Subgroups — C₂₃×#61591 #19209217

Order 5888.

2632 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3325	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3318	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3295	C₂	1	2	yes	maximal, complemented
6	D₄×D₈×C₂₃	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3274	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3264	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3192	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3188	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3003	C₂	1	2	yes	maximal, complemented
16	C₂×C₂₃×#447	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₂₃	—	2	1	no	—
19	C₂³×D₄×C₂₃	C₂²	1	2	yes	complemented
20	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
21	C₂²×D₈×C₂₃	C₂²	1	4	yes	complemented
22	C₂₃×#555	C₂²	1	1	yes	characteristic, complemented
23	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#553	—	2	1	no	—
25	C₂₃×#553	C₂²	1	2	yes	complemented
26	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
27	C₂₃×#546	—	2	2	no	—
28	C₂₃×#546	C₂²	1	2	yes	complemented
29	D₄²×C₂₃	—	2	1	no	—
30	D₄²×C₂₃	—	2	1	no	—
31	D₄²×C₂₃	—	2	2	no	—
32	D₄²×C₂₃	—	2	1	no	—
33	D₄²×C₂₃	C₂²	1	2	yes	—
34	D₄²×C₂₃	C₂²	1	4	yes	complemented
35	D₄²×C₂₃	C₂²	1	2	yes	complemented
36	D₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#540	—	2	1	no	—
38	C₂₃×#538	—	2	2	no	—
39	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#529	C₂²	1	1	yes	characteristic, complemented
42	C₂₃×#525	C₂²	1	2	yes	complemented
43	C₂×C₂₃×#121	—	2	1	no	—
44	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
45	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
46	C₂×C₂₃×#120	—	2	2	no	—
47	C₂₃×#518	—	2	1	no	—
48	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#496	C₂²	1	2	yes	complemented
51	C₂₃×#493	C₂²	1	2	yes	complemented
52	C₂₃×#490	C₂²	1	2	yes	complemented
53	C₂₃×#486	C₂²	1	2	yes	complemented
54	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#482	C₂²	1	4	yes	complemented
56	C₂₃×#481	C₂²	1	2	yes	complemented
57	C₂₃×#481	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#481	C₂²	1	4	yes	complemented
59	C₂₃×#478	C₂²	1	2	yes	complemented
60	C₂₃×#476	C₂²	1	2	yes	complemented
61	C₂₃×#469	C₂²	1	4	yes	complemented
62	C₂₃×#469	C₂²	1	4	yes	complemented
63	C₂₃×#466	C₂²	1	4	yes	complemented
64	C₂₃×#465	C₂²	1	4	yes	complemented
65	C₂₃×#463	C₂²	1	2	yes	complemented
66	C₂₃×#460	C₂²	1	2	yes	complemented
67	C₂₃×#459	C₂²	1	2	yes	complemented
68	C₂₃×#459	C₂²	1	4	yes	complemented
69	C₂₃×#459	C₂²	1	2	yes	complemented
70	C₂₃×#450	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#450	C₂²	1	4	yes	complemented
72	C₂₃×#450	C₂²	1	2	yes	complemented
73	C₂₃×#449	C₂²	1	4	yes	complemented
74	C₂₃×#447	C₂²	1	1	yes	characteristic
75	C₂₃×#447	C₂²	1	2	yes	complemented
76	C₂₃×#447	C₂²	1	4	yes	complemented
77	C₂₃×#447	C₂²	1	4	yes	complemented
78	C₂₃×#447	C₂²	1	4	yes	complemented
79	C₂₃×#447	C₂²	1	2	yes	complemented
80	C₂₃×#447	C₂²	1	2	yes	complemented
81	C₂₃×#447	C₂²	1	2	yes	complemented
82	C₂₃×#447	C₂²	1	4	yes	complemented
83	C₂₃×#442	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
85	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
86	C₂₃×#436	C₂²	1	2	yes	complemented
87	C₂₃×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
89	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#418	C₂²	1	4	yes	complemented
92	C₂×C₂₃×#102	C₂²	1	4	yes	complemented
93	C₂₃×#407	C₂²	1	2	yes	complemented
94	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
95	C₂⁵×C₂₃	—	2	2	no	—
96	C₂×#41×C₂₃	—	2	1	no	—
97	C₂×#41×C₂₃	C₂³	1	2	yes	complemented
98	C₂²×D₄×C₂₃	—	2	2	no	—
99	C₂²×D₄×C₂₃	—	2	2	no	—
100	C₂²×D₄×C₂₃	—	2	2	no	—
101	C₂²×D₄×C₂₃	—	2	4	no	—
102	C₂²×D₄×C₂₃	—	2	2	no	—
103	C₂²×D₄×C₂₃	—	2	1	no	—
104	C₂²×D₄×C₂₃	—	2	1	no	—
105	C₂²×D₄×C₂₃	—	2	2	no	—
106	C₂²×D₄×C₂₃	—	2	2	no	—
107	C₂²×D₄×C₂₃	—	2	2	no	—
108	C₂²×D₄×C₂₃	—	2	1	no	—
109	C₂²×D₄×C₂₃	—	4	8	no	—
110	C₂²×D₄×C₂₃	—	4	8	no	—
111	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
112	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
114	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
115	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₂₃	C₂³	1	2	yes	complemented
117	C₂³×C₄×C₂₃	—	2	1	no	—
118	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
119	C₂₃×AGL(1,ℤ/8)	—	4	8	no	—
120	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
121	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
122	C₂×D₈×C₂₃	—	4	8	no	—
123	C₂×D₈×C₂₃	C₂³	1	2	yes	—
124	C₂×D₈×C₂₃	C₂³	1	4	yes	—
125	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
126	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
127	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
128	C₂×M₁₆×C₂₃	C₂³	1	4	yes	complemented
