Subgroups — C₂₃×#60292 #19207918

Order 5888.

1806 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2991	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2990	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2989	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2988	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2986	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2979	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2976	C₂	1	4	yes	maximal, complemented
9	C₂₃×#2969	C₂	1	4	yes	maximal, complemented
10	C₂₃×#2966	C₂	1	4	yes	maximal, complemented
11	C₂₃×#2925	C₂	1	4	yes	maximal, complemented
12	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#533	C₄	1	1	yes	characteristic
15	C₂₃×#533	C₄	1	1	yes	characteristic
16	C₂₃×#533	C₂²	1	1	yes	characteristic
17	C₂₃×#532	C₄	1	1	yes	characteristic
18	C₂₃×#532	C₄	1	1	yes	characteristic
19	C₂₃×#532	C₂²	1	1	yes	characteristic
20	C₂₃×#529	C₄	1	2	yes	—
21	C₂₃×#529	C₄	1	2	yes	—
22	C₂₃×#529	C₄	1	2	yes	—
23	C₂₃×#529	C₄	1	2	yes	—
24	C₂₃×#529	C₂²	1	2	yes	—
25	C₂₃×#529	C₂²	1	2	yes	—
26	C₂₃×#525	C₄	1	2	yes	—
27	C₂₃×#525	C₄	1	2	yes	—
28	C₂₃×#525	C₂²	1	2	yes	—
29	C₄×#41×C₂₃	C₂²	1	2	yes	—
30	C₄×#41×C₂₃	C₂²	1	2	yes	—
31	C₄×#41×C₂₃	C₂²	1	2	yes	—
32	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
33	C₂₃×#446	C₂²	1	4	yes	complemented
34	C₂₃×#446	C₂²	1	4	yes	complemented
35	C₈×Q₈×C₂₃	C₂²	1	4	yes	complemented
36	C₈×Q₈×C₂₃	C₂²	1	4	yes	complemented
37	C₂₃×#436	C₂²	1	8	yes	—
38	C₂₃×#436	C₂²	1	4	yes	complemented
39	C₂₃×#436	C₂²	1	4	yes	complemented
40	C₂₃×#435	C₂²	1	8	yes	—
41	C₂₃×#435	C₂²	1	8	yes	—
42	C₈×D₄×C₂₃	C₂²	1	8	yes	—
43	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
44	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
45	C₂₃×#433	C₂²	1	8	yes	—
46	C₂₃×#433	C₂²	1	8	yes	complemented
47	C₂₃×#432	C₂²	1	2	yes	—
48	C₂₃×#432	C₂²	1	2	yes	—
49	C₂₃×#432	C₂²	1	4	yes	complemented
50	C₂₃×#431	C₂²	1	2	yes	—
51	C₂₃×#431	C₂²	1	2	yes	—
52	C₂₃×#431	C₂²	1	2	yes	—
53	C₂₃×#431	C₂²	1	2	yes	—
54	C₂₃×#431	C₂²	1	2	yes	—
55	C₂₃×#431	C₂²	1	2	yes	—
56	C₂₃×#431	C₂²	1	4	yes	complemented
57	C₂₃×#423	C₂²	1	1	yes	characteristic
58	C₂₃×#423	C₂²	1	1	yes	characteristic
59	C₂₃×#423	C₂²	1	4	yes	complemented
60	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×C₄⋊C₈	C₂²	1	4	yes	complemented
63	C₂₃×#408	C₂²	1	8	yes	—
64	C₂₃×#407	C₂²	1	2	yes	—
65	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
66	C₂₃×#405	C₂²	1	8	yes	complemented
67	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
68	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
69	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
70	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
71	C₂×#41×C₂₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
76	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
77	C₂×M₁₆×C₂₃	C₂³	1	8	yes	—
78	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
79	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
80	C₂²×C₈×C₂₃	C₂³	1	8	yes	—
81	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
82	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
83	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
84	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
85	C₂₃×#126	C₂×C₄	1	4	yes	—
86	C₂₃×#126	C₂×C₄	1	4	yes	—
87	C₂₃×#125	C₂×C₄	1	2	yes	—
88	C₂₃×#125	C₂×C₄	1	2	yes	—
89	C₂₃×#125	C₂×C₄	1	2	yes	—
90	C₂₃×#124	C₂×C₄	1	2	yes	—
91	C₂₃×#124	C₂×C₄	1	2	yes	—
92	C₂₃×#124	C₂×C₄	1	2	yes	—
93	C₂₃×#123	C₂×C₄	1	4	yes	—
94	C₂₃×#123	C₂×C₄	1	4	yes	—
95	C₂₃×#123	C₂×C₄	1	4	yes	—
96	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
97	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
98	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
99	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
100	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
101	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
102	C₂₃×#121	C₂×C₄	1	2	yes	—
103	C₂₃×#121	C₂×C₄	1	2	yes	—
104	C₂₃×#121	C₂×C₄	1	2	yes	—
105	C₂₃×#121	C₂×C₄	1	2	yes	—
106	C₂₃×#121	C₂×C₄	1	2	yes	—
107	C₂₃×#121	C₂×C₄	1	2	yes	—
108	C₂₃×#120	C₂×C₄	1	4	yes	—
109	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
110	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
111	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
112	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
113	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
114	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
115	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
116	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
117	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
118	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
119	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
