Subgroups — C₂₃×#60583 #19208209

Order 5888.

1998 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3127	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3121	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3117	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3113	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3108	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3104	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3091	C₂	1	1	yes	maximal, characteristic
11	C₂₃×#3082	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3044	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3004	C₂	1	1	yes	maximal, characteristic
14	C₂×C₂₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2950	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2947	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#137	C₂²	1	2	yes	—
20	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	—
21	C₂₃×#556	—	2	1	no	—
22	C₂₃×#554	—	2	1	no	—
23	C₂₃×#552	—	2	2	no	—
24	C₂₃×#552	—	2	1	no	—
25	C₂₃×#552	—	2	1	no	—
26	C₂₃×#551	—	2	2	no	—
27	C₂₃×#544	C₂²	1	1	yes	characteristic
28	C₂₃×#542	C₂²	1	2	yes	—
29	C₂₃×#541	C₂²	1	2	yes	—
30	C₂₃×#536	C₂²	1	1	yes	characteristic
31	C₂₃×#533	C₂²	1	2	yes	—
32	C₂₃×#529	C₂²	1	2	yes	—
33	C₂₃×#525	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂₃×#520	C₂²	1	1	yes	characteristic
36	C₂₃×#519	—	2	2	no	—
37	C₂₃×#519	—	2	1	no	—
38	C₂₃×#519	—	2	1	no	—
39	C₂₃×#519	C₂²	1	2	yes	—
40	C₂₃×#519	C₂²	1	2	yes	—
41	C₂₃×#519	C₂²	1	4	yes	—
42	C₂₃×#519	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
44	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
45	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
47	C₂×C₂₃×#117	—	2	2	no	—
48	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
49	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
50	C₂₃×#485	C₂²	1	2	yes	—
51	C₂₃×#485	C₂²	1	4	yes	—
52	C₂₃×#484	C₂²	1	1	yes	characteristic
53	C₂₃×#484	C₂²	1	2	yes	—
54	C₂₃×#483	C₂²	1	1	yes	characteristic
55	C₂₃×#483	C₂²	1	2	yes	—
56	C₂₃×#482	C₂²	1	2	yes	—
57	C₂₃×#481	C₂²	1	1	yes	characteristic
58	C₂₃×#480	C₂²	1	1	yes	characteristic
59	C₂₃×#479	C₂²	1	4	yes	complemented
60	C₂₃×#479	C₂²	1	4	yes	complemented
61	C₂₃×#477	C₂²	1	4	yes	complemented
62	C₂₃×#475	C₂²	1	4	yes	complemented
63	C₂₃×#464	C₂²	1	4	yes	complemented
64	C₂₃×#464	C₂²	1	4	yes	complemented
65	C₂₃×#462	C₂²	1	4	yes	complemented
66	C₂₃×#462	C₂²	1	4	yes	complemented
67	C₂₃×#451	C₂²	1	2	yes	—
68	C₂₃×#451	C₂²	1	2	yes	—
69	C₂₃×#451	C₂²	1	4	yes	—
70	C₂₃×#451	C₂²	1	2	yes	—
71	C₂₃×#451	C₂²	1	2	yes	—
72	C₂₃×#448	C₂²	1	2	yes	—
73	C₂₃×#448	C₂²	1	2	yes	—
74	C₂₃×#441	C₂²	1	4	yes	complemented
75	C₂₃×#441	C₂²	1	4	yes	complemented
76	C₂₃×#441	C₂²	1	4	yes	complemented
77	C₂₃×#440	C₂²	1	4	yes	complemented
78	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
79	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
80	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
81	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
82	C₂₃×#433	C₂²	1	4	yes	—
83	C₂₃×#432	C₂²	1	2	yes	—
84	C₂₃×#431	C₂²	1	2	yes	—