129	C₂²×C₈×C₂₃	C₂³	1	4	yes	complemented
130	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
131	C₂₃×#127	—	2	1	no	—
132	C₂₃×#127	—	2	1	no	—
133	C₂₃×#127	—	2	1	no	—
134	C₂₃×#127	C₂³	1	2	yes	—
135	C₂₃×#127	C₂³	1	2	yes	—
136	C₂₃×#127	C₂³	1	1	yes	characteristic, complemented
137	C₂₃×#126	—	2	2	no	—
138	C₂₃×#126	—	2	1	no	—
139	C₂₃×#125	—	2	1	no	—
140	C₂₃×#125	C₂³	1	1	yes	characteristic, complemented
141	C₂₃×#124	—	2	2	no	—
142	C₂₃×#124	—	2	1	no	—
143	C₂₃×#124	C₂³	1	1	yes	characteristic, complemented
144	C₂₃×#123	—	2	2	no	—
145	C₂₃×#123	—	2	1	no	—
146	C₂₃×#123	—	2	2	no	—
147	C₂₃×#123	—	2	2	no	—
148	C₂₃×C₂²⋊Q₈	—	2	2	no	—
149	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
150	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	complemented
151	C₂₃×#121	—	2	2	no	—
152	C₂₃×#121	—	2	1	no	—
153	C₂₃×#121	—	2	2	no	—
154	C₂₃×#121	—	2	1	no	—
155	C₂₃×#121	—	2	2	no	—
156	C₂₃×#121	—	2	2	no	—
157	C₂₃×#121	—	2	2	no	—
158	C₂₃×#121	—	2	1	no	—
159	C₂₃×#121	—	2	2	no	—
160	C₂₃×#121	—	2	2	no	—
161	C₂₃×#121	—	2	4	no	—
162	C₂₃×#121	—	2	2	no	—
163	C₂₃×#121	—	2	2	no	—
164	C₂₃×#121	C₂³	1	1	yes	characteristic
165	C₂₃×#121	C₂³	1	2	yes	—
166	C₂₃×#121	C₂³	1	4	yes	—
167	C₂₃×#121	C₂³	1	4	yes	—
168	C₂₃×#121	C₂³	1	2	yes	complemented
169	C₂₃×#121	C₂³	1	2	yes	complemented
170	C₂₃×#121	C₂³	1	2	yes	complemented
171	C₂₃×#120	—	2	2	no	—
172	C₂₃×#120	—	2	2	no	—
173	C₂₃×#120	—	2	4	no	—
174	C₂₃×#120	—	2	4	no	—
175	C₂₃×#120	—	2	4	no	—
176	C₂₃×#120	—	2	4	no	—
177	C₂₃×#120	—	2	2	no	—
178	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic, complemented
179	C₄×D₄×C₂₃	—	2	1	no	—
180	C₄×D₄×C₂₃	—	2	2	no	—
181	C₄×D₄×C₂₃	—	2	1	no	—
182	C₄×D₄×C₂₃	—	2	2	no	—
183	C₄×D₄×C₂₃	—	2	1	no	—
184	C₄×D₄×C₂₃	—	2	2	no	—
185	C₄×D₄×C₂₃	—	2	1	no	—
186	C₄×D₄×C₂₃	—	2	1	no	—
187	C₄×D₄×C₂₃	—	2	1	no	—
188	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
189	C₄×D₄×C₂₃	D₄	1	2	yes	—
190	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
191	C₄×D₄×C₂₃	C₂³	1	2	yes	—
192	C₄×D₄×C₂₃	C₂³	1	2	yes	—
193	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₂₃	C₂³	1	2	yes	—
195	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₄×D₄×C₂₃	C₂³	1	2	yes	complemented
197	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
198	C₂₃×#117	—	2	1	no	—
199	C₂₃×#117	—	2	1	no	—
200	C₂₃×#117	C₂³	1	2	yes	complemented
201	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
204	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
205	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
207	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
208	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
209	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
210	C₂₃×#107	C₂³	1	2	yes	complemented
211	C₂₃×#106	C₂³	1	2	yes	complemented
212	C₂₃×#106	C₂³	1	4	yes	complemented
213	C₂₃×C₄⋊C₈	C₂³	1	2	yes	complemented
214	C₂₃×C₄⋊C₈	C₂³	1	2	yes	complemented
215	C₂₃×#103	C₂³	1	2	yes	complemented
216	C₂₃×#102	C₂³	1	2	yes	—
217	C₂₃×#102	C₂³	1	4	yes	—
218	C₂₃×#102	C₂³	1	2	yes	—
219	C₂₃×#102	C₂³	1	4	yes	complemented
220	C₂₃×#102	C₂³	1	4	yes	complemented
221	C₂₃×#102	C₂³	1	4	yes	complemented
222	C₂₃×#102	C₂³	1	4	yes	complemented
223	C₂₃×#102	C₂³	1	2	yes	complemented
224	C₂₃×#102	C₂³	1	4	yes	complemented
225	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
226	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
229	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
230	C₂₃×#97	C₂³	1	2	yes	complemented
231	C₄×C₈×C₂₃	C₂³	1	2	yes	complemented
232	C₂⁴×C₂₃	—	2	1	no	—
233	C₂⁴×C₂₃	—	2	2	no	—
234	C₂⁴×C₂₃	—	2	4	no	—
235	C₂⁴×C₂₃	—	2	4	no	—
236	C₂⁴×C₂₃	—	2	2	no	—
237	C₂⁴×C₂₃	—	4	8	no	—
238	C₂⁴×C₂₃	—	4	8	no	—
239	C₂⁴×C₂₃	—	8	4	no	—
240	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
241	#41×C₂₃	—	4	4	no	—
242	#41×C₂₃	—	8	2	no	—
243	C₂×Q₈×C₂₃	—	2	1	no	—
244	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₂₃	—	2	4	no	—
246	C₂×D₄×C₂₃	—	2	4	no	—
247	C₂×D₄×C₂₃	—	2	8	no	—
248	C₂×D₄×C₂₃	—	2	8	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	2	2	no	—
251	C₂×D₄×C₂₃	—	2	1	no	—
252	C₂×D₄×C₂₃	—	2	4	no	—
253	C₂×D₄×C₂₃	—	2	4	no	—
254	C₂×D₄×C₂₃	—	2	2	no	—
255	C₂×D₄×C₂₃	—	2	2	no	—
256	C₂×D₄×C₂₃	—	2	2	no	—
257	C₂×D₄×C₂₃	—	2	1	no	—
258	C₂×D₄×C₂₃	—	2	1	no	—
259	C₂×D₄×C₂₃	—	2	4	no	—
260	C₂×D₄×C₂₃	—	2	4	no	—
261	C₂×D₄×C₂₃	—	2	2	no	—
262	C₂×D₄×C₂₃	—	2	2	no	—
263	C₂×D₄×C₂₃	—	2	2	no	—
264	C₂×D₄×C₂₃	—	2	2	no	—
265	C₂×D₄×C₂₃	—	2	2	no	—
266	C₂×D₄×C₂₃	—	2	1	no	—
267	C₂×D₄×C₂₃	—	2	2	no	—
268	C₂×D₄×C₂₃	—	4	4	no	—
269	C₂×D₄×C₂₃	—	4	4	no	—
270	C₂×D₄×C₂₃	—	4	4	no	—
271	C₂×D₄×C₂₃	—	4	4	no	—
272	C₂×D₄×C₂₃	—	4	4	no	—
273	C₂×D₄×C₂₃	—	4	8	no	—
274	C₂×D₄×C₂₃	—	4	8	no	—
275	C₂×D₄×C₂₃	—	4	16	no	—
276	C₂×D₄×C₂₃	—	4	8	no	—
277	C₂×D₄×C₂₃	—	4	8	no	—
278	C₂×D₄×C₂₃	—	4	8	no	—
279	C₂×D₄×C₂₃	—	4	4	no	—
280	C₂×D₄×C₂₃	—	4	8	no	—
281	C₂×D₄×C₂₃	—	8	2	no	—