120	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
121	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
122	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
123	C₄×D₄×C₂₃	C₂³	1	4	yes	—
124	C₄×D₄×C₂₃	C₂³	1	2	yes	—
125	C₄×D₄×C₂₃	C₂³	1	2	yes	—
126	C₄×D₄×C₂₃	C₂³	1	4	yes	—
127	C₂₃×#117	C₂×C₄	1	2	yes	—
128	C₂₃×#117	C₂×C₄	1	2	yes	—
129	C₂₃×#117	C₂×C₄	1	4	yes	—
130	C₂₃×#117	C₂×C₄	1	4	yes	—
131	C₂₃×#117	C₂³	1	4	yes	—
132	C₂₃×#117	C₂³	1	2	yes	—
133	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
135	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
136	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
137	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
138	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
139	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
143	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
146	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
147	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
148	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
149	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
150	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
151	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
152	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
153	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
154	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
155	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
156	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
157	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
158	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
159	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
160	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
161	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
162	C₂₃×#97	C₂³	1	4	yes	—
163	C₂₃×#97	C₂³	1	8	yes	—
164	C₄×C₈×C₂₃	C₂³	1	4	yes	—
165	C₄×C₈×C₂₃	C₂³	1	4	yes	—
166	C₄×C₈×C₂₃	C₂³	1	4	yes	—
167	C₄×C₈×C₂₃	C₂³	1	8	yes	—
168	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
169	#41×C₂₃	—	2	8	no	—
170	#41×C₂₃	—	4	2	no	—
171	#41×C₂₃	—	4	2	no	—
172	#41×C₂₃	—	4	4	no	—
173	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
174	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
175	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
176	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
177	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
178	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
179	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
180	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
181	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₂₃	—	2	4	no	—
183	C₂²×C₄×C₂₃	—	4	2	no	—
184	C₂²×C₄×C₂₃	—	4	1	no	—
185	C₂²×C₄×C₂₃	—	4	1	no	—
186	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
202	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
207	M₁₆×C₂₃	—	4	2	no	—
208	M₁₆×C₂₃	—	4	8	no	—
209	M₁₆×C₂₃	—	4	2	no	—
210	C₂×C₈×C₂₃	—	4	2	no	—
211	C₂×C₈×C₂₃	—	4	8	no	—
212	C₂×C₈×C₂₃	—	4	2	no	—
213	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
214	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
215	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
216	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
217	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
218	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
219	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
220	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
221	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
222	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
223	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
224	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
225	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
226	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
227	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
228	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
229	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
230	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
231	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
232	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
233	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
234	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
235	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
236	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
237	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
238	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
239	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
240	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
241	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