85	C₂₃×#428	C₂²	1	2	yes	—
86	C₂₃×#427	C₂²	1	2	yes	—
87	C₂₃×#424	C₂²	1	2	yes	—
88	C₂₃×#419	C₂²	1	2	yes	—
89	C₂₃×#419	C₂²	1	2	yes	—
90	C₂₃×#416	C₂²	1	2	yes	—
91	C₂×C₂₃×#103	C₂²	1	2	yes	—
92	C₂₃×#407	C₂²	1	1	yes	characteristic
93	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₂₃×#405	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₂₃	—	2	8	no	—
97	C₂²×Q₈×C₂₃	—	2	1	no	—
98	C₂²×Q₈×C₂₃	—	2	1	no	—
99	C₂²×Q₈×C₂₃	—	2	1	no	—
100	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
103	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
104	C₂³×C₄×C₂₃	—	2	1	no	—
105	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂₃×#137	—	2	8	no	—
107	C₂×Q₁₆×C₂₃	—	2	8	no	—
108	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
109	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
110	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
112	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
114	C₂₃×C₄⋊Q₈	—	2	1	no	—
115	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₂₃×#126	—	2	2	no	—
118	C₂₃×#126	—	2	2	no	—
119	C₂₃×#126	—	2	2	no	—
120	C₂₃×#126	—	2	2	no	—
121	C₂₃×#125	—	2	2	no	—
122	C₂₃×#125	—	2	1	no	—
123	C₂₃×#125	—	2	2	no	—
124	C₂₃×#125	—	2	2	no	—
125	C₂₃×#125	C₂³	1	2	yes	—
126	C₂₃×#124	—	2	2	no	—
127	C₂₃×#124	C₂³	1	2	yes	—
128	C₂₃×#123	—	2	2	no	—
129	C₂₃×#123	—	2	1	no	—
130	C₂₃×#123	—	2	2	no	—
131	C₂₃×#123	—	2	2	no	—
132	C₂₃×C₂²⋊Q₈	—	2	2	no	—
133	C₂₃×C₂²⋊Q₈	—	2	1	no	—
134	C₂₃×C₂²⋊Q₈	—	2	1	no	—
135	C₂₃×C₂²⋊Q₈	—	2	1	no	—
136	C₂₃×C₂²⋊Q₈	—	2	2	no	—
137	C₂₃×C₂²⋊Q₈	—	2	1	no	—
138	C₂₃×C₂²⋊Q₈	—	2	2	no	—
139	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
140	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
141	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
143	C₂₃×#121	C₂³	1	1	yes	characteristic
144	C₂₃×#121	C₂³	1	1	yes	characteristic
145	C₂₃×#120	—	2	1	no	—
146	C₄×Q₈×C₂₃	—	2	1	no	—
147	C₄×Q₈×C₂₃	—	2	1	no	—
148	C₄×Q₈×C₂₃	—	2	2	no	—
149	C₄×Q₈×C₂₃	—	2	2	no	—
150	C₄×Q₈×C₂₃	—	2	2	no	—
151	C₄×Q₈×C₂₃	—	2	4	no	—
152	C₄×Q₈×C₂₃	—	2	2	no	—
153	C₄×Q₈×C₂₃	—	2	4	no	—
154	C₄×Q₈×C₂₃	—	2	2	no	—
155	C₄×Q₈×C₂₃	—	2	2	no	—
156	C₄×Q₈×C₂₃	—	2	2	no	—
157	C₄×Q₈×C₂₃	—	2	2	no	—
158	C₄×Q₈×C₂₃	—	2	2	no	—
159	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
160	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
161	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
163	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
165	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
166	C₄×D₄×C₂₃	—	2	2	no	—
167	C₄×D₄×C₂₃	—	2	1	no	—
168	C₄×D₄×C₂₃	—	2	1	no	—
169	C₄×D₄×C₂₃	—	2	2	no	—
170	C₄×D₄×C₂₃	C₂³	1	2	yes	—
171	C₂₃×#117	—	2	2	no	—
172	C₂₃×#117	—	2	1	no	—
173	C₂₃×#117	—	2	1	no	—
174	C₂₃×#117	—	2	1	no	—
175	C₂₃×#117	—	2	2	no	—
176	C₂₃×#117	—	2	4	no	—
177	C₂₃×#117	—	2	4	no	—
178	C₂₃×#117	—	2	4	no	—
179	C₂₃×#117	—	2	4	no	—
180	C₂₃×#117	—	2	2	no	—
181	C₂₃×#117	D₄	1	1	yes	characteristic
182	C₂₃×#117	D₄	1	2	yes	—
183	C₂₃×#117	D₄	1	1	yes	characteristic
184	C₂₃×#117	C₂³	1	2	yes	—
185	C₂₃×#117	C₂³	1	1	yes	characteristic
186	C₂₃×#117	C₂³	1	2	yes	—