282	C₂×D₄×C₂₃	—	8	4	no	—
283	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
284	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
285	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
287	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
288	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
289	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₂₃	—	2	1	no	—
291	C₂²×C₄×C₂₃	—	2	2	no	—
292	C₂²×C₄×C₂₃	—	2	1	no	—
293	C₂²×C₄×C₂₃	—	2	2	no	—
294	C₂²×C₄×C₂₃	—	2	2	no	—
295	C₂²×C₄×C₂₃	—	2	2	no	—
296	C₂²×C₄×C₂₃	—	2	2	no	—
297	C₂²×C₄×C₂₃	—	4	4	no	—
298	C₂²×C₄×C₂₃	—	4	4	no	—
299	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
302	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
303	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
304	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
307	SD₁₆×C₂₃	—	2	4	no	—
308	SD₁₆×C₂₃	—	4	4	no	—
309	D₈×C₂₃	—	2	4	no	—
310	D₈×C₂₃	—	2	8	no	—
311	D₈×C₂₃	—	4	4	no	—
312	D₈×C₂₃	—	4	4	no	—
313	D₈×C₂₃	—	4	4	no	—
314	M₁₆×C₂₃	—	4	4	no	—
315	C₂×C₈×C₂₃	—	4	4	no	—
316	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
317	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
318	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
319	C₄⋊C₄×C₂₃	—	2	1	no	—
320	C₄⋊C₄×C₂₃	—	2	2	no	—
321	C₄⋊C₄×C₂₃	—	2	1	no	—
322	C₄⋊C₄×C₂₃	—	2	1	no	—
323	C₄⋊C₄×C₂₃	—	2	1	no	—
324	C₄⋊C₄×C₂₃	—	2	1	no	—
325	C₄⋊C₄×C₂₃	—	2	2	no	—
326	C₄⋊C₄×C₂₃	—	2	1	no	—
327	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
328	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
329	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
330	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
332	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
334	C₂²⋊C₄×C₂₃	—	2	2	no	—
335	C₂²⋊C₄×C₂₃	—	2	2	no	—
336	C₂²⋊C₄×C₂₃	—	2	1	no	—
337	C₂²⋊C₄×C₂₃	—	2	1	no	—
338	C₂²⋊C₄×C₂₃	—	2	1	no	—
339	C₂²⋊C₄×C₂₃	—	2	2	no	—
340	C₂²⋊C₄×C₂₃	—	2	2	no	—
341	C₂²⋊C₄×C₂₃	—	2	2	no	—
342	C₂²⋊C₄×C₂₃	—	2	2	no	—
343	C₂²⋊C₄×C₂₃	—	2	2	no	—
344	C₂²⋊C₄×C₂₃	—	2	4	no	—
345	C₂²⋊C₄×C₂₃	—	2	4	no	—
346	C₂²⋊C₄×C₂₃	—	2	1	no	—
347	C₂²⋊C₄×C₂₃	—	2	2	no	—
348	C₂²⋊C₄×C₂₃	—	2	1	no	—
349	C₂²⋊C₄×C₂₃	—	2	2	no	—
350	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
351	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
352	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
353	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
354	C₄²×C₂₃	—	2	2	no	—
355	C₄²×C₂₃	—	2	1	no	—
356	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
357	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
358	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
360	#61591	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂³×C₂₃	—	2	4	no	—
362	C₂³×C₂₃	—	2	4	no	—
363	C₂³×C₂₃	—	2	4	no	—
364	C₂³×C₂₃	—	2	2	no	—
365	C₂³×C₂₃	—	2	1	no	—
366	C₂³×C₂₃	—	2	2	no	—
367	C₂³×C₂₃	—	2	4	no	—
368	C₂³×C₂₃	—	4	2	no	—
369	C₂³×C₂₃	—	4	8	no	—
370	C₂³×C₂₃	—	4	8	no	—
371	C₂³×C₂₃	—	4	2	no	—
372	C₂³×C₂₃	—	4	4	no	—
373	C₂³×C₂₃	—	4	4	no	—
374	C₂³×C₂₃	—	4	8	no	—
375	C₂³×C₂₃	—	4	2	no	—
376	C₂³×C₂₃	—	4	8	no	—
377	C₂³×C₂₃	—	4	4	no	—
378	C₂³×C₂₃	—	4	4	no	—
379	C₂³×C₂₃	—	8	4	no	—
380	C₂³×C₂₃	—	8	4	no	—
381	C₂³×C₂₃	—	8	2	no	—
382	C₂³×C₂₃	—	8	2	no	—
383	C₂³×C₂₃	—	8	32	no	—
384	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
385	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
386	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	Q₈×C₂₃	—	2	2	no	—
388	Q₈×C₂₃	—	8	1	no	—
389	D₄×C₂₃	—	2	4	no	—
390	D₄×C₂₃	—	2	4	no	—
391	D₄×C₂₃	—	2	2	no	—
392	D₄×C₂₃	—	2	2	no	—
393	D₄×C₂₃	—	2	2	no	—
394	D₄×C₂₃	—	2	4	no	—
395	D₄×C₂₃	—	2	4	no	—
396	D₄×C₂₃	—	2	4	no	—
397	D₄×C₂₃	—	4	8	no	—
398	D₄×C₂₃	—	4	8	no	—
399	D₄×C₂₃	—	4	4	no	—
400	D₄×C₂₃	—	4	4	no	—
401	D₄×C₂₃	—	4	8	no	—
402	D₄×C₂₃	—	4	4	no	—
403	D₄×C₂₃	—	4	8	no	—
404	D₄×C₂₃	—	4	2	no	—
405	D₄×C₂₃	—	4	4	no	—
406	D₄×C₂₃	—	4	2	no	—
407	D₄×C₂₃	—	4	4	no	—
408	D₄×C₂₃	—	8	2	no	—
409	D₄×C₂₃	—	8	2	no	—
410	D₄×C₂₃	—	8	2	no	—
411	D₄×C₂₃	—	8	1	no	—
412	D₄×C₂₃	—	8	2	no	—
413	D₄×C₂₃	—	8	2	no	—
414	D₄×C₂₃	—	8	2	no	—
415	D₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	complemented
416	D₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
417	C₂×C₄×C₂₃	—	2	2	no	—
418	C₂×C₄×C₂₃	—	2	2	no	—
419	C₂×C₄×C₂₃	—	2	4	no	—
420	C₂×C₄×C₂₃	—	2	4	no	—
421	C₂×C₄×C₂₃	—	2	2	no	—
422	C₂×C₄×C₂₃	—	2	1	no	—
423	C₂×C₄×C₂₃	—	2	1	no	—
424	C₂×C₄×C₂₃	—	2	2	no	—
425	C₂×C₄×C₂₃	—	2	1	no	—
426	C₂×C₄×C₂₃	—	2	2	no	—
427	C₂×C₄×C₂₃	—	4	2	no	—
428	C₂×C₄×C₂₃	—	4	2	no	—
429	C₂×C₄×C₂₃	—	4	2	no	—
430	C₂×C₄×C₂₃	—	4	4	no	—
431	C₂×C₄×C₂₃	—	4	2	no	—
432	C₂×C₄×C₂₃	—	4	4	no	—
433	C₂×C₄×C₂₃	—	4	2	no	—
434	C₂×C₄×C₂₃	—	8	2	no	—
435	C₂×C₄×C₂₃	—	8	2	no	—
436	C₂×C₄×C₂₃	—	8	2	no	—
437	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
445	C₈×C₂₃	—	2	2	no	—
446	C₈×C₂₃	—	2	4	no	—
