#121	C₂×C₄	1	2	yes	—
183	C₂₃×#120	C₂×C₄	1	2	yes	—
184	C₂₃×#120	C₂×C₄	1	1	yes	characteristic
185	C₂₃×#120	C₂×C₄	1	1	yes	characteristic
186	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
187	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
188	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
189	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
190	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
191	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
192	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
193	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
194	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
195	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
196	C₄×D₄×C₂₃	C₂³	1	2	yes	—
197	C₄×D₄×C₂₃	C₂³	1	2	yes	—
198	C₄×D₄×C₂₃	C₂³	1	2	yes	—
199	C₄×D₄×C₂₃	C₂³	1	2	yes	—
200	C₄×D₄×C₂₃	C₂³	1	2	yes	—
201	C₄×D₄×C₂₃	C₂³	1	2	yes	—
202	C₂₃×#117	C₂×C₄	1	2	yes	—
203	C₂₃×#117	C₂×C₄	1	2	yes	—
204	C₂₃×#117	C₂³	1	2	yes	—
205	C₂₃×#117	C₂³	1	2	yes	—
206	C₂₃×#117	C₂³	1	2	yes	—
207	C₂₃×#117	C₂³	1	1	yes	characteristic
208	C₂₃×#117	C₂³	1	1	yes	characteristic
209	C₂₃×#117	C₂³	1	1	yes	characteristic
210	C₂₃×#117	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
212	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
213	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
216	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
218	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
219	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
220	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
221	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
222	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
223	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
224	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
225	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
226	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
227	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
228	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
229	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
230	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
231	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
232	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
233	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
234	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
235	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
236	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
237	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
238	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
239	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
240	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
241	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
242	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
243	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
244	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
245	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
246	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
249	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
250	C₂₃×#97	C₂³	1	2	yes	—
251	C₂₃×#97	C₂³	1	2	yes	—
252	C₂₃×#97	C₂³	1	2	yes	—
253	C₂₃×#97	C₂³	1	2	yes	—
254	C₂₃×#97	C₂³	1	2	yes	—
255	C₂₃×#97	C₂³	1	2	yes	—
256	C₂₃×#97	C₂³	1	2	yes	—
257	C₂₃×#97	C₂³	1	2	yes	—
258	C₄×C₈×C₂₃	C₂³	1	2	yes	—
259	C₄×C₈×C₂₃	C₂³	1	2	yes	—
260	C₄×C₈×C₂₃	C₂³	1	2	yes	—
261	C₄×C₈×C₂₃	C₂³	1	2	yes	—
262	C₄×C₈×C₂₃	C₂³	1	2	yes	—
263	C₄×C₈×C₂₃	C₂³	1	2	yes	—
264	C₄×C₈×C₂₃	C₂³	1	2	yes	—
265	C₄×C₈×C₂₃	C₂³	1	2	yes	—
266	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
267	#41×C₂₃	—	4	1	no	—
268	#41×C₂₃	—	4	1	no	—
269	#41×C₂₃	—	4	1	no	—
270	#41×C₂₃	—	4	1	no	—
271	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
272	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
273	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
274	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
275	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
276	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
277	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
278	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
279	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
280	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
281	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
