Subgroups — C₂₃×#61602 #19209228

Order 5888.

2084 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3520	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3328	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3312	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3298	C₂	1	2	yes	maximal, complemented
6	D₄×Q₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3276	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3270	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3195	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3190	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3004	C₂	1	2	yes	maximal, complemented
16	C₂×C₂₃×#451	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₂₃	C₂²	1	2	yes	—
19	C₂×C₂₃×#137	C₂²	1	4	yes	complemented
20	C₂²×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
21	C₂₃×#556	C₂²	1	1	yes	characteristic
22	C₂₃×#554	—	2	1	no	—
23	C₂₃×#552	C₂²	1	2	yes	—
24	C₂₃×#551	—	2	2	no	—
25	D₄×Q₈×C₂₃	—	2	1	no	—
26	D₄×Q₈×C₂₃	—	2	2	no	—
27	D₄×Q₈×C₂₃	—	2	1	no	—
28	D₄×Q₈×C₂₃	C₂²	1	4	yes	—
29	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
30	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
31	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
32	C₂₃×#548	C₂²	1	2	yes	—
33	C₂₃×#547	C₂²	1	1	yes	characteristic
34	C₂₃×#547	C₂²	1	1	yes	characteristic
35	C₂₃×#546	—	2	1	no	—
36	C₂₃×#542	—	2	1	no	—
37	C₂₃×#539	—	2	2	no	—
38	C₂₃×#533	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
40	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂₃×#529	C₂²	1	1	yes	characteristic
42	C₂₃×#525	C₂²	1	2	yes	—
43	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
44	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
46	C₂₃×#520	—	2	1	no	—
47	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₂₃	—	2	1	no	—
49	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₂₃×#497	C₂²	1	2	yes	complemented
51	C₂₃×#494	C₂²	1	2	yes	complemented
52	C₂₃×#491	C₂²	1	2	yes	complemented
53	C₂₃×#487	C₂²	1	2	yes	complemented
54	C₂₃×#485	C₂²	1	4	yes	complemented
55	C₂₃×#483	C₂²	1	2	yes	—
56	C₂₃×#483	C₂²	1	1	yes	characteristic
57	C₂₃×#483	C₂²	1	4	yes	complemented
58	C₂₃×#480	C₂²	1	1	yes	characteristic
59	C₂₃×#479	C₂²	1	2	yes	complemented
60	C₂₃×#475	C₂²	1	2	yes	complemented
61	C₂₃×#470	C₂²	1	4	yes	complemented
62	C₂₃×#470	C₂²	1	4	yes	complemented
63	C₂₃×#467	C₂²	1	4	yes	complemented
64	C₂₃×#465	C₂²	1	4	yes	complemented
65	C₂₃×#464	C₂²	1	2	yes	complemented
66	C₂₃×#462	C₂²	1	4	yes	complemented
67	C₂₃×#462	C₂²	1	2	yes	complemented
68	C₂₃×#462	C₂²	1	2	yes	complemented
69	C₂₃×#461	C₂²	1	2	yes	complemented
70	C₂₃×#452	C₂²	1	4	yes	complemented
71	C₂₃×#451	C₂²	1	2	yes	—
72	C₂₃×#451	C₂²	1	2	yes	—
73	C₂₃×#451	C₂²	1	2	yes	—
74	C₂₃×#451	C₂²	1	1	yes	characteristic
75	C₂₃×#451	C₂²	1	2	yes	—
76	C₂₃×#451	C₂²	1	4	yes	complemented
77	C₂₃×#451	C₂²	1	4	yes	complemented
78	C₂₃×#451	C₂²	1	4	yes	complemented
79	C₂₃×#451	C₂²	1	4	yes	complemented
80	C₂₃×#448	C₂²	1	2	yes	—
81	C₂₃×#448	C₂²	1	1	yes	characteristic
82	C₂₃×#448	C₂²	1	4	yes	complemented
83	C₂₃×#441	C₂²	1	4	yes	complemented
84	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
86	C₂₃×#436	C₂²	1	2	yes	—
87	C₂₃×#435	C₂²	1	4	yes	—
88	C₈×D₄×C₂₃	C₂²	1	2	yes	—
89	C₂₃×#432	C₂²	1	1	yes	characteristic
90	C₂₃×#431	C₂²	1	1	yes	characteristic
91	C₂₃×#419	C₂²	1	4	yes	complemented
92	C₂×C₂₃×#103	C₂²	1	4	yes	complemented
93	C₂₃×#407	C₂²	1	2	yes	—
94	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	—	2	1	no	—
96	C₂×#41×C₂₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₂₃	—	2	2	no	—
98	C₂²×Q₈×C₂₃	—	2	2	no	—
99	C₂²×Q₈×C₂₃	—	2	2	no	—