187	C₂₃×#117	C₂³	1	1	yes	characteristic
188	C₂₃×#117	C₂³	1	1	yes	characteristic
189	C₂₃×#117	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
193	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
194	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
201	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
202	C₂×C₄²×C₂₃	—	2	2	no	—
203	C₂×C₄²×C₂₃	—	2	2	no	—
204	C₂×C₄²×C₂₃	—	2	1	no	—
205	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
206	C₂₃×#107	C₂³	1	2	yes	—
207	C₂₃×#107	C₂³	1	2	yes	—
208	C₂₃×#107	C₂³	1	4	yes	—
209	C₂₃×#106	C₂³	1	2	yes	—
210	C₂₃×#106	C₂³	1	2	yes	—
211	C₂₃×#106	C₂³	1	4	yes	—
212	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	2	yes	—
217	C₂₃×#103	C₂³	1	2	yes	—
218	C₂₃×#103	C₂³	1	4	yes	—
219	C₂₃×#103	C₂³	1	4	yes	—
220	C₂₃×#103	C₂³	1	4	yes	—
221	C₂₃×#103	C₂³	1	4	yes	—
222	C₂₃×#102	C₂³	1	2	yes	—
223	C₂₃×#102	C₂³	1	2	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
226	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
229	C₂₃×#97	C₂³	1	4	yes	—
230	C₄×C₈×C₂₃	C₂³	1	4	yes	—
231	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
232	#41×C₂₃	—	2	4	no	—
233	C₂×Q₈×C₂₃	—	2	8	no	—
234	C₂×Q₈×C₂₃	—	2	8	no	—
235	C₂×Q₈×C₂₃	—	2	8	no	—
236	C₂×Q₈×C₂₃	—	2	8	no	—
237	C₂×Q₈×C₂₃	—	2	8	no	—
238	C₂×Q₈×C₂₃	—	2	2	no	—
239	C₂×Q₈×C₂₃	—	2	2	no	—
240	C₂×Q₈×C₂₃	—	2	2	no	—
241	C₂×Q₈×C₂₃	—	2	1	no	—
242	C₂×Q₈×C₂₃	—	2	2	no	—
243	C₂×Q₈×C₂₃	—	2	4	no	—
244	C₂×Q₈×C₂₃	—	2	4	no	—
245	C₂×Q₈×C₂₃	#41	1	8	yes	—
246	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
248	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
249	C₂×D₄×C₂₃	—	2	1	no	—
250	C₂×D₄×C₂₃	—	2	1	no	—
251	C₂×D₄×C₂₃	—	2	1	no	—
252	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	—	2	8	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	2	2	no	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	2	4	no	—
258	C₂²×C₄×C₂₃	—	2	1	no	—
259	C₂²×C₄×C₂₃	—	2	1	no	—
260	C₂²×C₄×C₂₃	—	2	1	no	—
261	C₂²×C₄×C₂₃	—	2	1	no	—
262	C₂²×C₄×C₂₃	—	2	1	no	—
263	C₂²×C₄×C₂₃	—	2	2	no	—
264	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
272	Q₁₆×C₂₃	—	2	8	no	—
273	Q₁₆×C₂₃	—	2	8	no	—
274	Q₁₆×C₂₃	—	2	8	no	—
275	SD₁₆×C₂₃	—	2	8	no	—
276	M₁₆×C₂₃	—	2	4	no	—
277	C₂×C₈×C₂₃	—	2	4	no	—
278	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
279	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
280	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₄⋊C₄×C₂₃	—	2	4	no	—
283	C₄⋊C₄×C₂₃	—	2	4	no	—
284	C₄⋊C₄×C₂₃	—	2	4	no	—
285	C₄⋊C₄×C₂₃	—	2	4	no	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	1	no	—
290	C₄⋊C₄×C₂₃	—	2	1	no	—
291	C₄⋊C₄×C₂₃	—	2	2	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	1	no	—
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	1	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
305	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
309	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
311	C₂²⋊C₄×C₂₃	—	2	2	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	2	no	—
314	C₂²⋊C₄×C₂₃	—	2	2	no	—
315	C₂²⋊C₄×C₂₃	—	2	1	no	—
316	C₂²⋊C₄×C₂₃	—	2	1	no	—
317	C₂²⋊C₄×C₂₃	—	2	1	no	—