282	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
283	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
284	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
285	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
286	C₂²×C₄×C₂₃	—	4	1	no	—
287	C₂²×C₄×C₂₃	—	4	1	no	—
288	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
289	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
290	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
291	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
292	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
293	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
294	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
295	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
296	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
301	M₁₆×C₂₃	—	4	1	no	—
302	M₁₆×C₂₃	—	4	2	no	—
303	M₁₆×C₂₃	—	4	2	no	—
304	M₁₆×C₂₃	—	4	1	no	—
305	M₁₆×C₂₃	—	4	1	no	—
306	M₁₆×C₂₃	—	4	2	no	—
307	M₁₆×C₂₃	—	4	2	no	—
308	M₁₆×C₂₃	—	4	1	no	—
309	C₂×C₈×C₂₃	—	4	1	no	—
310	C₂×C₈×C₂₃	—	4	2	no	—
311	C₂×C₈×C₂₃	—	4	2	no	—
312	C₂×C₈×C₂₃	—	4	1	no	—
313	C₂×C₈×C₂₃	—	4	1	no	—
314	C₂×C₈×C₂₃	—	4	2	no	—
315	C₂×C₈×C₂₃	—	4	2	no	—
316	C₂×C₈×C₂₃	—	4	1	no	—
317	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
318	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
319	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
320	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
321	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
322	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
323	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
324	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
325	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
326	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
327	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
328	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
329	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
330	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
331	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
332	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
333	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
334	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
335	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
336	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
337	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
338	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
339	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
340	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
341	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
342	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
343	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
344	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
345	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
346	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
347	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
348	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
349	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
350	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
351	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
352	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
353	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
354	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
355	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
356	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
357	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
358	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
359	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
360	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
361	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
362	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
363	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
364	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
365	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
366	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
367	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
368	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
369	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
370	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