100	C₂²×Q₈×C₂₃	—	4	8	no	—
101	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
103	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
104	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
105	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
106	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₂₃	—	2	2	no	—
108	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
109	C₂₃×#137	—	4	8	no	—
110	C₂×Q₁₆×C₂₃	—	4	8	no	—
111	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
112	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
113	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
114	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
115	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
118	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
119	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
120	C₂₃×C₄⋊Q₈	—	2	2	no	—
121	C₂₃×C₄⋊Q₈	—	2	4	no	—
122	C₂₃×C₄⋊Q₈	—	2	2	no	—
123	C₂₃×C₄⋊Q₈	—	2	1	no	—
124	C₂₃×C₄⋊Q₈	—	2	1	no	—
125	C₂₃×C₄⋊Q₈	—	2	1	no	—
126	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
128	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₂₃×#126	—	2	2	no	—
131	C₂₃×#126	—	2	2	no	—
132	C₂₃×#126	—	2	1	no	—
133	C₂₃×#125	—	2	2	no	—
134	C₂₃×#125	—	2	1	no	—
135	C₂₃×#125	C₂³	1	1	yes	characteristic
136	C₂₃×#124	—	2	1	no	—
137	C₂₃×#124	—	2	2	no	—
138	C₂₃×#124	C₂³	1	1	yes	characteristic
139	C₂₃×#123	—	2	2	no	—
140	C₂₃×#123	—	2	1	no	—
141	C₂₃×#123	—	2	2	no	—
142	C₂₃×#123	—	2	2	no	—
143	C₂₃×#123	—	2	2	no	—
144	C₂₃×C₂²⋊Q₈	—	2	2	no	—
145	C₂₃×C₂²⋊Q₈	—	2	2	no	—
146	C₂₃×C₂²⋊Q₈	—	2	2	no	—
147	C₂₃×C₂²⋊Q₈	—	2	1	no	—
148	C₂₃×C₂²⋊Q₈	—	2	2	no	—
149	C₂₃×C₂²⋊Q₈	—	2	1	no	—
150	C₂₃×C₂²⋊Q₈	—	2	2	no	—
151	C₂₃×C₂²⋊Q₈	—	2	4	no	—
152	C₂₃×C₂²⋊Q₈	—	2	4	no	—
153	C₂₃×C₂²⋊Q₈	—	2	4	no	—
154	C₂₃×C₂²⋊Q₈	—	2	4	no	—
155	C₂₃×C₂²⋊Q₈	—	2	2	no	—
156	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
157	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
159	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
160	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
161	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
163	C₂₃×#121	—	2	1	no	—
164	C₂₃×#121	—	2	2	no	—
165	C₂₃×#121	C₂³	1	2	yes	—
166	C₂₃×#121	C₂³	1	1	yes	characteristic
167	C₂₃×#120	—	2	2	no	—
168	C₄×Q₈×C₂₃	—	2	1	no	—
169	C₄×Q₈×C₂₃	—	2	1	no	—
170	C₄×Q₈×C₂₃	—	2	1	no	—
171	C₄×Q₈×C₂₃	—	2	1	no	—
172	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
174	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
175	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₂₃	—	2	4	no	—
177	C₄×D₄×C₂₃	—	2	2	no	—
178	C₄×D₄×C₂₃	—	2	2	no	—
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	2	no	—
184	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
185	C₄×D₄×C₂₃	D₄	1	2	yes	—
186	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
187	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₂₃	C₂³	1	2	yes	—
191	C₂₃×#117	—	2	1	no	—
192	C₂₃×#117	—	2	2	no	—
193	C₂₃×#117	—	2	1	no	—
194	C₂₃×#117	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
196	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
197	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
198	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
199	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
200	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
201	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
207	C₂×C₄²×C₂₃	—	2	1	no	—
208	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
209	C₂₃×#107	C₂³	1	2	yes	—
210	C₂₃×#106	C₂³	1	2	yes	—
211	C₂₃×#106	C₂³	1	4	yes	—
212	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₂₃×#103	C₂³	1	2	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	4	yes	—