242	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
243	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
244	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
245	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
246	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
247	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
248	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
249	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
250	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
251	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
252	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
253	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
254	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
255	C₄²×C₂₃	C₂⁴	1	4	yes	—
256	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
257	#60292	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂³×C₂₃	—	2	2	no	—
259	C₂³×C₂₃	—	4	1	no	—
260	C₂³×C₂₃	—	4	1	no	—
261	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
262	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
263	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
264	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
265	Q₈×C₂₃	—	2	4	no	—
266	Q₈×C₂₃	—	2	4	no	—
267	Q₈×C₂₃	—	4	2	no	—
268	D₄×C₂₃	—	2	8	no	—
269	D₄×C₂₃	—	2	4	no	—
270	D₄×C₂₃	—	2	4	no	—
271	D₄×C₂₃	—	4	2	no	—
272	D₄×C₂₃	—	4	4	no	—
273	D₄×C₂₃	—	4	4	no	—
274	C₂×C₄×C₂₃	—	2	2	no	—
275	C₂×C₄×C₂₃	—	2	2	no	—
276	C₂×C₄×C₂₃	—	2	2	no	—
277	C₂×C₄×C₂₃	—	2	2	no	—
278	C₂×C₄×C₂₃	—	2	2	no	—
279	C₂×C₄×C₂₃	—	2	8	no	—
280	C₂×C₄×C₂₃	—	2	2	no	—
281	C₂×C₄×C₂₃	—	2	2	no	—
282	C₂×C₄×C₂₃	—	2	2	no	—
283	C₂×C₄×C₂₃	—	2	1	no	—
284	C₂×C₄×C₂₃	—	2	1	no	—
285	C₂×C₄×C₂₃	—	2	4	no	—
286	C₂×C₄×C₂₃	—	2	1	no	—
287	C₂×C₄×C₂₃	—	2	1	no	—
288	C₂×C₄×C₂₃	—	2	4	no	—
289	C₂×C₄×C₂₃	—	2	1	no	—
290	C₂×C₄×C₂₃	—	2	1	no	—
291	C₂×C₄×C₂₃	—	4	1	no	—
292	C₂×C₄×C₂₃	—	4	1	no	—
293	C₂×C₄×C₂₃	—	4	1	no	—
294	C₂×C₄×C₂₃	—	4	1	no	—
295	C₂×C₄×C₂₃	—	4	1	no	—
296	C₂×C₄×C₂₃	—	4	1	no	—
297	C₂×C₄×C₂₃	—	4	4	no	—
298	C₂×C₄×C₂₃	#131	1	4	yes	—
299	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
301	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
302	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
303	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
304	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
308	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
309	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
310	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
311	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
312	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
313	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
314	C₈×C₂₃	—	2	4	no	—
315	C₈×C₂₃	—	2	4	no	—
316	C₈×C₂₃	—	2	4	no	—
317	C₈×C₂₃	—	2	4	no	—
318	#3444	C₂×C₂₃	1	1	yes	characteristic
319	#2991	C₂×C₂₃	1	2	yes	complemented
320	#2990	C₂×C₂₃	1	2	yes	complemented
321	#2989	C₂×C₂₃	1	2	yes	complemented
322	#2988	C₂×C₂₃	1	2	yes	complemented
323	#2986	C₂×C₂₃	1	2	yes	complemented
324	#2979	C₂×C₂₃	1	2	yes	complemented
325	#2976	C₂×C₂₃	1	4	yes	complemented
326	#2969	C₂×C₂₃	1	4	yes	complemented
327	#2966	C₂×C₂₃	1	4	yes	complemented
328	#2925	C₂×C₂₃	1	4	yes	complemented
329	#2920	C₂×C₂₃	1	1	yes	characteristic, complemented
330	C₂×#431	C₂×C₂₃	1	1	yes	characteristic, complemented
331	C₂²×C₂₃	—	2	1	no	—
332	C₂²×C₂₃	—	2	1	no	—
333	C₂²×C₂₃	—	2	1	no	—
334	C₂²×C₂₃	—	2	1	no	—
335	C₂²×C₂₃	—	2	4	no	—
336	C₂²×C₂₃	—	2	1	no	—
337	C₂²×C₂₃	—	2	1	no	—
338	C₂²×C₂₃	—	2	4	no	—
339	C₂²×C₂₃	—	2	1	no	—
340	C₂²×C₂₃	—	2	1	no	—
341	C₂²×C₂₃	—	2	4	no	—
342	C₂²×C₂₃	—	4	4	no	—
343	C₂²×C₂₃	C₂×#131	1	2	yes	—
344	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
345	C₄×C₂₃	—	2	1	no	—
346	C₄×C₂₃	—	2	1	no	—
347	C₄×C₂₃	—	2	1	no	—
348	C₄×C₂₃	—	2	4	no	—
349	C₄×C₂₃	—	2	1	no	—
350	C₄×C₂₃	—	2	1	no	—
351	C₄×C₂₃	—	2	4	no	—
352	C₄×C₂₃	—	2	1	no	—
353	C₄×C₂₃	—	2	1	no	—
354	C₄×C₂₃	—	2	1	no	—
355	C₄×C₂₃	—	2	4	no	—
356	C₄×C₂₃	C₂×#131	1	2	yes	—
357	C₄×C₂₃	C₂×#131	1	2	yes	—
358	C₄×C₂₃	#568	1	2	yes	—
359	C₄×C₂₃	#585	1	1	yes	characteristic
360	C₄×C₂₃	#585	1	1	yes	characteristic
361	#533	C₄×C₂₃	1	1	yes	characteristic
362	#533	C₄×C₂₃	1	1	yes	characteristic
363	#533	C₂²×C₂₃	1	1	yes	characteristic
364	#532	C₄×C₂₃	1	1	yes	characteristic
365	#532	C₄×C₂₃	1	1	yes	characteristic
366	#532	C₂²×C₂₃	1	1	yes	characteristic
367	#529	C₄×C₂₃	1	2	yes	—
368	#529	C₄×C₂₃	1	2	yes	—
369	#529	C₄×C₂₃	1	2	yes	—
370	#529	C₄×C₂₃	1	2	yes	—
371	#529	C₂²×C₂₃	1	2	yes	—
372	#529	C₂²×C₂₃	1	2	yes	—
373	#525	C₄×C₂₃	1	2	yes	—
374	#525	C₄×C₂₃	1	2	yes	—
375	#525	C₂²×C₂₃	1	2	yes	—
376	C₄×#41	C₂²×C₂₃	1	2	yes	—
377	C₄×#41	C₂²×C₂₃	1	2	yes	—
378	C₄×#41	C₂²×C₂₃	1	2	yes	—
379	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