371	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
372	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
373	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
374	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
375	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
376	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
377	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
378	C₄²×C₂₃	C₂⁴	1	2	yes	—
379	C₄²×C₂₃	C₂⁴	1	2	yes	—
380	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
381	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
382	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
383	#60296	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₂³×C₂₃	—	4	1	no	—
385	C₂³×C₂₃	—	4	2	no	—
386	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
387	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
388	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
389	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
390	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
391	Q₈×C₂₃	—	4	2	no	—
392	Q₈×C₂₃	—	4	2	no	—
393	Q₈×C₂₃	—	4	1	no	—
394	Q₈×C₂₃	—	4	1	no	—
395	D₄×C₂₃	—	4	2	no	—
396	D₄×C₂₃	—	4	2	no	—
397	D₄×C₂₃	—	4	2	no	—
398	D₄×C₂₃	—	4	2	no	—
399	D₄×C₂₃	—	4	2	no	—
400	D₄×C₂₃	—	4	2	no	—
401	D₄×C₂₃	—	4	1	no	—
402	D₄×C₂₃	—	4	1	no	—
403	D₄×C₂₃	—	4	2	no	—
404	D₄×C₂₃	—	4	1	no	—
405	D₄×C₂₃	—	4	1	no	—
406	C₂×C₄×C₂₃	—	2	2	no	—
407	C₂×C₄×C₂₃	—	2	2	no	—
408	C₂×C₄×C₂₃	—	2	2	no	—
409	C₂×C₄×C₂₃	—	2	1	no	—
410	C₂×C₄×C₂₃	—	2	1	no	—
411	C₂×C₄×C₂₃	—	2	1	no	—
412	C₂×C₄×C₂₃	—	2	1	no	—
413	C₂×C₄×C₂₃	—	2	2	no	—
414	C₂×C₄×C₂₃	—	2	1	no	—
415	C₂×C₄×C₂₃	—	2	1	no	—
416	C₂×C₄×C₂₃	—	4	1	no	—
417	C₂×C₄×C₂₃	—	4	2	no	—
418	C₂×C₄×C₂₃	—	4	2	no	—
419	C₂×C₄×C₂₃	—	4	2	no	—
420	C₂×C₄×C₂₃	—	4	2	no	—
421	C₂×C₄×C₂₃	—	4	2	no	—
422	C₂×C₄×C₂₃	—	4	2	no	—
423	C₂×C₄×C₂₃	—	4	2	no	—
424	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
425	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
426	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
427	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
428	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
429	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
430	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
431	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
432	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
433	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
434	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
435	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
436	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
437	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
438	C₈×C₂₃	—	2	2	no	—
439	C₈×C₂₃	—	2	2	no	—
440	C₈×C₂₃	—	2	2	no	—
441	C₈×C₂₃	—	2	2	no	—
442	C₈×C₂₃	—	2	2	no	—
443	C₈×C₂₃	—	2	2	no	—
444	C₈×C₂₃	—	2	2	no	—
445	C₈×C₂₃	—	2	2	no	—
446	#3455	C₂×C₂₃	1	1	yes	characteristic
447	#2995	C₂×C₂₃	1	2	yes	complemented
448	#2994	C₂×C₂₃	1	2	yes	complemented
449	#2993	C₂×C₂₃	1	2	yes	complemented
450	#2992	C₂×C₂₃	1	2	yes	complemented
451	#2985	C₂×C₂₃	1	2	yes	complemented
452	#2980	C₂×C₂₃	1	1	yes	characteristic, complemented
453	#2979	C₂×C₂₃	1	1	yes	characteristic, complemented
454	#2978	C₂×C₂₃	1	1	yes	characteristic, complemented
455	#2977	C₂×C₂₃	1	1	yes	characteristic, complemented
456	#2976	C₂×C₂₃	1	2	yes	complemented
457	#2969	C₂×C₂₃	1	2	yes	complemented
458	#2968	C₂×C₂₃	1	2	yes	complemented
459	#2967	C₂×C₂₃	1	2	yes	complemented
460	#2966	C₂×C₂₃	1	2	yes	complemented
461	#2925	C₂×C₂₃	1	2	yes	complemented
462	#2924	C₂×C₂₃	1	2	yes	complemented
463	#2923	C₂×C₂₃	1	1	yes	characteristic, complemented
464	#2922	C₂×C₂₃	1	1	yes	characteristic, complemented
465	C₂²×C₂₃	—	2	1	no	—
466	C₂²×C₂₃	—	2	2	no	—
467	C₂²×C₂₃	—	2	2	no	—
468	C₂²×C₂₃	—	2	1	no	—
469	C₂²×C₂₃	—	2	1	no	—
470	C₂²×C₂₃	—	2	2	no	—
471	C₂²×C₂₃	—	2	2	no	—
472	C₂²×C₂₃	—	2	2	no	—
473	C₂²×C₂₃	—	2	2	no	—
474	C₂²×C₂₃	—	2	2	no	—
475	C₂²×C₂₃	—	2	2	no	—
476	C₂²×C₂₃	—	2	2	no	—
477	C₂²×C₂₃	—	8	2	no	—
478	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
479	C₄×C₂₃	—	2	2	no	—
480	C₄×C₂₃	—	2	1	no	—
481	C₄×C₂₃	—	2	2	no	—
482	C₄×C₂₃	—	2	1	no	—
483	C₄×C₂₃	—	2	1	no	—
484	C₄×C₂₃	—	2	2	no	—
485	C₄×C₂₃	—	2	2	no	—
486	C₄×C₂₃	—	2	2	no	—
487	C₄×C₂₃	—	2	2	no	—
488	C₄×C₂₃	—	2	2	no	—
489	C₄×C₂₃	—	2	2	no	—
490	C₄×C₂₃	—	2	2	no	—
491	C₄×C₂₃	—	2	2	no	—
492	C₄×C₂₃	#585	1	1	yes	characteristic
493	C₄×C₂₃	#585	1	1	yes	characteristic