217	C₂₃×#103	C₂³	1	4	yes	—
218	C₂₃×#103	C₂³	1	2	yes	—
219	C₂₃×#103	C₂³	1	4	yes	—
220	C₂₃×#103	C₂³	1	4	yes	—
221	C₂₃×#103	C₂³	1	2	yes	—
222	C₂₃×#103	C₂³	1	4	yes	—
223	C₂₃×#102	C₂³	1	2	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₂₃×#97	C₂³	1	2	yes	—
230	C₄×C₈×C₂₃	C₂³	1	2	yes	—
231	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
232	#41×C₂₃	—	4	4	no	—
233	#41×C₂₃	—	4	4	no	—
234	C₂×Q₈×C₂₃	—	2	4	no	—
235	C₂×Q₈×C₂₃	—	2	1	no	—
236	C₂×Q₈×C₂₃	—	2	1	no	—
237	C₂×Q₈×C₂₃	—	2	4	no	—
238	C₂×Q₈×C₂₃	—	2	4	no	—
239	C₂×Q₈×C₂₃	—	2	2	no	—
240	C₂×Q₈×C₂₃	—	2	2	no	—
241	C₂×Q₈×C₂₃	—	2	8	no	—
242	C₂×Q₈×C₂₃	—	2	8	no	—
243	C₂×Q₈×C₂₃	—	4	4	no	—
244	C₂×Q₈×C₂₃	—	4	4	no	—
245	C₂×Q₈×C₂₃	—	4	4	no	—
246	C₂×Q₈×C₂₃	—	4	8	no	—
247	C₂×Q₈×C₂₃	—	4	4	no	—
248	C₂×Q₈×C₂₃	—	4	8	no	—
249	C₂×Q₈×C₂₃	—	4	8	no	—
250	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
251	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
253	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
254	C₂×D₄×C₂₃	—	2	4	no	—
255	C₂×D₄×C₂₃	—	2	1	no	—
256	C₂×D₄×C₂₃	—	2	2	no	—
257	C₂×D₄×C₂₃	—	2	2	no	—
258	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
260	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
261	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₂₃	—	2	1	no	—
263	C₂²×C₄×C₂₃	—	2	1	no	—
264	C₂²×C₄×C₂₃	—	2	2	no	—
265	C₂²×C₄×C₂₃	—	2	2	no	—
266	C₂²×C₄×C₂₃	—	2	4	no	—
267	C₂²×C₄×C₂₃	—	2	4	no	—
268	C₂²×C₄×C₂₃	—	2	2	no	—
269	C₂²×C₄×C₂₃	—	2	1	no	—
270	C₂²×C₄×C₂₃	—	2	2	no	—
271	C₂²×C₄×C₂₃	—	4	4	no	—
272	C₂²×C₄×C₂₃	—	4	8	no	—
273	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
278	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
281	Q₁₆×C₂₃	—	2	4	no	—
282	Q₁₆×C₂₃	—	2	8	no	—
283	Q₁₆×C₂₃	—	4	4	no	—
284	Q₁₆×C₂₃	—	4	4	no	—
285	Q₁₆×C₂₃	—	4	4	no	—
286	SD₁₆×C₂₃	—	2	4	no	—
287	SD₁₆×C₂₃	—	4	4	no	—
288	M₁₆×C₂₃	—	4	4	no	—
289	C₂×C₈×C₂₃	—	4	4	no	—
290	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
291	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
292	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	1	no	—
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	—	2	2	no	—
301	C₄⋊C₄×C₂₃	—	2	2	no	—
302	C₄⋊C₄×C₂₃	—	2	2	no	—
303	C₄⋊C₄×C₂₃	—	2	2	no	—
304	C₄⋊C₄×C₂₃	—	2	4	no	—
305	C₄⋊C₄×C₂₃	—	2	4	no	—
306	C₄⋊C₄×C₂₃	—	2	1	no	—
307	C₄⋊C₄×C₂₃	—	2	2	no	—
308	C₄⋊C₄×C₂₃	—	2	1	no	—
309	C₄⋊C₄×C₂₃	—	2	1	no	—
310	C₄⋊C₄×C₂₃	—	2	1	no	—
311	C₄⋊C₄×C₂₃	—	2	2	no	—
312	C₄⋊C₄×C₂₃	—	2	1	no	—
313	C₄⋊C₄×C₂₃	—	2	2	no	—
314	C₄⋊C₄×C₂₃	—	2	1	no	—
315	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
316	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
317	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
318	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
319	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
322	C₂²⋊C₄×C₂₃	—	2	1	no	—
323	C₂²⋊C₄×C₂₃	—	2	2	no	—
324	C₂²⋊C₄×C₂₃	—	2	4	no	—
325	C₂²⋊C₄×C₂₃	—	2	4	no	—
326	C₂²⋊C₄×C₂₃	—	2	2	no	—
327	C₂²⋊C₄×C₂₃	—	2	2	no	—
328	C₂²⋊C₄×C₂₃	—	2	2	no	—
329	C₂²⋊C₄×C₂₃	—	2	2	no	—
330	C₂²⋊C₄×C₂₃	—	2	1	no	—
331	C₂²⋊C₄×C₂₃	—	2	1	no	—
332	C₂²⋊C₄×C₂₃	—	2	1	no	—
333	C₂²⋊C₄×C₂₃	—	2	2	no	—
334	C₂²⋊C₄×C₂₃	—	2	1	no	—
335	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
336	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
337	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
338	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
339	C₄²×C₂₃	—	2	2	no	—
340	C₄²×C₂₃	—	2	2	no	—
341	C₄²×C₂₃	—	2	2	no	—
342	C₄²×C₂₃	—	2	2	no	—
343	C₄²×C₂₃	—	2	1	no	—
344	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