380	#446	C₂²×C₂₃	1	4	yes	complemented
381	#446	C₂²×C₂₃	1	4	yes	complemented
382	C₈×Q₈	C₂²×C₂₃	1	4	yes	complemented
383	C₈×Q₈	C₂²×C₂₃	1	4	yes	complemented
384	#436	C₂²×C₂₃	1	8	yes	—
385	#436	C₂²×C₂₃	1	4	yes	complemented
386	#436	C₂²×C₂₃	1	4	yes	complemented
387	#435	C₂²×C₂₃	1	8	yes	—
388	#435	C₂²×C₂₃	1	8	yes	—
389	C₈×D₄	C₂²×C₂₃	1	8	yes	—
390	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
391	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
392	#433	C₂²×C₂₃	1	8	yes	—
393	#433	C₂²×C₂₃	1	8	yes	complemented
394	#432	C₂²×C₂₃	1	2	yes	—
395	#432	C₂²×C₂₃	1	2	yes	—
396	#432	C₂²×C₂₃	1	4	yes	complemented
397	#431	C₂²×C₂₃	1	2	yes	—
398	#431	C₂²×C₂₃	1	2	yes	—
399	#431	C₂²×C₂₃	1	2	yes	—
400	#431	C₂²×C₂₃	1	2	yes	—
401	#431	C₂²×C₂₃	1	2	yes	—
402	#431	C₂²×C₂₃	1	2	yes	—
403	#431	C₂²×C₂₃	1	4	yes	complemented
404	#423	C₂²×C₂₃	1	1	yes	characteristic
405	#423	C₂²×C₂₃	1	1	yes	characteristic
406	#423	C₂²×C₂₃	1	4	yes	complemented
407	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
408	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×C₄⋊C₈	C₂²×C₂₃	1	4	yes	complemented
410	#408	C₂²×C₂₃	1	8	yes	—
411	#407	C₂²×C₂₃	1	2	yes	—
412	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
413	#405	C₂²×C₂₃	1	8	yes	complemented
414	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
415	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
416	C₂×C₂₃	—	2	2	no	—
417	C₂×C₂₃	—	4	4	no	—
418	C₂×C₂₃	—	4	1	no	—
419	C₂×C₂₃	—	4	1	no	—
420	C₂×C₂₃	#3428	1	1	yes	characteristic
421	C₂×C₂₃	C₂²×#131	1	1	yes	characteristic
422	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
423	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
424	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
425	C₂×#41	C₂³×C₂₃	1	2	yes	—
426	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
427	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
429	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
430	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
431	C₂×M₁₆	C₂³×C₂₃	1	8	yes	—
432	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
433	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
434	C₂²×C₈	C₂³×C₂₃	1	8	yes	—
435	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
436	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
437	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
438	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
439	#126	C₂×C₄×C₂₃	1	4	yes	—
440	#126	C₂×C₄×C₂₃	1	4	yes	—
441	#125	C₂×C₄×C₂₃	1	2	yes	—
442	#125	C₂×C₄×C₂₃	1	2	yes	—
443	#125	C₂×C₄×C₂₃	1	2	yes	—
444	#124	C₂×C₄×C₂₃	1	2	yes	—
445	#124	C₂×C₄×C₂₃	1	2	yes	—
446	#124	C₂×C₄×C₂₃	1	2	yes	—
447	#123	C₂×C₄×C₂₃	1	4	yes	—
448	#123	C₂×C₄×C₂₃	1	4	yes	—
449	#123	C₂×C₄×C₂₃	1	4	yes	—
450	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
451	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
452	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
453	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
454	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
455	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
456	#121	C₂×C₄×C₂₃	1	2	yes	—
457	#121	C₂×C₄×C₂₃	1	2	yes	—
458	#121	C₂×C₄×C₂₃	1	2	yes	—
459	#121	C₂×C₄×C₂₃	1	2	yes	—
460	#121	C₂×C₄×C₂₃	1	2	yes	—
461	#121	C₂×C₄×C₂₃	1	2	yes	—
462	#120	C₂×C₄×C₂₃	1	4	yes	—
463	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
464	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
465	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
466	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
467	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
468	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
469	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
470	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
471	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
472	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
473	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
474	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
475	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
476	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
477	C₄×D₄	C₂³×C₂₃	1	4	yes	—
478	C₄×D₄	C₂³×C₂₃	1	4	yes	—
479	C₄×D₄	C₂³×C₂₃	1	2	yes	—
480	C₄×D₄	C₂³×C₂₃	1	2	yes	—
481	#117	C₂×C₄×C₂₃	1	2	yes	—
482	#117	C₂×C₄×C₂₃	1	2	yes	—
483	#117	C₂×C₄×C₂₃	1	4	yes	—
484	#117	C₂×C₄×C₂₃	1	4	yes	—
485	#117	C₂³×C₂₃	1	2	yes	—
486	#117	C₂³×C₂₃	1	4	yes	—
487	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
488	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
489	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
490	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
491	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
492	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