318	C₂²⋊C₄×C₂₃	—	2	1	no	—
319	C₂²⋊C₄×C₂₃	—	2	2	no	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	1	no	—
322	C₂²⋊C₄×C₂₃	—	2	2	no	—
323	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
327	C₄²×C₂₃	—	2	4	no	—
328	C₄²×C₂₃	—	2	4	no	—
329	C₄²×C₂₃	—	2	4	no	—
330	C₄²×C₂₃	—	2	4	no	—
331	C₄²×C₂₃	—	2	2	no	—
332	C₄²×C₂₃	—	2	2	no	—
333	C₄²×C₂₃	—	2	2	no	—
334	C₄²×C₂₃	—	2	2	no	—
335	C₄²×C₂₃	—	2	2	no	—
336	C₄²×C₂₃	—	2	1	no	—
337	C₄²×C₂₃	C₂×D₄	1	2	yes	—
338	C₄²×C₂₃	C₂×D₄	1	2	yes	—
339	C₄²×C₂₃	C₂⁴	1	2	yes	—
340	C₄²×C₂₃	C₂⁴	1	2	yes	—
341	#60583	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₂³×C₂₃	—	2	2	no	—
343	C₂³×C₂₃	—	2	2	no	—
344	C₂³×C₂₃	—	2	1	no	—
345	C₂³×C₂₃	—	4	1	no	—
346	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
347	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
348	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
349	Q₈×C₂₃	—	2	8	no	—
350	Q₈×C₂₃	—	2	8	no	—
351	Q₈×C₂₃	—	2	8	no	—
352	Q₈×C₂₃	—	2	4	no	—
353	Q₈×C₂₃	—	2	4	no	—
354	Q₈×C₂₃	—	2	2	no	—
355	Q₈×C₂₃	—	4	2	no	—
356	Q₈×C₂₃	—	8	2	no	—
357	Q₈×C₂₃	C₂×#41	1	8	yes	—
358	D₄×C₂₃	—	2	2	no	—
359	D₄×C₂₃	—	4	2	no	—
360	D₄×C₂₃	—	4	2	no	—
361	D₄×C₂₃	—	8	1	no	—
362	C₂×C₄×C₂₃	—	2	8	no	—
363	C₂×C₄×C₂₃	—	2	8	no	—
364	C₂×C₄×C₂₃	—	2	8	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	4	no	—
367	C₂×C₄×C₂₃	—	2	4	no	—
368	C₂×C₄×C₂₃	—	2	2	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	2	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	2	1	no	—
375	C₂×C₄×C₂₃	—	2	1	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	1	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	4	2	no	—
380	C₂×C₄×C₂₃	—	4	2	no	—
381	C₂×C₄×C₂₃	—	4	2	no	—
382	C₂×C₄×C₂₃	—	4	2	no	—
383	C₂×C₄×C₂₃	—	4	2	no	—
384	C₂×C₄×C₂₃	—	8	2	no	—
385	C₂×C₄×C₂₃	—	8	1	no	—
386	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
394	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
395	C₈×C₂₃	—	2	2	no	—
396	C₈×C₂₃	—	2	2	no	—
397	C₈×C₂₃	—	2	4	no	—
398	#3495	C₂×C₂₃	1	1	yes	characteristic
399	C₂×#519	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#3127	C₂×C₂₃	1	4	yes	complemented
401	#3121	C₂×C₂₃	1	4	yes	complemented
402	#3117	C₂×C₂₃	1	2	yes	complemented
403	#3113	C₂×C₂₃	1	2	yes	complemented
404	#3108	C₂×C₂₃	1	2	yes	complemented
405	#3104	C₂×C₂₃	1	2	yes	complemented
406	#3095	C₂×C₂₃	1	1	yes	characteristic, complemented
407	#3091	C₂×C₂₃	1	1	yes	characteristic
408	#3082	C₂×C₂₃	1	2	yes	complemented
409	#3044	C₂×C₂₃	1	2	yes	complemented
410	#3004	C₂×C₂₃	1	1	yes	characteristic
411	C₂×#451	C₂×C₂₃	1	1	yes	characteristic, complemented
412	#2950	C₂×C₂₃	1	2	yes	complemented
413	#2947	C₂×C₂₃	1	2	yes	complemented
414	#2924	C₂×C₂₃	1	1	yes	characteristic, complemented
415	C₂²×C₂₃	—	2	1	no	—
416	C₂²×C₂₃	—	2	1	no	—
417	C₂²×C₂₃	—	2	1	no	—
418	C₂²×C₂₃	—	2	1	no	—
419	C₂²×C₂₃	—	2	1	no	—
420	C₂²×C₂₃	—	2	1	no	—
421	C₂²×C₂₃	—	2	1	no	—
422	C₂²×C₂₃	—	4	4	no	—
423	C₂²×C₂₃	—	4	1	no	—
424	C₂²×C₂₃	—	4	1	no	—
425	C₂²×C₂₃	—	4	1	no	—
426	C₂²×C₂₃	#525	1	2	yes	—
427	C₂²×C₂₃	#578	1	2	yes	—
428	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