345	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
347	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
348	#61602	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
349	C₂³×C₂₃	—	2	4	no	—
350	C₂³×C₂₃	—	2	4	no	—
351	C₂³×C₂₃	—	2	1	no	—
352	C₂³×C₂₃	—	4	2	no	—
353	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
354	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
355	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
356	Q₈×C₂₃	—	2	4	no	—
357	Q₈×C₂₃	—	2	2	no	—
358	Q₈×C₂₃	—	2	4	no	—
359	Q₈×C₂₃	—	2	2	no	—
360	Q₈×C₂₃	—	2	4	no	—
361	Q₈×C₂₃	—	2	4	no	—
362	Q₈×C₂₃	—	4	8	no	—
363	Q₈×C₂₃	—	4	8	no	—
364	Q₈×C₂₃	—	4	4	no	—
365	Q₈×C₂₃	—	4	2	no	—
366	Q₈×C₂₃	—	8	2	no	—
367	Q₈×C₂₃	H(5,𝔽₂)	1	4	yes	—
368	D₄×C₂₃	—	2	4	no	—
369	D₄×C₂₃	—	2	2	no	—
370	D₄×C₂₃	—	2	2	no	—
371	D₄×C₂₃	—	4	4	no	—
372	D₄×C₂₃	—	4	2	no	—
373	D₄×C₂₃	—	8	2	no	—
374	D₄×C₂₃	#137	1	4	yes	complemented
375	C₂×C₄×C₂₃	—	2	4	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	4	no	—
380	C₂×C₄×C₂₃	—	2	4	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	1	no	—
383	C₂×C₄×C₂₃	—	2	2	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	1	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	2	1	no	—
388	C₂×C₄×C₂₃	—	2	4	no	—
389	C₂×C₄×C₂₃	—	4	2	no	—
390	C₂×C₄×C₂₃	—	4	2	no	—
391	C₂×C₄×C₂₃	—	4	2	no	—
392	C₂×C₄×C₂₃	—	4	8	no	—
393	C₂×C₄×C₂₃	—	4	8	no	—
394	C₂×C₄×C₂₃	—	4	4	no	—
395	C₂×C₄×C₂₃	—	4	4	no	—
396	C₂×C₄×C₂₃	—	4	2	no	—
397	C₂×C₄×C₂₃	—	4	2	no	—
398	C₂×C₄×C₂₃	—	8	2	no	—
399	C₂×C₄×C₂₃	—	8	2	no	—
400	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
408	C₈×C₂₃	—	2	2	no	—
409	C₈×C₂₃	—	2	4	no	—
410	C₈×C₂₃	—	2	2	no	—
411	#3520	C₂×C₂₃	1	1	yes	characteristic
412	C₂×D₄×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
413	#3328	C₂×C₂₃	1	2	yes	complemented
414	#3312	C₂×C₂₃	1	4	yes	complemented
415	#3298	C₂×C₂₃	1	2	yes	complemented
416	D₄×Q₁₆	C₂×C₂₃	1	2	yes	complemented
417	#3276	C₂×C₂₃	1	2	yes	complemented
418	#3270	C₂×C₂₃	1	4	yes	complemented
419	#3218	C₂×C₂₃	1	1	yes	characteristic, complemented
420	#3209	C₂×C₂₃	1	1	yes	characteristic, complemented
421	#3195	C₂×C₂₃	1	2	yes	complemented
422	#3190	C₂×C₂₃	1	2	yes	complemented
423	#3113	C₂×C₂₃	1	1	yes	characteristic, complemented
424	#3108	C₂×C₂₃	1	1	yes	characteristic, complemented
425	#3004	C₂×C₂₃	1	2	yes	complemented
426	C₂×#451	C₂×C₂₃	1	2	yes	complemented
427	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
428	C₂²×C₂₃	—	2	1	no	—
429	C₂²×C₂₃	—	2	2	no	—
430	C₂²×C₂₃	—	2	1	no	—
431	C₂²×C₂₃	—	2	2	no	—
432	C₂²×C₂₃	—	2	2	no	—
433	C₂²×C₂₃	—	2	2	no	—
434	C₂²×C₂₃	—	2	2	no	—
435	C₂²×C₂₃	—	4	8	no	—
436	C₂²×C₂₃	—	4	1	no	—
437	C₂²×C₂₃	—	4	1	no	—
438	C₂²×C₂₃	—	4	1	no	—
439	C₂²×C₂₃	C₂×#137	1	4	yes	—
440	C₂²×C₂₃	#578	1	2	yes	—
441	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
442	C₄×C₂₃	—	2	4	no	—
443	C₄×C₂₃	—	2	1	no	—
444	C₄×C₂₃	—	2	2	no	—
445	C₄×C₂₃	—	2	2	no	—
446	C₄×C₂₃	—	2	1	no	—
447	C₄×C₂₃	—	2	1	no	—
448	C₄×C₂₃	—	2	1	no	—
449	C₄×C₂₃	—	4	4	no	—
450	C₄×C₂₃	—	4	2	no	—
451	C₄×C₂₃	—	4	1	no	—
452	C₄×C₂₃	—	4	1	no	—
453	C₄×C₂₃	—	4	2	no	—
454	C₄×C₂₃	—	4	2	no	—
455	C₄×C₂₃	—	4	1	no	—
456	C₄×C₂₃	C₂×#137	1	2	yes	—
457	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
458	C₂³×Q₈	C₂²×C₂₃	1	2	yes	—
459	C₂×#137	C₂²×C₂₃	1	4	yes	complemented
460	C₂²×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
461	#556	C₂²×C₂₃	1	1	yes	characteristic
462	#554	—	2	1	no	—
463	#552	C₂²×C₂₃	1	2	yes	—
464	#551	—	2	2	no	—
465	D₄×Q₈	—	2	1	no	—
466	D₄×Q₈	—	2	2	no	—
467	D₄×Q₈	—	2	1	no	—
468	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
469	D₄×Q₈	C₂²×C₂₃	1	4	yes	—
470	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