447	C₈×C₂₃	—	2	2	no	—
448	#3519	C₂×C₂₃	1	1	yes	characteristic, complemented
449	C₂×D₄²	C₂×C₂₃	1	1	yes	characteristic, complemented
450	#3325	C₂×C₂₃	1	2	yes	complemented
451	#3318	C₂×C₂₃	1	4	yes	complemented
452	#3295	C₂×C₂₃	1	2	yes	complemented
453	D₄×D₈	C₂×C₂₃	1	2	yes	complemented
454	#3274	C₂×C₂₃	1	2	yes	complemented
455	#3264	C₂×C₂₃	1	4	yes	complemented
456	#3217	C₂×C₂₃	1	1	yes	characteristic, complemented
457	#3205	C₂×C₂₃	1	1	yes	characteristic, complemented
458	#3192	C₂×C₂₃	1	2	yes	complemented
459	#3188	C₂×C₂₃	1	2	yes	complemented
460	#3109	C₂×C₂₃	1	1	yes	characteristic, complemented
461	#3105	C₂×C₂₃	1	1	yes	characteristic, complemented
462	#3003	C₂×C₂₃	1	2	yes	complemented
463	C₂×#447	C₂×C₂₃	1	2	yes	complemented
464	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
465	C₂²×C₂₃	—	2	1	no	—
466	C₂²×C₂₃	—	2	2	no	—
467	C₂²×C₂₃	—	2	1	no	—
468	C₂²×C₂₃	—	2	2	no	—
469	C₂²×C₂₃	—	2	2	no	—
470	C₂²×C₂₃	—	2	4	no	—
471	C₂²×C₂₃	—	2	2	no	—
472	C₂²×C₂₃	—	2	2	no	—
473	C₂²×C₂₃	—	4	8	no	—
474	C₂²×C₂₃	—	4	8	no	—
475	C₂²×C₂₃	—	4	2	no	—
476	C₂²×C₂₃	—	4	2	no	—
477	C₂²×C₂₃	—	4	2	no	—
478	C₂²×C₂₃	—	4	4	no	—
479	C₂²×C₂₃	—	4	1	no	—
480	C₂²×C₂₃	—	4	1	no	—
481	C₂²×C₂₃	—	4	4	no	—
482	C₂²×C₂₃	—	4	2	no	—
483	C₂²×C₂₃	—	4	2	no	—
484	C₂²×C₂₃	—	4	1	no	—
485	C₂²×C₂₃	—	4	4	no	—
486	C₂²×C₂₃	—	8	16	no	—
487	C₂²×C₂₃	—	8	8	no	—
488	C₂²×C₂₃	—	8	16	no	—
489	C₂²×C₂₃	—	16	4	no	—
490	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
491	C₂²×C₂₃	#576	1	2	yes	—
492	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
493	C₄×C₂₃	—	2	1	no	—
494	C₄×C₂₃	—	2	2	no	—
495	C₄×C₂₃	—	2	2	no	—
496	C₄×C₂₃	—	2	1	no	—
497	C₄×C₂₃	—	2	1	no	—
498	C₄×C₂₃	—	2	1	no	—
499	C₄×C₂₃	—	4	1	no	—
500	C₄×C₂₃	—	4	2	no	—
501	C₄×C₂₃	—	4	1	no	—
502	C₄×C₂₃	—	4	1	no	—
503	C₄×C₂₃	—	4	2	no	—
504	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
505	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
506	C₂³×D₄	—	2	1	no	—
507	C₂³×D₄	C₂²×C₂₃	1	2	yes	complemented
508	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
509	C₂²×D₈	C₂²×C₂₃	1	4	yes	complemented
510	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
511	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
512	#553	—	2	1	no	—
513	#553	C₂²×C₂₃	1	2	yes	complemented
514	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
515	#546	—	2	2	no	—
516	#546	C₂²×C₂₃	1	2	yes	complemented
517	D₄²	—	2	1	no	—
518	D₄²	—	2	1	no	—
519	D₄²	—	2	2	no	—
520	D₄²	—	2	1	no	—
521	D₄²	C₂²×C₂₃	1	2	yes	—
522	D₄²	C₂²×C₂₃	1	4	yes	complemented
523	D₄²	C₂²×C₂₃	1	2	yes	complemented
524	D₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
525	#540	—	2	1	no	—
526	#538	—	2	2	no	—
527	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
528	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic, complemented
529	#529	C₂²×C₂₃	1	1	yes	characteristic, complemented
530	#525	C₂²×C₂₃	1	2	yes	complemented
531	C₂×#121	—	2	1	no	—
532	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
533	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
534	C₂×#120	—	2	2	no	—
535	#518	—	2	1	no	—
536	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
537	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
538	#496	C₂²×C₂₃	1	2	yes	complemented
539	#493	C₂²×C₂₃	1	2	yes	complemented
540	#490	C₂²×C₂₃	1	2	yes	complemented
541	#486	C₂²×C₂₃	1	2	yes	complemented
542	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
543	#482	C₂²×C₂₃	1	4	yes	complemented
544	#481	C₂²×C₂₃	1	1	yes	characteristic, complemented
545	#481	C₂²×C₂₃	1	2	yes	complemented
546	#481	C₂²×C₂₃	1	4	yes	complemented
547	#478	C₂²×C₂₃	1	2	yes	complemented
548	#476	C₂²×C₂₃	1	2	yes	complemented
549	#469	C₂²×C₂₃	1	4	yes	complemented
550	#469	C₂²×C₂₃	1	4	yes	complemented
551	#466	C₂²×C₂₃	1	4	yes	complemented
552	#465	C₂²×C₂₃	1	4	yes	complemented
553	#463	C₂²×C₂₃	1	2	yes	complemented
554	#460	C₂²×C₂₃	1	2	yes	complemented
555	#459	C₂²×C₂₃	1	2	yes	complemented
556	#459	C₂²×C₂₃	1	4	yes	complemented
557	#459	C₂²×C₂₃	1	2	yes	complemented
558	#450	C₂²×C₂₃	1	1	yes	characteristic, complemented
559	#450	C₂²×C₂₃	1	2	yes	complemented
560	#450	C₂²×C₂₃	1	4	yes	complemented
561	#449	C₂²×C₂₃	1	4	yes	complemented
562	#447	C₂²×C₂₃	1	1	yes	characteristic
563	#447	C₂²×C₂₃	1	2	yes	complemented
564	#447	C₂²×C₂₃	1	2	yes	complemented
565	#447	C₂²×C₂₃	1	2	yes	complemented
566	#447	C₂²×C₂₃	1	2	yes	complemented
567	#447	C₂²×C₂₃	1	4	yes	complemented
568	#447	C₂²×C₂₃	1	4	yes	complemented
569	#447	C₂²×C₂₃	1	4	yes	complemented
570	#447	C₂²×C₂₃	1	4	yes	complemented
571	#442	C₂²×C₂₃	1	4	yes	complemented
572	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
573	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
574	#436	C₂²×C₂₃	1	2	yes	complemented
575	#435	C₂²×C₂₃	1	4	yes	complemented
576	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