494	#542	C₄×C₂₃	1	2	yes	—
495	#542	C₄×C₂₃	1	2	yes	—
496	#541	C₄×C₂₃	1	2	yes	—
497	#540	C₄×C₂₃	1	2	yes	—
498	#539	C₄×C₂₃	1	2	yes	—
499	#539	C₄×C₂₃	1	2	yes	—
500	#538	C₄×C₂₃	1	2	yes	—
501	#538	C₄×C₂₃	1	2	yes	—
502	#533	C₂²×C₂₃	1	1	yes	characteristic
503	#532	C₂²×C₂₃	1	1	yes	characteristic
504	#529	C₂²×C₂₃	1	2	yes	—
505	#529	C₂²×C₂₃	1	2	yes	—
506	#529	C₂²×C₂₃	1	2	yes	—
507	#529	C₂²×C₂₃	1	2	yes	—
508	#525	C₂²×C₂₃	1	1	yes	characteristic
509	#525	C₂²×C₂₃	1	1	yes	characteristic
510	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
511	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
512	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
513	#446	C₂²×C₂₃	1	2	yes	complemented
514	#446	C₂²×C₂₃	1	2	yes	complemented
515	#446	C₂²×C₂₃	1	2	yes	complemented
516	#446	C₂²×C₂₃	1	2	yes	complemented
517	#446	C₂²×C₂₃	1	2	yes	complemented
518	#446	C₂²×C₂₃	1	2	yes	complemented
519	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
520	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
521	#436	C₂²×C₂₃	1	2	yes	—
522	#436	C₂²×C₂₃	1	2	yes	—
523	#436	C₂²×C₂₃	1	2	yes	—
524	#436	C₂²×C₂₃	1	2	yes	—
525	#436	C₂²×C₂₃	1	2	yes	complemented
526	#436	C₂²×C₂₃	1	2	yes	complemented
527	#435	C₂²×C₂₃	1	2	yes	—
528	#435	C₂²×C₂₃	1	2	yes	—
529	#435	C₂²×C₂₃	1	2	yes	—
530	#435	C₂²×C₂₃	1	2	yes	—
531	#435	C₂²×C₂₃	1	2	yes	—
532	#435	C₂²×C₂₃	1	2	yes	—
533	#435	C₂²×C₂₃	1	2	yes	—
534	#435	C₂²×C₂₃	1	2	yes	—
535	#435	C₂²×C₂₃	1	2	yes	complemented
536	#435	C₂²×C₂₃	1	2	yes	complemented
537	#435	C₂²×C₂₃	1	2	yes	complemented
538	#435	C₂²×C₂₃	1	2	yes	complemented
539	C₈×D₄	C₂²×C₂₃	1	2	yes	—
540	C₈×D₄	C₂²×C₂₃	1	2	yes	—
541	C₈×D₄	C₂²×C₂₃	1	2	yes	—
542	C₈×D₄	C₂²×C₂₃	1	2	yes	—
543	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
544	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
545	#433	C₂²×C₂₃	1	2	yes	—
546	#433	C₂²×C₂₃	1	2	yes	—
547	#433	C₂²×C₂₃	1	2	yes	—
548	#433	C₂²×C₂₃	1	2	yes	—
549	#433	C₂²×C₂₃	1	2	yes	—
550	#433	C₂²×C₂₃	1	2	yes	—
551	#433	C₂²×C₂₃	1	2	yes	—
552	#433	C₂²×C₂₃	1	2	yes	—
553	#433	C₂²×C₂₃	1	2	yes	complemented
554	#433	C₂²×C₂₃	1	2	yes	complemented
555	#433	C₂²×C₂₃	1	2	yes	complemented
556	#433	C₂²×C₂₃	1	2	yes	complemented
557	#432	C₂²×C₂₃	1	2	yes	—
558	#432	C₂²×C₂₃	1	2	yes	—
559	#432	C₂²×C₂₃	1	2	yes	complemented
560	#432	C₂²×C₂₃	1	2	yes	complemented
561	#431	C₂²×C₂₃	1	2	yes	—
562	#431	C₂²×C₂₃	1	2	yes	—
563	#431	C₂²×C₂₃	1	2	yes	complemented
564	#431	C₂²×C₂₃	1	2	yes	complemented
565	#424	C₂²×C₂₃	1	2	yes	—
566	#424	C₂²×C₂₃	1	2	yes	—
567	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
568	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
569	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
570	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
571	#423	C₂²×C₂₃	1	2	yes	complemented
572	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
573	#408	C₂²×C₂₃	1	1	yes	characteristic
574	#408	C₂²×C₂₃	1	1	yes	characteristic
575	#408	C₂²×C₂₃	1	1	yes	characteristic
576	#408	C₂²×C₂₃	1	1	yes	characteristic
577	#408	C₂²×C₂₃	1	2	yes	—
578	#408	C₂²×C₂₃	1	2	yes	—
579	#407	C₂²×C₂₃	1	2	yes	—
580	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
581	#405	C₂²×C₂₃	1	2	yes	—
582	#405	C₂²×C₂₃	1	2	yes	—
583	#405	C₂²×C₂₃	1	2	yes	complemented
584	#405	C₂²×C₂₃	1	2	yes	complemented
585	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
586	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
587	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
588	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
589	C₂×C₂₃	—	4	2	no	—
590	C₂×C₂₃	—	4	1	no	—
591	C₂×C₂₃	—	4	1	no	—
592	C₂×C₂₃	—	4	1	no	—
593	C₂×C₂₃	—	4	2	no	—
594	C₂×C₂₃	#3428	1	1	yes	characteristic
595	C₂×C₂₃	#3573	1	2	yes	—
596	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
597	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
598	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
599	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
600	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
601	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
602	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
603	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
604	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
605	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
606	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
607	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