471	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
472	#548	C₂²×C₂₃	1	2	yes	—
473	#547	C₂²×C₂₃	1	1	yes	characteristic
474	#547	C₂²×C₂₃	1	1	yes	characteristic
475	#546	—	2	1	no	—
476	#542	—	2	1	no	—
477	#539	—	2	2	no	—
478	#533	C₂²×C₂₃	1	1	yes	characteristic
479	C₂×C₄⋊Q₈	—	2	1	no	—
480	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
481	#529	C₂²×C₂₃	1	1	yes	characteristic
482	#525	C₂²×C₂₃	1	2	yes	—
483	C₂×C₂²⋊Q₈	—	2	2	no	—
484	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
485	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
486	#520	—	2	1	no	—
487	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
488	C₂×C₄×D₄	—	2	1	no	—
489	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
490	#497	C₂²×C₂₃	1	2	yes	complemented
491	#494	C₂²×C₂₃	1	2	yes	complemented
492	#491	C₂²×C₂₃	1	2	yes	complemented
493	#487	C₂²×C₂₃	1	2	yes	complemented
494	#485	C₂²×C₂₃	1	4	yes	complemented
495	#483	C₂²×C₂₃	1	1	yes	characteristic
496	#483	C₂²×C₂₃	1	2	yes	—
497	#483	C₂²×C₂₃	1	4	yes	complemented
498	#480	C₂²×C₂₃	1	1	yes	characteristic
499	#479	C₂²×C₂₃	1	2	yes	complemented
500	#475	C₂²×C₂₃	1	2	yes	complemented
501	#470	C₂²×C₂₃	1	4	yes	complemented
502	#470	C₂²×C₂₃	1	4	yes	complemented
503	#467	C₂²×C₂₃	1	4	yes	complemented
504	#465	C₂²×C₂₃	1	4	yes	complemented
505	#464	C₂²×C₂₃	1	2	yes	complemented
506	#462	C₂²×C₂₃	1	2	yes	complemented
507	#462	C₂²×C₂₃	1	2	yes	complemented
508	#462	C₂²×C₂₃	1	4	yes	complemented
509	#461	C₂²×C₂₃	1	2	yes	complemented
510	#452	C₂²×C₂₃	1	4	yes	complemented
511	#451	C₂²×C₂₃	1	1	yes	characteristic
512	#451	C₂²×C₂₃	1	2	yes	—
513	#451	C₂²×C₂₃	1	2	yes	—
514	#451	C₂²×C₂₃	1	2	yes	—
515	#451	C₂²×C₂₃	1	2	yes	—
516	#451	C₂²×C₂₃	1	4	yes	complemented
517	#451	C₂²×C₂₃	1	4	yes	complemented
518	#451	C₂²×C₂₃	1	4	yes	complemented
519	#451	C₂²×C₂₃	1	4	yes	complemented
520	#448	C₂²×C₂₃	1	1	yes	characteristic
521	#448	C₂²×C₂₃	1	2	yes	—
522	#448	C₂²×C₂₃	1	4	yes	complemented
523	#441	C₂²×C₂₃	1	4	yes	complemented
524	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
525	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
526	#436	C₂²×C₂₃	1	2	yes	—
527	#435	C₂²×C₂₃	1	4	yes	—
528	C₈×D₄	C₂²×C₂₃	1	2	yes	—
529	#432	C₂²×C₂₃	1	1	yes	characteristic
530	#431	C₂²×C₂₃	1	1	yes	characteristic
531	#419	C₂²×C₂₃	1	4	yes	complemented
532	C₂×#103	C₂²×C₂₃	1	4	yes	complemented
533	#407	C₂²×C₂₃	1	2	yes	—
534	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
535	C₂×C₂₃	—	2	2	no	—
536	C₂×C₂₃	—	2	4	no	—
537	C₂×C₂₃	—	4	2	no	—
538	C₂×C₂₃	—	8	1	no	—
539	C₂×C₂₃	#3484	1	1	yes	characteristic
540	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
541	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
542	C₂×#41	—	2	1	no	—
543	C₂×#41	C₂³×C₂₃	1	2	yes	—
544	C₂²×Q₈	—	2	2	no	—
545	C₂²×Q₈	—	2	2	no	—
546	C₂²×Q₈	—	2	2	no	—
547	C₂²×Q₈	—	4	8	no	—
548	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
550	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
551	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
552	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
553	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
554	C₂³×C₄	—	2	2	no	—
555	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
556	#137	—	4	8	no	—
557	C₂×Q₁₆	—	4	8	no	—
558	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
559	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
560	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
561	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
562	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
563	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