577	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
578	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
579	#418	C₂²×C₂₃	1	4	yes	complemented
580	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
581	#407	C₂²×C₂₃	1	2	yes	complemented
582	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
583	C₂×C₂₃	—	2	2	no	—
584	C₂×C₂₃	—	2	4	no	—
585	C₂×C₂₃	—	4	2	no	—
586	C₂×C₂₃	—	4	4	no	—
587	C₂×C₂₃	—	8	4	no	—
588	C₂×C₂₃	—	8	2	no	—
589	C₂×C₂₃	—	8	1	no	—
590	C₂×C₂₃	#3484	1	1	yes	characteristic
591	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
592	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
593	C₂⁵	—	2	2	no	—
594	C₂×#41	—	2	1	no	—
595	C₂×#41	C₂³×C₂₃	1	2	yes	complemented
596	C₂²×D₄	—	2	2	no	—
597	C₂²×D₄	—	2	2	no	—
598	C₂²×D₄	—	2	1	no	—
599	C₂²×D₄	—	2	2	no	—
600	C₂²×D₄	—	2	4	no	—
601	C₂²×D₄	—	2	2	no	—
602	C₂²×D₄	—	2	2	no	—
603	C₂²×D₄	—	2	1	no	—
604	C₂²×D₄	—	2	2	no	—
605	C₂²×D₄	—	2	2	no	—
606	C₂²×D₄	—	2	1	no	—
607	C₂²×D₄	—	4	8	no	—
608	C₂²×D₄	—	4	8	no	—
609	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
610	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
611	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
612	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
613	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
614	C₂²×D₄	C₂³×C₂₃	1	2	yes	complemented
615	C₂³×C₄	—	2	1	no	—
616	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
617	AGL(1,ℤ/8)	—	4	8	no	—
618	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
619	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
620	C₂×D₈	—	4	8	no	—
621	C₂×D₈	C₂³×C₂₃	1	2	yes	—
622	C₂×D₈	C₂³×C₂₃	1	4	yes	—
623	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
624	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
625	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
626	C₂×M₁₆	C₂³×C₂₃	1	4	yes	complemented
627	C₂²×C₈	C₂³×C₂₃	1	4	yes	complemented
628	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
629	#127	—	2	1	no	—
630	#127	—	2	1	no	—
631	#127	—	2	1	no	—
632	#127	C₂³×C₂₃	1	2	yes	—
633	#127	C₂³×C₂₃	1	2	yes	—
634	#127	C₂³×C₂₃	1	1	yes	characteristic, complemented
635	#126	—	2	2	no	—
636	#126	—	2	1	no	—
637	#125	—	2	1	no	—
638	#125	C₂³×C₂₃	1	1	yes	characteristic, complemented
639	#124	—	2	2	no	—
640	#124	—	2	1	no	—
641	#124	C₂³×C₂₃	1	1	yes	characteristic, complemented
642	#123	—	2	2	no	—
643	#123	—	2	1	no	—
644	#123	—	2	2	no	—
645	#123	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
648	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
649	#121	—	2	2	no	—
650	#121	—	2	1	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	1	no	—
656	#121	—	2	2	no	—
657	#121	—	2	2	no	—
658	#121	—	2	4	no	—
659	#121	—	2	1	no	—
660	#121	—	2	2	no	—
661	#121	—	2	2	no	—
662	#121	C₂³×C₂₃	1	1	yes	characteristic
663	#121	C₂³×C₂₃	1	2	yes	—
664	#121	C₂³×C₂₃	1	4	yes	—
665	#121	C₂³×C₂₃	1	4	yes	—
666	#121	C₂³×C₂₃	1	2	yes	complemented
667	#121	C₂³×C₂₃	1	2	yes	complemented
668	#121	C₂³×C₂₃	1	2	yes	complemented
669	#120	—	2	2	no	—
670	#120	—	2	2	no	—
671	#120	—	2	4	no	—
672	#120	—	2	4	no	—
673	#120	—	2	4	no	—
674	#120	—	2	4	no	—
675	#120	—	2	2	no	—
676	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
677	C₄×D₄	—	2	1	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	—	2	1	no	—
684	C₄×D₄	—	2	1	no	—
685	C₄×D₄	—	2	1	no	—
686	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
687	C₄×D₄	D₄×C₂₃	1	2	yes	—
688	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
689	C₄×D₄	C₂³×C₂₃	1	2	yes	—
690	C₄×D₄	C₂³×C₂₃	1	2	yes	—
691	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
692	C₄×D₄	C₂³×C₂₃	1	2	yes	—
693	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
694	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic, complemented
695	C₄×D₄	C₂³×C₂₃	1	2	yes	complemented
696	#117	—	2	1	no	—
697	#117	—	2	1	no	—
698	#117	C₂³×C₂₃	1	2	yes	complemented
699	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	complemented
702	C₂×C₂²⋊C₄	—	2	1	no	—
703	C₂×C₂²⋊C₄	—	2	2	no	—
704	C₂×C₂²⋊C₄	—	2	2	no	—
705	C₂×C₂²⋊C₄	—	2	2	no	—
706	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
707	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
708	#107	C₂³×C₂₃	1	2	yes	complemented
709	#106	C₂³×C₂₃	1	2	yes	complemented
710	#106	C₂³×C₂₃	1	4	yes	complemented
711	C₄⋊C₈	C₂³×C₂₃	1	2	yes	complemented
712	C₄⋊C₈	C₂³×C₂₃	1	2	yes	complemented
713	#103	C₂³×C₂₃	1	2	yes	complemented
714	#102	C₂³×C₂₃	1	2	yes	—
715	#102	C₂³×C₂₃	1	4	yes	—
716	#102	C₂³×C₂₃	1	2	yes	—
717	#102	C₂³×C₂₃	1	4	yes	complemented
718	#102	C₂³×C₂₃	1	4	yes	complemented
719	#102	C₂³×C₂₃	1	4	yes	complemented
720	#102	C₂³×C₂₃	1	4	yes	complemented
721	#102	C₂³×C₂₃	1	2	yes	complemented
722	#102	C₂³×C₂₃	1	4	yes	complemented
723	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