429	C₄×C₂₃	—	2	2	no	—
430	C₄×C₂₃	—	2	2	no	—
431	C₄×C₂₃	—	2	8	no	—
432	C₄×C₂₃	—	2	1	no	—
433	C₄×C₂₃	—	2	1	no	—
434	C₄×C₂₃	—	2	2	no	—
435	C₄×C₂₃	—	2	2	no	—
436	C₄×C₂₃	—	4	2	no	—
437	C₄×C₂₃	—	4	2	no	—
438	C₄×C₂₃	—	4	1	no	—
439	C₄×C₂₃	—	4	1	no	—
440	C₄×C₂₃	—	4	2	no	—
441	C₄×C₂₃	—	4	2	no	—
442	C₄×C₂₃	—	4	1	no	—
443	C₄×C₂₃	#525	1	2	yes	—
444	C₄×C₂₃	C₂²×#41	1	2	yes	—
445	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×#137	C₂²×C₂₃	1	2	yes	—
447	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	—
448	#556	—	2	1	no	—
449	#554	—	2	1	no	—
450	#552	—	2	2	no	—
451	#552	—	2	1	no	—
452	#552	—	2	1	no	—
453	#551	—	2	2	no	—
454	#544	C₂²×C₂₃	1	1	yes	characteristic
455	#542	C₂²×C₂₃	1	2	yes	—
456	#541	C₂²×C₂₃	1	2	yes	—
457	#536	C₂²×C₂₃	1	1	yes	characteristic
458	#533	C₂²×C₂₃	1	2	yes	—
459	#529	C₂²×C₂₃	1	2	yes	—
460	#525	C₂²×C₂₃	1	1	yes	characteristic
461	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
462	#520	C₂²×C₂₃	1	1	yes	characteristic
463	#519	—	2	2	no	—
464	#519	—	2	1	no	—
465	#519	—	2	1	no	—
466	#519	C₂²×C₂₃	1	2	yes	—
467	#519	C₂²×C₂₃	1	4	yes	—
468	#519	C₂²×C₂₃	1	2	yes	—
469	#519	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×C₄×Q₈	—	2	1	no	—
471	C₂×C₄×Q₈	—	2	1	no	—
472	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
473	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
474	C₂×#117	—	2	2	no	—
475	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
476	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
477	#485	C₂²×C₂₃	1	2	yes	—
478	#485	C₂²×C₂₃	1	4	yes	—
479	#484	C₂²×C₂₃	1	1	yes	characteristic
480	#484	C₂²×C₂₃	1	2	yes	—
481	#483	C₂²×C₂₃	1	1	yes	characteristic
482	#483	C₂²×C₂₃	1	2	yes	—
483	#482	C₂²×C₂₃	1	2	yes	—
484	#481	C₂²×C₂₃	1	1	yes	characteristic
485	#480	C₂²×C₂₃	1	1	yes	characteristic
486	#479	C₂²×C₂₃	1	4	yes	complemented
487	#479	C₂²×C₂₃	1	4	yes	complemented
488	#477	C₂²×C₂₃	1	4	yes	complemented
489	#475	C₂²×C₂₃	1	4	yes	complemented
490	#464	C₂²×C₂₃	1	4	yes	complemented
491	#464	C₂²×C₂₃	1	4	yes	complemented
492	#462	C₂²×C₂₃	1	4	yes	complemented
493	#462	C₂²×C₂₃	1	4	yes	complemented
494	#451	C₂²×C₂₃	1	2	yes	—
495	#451	C₂²×C₂₃	1	2	yes	—
496	#451	C₂²×C₂₃	1	2	yes	—
497	#451	C₂²×C₂₃	1	4	yes	—
498	#451	C₂²×C₂₃	1	2	yes	—
499	#448	C₂²×C₂₃	1	2	yes	—
500	#448	C₂²×C₂₃	1	2	yes	—
501	#441	C₂²×C₂₃	1	4	yes	complemented
502	#441	C₂²×C₂₃	1	4	yes	complemented
503	#441	C₂²×C₂₃	1	4	yes	complemented
504	#440	C₂²×C₂₃	1	4	yes	complemented
505	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
506	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
507	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
508	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
509	#433	C₂²×C₂₃	1	4	yes	—
510	#432	C₂²×C₂₃	1	2	yes	—
511	#431	C₂²×C₂₃	1	2	yes	—
512	#428	C₂²×C₂₃	1	2	yes	—
513	#427	C₂²×C₂₃	1	2	yes	—
514	#424	C₂²×C₂₃	1	2	yes	—
515	#419	C₂²×C₂₃	1	2	yes	—
516	#419	C₂²×C₂₃	1	2	yes	—
517	#416	C₂²×C₂₃	1	2	yes	—
518	C₂×#103	C₂²×C₂₃	1	2	yes	—
519	#407	C₂²×C₂₃	1	1	yes	characteristic
520	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
521	#405	C₂²×C₂₃	1	2	yes	—