564	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
565	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
566	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
567	C₄⋊Q₈	—	2	2	no	—
568	C₄⋊Q₈	—	2	4	no	—
569	C₄⋊Q₈	—	2	2	no	—
570	C₄⋊Q₈	—	2	1	no	—
571	C₄⋊Q₈	—	2	1	no	—
572	C₄⋊Q₈	—	2	1	no	—
573	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
574	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
575	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
576	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
577	#126	—	2	2	no	—
578	#126	—	2	2	no	—
579	#126	—	2	1	no	—
580	#125	—	2	2	no	—
581	#125	—	2	1	no	—
582	#125	C₂³×C₂₃	1	1	yes	characteristic
583	#124	—	2	1	no	—
584	#124	—	2	2	no	—
585	#124	C₂³×C₂₃	1	1	yes	characteristic
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	1	no	—
589	#123	—	2	2	no	—
590	#123	—	2	2	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	1	no	—
598	C₂²⋊Q₈	—	2	4	no	—
599	C₂²⋊Q₈	—	2	4	no	—
600	C₂²⋊Q₈	—	2	4	no	—
601	C₂²⋊Q₈	—	2	4	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
604	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
605	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
606	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
607	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
608	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
609	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
610	#121	—	2	2	no	—
611	#121	—	2	1	no	—
612	#121	C₂³×C₂₃	1	1	yes	characteristic
613	#121	C₂³×C₂₃	1	2	yes	—
614	#120	—	2	2	no	—
615	C₄×Q₈	—	2	1	no	—
616	C₄×Q₈	—	2	1	no	—
617	C₄×Q₈	—	2	1	no	—
618	C₄×Q₈	—	2	1	no	—
619	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
620	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
621	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
622	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
623	C₄×D₄	—	2	4	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
632	C₄×D₄	D₄×C₂₃	1	2	yes	—
633	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
634	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
635	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₂₃	1	2	yes	—
638	#117	—	2	1	no	—
639	#117	—	2	2	no	—
640	#117	—	2	1	no	—
641	#117	C₂³×C₂₃	1	2	yes	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	2	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	2	no	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
651	C₂×C₂²⋊C₄	—	2	2	no	—
652	C₂×C₂²⋊C₄	—	2	2	no	—
653	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
656	#107	C₂³×C₂₃	1	2	yes	—
657	#106	C₂³×C₂₃	1	2	yes	—
658	#106	C₂³×C₂₃	1	4	yes	—
659	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
660	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
661	#103	C₂³×C₂₃	1	2	yes	—
662	#103	C₂³×C₂₃	1	4	yes	—
663	#103	C₂³×C₂₃	1	4	yes	—
664	#103	C₂³×C₂₃	1	4	yes	—
665	#103	C₂³×C₂₃	1	2	yes	—
666	#103	C₂³×C₂₃	1	4	yes	—
667	#103	C₂³×C₂₃	1	4	yes	—
668	#103	C₂³×C₂₃	1	2	yes	—
669	#103	C₂³×C₂₃	1	4	yes	—
670	#102	C₂³×C₂₃	1	2	yes	—
671	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
672	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
673	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
674	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
675	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
676	#97	C₂³×C₂₃	1	2	yes	—
677	C₄×C₈	C₂³×C₂₃	1	2	yes	—
678	C₂₃	#61602	1	1	yes	characteristic, direct product factor, Sylow
679	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
680	#41	—	4	4	no	—
681	#41	—	4	4	no	—
682	C₂×Q₈	—	2	4	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	—	2	4	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	8	no	—