724	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
725	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
726	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
727	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
728	#97	C₂³×C₂₃	1	2	yes	complemented
729	C₄×C₈	C₂³×C₂₃	1	2	yes	complemented
730	C₂₃	#61591	1	1	yes	characteristic, direct product factor, Sylow
731	C₂⁴	—	2	1	no	—
732	C₂⁴	—	2	2	no	—
733	C₂⁴	—	2	4	no	—
734	C₂⁴	—	2	4	no	—
735	C₂⁴	—	2	2	no	—
736	C₂⁴	—	4	8	no	—
737	C₂⁴	—	4	8	no	—
738	C₂⁴	—	8	4	no	—
739	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
740	#41	—	4	4	no	—
741	#41	—	8	2	no	—
742	C₂×Q₈	—	2	1	no	—
743	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	8	no	—
747	C₂×D₄	—	2	8	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	1	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	2	4	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	1	no	—
757	C₂×D₄	—	2	1	no	—
758	C₂×D₄	—	2	4	no	—
759	C₂×D₄	—	2	4	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	4	4	no	—
768	C₂×D₄	—	4	4	no	—
769	C₂×D₄	—	4	4	no	—
770	C₂×D₄	—	4	4	no	—
771	C₂×D₄	—	4	4	no	—
772	C₂×D₄	—	4	8	no	—
773	C₂×D₄	—	4	8	no	—
774	C₂×D₄	—	4	16	no	—
775	C₂×D₄	—	4	8	no	—
776	C₂×D₄	—	4	8	no	—
777	C₂×D₄	—	4	8	no	—
778	C₂×D₄	—	4	8	no	—
779	C₂×D₄	—	4	4	no	—
780	C₂×D₄	—	8	2	no	—
781	C₂×D₄	—	8	4	no	—
782	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
783	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
784	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
785	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
786	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
787	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
788	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	4	4	no	—
797	C₂²×C₄	—	4	4	no	—
798	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
799	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
800	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
801	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
802	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
803	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
806	SD₁₆	—	2	4	no	—
807	SD₁₆	—	4	4	no	—
808	D₈	—	2	4	no	—
809	D₈	—	2	8	no	—
810	D₈	—	4	4	no	—
811	D₈	—	4	4	no	—
812	D₈	—	4	4	no	—
813	M₁₆	—	4	4	no	—
814	C₂×C₈	—	4	4	no	—
815	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
816	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
817	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
827	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
828	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
829	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
830	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
831	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
832	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	1	no	—
836	C₂²⋊C₄	—	2	1	no	—
837	C₂²⋊C₄	—	2	1	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	4	no	—
845	C₂²⋊C₄	—	2	1	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	1	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
850	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
851	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
852	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	1	no	—
855	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
856	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
857	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
858	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
859	C₂³	—	2	4	no	—
860	C₂³	—	2	4	no	—
861	C₂³	—	2	4	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	4	no	—
866	C₂³	—	4	2	no	—
867	C₂³	—	4	8	no	—
868	C₂³	—	4	8	no	—
869	C₂³	—	4	2	no	—
870	C₂³	—	4	4	no	—
871	C₂³	—	4	4	no	—
872	C₂³	—	4	8	no	—
873	C₂³	—	4	2	no	—
874	C₂³	—	4	8	no	—
875	C₂³	—	4	4	no	—
876	C₂³	—	4	4	no	—
877	C₂³	—	8	4	no	—
878	C₂³	—	8	4	no	—
879	C₂³	—	8	2	no	—
880	C₂³	—	8	2	no	—
881	C₂³	—	8	32	no	—
882	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
883	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
884	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
885	Q₈	—	2	2	no	—
886	Q₈	—	8	1	no	—
887	D₄	—	2	4	no	—
888	D₄	—	2	4	no	—
889	D₄	—	2	2	no	—
890	D₄	—	2	2	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	4	no	—
893	D₄	—	2	4	no	—
894	D₄	—	2	4	no	—
895	D₄	—	4	8	no	—
896	D₄	—	4	8	no	—
897	D₄	—	4	4	no	—
898	D₄	—	4	4	no	—
899	D₄	—	4	8	no	—
900	D₄	—	4	8	no	—
901	D₄	—	4	4	no	—
902	D₄	—	4	2	no	—
903	D₄	—	4	4	no	—
904	D₄	—	4	4	no	—
905	D₄	—	4	2	no	—
906	D₄	—	8	2	no	—
907	D₄	—	8	2	no	—
908	D₄	—	8	2	no	—
909	D₄	—	8	1	no	—
910	D₄	—	8	2	no	—
911	D₄	—	8	2	no	—
912	D₄	—	8	2	no	—
913	D₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	complemented
914	D₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	4	no	—