522	C₂×C₂₃	—	2	2	no	—
523	C₂×C₂₃	—	2	2	no	—
524	C₂×C₂₃	—	4	1	no	—
525	C₂×C₂₃	—	8	1	no	—
526	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
527	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
528	C₂×C₂₃	#3586	1	1	yes	characteristic
529	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
530	C₂²×Q₈	—	2	8	no	—
531	C₂²×Q₈	—	2	1	no	—
532	C₂²×Q₈	—	2	1	no	—
533	C₂²×Q₈	—	2	1	no	—
534	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
535	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
536	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
537	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
538	C₂³×C₄	—	2	1	no	—
539	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
540	#137	—	2	8	no	—
541	C₂×Q₁₆	—	2	8	no	—
542	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
543	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
544	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
545	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
546	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
547	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
551	#126	—	2	2	no	—
552	#126	—	2	2	no	—
553	#126	—	2	2	no	—
554	#126	—	2	2	no	—
555	#125	—	2	2	no	—
556	#125	—	2	2	no	—
557	#125	—	2	1	no	—
558	#125	—	2	2	no	—
559	#125	C₂³×C₂₃	1	2	yes	—
560	#124	—	2	2	no	—
561	#124	C₂³×C₂₃	1	2	yes	—
562	#123	—	2	1	no	—
563	#123	—	2	2	no	—
564	#123	—	2	2	no	—
565	#123	—	2	2	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
574	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
575	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
576	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
577	#121	C₂³×C₂₃	1	1	yes	characteristic
578	#121	C₂³×C₂₃	1	1	yes	characteristic
579	#120	—	2	1	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	4	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	4	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
594	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
595	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
596	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
597	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
598	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
599	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	C₂³×C₂₃	1	2	yes	—
605	#117	—	2	1	no	—
606	#117	—	2	1	no	—
607	#117	—	2	2	no	—
608	#117	—	2	1	no	—
609	#117	—	2	4	no	—
610	#117	—	2	4	no	—
611	#117	—	2	4	no	—
612	#117	—	2	4	no	—
613	#117	—	2	2	no	—
614	#117	—	2	2	no	—
615	#117	D₄×C₂₃	1	1	yes	characteristic
616	#117	D₄×C₂₃	1	2	yes	—
617	#117	D₄×C₂₃	1	1	yes	characteristic
618	#117	C₂³×C₂₃	1	2	yes	—
619	#117	C₂³×C₂₃	1	2	yes	—
620	#117	C₂³×C₂₃	1	1	yes	characteristic
621	#117	C₂³×C₂₃	1	1	yes	characteristic
622	#117	C₂³×C₂₃	1	1	yes	characteristic
623	#117	C₂³×C₂₃	1	2	yes	—
624	C₂×C₄⋊C₄	—	2	2	no	—
625	C₂×C₄⋊C₄	—	2	2	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
636	C₂×C₄²	—	2	2	no	—
637	C₂×C₄²	—	2	2	no	—
638	C₂×C₄²	—	2	1	no	—
639	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
640	#107	C₂³×C₂₃	1	2	yes	—