494	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
500	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
501	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
502	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
503	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
504	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
505	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
506	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
507	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
508	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
509	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
510	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
511	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
512	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
513	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
514	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
515	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
516	#97	C₂³×C₂₃	1	4	yes	—
517	#97	C₂³×C₂₃	1	8	yes	—
518	C₄×C₈	C₂³×C₂₃	1	4	yes	—
519	C₄×C₈	C₂³×C₂₃	1	4	yes	—
520	C₄×C₈	C₂³×C₂₃	1	4	yes	—
521	C₄×C₈	C₂³×C₂₃	1	8	yes	—
522	C₂₃	#60292	1	1	yes	characteristic, direct product factor, Sylow
523	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
524	#41	—	2	8	no	—
525	#41	—	4	2	no	—
526	#41	—	4	2	no	—
527	#41	—	4	4	no	—
528	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
529	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
530	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
531	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
532	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
533	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
534	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
535	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
536	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	1	no	—
540	C₂²×C₄	—	4	1	no	—
541	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
547	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
548	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
549	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
550	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
551	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
552	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
553	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
554	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
555	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
556	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
557	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
562	M₁₆	—	4	2	no	—
563	M₁₆	—	4	8	no	—
564	M₁₆	—	4	2	no	—
565	C₂×C₈	—	4	2	no	—
566	C₂×C₈	—	4	8	no	—
567	C₂×C₈	—	4	2	no	—
568	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
569	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
570	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
571	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
573	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
574	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
575	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
576	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
577	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
578	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
579	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
580	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
581	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
582	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
583	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
584	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
585	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
586	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
587	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
588	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
589	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
590	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
591	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
592	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
593	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
594	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
595	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
596	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
597	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
598	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
599	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
600	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
601	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