608	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
609	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
610	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
611	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
612	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
613	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
614	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
615	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
616	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
617	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
618	#126	C₂×C₄×C₂₃	1	2	yes	—
619	#126	C₂×C₄×C₂₃	1	2	yes	—
620	#126	C₂×C₄×C₂₃	1	2	yes	—
621	#126	C₂×C₄×C₂₃	1	2	yes	—
622	#126	C₂×C₄×C₂₃	1	2	yes	—
623	#126	C₂×C₄×C₂₃	1	2	yes	—
624	#126	C₂×C₄×C₂₃	1	2	yes	—
625	#126	C₂×C₄×C₂₃	1	2	yes	—
626	#125	C₂×C₄×C₂₃	1	2	yes	—
627	#125	C₂×C₄×C₂₃	1	2	yes	—
628	#125	C₂×C₄×C₂₃	1	2	yes	—
629	#125	C₂×C₄×C₂₃	1	2	yes	—
630	#125	C₂×C₄×C₂₃	1	2	yes	—
631	#124	C₂×C₄×C₂₃	1	2	yes	—
632	#124	C₂×C₄×C₂₃	1	2	yes	—
633	#124	C₂×C₄×C₂₃	1	2	yes	—
634	#124	C₂×C₄×C₂₃	1	2	yes	—
635	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
636	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
637	#123	C₂×C₄×C₂₃	1	2	yes	—
638	#123	C₂×C₄×C₂₃	1	1	yes	characteristic
639	#123	C₂×C₄×C₂₃	1	1	yes	characteristic
640	#123	C₂×C₄×C₂₃	1	2	yes	—
641	#123	C₂×C₄×C₂₃	1	2	yes	—
642	#123	C₂×C₄×C₂₃	1	2	yes	—
643	#123	C₂×C₄×C₂₃	1	2	yes	—
644	#123	C₂×C₄×C₂₃	1	2	yes	—
645	#123	C₂×C₄×C₂₃	1	2	yes	—
646	#123	C₂×C₄×C₂₃	1	2	yes	—
647	#123	C₂×C₄×C₂₃	1	2	yes	—
648	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
649	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
650	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
651	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
652	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
653	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
654	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
655	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
656	#121	C₂×C₄×C₂₃	1	2	yes	—
657	#121	C₂×C₄×C₂₃	1	2	yes	—
658	#121	C₂×C₄×C₂₃	1	2	yes	—
659	#121	C₂×C₄×C₂₃	1	2	yes	—
660	#121	C₂×C₄×C₂₃	1	2	yes	—
661	#121	C₂×C₄×C₂₃	1	2	yes	—
662	#121	C₂×C₄×C₂₃	1	2	yes	—
663	#121	C₂×C₄×C₂₃	1	2	yes	—
664	#120	C₂×C₄×C₂₃	1	2	yes	—
665	#120	C₂×C₄×C₂₃	1	1	yes	characteristic
666	#120	C₂×C₄×C₂₃	1	1	yes	characteristic
667	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
668	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
669	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
670	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
671	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
672	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
673	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
674	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
675	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
676	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
677	C₄×D₄	C₂³×C₂₃	1	2	yes	—
678	C₄×D₄	C₂³×C₂₃	1	2	yes	—
679	C₄×D₄	C₂³×C₂₃	1	2	yes	—
680	C₄×D₄	C₂³×C₂₃	1	2	yes	—
681	C₄×D₄	C₂³×C₂₃	1	2	yes	—
682	C₄×D₄	C₂³×C₂₃	1	2	yes	—
683	#117	C₂×C₄×C₂₃	1	2	yes	—
684	#117	C₂×C₄×C₂₃	1	2	yes	—
685	#117	C₂³×C₂₃	1	2	yes	—
686	#117	C₂³×C₂₃	1	2	yes	—
687	#117	C₂³×C₂₃	1	1	yes	characteristic
688	#117	C₂³×C₂₃	1	1	yes	characteristic
689	#117	C₂³×C₂₃	1	2	yes	—
690	#117	C₂³×C₂₃	1	1	yes	characteristic
691	#117	C₂³×C₂₃	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
694	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
699	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
700	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
701	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
702	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
703	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
704	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
705	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
706	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
707	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
708	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
709	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
710	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
711	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
712	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
713	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