641	#107	C₂³×C₂₃	1	2	yes	—
642	#107	C₂³×C₂₃	1	4	yes	—
643	#106	C₂³×C₂₃	1	2	yes	—
644	#106	C₂³×C₂₃	1	2	yes	—
645	#106	C₂³×C₂₃	1	4	yes	—
646	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
647	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
648	#103	C₂³×C₂₃	1	4	yes	—
649	#103	C₂³×C₂₃	1	4	yes	—
650	#103	C₂³×C₂₃	1	2	yes	—
651	#103	C₂³×C₂₃	1	2	yes	—
652	#103	C₂³×C₂₃	1	4	yes	—
653	#103	C₂³×C₂₃	1	4	yes	—
654	#103	C₂³×C₂₃	1	4	yes	—
655	#103	C₂³×C₂₃	1	4	yes	—
656	#102	C₂³×C₂₃	1	2	yes	—
657	#102	C₂³×C₂₃	1	2	yes	—
658	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
659	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
660	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
661	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
662	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
663	#97	C₂³×C₂₃	1	4	yes	—
664	C₄×C₈	C₂³×C₂₃	1	4	yes	—
665	C₂₃	#60583	1	1	yes	characteristic, direct product factor, Sylow
666	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
667	#41	—	2	4	no	—
668	C₂×Q₈	—	2	8	no	—
669	C₂×Q₈	—	2	8	no	—
670	C₂×Q₈	—	2	8	no	—
671	C₂×Q₈	—	2	8	no	—
672	C₂×Q₈	—	2	8	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	4	no	—
679	C₂×Q₈	—	2	4	no	—
680	C₂×Q₈	#41×C₂₃	1	8	yes	—
681	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
682	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
683	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
688	C₂²×C₄	—	2	8	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
700	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
702	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
707	Q₁₆	—	2	8	no	—
708	Q₁₆	—	2	8	no	—
709	Q₁₆	—	2	8	no	—
710	SD₁₆	—	2	8	no	—
711	M₁₆	—	2	4	no	—
712	C₂×C₈	—	2	4	no	—
713	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
714	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
715	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
738	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
743	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
745	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
759	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
760	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
762	C₄²	—	2	4	no	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	4	no	—
765	C₄²	—	2	4	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	1	no	—
772	C₄²	C₂×D₄×C₂₃	1	2	yes	—
773	C₄²	C₂×D₄×C₂₃	1	2	yes	—
774	C₄²	C₂⁴×C₂₃	1	2	yes	—
775	C₄²	C₂⁴×C₂₃	1	2	yes	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	4	1	no	—
780	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
781	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
782	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
783	Q₈	—	2	8	no	—
784	Q₈	—	2	8	no	—
785	Q₈	—	2	4	no	—
786	Q₈	—	2	8	no	—
787	Q₈	—	2	4	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	4	2	no	—
790	Q₈	—	8	2	no	—
791	Q₈	C₂×#41×C₂₃	1	8	yes	—
792	D₄	—	2	2	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	2	no	—
795	D₄	—	8	1	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	8	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	8	2	no	—