602	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
603	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
604	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
605	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
606	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
607	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
608	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
609	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
610	C₄²	C₂⁴×C₂₃	1	4	yes	—
611	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
612	C₂³	—	2	2	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
616	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
617	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
618	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
619	Q₈	—	2	4	no	—
620	Q₈	—	2	4	no	—
621	Q₈	—	4	2	no	—
622	D₄	—	2	8	no	—
623	D₄	—	2	4	no	—
624	D₄	—	2	4	no	—
625	D₄	—	4	2	no	—
626	D₄	—	4	4	no	—
627	D₄	—	4	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	8	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	4	no	—
652	C₂×C₄	C₂₃×#131	1	4	yes	—
653	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
654	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
655	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
656	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
657	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
658	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
659	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
660	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
661	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
662	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
663	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
664	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
665	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
666	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
667	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
668	C₈	—	2	4	no	—
669	C₈	—	2	4	no	—
670	C₈	—	2	4	no	—
671	C₈	—	2	4	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	4	4	no	—
684	C₂²	C₂×C₂₃×#131	1	2	yes	—
685	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	2	4	no	—
690	C₄	—	2	1	no	—
691	C₄	—	2	1	no	—
692	C₄	—	2	4	no	—
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	4	no	—
697	C₄	C₂×C₂₃×#131	1	2	yes	—
698	C₄	C₂×C₂₃×#131	1	2	yes	—
699	C₄	C₂₃×#568	1	2	yes	—
700	C₄	C₂₃×#585	1	1	yes	characteristic
701	C₄	C₂₃×#585	1	1	yes	characteristic
702	C₂	—	2	2	no	—
703	C₂	—	4	1	no	—
704	C₂	—	4	1	no	—
705	C₂	—	4	4	no	—
706	C₂	C₂₃×#3428	1	1	yes	characteristic
707	C₂	C₂²×C₂₃×#131	1	1	yes	characteristic
708	C₂	C₂×C₂₃×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	C₂₃×#3444	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2991	C₂	semidirect
3. C₂₃×#2990	C₂	semidirect
4. C₂₃×#2989	C₂	semidirect
5. C₂₃×#2988	C₂	semidirect
6. C₂₃×#2986	C₂	semidirect
7. C₂₃×#2979	C₂	semidirect
8. C₂₃×#2976	C₂	semidirect
9. C₂₃×#2969	C₂	semidirect
10. C₂₃×#2966	C₂	semidirect
11. C₂₃×#2925	C₂	semidirect
12. C₂₃×#2920	C₂	semidirect
13. C₂×C₂₃×#431	C₂	semidirect
33. C₂₃×#446	C₂²	semidirect
34. C₂₃×#446	C₂²	semidirect
35. C₈×Q₈×C₂₃	C₂²	semidirect
36. C₈×Q₈×C₂₃	C₂²	semidirect
38. C₂₃×#436	C₂²	semidirect
39. C₂₃×#436	C₂²	semidirect
43. C₈×D₄×C₂₃	C₂²	semidirect
44. C₈×D₄×C₂₃	C₂²	semidirect
46. C₂₃×#433	C₂²	semidirect
49. C₂₃×#432	C₂²	semidirect
56. C₂₃×#431	C₂²	semidirect
59. C₂₃×#423	C₂²	semidirect
62. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
66. C₂₃×#405	C₂²	semidirect
257. #60292	C₂₃	direct (N × H)
319. #2991	C₂×C₂₃	semidirect
320. #2990	C₂×C₂₃	semidirect
321. #2989	C₂×C₂₃	semidirect
322. #2988	C₂×C₂₃	semidirect
323. #2986	C₂×C₂₃	semidirect
324. #2979	C₂×C₂₃	semidirect
325. #2976	C₂×C₂₃	semidirect
326. #2969	C₂×C₂₃	semidirect
327. #2966	C₂×C₂₃	semidirect
328. #2925	C₂×C₂₃	semidirect
329. #2920	C₂×C₂₃	semidirect
330. C₂×#431	C₂×C₂₃	semidirect
380. #446	C₂²×C₂₃	semidirect
381. #446	C₂²×C₂₃	semidirect
382. C₈×Q₈	C₂²×C₂₃	semidirect
383. C₈×Q₈	C₂²×C₂₃	semidirect
385. #436	C₂²×C₂₃	semidirect
386. #436	C₂²×C₂₃	semidirect
390. C₈×D₄	C₂²×C₂₃	semidirect
391. C₈×D₄	C₂²×C₂₃	semidirect
393. #433	C₂²×C₂₃	semidirect
396. #432	C₂²×C₂₃	semidirect
403. #431	C₂²×C₂₃	semidirect
406. #423	C₂²×C₂₃	semidirect
409. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
413. #405	C₂²×C₂₃	semidirect
522. C₂₃	#60292	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×#3444	2
C₂₃×#2991	2
C₂₃×#2990	2
C₂₃×#2989	2
C₂₃×#2988	2
C₂₃×#2986	2
C₂₃×#2979	2
C₂₃×#2976	2
C₂₃×#2969	2
C₂₃×#2966	2
C₂₃×#2925	2
C₂₃×#2920	2
C₂×C₂₃×#431	2
#60292	23

Subgroups — C23×#60292 #19207918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60292 #19207918