918	C₂×C₄	—	2	4	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	4	2	no	—
926	C₂×C₄	—	4	2	no	—
927	C₂×C₄	—	4	2	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	4	2	no	—
930	C₂×C₄	—	4	4	no	—
931	C₂×C₄	—	4	2	no	—
932	C₂×C₄	—	8	2	no	—
933	C₂×C₄	—	8	2	no	—
934	C₂×C₄	—	8	2	no	—
935	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
936	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
937	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
938	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
939	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
940	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
941	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
942	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
943	C₈	—	2	2	no	—
944	C₈	—	2	4	no	—
945	C₈	—	2	2	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	1	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	4	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	4	8	no	—
955	C₂²	—	4	8	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	4	no	—
960	C₂²	—	4	1	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	4	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	8	16	no	—
968	C₂²	—	8	8	no	—
969	C₂²	—	8	16	no	—
970	C₂²	—	16	4	no	—
971	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	4	yes	—
972	C₂²	C₂₃×#576	1	2	yes	—
973	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
974	C₄	—	2	1	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	1	no	—
978	C₄	—	2	1	no	—
979	C₄	—	2	1	no	—
980	C₄	—	4	1	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	2	no	—
985	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
986	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
987	C₂	—	2	2	no	—
988	C₂	—	2	4	no	—
989	C₂	—	4	2	no	—
990	C₂	—	4	4	no	—
991	C₂	—	8	4	no	—
992	C₂	—	8	1	no	—
993	C₂	—	8	2	no	—
994	C₂	C₂₃×#3484	1	1	yes	characteristic
995	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
996	C₂	C₂×C₂₃×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3519	C₂	semidirect
2. C₂×D₄²×C₂₃	C₂	semidirect
3. C₂₃×#3325	C₂	semidirect
4. C₂₃×#3318	C₂	semidirect
5. C₂₃×#3295	C₂	semidirect
6. D₄×D₈×C₂₃	C₂	semidirect
7. C₂₃×#3274	C₂	semidirect
8. C₂₃×#3264	C₂	semidirect
9. C₂₃×#3217	C₂	semidirect
10. C₂₃×#3205	C₂	semidirect
11. C₂₃×#3192	C₂	semidirect
12. C₂₃×#3188	C₂	semidirect
13. C₂₃×#3109	C₂	semidirect
14. C₂₃×#3105	C₂	semidirect
15. C₂₃×#3003	C₂	semidirect
16. C₂×C₂₃×#447	C₂	semidirect
17. C₂₃×#2974	C₂	semidirect
19. C₂³×D₄×C₂₃	C₂²	semidirect
20. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂²×D₈×C₂₃	C₂²	semidirect
22. C₂₃×#555	C₂²	semidirect
23. C₂₃×#554	C₂²	semidirect
25. C₂₃×#553	C₂²	semidirect
26. C₂₃×#550	C₂²	semidirect
28. C₂₃×#546	C₂²	semidirect
34. D₄²×C₂₃	C₂²	semidirect
35. D₄²×C₂₃	C₂²	semidirect
36. D₄²×C₂₃	C₂²	semidirect
39. C₂₃×#532	C₂²	semidirect
40. C₂×C₂₃×#127	C₂²	semidirect
41. C₂₃×#529	C₂²	semidirect
42. C₂₃×#525	C₂²	semidirect
44. C₂×C₂₃×#121	C₂²	semidirect
45. C₂×C₂₃×#121	C₂²	semidirect
49. C₂×C₄×D₄×C₂₃	C₂²	semidirect
50. C₂₃×#496	C₂²	semidirect
51. C₂₃×#493	C₂²	semidirect
52. C₂₃×#490	C₂²	semidirect
53. C₂₃×#486	C₂²	semidirect
54. C₂₃×#484	C₂²	semidirect
55. C₂₃×#482	C₂²	semidirect
56. C₂₃×#481	C₂²	semidirect
57. C₂₃×#481	C₂²	semidirect
58. C₂₃×#481	C₂²	semidirect
59. C₂₃×#478	C₂²	semidirect
60. C₂₃×#476	C₂²	semidirect
61. C₂₃×#469	C₂²	semidirect
62. C₂₃×#469	C₂²	semidirect
63. C₂₃×#466	C₂²	semidirect
64. C₂₃×#465	C₂²	semidirect
65. C₂₃×#463	C₂²	semidirect
66. C₂₃×#460	C₂²	semidirect
67. C₂₃×#459	C₂²	semidirect
68. C₂₃×#459	C₂²	semidirect
69. C₂₃×#459	C₂²	semidirect
70. C₂₃×#450	C₂²	semidirect
71. C₂₃×#450	C₂²	semidirect
72. C₂₃×#450	C₂²	semidirect
73. C₂₃×#449	C₂²	semidirect
75. C₂₃×#447	C₂²	semidirect
76. C₂₃×#447	C₂²	semidirect
77. C₂₃×#447	C₂²	semidirect
78. C₂₃×#447	C₂²	semidirect
79. C₂₃×#447	C₂²	semidirect
80. C₂₃×#447	C₂²	semidirect
81. C₂₃×#447	C₂²	semidirect
82. C₂₃×#447	C₂²	semidirect
83. C₂₃×#442	C₂²	semidirect
84. C₄×SD₁₆×C₂₃	C₂²	semidirect
85. C₄×D₈×C₂₃	C₂²	semidirect
86. C₂₃×#436	C₂²	semidirect
87. C₂₃×#435	C₂²	semidirect
88. C₈×D₄×C₂₃	C₂²	semidirect
89. C₂₃×#432	C₂²	semidirect
90. C₂₃×#431	C₂²	semidirect
91. C₂₃×#418	C₂²	semidirect
92. C₂×C₂₃×#102	C₂²	semidirect
93. C₂₃×#407	C₂²	semidirect
94. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
97. C₂×#41×C₂₃	C₂³	semidirect
116. C₂²×D₄×C₂₃	C₂³	semidirect
121. C₂×SD₁₆×C₂₃	C₂³	semidirect
125. C₂×D₈×C₂₃	C₂³	semidirect
126. C₂×D₈×C₂₃	C₂³	semidirect
127. C₂×D₈×C₂₃	C₂³	semidirect
128. C₂×M₁₆×C₂₃	C₂³	semidirect
129. C₂²×C₈×C₂₃	C₂³	semidirect
130. C₂₃×C₄⋊Q₈	C₂³	semidirect
136. C₂₃×#127	C₂³	semidirect
140. C₂₃×#125	C₂³	semidirect
143. C₂₃×#124	C₂³	semidirect
150. C₂₃×C₂²⋊Q₈	C₂³	semidirect
168. C₂₃×#121	C₂³	semidirect