819	C₂×C₄	—	8	1	no	—
820	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
827	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
828	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
829	C₈	—	2	2	no	—
830	C₈	—	2	2	no	—
831	C₈	—	2	4	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	4	4	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	C₂₃×#525	1	2	yes	—
844	C₂²	C₂₃×#578	1	2	yes	—
845	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
846	C₄	—	2	8	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	C₂₃×#525	1	2	yes	—
861	C₄	C₂²×#41×C₂₃	1	2	yes	—
862	C₂	—	2	2	no	—
863	C₂	—	2	2	no	—
864	C₂	—	4	1	no	—
865	C₂	—	8	1	no	—
866	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
867	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
868	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#519	C₂	semidirect
3. C₂₃×#3127	C₂	semidirect
4. C₂₃×#3121	C₂	semidirect
5. C₂₃×#3117	C₂	semidirect
6. C₂₃×#3113	C₂	semidirect
7. C₂₃×#3108	C₂	semidirect
8. C₂₃×#3104	C₂	semidirect
9. C₂₃×#3095	C₂	semidirect
11. C₂₃×#3082	C₂	semidirect
12. C₂₃×#3044	C₂	semidirect
14. C₂×C₂₃×#451	C₂	semidirect
15. C₂₃×#2950	C₂	semidirect
16. C₂₃×#2947	C₂	semidirect
17. C₂₃×#2924	C₂	semidirect
59. C₂₃×#479	C₂²	semidirect
60. C₂₃×#479	C₂²	semidirect
61. C₂₃×#477	C₂²	semidirect
62. C₂₃×#475	C₂²	semidirect
63. C₂₃×#464	C₂²	semidirect
64. C₂₃×#464	C₂²	semidirect
65. C₂₃×#462	C₂²	semidirect
66. C₂₃×#462	C₂²	semidirect
74. C₂₃×#441	C₂²	semidirect
75. C₂₃×#441	C₂²	semidirect
76. C₂₃×#441	C₂²	semidirect
77. C₂₃×#440	C₂²	semidirect
78. C₄×Q₁₆×C₂₃	C₂²	semidirect
79. C₄×Q₁₆×C₂₃	C₂²	semidirect
80. C₄×Q₁₆×C₂₃	C₂²	semidirect
81. C₄×SD₁₆×C₂₃	C₂²	semidirect
341. #60583	C₂₃	direct (N × H)
399. C₂×#519	C₂×C₂₃	semidirect
400. #3127	C₂×C₂₃	semidirect
401. #3121	C₂×C₂₃	semidirect
402. #3117	C₂×C₂₃	semidirect
403. #3113	C₂×C₂₃	semidirect
404. #3108	C₂×C₂₃	semidirect
405. #3104	C₂×C₂₃	semidirect
406. #3095	C₂×C₂₃	semidirect
408. #3082	C₂×C₂₃	semidirect
409. #3044	C₂×C₂₃	semidirect
411. C₂×#451	C₂×C₂₃	semidirect
412. #2950	C₂×C₂₃	semidirect
413. #2947	C₂×C₂₃	semidirect
414. #2924	C₂×C₂₃	semidirect
486. #479	C₂²×C₂₃	semidirect
487. #479	C₂²×C₂₃	semidirect
488. #477	C₂²×C₂₃	semidirect
489. #475	C₂²×C₂₃	semidirect
490. #464	C₂²×C₂₃	semidirect
491. #464	C₂²×C₂₃	semidirect
492. #462	C₂²×C₂₃	semidirect
493. #462	C₂²×C₂₃	semidirect
501. #441	C₂²×C₂₃	semidirect
502. #441	C₂²×C₂₃	semidirect
503. #441	C₂²×C₂₃	semidirect
504. #440	C₂²×C₂₃	semidirect
505. C₄×Q₁₆	C₂²×C₂₃	semidirect
506. C₄×Q₁₆	C₂²×C₂₃	semidirect
507. C₄×Q₁₆	C₂²×C₂₃	semidirect
508. C₄×SD₁₆	C₂²×C₂₃	semidirect
665. C₂₃	#60583	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×#3495	2
C₂×C₂₃×#519	2
C₂₃×#3127	2
C₂₃×#3121	2
C₂₃×#3117	2
C₂₃×#3113	2
C₂₃×#3108	2
C₂₃×#3104	2
C₂₃×#3095	2
C₂₃×#3091	2
C₂₃×#3082	2
C₂₃×#3044	2
C₂₃×#3004	2
C₂×C₂₃×#451	2
C₂₃×#2950	2
C₂₃×#2947	2
C₂₃×#2924	2
#60583	23

Subgroups — C23×#60583 #19208209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60583 #19208209