714	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
715	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
716	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
717	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
718	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
719	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
720	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
721	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
722	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
723	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
724	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
725	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
726	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
727	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
728	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
729	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
730	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
731	#97	C₂³×C₂₃	1	2	yes	—
732	#97	C₂³×C₂₃	1	2	yes	—
733	#97	C₂³×C₂₃	1	2	yes	—
734	#97	C₂³×C₂₃	1	2	yes	—
735	#97	C₂³×C₂₃	1	2	yes	—
736	#97	C₂³×C₂₃	1	2	yes	—
737	#97	C₂³×C₂₃	1	2	yes	—
738	#97	C₂³×C₂₃	1	2	yes	—
739	C₄×C₈	C₂³×C₂₃	1	2	yes	—
740	C₄×C₈	C₂³×C₂₃	1	2	yes	—
741	C₄×C₈	C₂³×C₂₃	1	2	yes	—
742	C₄×C₈	C₂³×C₂₃	1	2	yes	—
743	C₄×C₈	C₂³×C₂₃	1	2	yes	—
744	C₄×C₈	C₂³×C₂₃	1	2	yes	—
745	C₄×C₈	C₂³×C₂₃	1	2	yes	—
746	C₄×C₈	C₂³×C₂₃	1	2	yes	—
747	C₂₃	#60296	1	1	yes	characteristic, direct product factor, Sylow
748	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
749	#41	—	4	1	no	—
750	#41	—	4	1	no	—
751	#41	—	4	1	no	—
752	#41	—	4	1	no	—
753	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
754	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
755	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
756	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
757	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
758	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
759	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
760	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
761	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
762	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
763	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
764	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
765	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
766	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
767	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	1	no	—
770	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
771	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
772	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
773	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
774	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
775	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
776	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
777	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
783	M₁₆	—	4	1	no	—
784	M₁₆	—	4	2	no	—
785	M₁₆	—	4	2	no	—
786	M₁₆	—	4	1	no	—
787	M₁₆	—	4	1	no	—
788	M₁₆	—	4	2	no	—
789	M₁₆	—	4	2	no	—
790	M₁₆	—	4	1	no	—
791	C₂×C₈	—	4	1	no	—
792	C₂×C₈	—	4	2	no	—
793	C₂×C₈	—	4	2	no	—
794	C₂×C₈	—	4	1	no	—
795	C₂×C₈	—	4	1	no	—
796	C₂×C₈	—	4	2	no	—
797	C₂×C₈	—	4	2	no	—
798	C₂×C₈	—	4	1	no	—
799	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
800	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
801	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
802	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
803	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
804	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
805	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
806	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
807	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
808	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
809	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
810	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
811	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
812	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
813	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
814	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
815	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
816	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