690	C₂×Q₈	—	2	8	no	—
691	C₂×Q₈	—	4	4	no	—
692	C₂×Q₈	—	4	4	no	—
693	C₂×Q₈	—	4	4	no	—
694	C₂×Q₈	—	4	8	no	—
695	C₂×Q₈	—	4	4	no	—
696	C₂×Q₈	—	4	8	no	—
697	C₂×Q₈	—	4	8	no	—
698	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
699	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
700	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
701	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
707	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
708	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
709	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	4	4	no	—
720	C₂²×C₄	—	4	8	no	—
721	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
723	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
724	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
725	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
729	Q₁₆	—	2	4	no	—
730	Q₁₆	—	2	8	no	—
731	Q₁₆	—	4	4	no	—
732	Q₁₆	—	4	4	no	—
733	Q₁₆	—	4	4	no	—
734	SD₁₆	—	2	4	no	—
735	SD₁₆	—	4	4	no	—
736	M₁₆	—	4	4	no	—
737	C₂×C₈	—	4	4	no	—
738	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
739	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
740	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
764	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
765	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
766	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
767	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
768	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	1	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
784	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
785	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
786	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	1	no	—
792	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
793	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
794	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
795	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
796	C₂³	—	2	4	no	—
797	C₂³	—	2	4	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	4	2	no	—
800	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
801	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
802	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
803	Q₈	—	2	4	no	—
804	Q₈	—	2	2	no	—
805	Q₈	—	2	4	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	2	4	no	—
808	Q₈	—	2	4	no	—
809	Q₈	—	4	8	no	—
810	Q₈	—	4	8	no	—
811	Q₈	—	4	4	no	—
812	Q₈	—	4	2	no	—
813	Q₈	—	8	2	no	—
814	Q₈	C₂₃×H(5,𝔽₂)	1	4	yes	—
815	D₄	—	2	4	no	—
816	D₄	—	2	2	no	—
817	D₄	—	2	2	no	—
818	D₄	—	4	4	no	—
819	D₄	—	4	2	no	—
820	D₄	—	8	2	no	—
821	D₄	C₂₃×#137	1	4	yes	complemented
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	4	8	no	—
840	C₂×C₄	—	4	8	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	8	2	no	—
846	C₂×C₄	—	8	2	no	—
847	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
850	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
852	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
853	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
854	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
855	C₈	—	2	2	no	—
856	C₈	—	2	4	no	—
857	C₈	—	2	2	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	4	8	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	C₂×C₂₃×#137	1	4	yes	—
870	C₂²	C₂₃×#578	1	2	yes	—
871	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
872	C₄	—	2	4	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	2	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	1	no	—