169. C₂₃×#121	C₂³	semidirect
170. C₂₃×#121	C₂³	semidirect
178. C₄×Q₈×C₂₃	C₂³	semidirect
196. C₄×D₄×C₂₃	C₂³	semidirect
197. C₄×D₄×C₂₃	C₂³	semidirect
200. C₂₃×#117	C₂³	semidirect
203. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
210. C₂₃×#107	C₂³	semidirect
211. C₂₃×#106	C₂³	semidirect
212. C₂₃×#106	C₂³	semidirect
213. C₂₃×C₄⋊C₈	C₂³	semidirect
214. C₂₃×C₄⋊C₈	C₂³	semidirect
215. C₂₃×#103	C₂³	semidirect
219. C₂₃×#102	C₂³	semidirect
220. C₂₃×#102	C₂³	semidirect
221. C₂₃×#102	C₂³	semidirect
222. C₂₃×#102	C₂³	semidirect
223. C₂₃×#102	C₂³	semidirect
224. C₂₃×#102	C₂³	semidirect
228. C₂₃×C₂²⋊C₈	C₂³	semidirect
229. C₂₃×C₂²⋊C₈	C₂³	semidirect
230. C₂₃×#97	C₂³	semidirect
231. C₄×C₈×C₂₃	C₂³	semidirect
360. #61591	C₂₃	direct (N × H)
415. D₄×C₂₃	AGL(1,ℤ/8)	semidirect
448. #3519	C₂×C₂₃	semidirect
449. C₂×D₄²	C₂×C₂₃	semidirect
450. #3325	C₂×C₂₃	semidirect
451. #3318	C₂×C₂₃	semidirect
452. #3295	C₂×C₂₃	semidirect
453. D₄×D₈	C₂×C₂₃	semidirect
454. #3274	C₂×C₂₃	semidirect
455. #3264	C₂×C₂₃	semidirect
456. #3217	C₂×C₂₃	semidirect
457. #3205	C₂×C₂₃	semidirect
458. #3192	C₂×C₂₃	semidirect
459. #3188	C₂×C₂₃	semidirect
460. #3109	C₂×C₂₃	semidirect
461. #3105	C₂×C₂₃	semidirect
462. #3003	C₂×C₂₃	semidirect
463. C₂×#447	C₂×C₂₃	semidirect
464. #2974	C₂×C₂₃	semidirect
507. C₂³×D₄	C₂²×C₂₃	semidirect
508. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
509. C₂²×D₈	C₂²×C₂₃	semidirect
510. #555	C₂²×C₂₃	semidirect
511. #554	C₂²×C₂₃	semidirect
513. #553	C₂²×C₂₃	semidirect
514. #550	C₂²×C₂₃	semidirect
516. #546	C₂²×C₂₃	semidirect
522. D₄²	C₂²×C₂₃	semidirect
523. D₄²	C₂²×C₂₃	semidirect
524. D₄²	C₂²×C₂₃	semidirect
527. #532	C₂²×C₂₃	semidirect
528. C₂×#127	C₂²×C₂₃	semidirect
529. #529	C₂²×C₂₃	semidirect
530. #525	C₂²×C₂₃	semidirect
532. C₂×#121	C₂²×C₂₃	semidirect
533. C₂×#121	C₂²×C₂₃	semidirect
537. C₂×C₄×D₄	C₂²×C₂₃	semidirect
538. #496	C₂²×C₂₃	semidirect
539. #493	C₂²×C₂₃	semidirect
540. #490	C₂²×C₂₃	semidirect
541. #486	C₂²×C₂₃	semidirect
542. #484	C₂²×C₂₃	semidirect
543. #482	C₂²×C₂₃	semidirect
544. #481	C₂²×C₂₃	semidirect
545. #481	C₂²×C₂₃	semidirect
546. #481	C₂²×C₂₃	semidirect
547. #478	C₂²×C₂₃	semidirect
548. #476	C₂²×C₂₃	semidirect
549. #469	C₂²×C₂₃	semidirect
550. #469	C₂²×C₂₃	semidirect
551. #466	C₂²×C₂₃	semidirect
552. #465	C₂²×C₂₃	semidirect
553. #463	C₂²×C₂₃	semidirect
554. #460	C₂²×C₂₃	semidirect
555. #459	C₂²×C₂₃	semidirect
556. #459	C₂²×C₂₃	semidirect
557. #459	C₂²×C₂₃	semidirect
558. #450	C₂²×C₂₃	semidirect
559. #450	C₂²×C₂₃	semidirect
560. #450	C₂²×C₂₃	semidirect
561. #449	C₂²×C₂₃	semidirect
563. #447	C₂²×C₂₃	semidirect
564. #447	C₂²×C₂₃	semidirect
565. #447	C₂²×C₂₃	semidirect
566. #447	C₂²×C₂₃	semidirect
567. #447	C₂²×C₂₃	semidirect
568. #447	C₂²×C₂₃	semidirect
569. #447	C₂²×C₂₃	semidirect
570. #447	C₂²×C₂₃	semidirect
571. #442	C₂²×C₂₃	semidirect
572. C₄×SD₁₆	C₂²×C₂₃	semidirect
573. C₄×D₈	C₂²×C₂₃	semidirect
574. #436	C₂²×C₂₃	semidirect
575. #435	C₂²×C₂₃	semidirect
576. C₈×D₄	C₂²×C₂₃	semidirect
577. #432	C₂²×C₂₃	semidirect
578. #431	C₂²×C₂₃	semidirect
579. #418	C₂²×C₂₃	semidirect
580. C₂×#102	C₂²×C₂₃	semidirect
581. #407	C₂²×C₂₃	semidirect
582. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
595. C₂×#41	C₂³×C₂₃	semidirect
614. C₂²×D₄	C₂³×C₂₃	semidirect
619. C₂×SD₁₆	C₂³×C₂₃	semidirect
623. C₂×D₈	C₂³×C₂₃	semidirect
624. C₂×D₈	C₂³×C₂₃	semidirect
625. C₂×D₈	C₂³×C₂₃	semidirect
626. C₂×M₁₆	C₂³×C₂₃	semidirect
627. C₂²×C₈	C₂³×C₂₃	semidirect
628. C₄⋊Q₈	C₂³×C₂₃	semidirect
634. #127	C₂³×C₂₃	semidirect
638. #125	C₂³×C₂₃	semidirect
641. #124	C₂³×C₂₃	semidirect
648. C₂²⋊Q₈	C₂³×C₂₃	semidirect
666. #121	C₂³×C₂₃	semidirect
667. #121	C₂³×C₂₃	semidirect
668. #121	C₂³×C₂₃	semidirect
676. C₄×Q₈	C₂³×C₂₃	semidirect
694. C₄×D₄	C₂³×C₂₃	semidirect
695. C₄×D₄	C₂³×C₂₃	semidirect
698. #117	C₂³×C₂₃	semidirect
701. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
708. #107	C₂³×C₂₃	semidirect
709. #106	C₂³×C₂₃	semidirect
710. #106	C₂³×C₂₃	semidirect
711. C₄⋊C₈	C₂³×C₂₃	semidirect
712. C₄⋊C₈	C₂³×C₂₃	semidirect
713. #103	C₂³×C₂₃	semidirect
717. #102	C₂³×C₂₃	semidirect
718. #102	C₂³×C₂₃	semidirect
719. #102	C₂³×C₂₃	semidirect
720. #102	C₂³×C₂₃	semidirect
721. #102	C₂³×C₂₃	semidirect
722. #102	C₂³×C₂₃	semidirect
726. C₂²⋊C₈	C₂³×C₂₃	semidirect
727. C₂²⋊C₈	C₂³×C₂₃	semidirect
728. #97	C₂³×C₂₃	semidirect
729. C₄×C₈	C₂³×C₂₃	semidirect
730. C₂₃	#61591	direct (N × H)
913. D₄	C₂₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3519	2
C₂×D₄²×C₂₃	2
C₂₃×#3325	2
C₂₃×#3318	2
C₂₃×#3295	2
D₄×D₈×C₂₃	2
C₂₃×#3274	2
C₂₃×#3264	2
C₂₃×#3217	2
C₂₃×#3205	2
C₂₃×#3192	2
C₂₃×#3188	2
C₂₃×#3109	2
C₂₃×#3105	2
C₂₃×#3003	2
C₂×C₂₃×#447	2
C₂₃×#2974	2
#61591	23

Subgroups — C23×#61591 #19209217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61591 #19209217