817	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
818	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
819	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
820	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
821	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
822	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
823	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
824	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
825	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
826	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
827	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
828	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
829	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
830	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
831	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
832	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
833	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
834	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
835	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
836	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
837	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
838	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
839	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
840	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
841	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
842	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
843	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
844	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
845	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
846	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
847	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
848	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
849	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
850	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
851	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
852	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
853	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
854	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
855	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
856	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
857	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
858	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
859	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
860	C₄²	C₂⁴×C₂₃	1	2	yes	—
861	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
862	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
863	C₄²	C₂⁴×C₂₃	1	2	yes	—
864	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
865	C₂³	—	4	1	no	—
866	C₂³	—	4	2	no	—
867	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
868	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
869	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
870	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
871	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
872	Q₈	—	4	1	no	—
873	Q₈	—	4	1	no	—
874	Q₈	—	4	2	no	—
875	Q₈	—	4	2	no	—
876	D₄	—	4	1	no	—
877	D₄	—	4	1	no	—
878	D₄	—	4	2	no	—
879	D₄	—	4	1	no	—
880	D₄	—	4	1	no	—
881	D₄	—	4	2	no	—
882	D₄	—	4	2	no	—
883	D₄	—	4	2	no	—
884	D₄	—	4	2	no	—
885	D₄	—	4	2	no	—
886	D₄	—	4	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	4	2	no	—
898	C₂×C₄	—	4	1	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	4	2	no	—
902	C₂×C₄	—	4	2	no	—
903	C₂×C₄	—	4	2	no	—
904	C₂×C₄	—	4	2	no	—
905	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
906	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
907	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
908	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
909	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
910	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
911	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
912	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
913	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
914	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
915	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
916	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
917	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
918	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