879	C₄	—	4	4	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	1	no	—
886	C₄	C₂×C₂₃×#137	1	2	yes	—
887	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
888	C₂	—	2	2	no	—
889	C₂	—	2	4	no	—
890	C₂	—	4	2	no	—
891	C₂	—	8	1	no	—
892	C₂	C₂₃×#3484	1	1	yes	characteristic
893	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
894	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3520	C₂
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
2. C₂×D₄×Q₈×C₂₃	C₂	semidirect
3. C₂₃×#3328	C₂	semidirect
4. C₂₃×#3312	C₂	semidirect
5. C₂₃×#3298	C₂	semidirect
6. D₄×Q₁₆×C₂₃	C₂	semidirect
7. C₂₃×#3276	C₂	semidirect
8. C₂₃×#3270	C₂	semidirect
9. C₂₃×#3218	C₂	semidirect
10. C₂₃×#3209	C₂	semidirect
11. C₂₃×#3195	C₂	semidirect
12. C₂₃×#3190	C₂	semidirect
13. C₂₃×#3113	C₂	semidirect
14. C₂₃×#3108	C₂	semidirect
15. C₂₃×#3004	C₂	semidirect
16. C₂×C₂₃×#451	C₂	semidirect
17. C₂₃×#2974	C₂	semidirect
19. C₂×C₂₃×#137	C₂²	semidirect
20. C₂²×Q₁₆×C₂₃	C₂²	semidirect
50. C₂₃×#497	C₂²	semidirect
51. C₂₃×#494	C₂²	semidirect
52. C₂₃×#491	C₂²	semidirect
53. C₂₃×#487	C₂²	semidirect
54. C₂₃×#485	C₂²	semidirect
57. C₂₃×#483	C₂²	semidirect
59. C₂₃×#479	C₂²	semidirect
60. C₂₃×#475	C₂²	semidirect
61. C₂₃×#470	C₂²	semidirect
62. C₂₃×#470	C₂²	semidirect
63. C₂₃×#467	C₂²	semidirect
64. C₂₃×#465	C₂²	semidirect
65. C₂₃×#464	C₂²	semidirect
66. C₂₃×#462	C₂²	semidirect
67. C₂₃×#462	C₂²	semidirect
68. C₂₃×#462	C₂²	semidirect
69. C₂₃×#461	C₂²	semidirect
70. C₂₃×#452	C₂²	semidirect
76. C₂₃×#451	C₂²	semidirect
77. C₂₃×#451	C₂²	semidirect
78. C₂₃×#451	C₂²	semidirect
79. C₂₃×#451	C₂²	semidirect
82. C₂₃×#448	C₂²	semidirect
83. C₂₃×#441	C₂²	semidirect
84. C₄×Q₁₆×C₂₃	C₂²	semidirect
85. C₄×SD₁₆×C₂₃	C₂²	semidirect
91. C₂₃×#419	C₂²	semidirect
92. C₂×C₂₃×#103	C₂²	semidirect
348. #61602	C₂₃	direct (N × H)
374. D₄×C₂₃	#137	semidirect
412. C₂×D₄×Q₈	C₂×C₂₃	semidirect
413. #3328	C₂×C₂₃	semidirect
414. #3312	C₂×C₂₃	semidirect
415. #3298	C₂×C₂₃	semidirect
416. D₄×Q₁₆	C₂×C₂₃	semidirect
417. #3276	C₂×C₂₃	semidirect
418. #3270	C₂×C₂₃	semidirect
419. #3218	C₂×C₂₃	semidirect
420. #3209	C₂×C₂₃	semidirect
421. #3195	C₂×C₂₃	semidirect
422. #3190	C₂×C₂₃	semidirect
423. #3113	C₂×C₂₃	semidirect
424. #3108	C₂×C₂₃	semidirect
425. #3004	C₂×C₂₃	semidirect
426. C₂×#451	C₂×C₂₃	semidirect
427. #2974	C₂×C₂₃	semidirect
459. C₂×#137	C₂²×C₂₃	semidirect
460. C₂²×Q₁₆	C₂²×C₂₃	semidirect
490. #497	C₂²×C₂₃	semidirect
491. #494	C₂²×C₂₃	semidirect
492. #491	C₂²×C₂₃	semidirect
493. #487	C₂²×C₂₃	semidirect
494. #485	C₂²×C₂₃	semidirect
497. #483	C₂²×C₂₃	semidirect
499. #479	C₂²×C₂₃	semidirect
500. #475	C₂²×C₂₃	semidirect
501. #470	C₂²×C₂₃	semidirect
502. #470	C₂²×C₂₃	semidirect
503. #467	C₂²×C₂₃	semidirect
504. #465	C₂²×C₂₃	semidirect
505. #464	C₂²×C₂₃	semidirect
506. #462	C₂²×C₂₃	semidirect
507. #462	C₂²×C₂₃	semidirect
508. #462	C₂²×C₂₃	semidirect
509. #461	C₂²×C₂₃	semidirect
510. #452	C₂²×C₂₃	semidirect
516. #451	C₂²×C₂₃	semidirect
517. #451	C₂²×C₂₃	semidirect
518. #451	C₂²×C₂₃	semidirect
519. #451	C₂²×C₂₃	semidirect
522. #448	C₂²×C₂₃	semidirect
523. #441	C₂²×C₂₃	semidirect
524. C₄×Q₁₆	C₂²×C₂₃	semidirect
525. C₄×SD₁₆	C₂²×C₂₃	semidirect
531. #419	C₂²×C₂₃	semidirect
532. C₂×#103	C₂²×C₂₃	semidirect
678. C₂₃	#61602	direct (N × H)
821. D₄	C₂₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3520	2
C₂×D₄×Q₈×C₂₃	2
C₂₃×#3328	2
C₂₃×#3312	2
C₂₃×#3298	2
D₄×Q₁₆×C₂₃	2
C₂₃×#3276	2
C₂₃×#3270	2
C₂₃×#3218	2
C₂₃×#3209	2
C₂₃×#3195	2
C₂₃×#3190	2
C₂₃×#3113	2
C₂₃×#3108	2
C₂₃×#3004	2
C₂×C₂₃×#451	2
C₂₃×#2974	2
#61602	23

Subgroups — C23×#61602 #19209228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61602 #19209228