919	C₈	—	2	2	no	—
920	C₈	—	2	2	no	—
921	C₈	—	2	2	no	—
922	C₈	—	2	2	no	—
923	C₈	—	2	2	no	—
924	C₈	—	2	2	no	—
925	C₈	—	2	2	no	—
926	C₈	—	2	2	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	8	2	no	—
940	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
941	C₄	—	2	1	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	1	no	—
945	C₄	—	2	1	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	2	no	—
954	C₄	C₂₃×#585	1	1	yes	characteristic
955	C₄	C₂₃×#585	1	1	yes	characteristic
956	C₂	—	4	1	no	—
957	C₂	—	4	2	no	—
958	C₂	—	4	2	no	—
959	C₂	—	4	1	no	—
960	C₂	—	4	1	no	—
961	C₂	C₂₃×#3428	1	1	yes	characteristic
962	C₂	C₂₃×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	C₂₃×#3455	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2995	C₂	semidirect
3. C₂₃×#2994	C₂	semidirect
4. C₂₃×#2993	C₂	semidirect
5. C₂₃×#2992	C₂	semidirect
6. C₂₃×#2985	C₂	semidirect
7. C₂₃×#2980	C₂	semidirect
8. C₂₃×#2979	C₂	semidirect
9. C₂₃×#2978	C₂	semidirect
10. C₂₃×#2977	C₂	semidirect
11. C₂₃×#2976	C₂	semidirect
12. C₂₃×#2969	C₂	semidirect
13. C₂₃×#2968	C₂	semidirect
14. C₂₃×#2967	C₂	semidirect
15. C₂₃×#2966	C₂	semidirect
16. C₂₃×#2925	C₂	semidirect
17. C₂₃×#2924	C₂	semidirect
18. C₂₃×#2923	C₂	semidirect
19. C₂₃×#2922	C₂	semidirect
39. C₂₃×#446	C₂²	semidirect
40. C₂₃×#446	C₂²	semidirect
41. C₂₃×#446	C₂²	semidirect
42. C₂₃×#446	C₂²	semidirect
43. C₂₃×#446	C₂²	semidirect
44. C₂₃×#446	C₂²	semidirect
45. C₈×Q₈×C₂₃	C₂²	semidirect
46. C₈×Q₈×C₂₃	C₂²	semidirect
51. C₂₃×#436	C₂²	semidirect
52. C₂₃×#436	C₂²	semidirect
61. C₂₃×#435	C₂²	semidirect
62. C₂₃×#435	C₂²	semidirect
63. C₂₃×#435	C₂²	semidirect
64. C₂₃×#435	C₂²	semidirect
69. C₈×D₄×C₂₃	C₂²	semidirect
70. C₈×D₄×C₂₃	C₂²	semidirect
79. C₂₃×#433	C₂²	semidirect
80. C₂₃×#433	C₂²	semidirect
81. C₂₃×#433	C₂²	semidirect
82. C₂₃×#433	C₂²	semidirect
85. C₂₃×#432	C₂²	semidirect
86. C₂₃×#432	C₂²	semidirect
89. C₂₃×#431	C₂²	semidirect
90. C₂₃×#431	C₂²	semidirect
93. C₂₃×#424	C₂²	semidirect
94. C₂₃×#424	C₂²	semidirect
95. C₂₃×#424	C₂²	semidirect
96. C₂₃×#424	C₂²	semidirect
97. C₂₃×#423	C₂²	semidirect
98. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
109. C₂₃×#405	C₂²	semidirect
110. C₂₃×#405	C₂²	semidirect
111. C₄×M₁₆×C₂₃	C₂²	semidirect
112. C₄×M₁₆×C₂₃	C₂²	semidirect
113. C₂×C₂₃×#97	C₂²	semidirect
114. C₂×C₄×C₈×C₂₃	C₂²	semidirect
383. #60296	C₂₃	direct (N × H)
447. #2995	C₂×C₂₃	semidirect
448. #2994	C₂×C₂₃	semidirect
449. #2993	C₂×C₂₃	semidirect
450. #2992	C₂×C₂₃	semidirect
451. #2985	C₂×C₂₃	semidirect
452. #2980	C₂×C₂₃	semidirect
453. #2979	C₂×C₂₃	semidirect
454. #2978	C₂×C₂₃	semidirect
455. #2977	C₂×C₂₃	semidirect
456. #2976	C₂×C₂₃	semidirect
457. #2969	C₂×C₂₃	semidirect
458. #2968	C₂×C₂₃	semidirect
459. #2967	C₂×C₂₃	semidirect
460. #2966	C₂×C₂₃	semidirect
461. #2925	C₂×C₂₃	semidirect
462. #2924	C₂×C₂₃	semidirect
463. #2923	C₂×C₂₃	semidirect
464. #2922	C₂×C₂₃	semidirect
513. #446	C₂²×C₂₃	semidirect
514. #446	C₂²×C₂₃	semidirect
515. #446	C₂²×C₂₃	semidirect
516. #446	C₂²×C₂₃	semidirect
517. #446	C₂²×C₂₃	semidirect
518. #446	C₂²×C₂₃	semidirect
519. C₈×Q₈	C₂²×C₂₃	semidirect
520. C₈×Q₈	C₂²×C₂₃	semidirect
525. #436	C₂²×C₂₃	semidirect
526. #436	C₂²×C₂₃	semidirect
535. #435	C₂²×C₂₃	semidirect
536. #435	C₂²×C₂₃	semidirect
537. #435	C₂²×C₂₃	semidirect
538. #435	C₂²×C₂₃	semidirect
543. C₈×D₄	C₂²×C₂₃	semidirect
544. C₈×D₄	C₂²×C₂₃	semidirect
553. #433	C₂²×C₂₃	semidirect
554. #433	C₂²×C₂₃	semidirect
555. #433	C₂²×C₂₃	semidirect
556. #433	C₂²×C₂₃	semidirect
559. #432	C₂²×C₂₃	semidirect
560. #432	C₂²×C₂₃	semidirect
563. #431	C₂²×C₂₃	semidirect
564. #431	C₂²×C₂₃	semidirect
567. #424	C₂²×C₂₃	semidirect
568. #424	C₂²×C₂₃	semidirect
569. #424	C₂²×C₂₃	semidirect
570. #424	C₂²×C₂₃	semidirect
571. #423	C₂²×C₂₃	semidirect
572. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
583. #405	C₂²×C₂₃	semidirect
584. #405	C₂²×C₂₃	semidirect
585. C₄×M₁₆	C₂²×C₂₃	semidirect
586. C₄×M₁₆	C₂²×C₂₃	semidirect
587. C₂×#97	C₂²×C₂₃	semidirect
588. C₂×C₄×C₈	C₂²×C₂₃	semidirect
747. C₂₃	#60296	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×#3455	2
C₂₃×#2995	2
C₂₃×#2994	2
C₂₃×#2993	2
C₂₃×#2992	2
C₂₃×#2985	2
C₂₃×#2980	2
C₂₃×#2979	2
C₂₃×#2978	2
C₂₃×#2977	2
C₂₃×#2976	2
C₂₃×#2969	2
C₂₃×#2968	2
C₂₃×#2967	2
C₂₃×#2966	2
C₂₃×#2925	2
C₂₃×#2924	2
C₂₃×#2923	2
C₂₃×#2922	2
#60296	23

Subgroups — C23×#60296 #19207922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60296 #19207922