Subgroups — C₂₃×#60290 #19207916

Order 5888.

1816 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2994	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2993	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2982	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2974	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2969	C₂	1	4	yes	maximal, complemented
10	C₂₃×#2966	C₂	1	4	yes	maximal, complemented
11	C₂₃×#2924	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×#529	C₄	1	2	yes	—
15	C₂₃×#529	C₄	1	2	yes	—
16	C₂₃×#529	C₄	1	2	yes	—
17	C₂₃×#529	C₄	1	2	yes	—
18	C₂₃×#529	C₂²	1	2	yes	—
19	C₂₃×#529	C₂²	1	2	yes	—
20	C₂₃×#529	C₂²	1	2	yes	—
21	C₂₃×#529	C₂²	1	2	yes	—
22	C₂×C₂₃×#126	C₄	1	2	yes	—
23	C₂×C₂₃×#125	C₄	1	1	yes	characteristic
24	C₂×C₂₃×#124	C₄	1	1	yes	characteristic
25	C₂×C₂₃×#123	C₄	1	2	yes	—
26	C₂×C₂₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
27	C₂×C₂₃×#121	C₄	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
31	C₂×C₂₃×#117	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	4	yes	complemented
38	C₂₃×#436	C₂²	1	8	yes	complemented
39	C₂₃×#436	C₂²	1	4	yes	complemented
40	C₂₃×#435	C₂²	1	8	yes	complemented
41	C₂₃×#435	C₂²	1	8	yes	complemented
42	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
43	C₈×D₄×C₂₃	C₂²	1	8	yes	complemented
44	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
45	C₂₃×#433	C₂²	1	8	yes	complemented
46	C₂₃×#433	C₂²	1	8	yes	complemented
47	C₂₃×#432	C₂²	1	2	yes	—
48	C₂₃×#432	C₂²	1	4	yes	—
49	C₂₃×#432	C₂²	1	2	yes	complemented
50	C₂₃×#431	C₂²	1	2	yes	—
51	C₂₃×#431	C₂²	1	1	yes	characteristic
52	C₂₃×#431	C₂²	1	1	yes	characteristic
53	C₂₃×#431	C₂²	1	1	yes	characteristic
54	C₂₃×#431	C₂²	1	1	yes	characteristic
55	C₂₃×#431	C₂²	1	4	yes	—
56	C₂₃×#431	C₂²	1	2	yes	complemented
57	C₂₃×#431	C₂²	1	2	yes	complemented
58	C₂₃×#431	C₂²	1	2	yes	complemented
59	C₂₃×#424	C₂²	1	8	yes	complemented
60	C₂₃×#423	C₂²	1	2	yes	complemented
61	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
62	C₂₃×#407	C₂²	1	2	yes	—
63	C₂₃×#407	C₂²	1	4	yes	—
64	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
65	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	—
66	C₂₃×#405	C₂²	1	8	yes	complemented
67	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
68	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
69	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
70	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
71	C₂²×D₄×C₂₃	C₂×C₄	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	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
76	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
77	C₂×M₁₆×C₂₃	C₂³	1	8	yes	—
78	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
79	C₂²×C₈×C₂₃	C₂³	1	8	yes	—
80	C₂₃×#126	C₂×C₄	1	4	yes	—
81	C₂₃×#126	C₂×C₄	1	4	yes	—
82	C₂₃×#126	C₂×C₄	1	4	yes	—
83	C₂₃×#126	C₂×C₄	1	4	yes	—
84	C₂₃×#125	C₂×C₄	1	2	yes	—
85	C₂₃×#125	C₂×C₄	1	2	yes	—
86	C₂₃×#125	C₂×C₄	1	2	yes	—
87	C₂₃×#125	C₂×C₄	1	2	yes	—
88	C₂₃×#124	C₂×C₄	1	2	yes	—
89	C₂₃×#124	C₂×C₄	1	2	yes	—
90	C₂₃×#124	C₂×C₄	1	2	yes	—
91	C₂₃×#124	C₂×C₄	1	2	yes	—
92	C₂₃×#123	C₂×C₄	1	4	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×#121	C₂×C₄	1	2	yes	—
101	C₂₃×#121	C₂×C₄	1	2	yes	—
102	C₂₃×#121	C₂×C₄	1	2	yes	—
103	C₂₃×#121	C₂×C₄	1	2	yes	—
104	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
105	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
106	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
107	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
108	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
109	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
110	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
111	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
112	C₄×D₄×C₂₃	C₂³	1	4	yes	—
113	C₄×D₄×C₂₃	C₂³	1	2	yes	—
114	C₄×D₄×C₂₃	C₂³	1	2	yes	—
115	C₄×D₄×C₂₃	C₂³	1	4	yes	—
116	C₂₃×#117	C₂×C₄	1	4	yes	—
117	C₂₃×#117	C₂×C₄	1	4	yes	—
118	C₂₃×#117	C₂³	1	4	yes	—
119	C₂₃×#117	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
121	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
122	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
124	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
126	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
127	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
128	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
129	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
130	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
131	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
132	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₂₃	C₂³	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	1	yes	characteristic
143	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
144	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
145	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
146	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
147	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
148	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
149	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
150	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
151	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
152	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
153	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
154	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
155	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
156	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
157	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
158	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
159	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
160	C₂₃×#97	C₂³	1	4	yes	—
161	C₂₃×#97	C₂³	1	8	yes	—
162	C₄×C₈×C₂₃	C₂³	1	4	yes	—
163	C₄×C₈×C₂₃	C₂³	1	2	yes	—
164	C₄×C₈×C₂₃	C₂³	1	2	yes	—
165	C₄×C₈×C₂₃	C₂³	1	2	yes	—
166	C₄×C₈×C₂₃	C₂³	1	2	yes	—
167	C₄×C₈×C₂₃	C₂³	1	8	yes	—
168	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
169	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
170	C₂×Q₈×C₂₃	—	2	4	no	—
171	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
172	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
173	C₂×D₄×C₂₃	—	2	4	no	—
174	C₂×D₄×C₂₃	—	4	4	no	—
175	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
176	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
177	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
178	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
179	C₂²×C₄×C₂₃	—	2	4	no	—
180	C₂²×C₄×C₂₃	—	4	2	no	—
181	C₂²×C₄×C₂₃	—	4	4	no	—
182	C₂²×C₄×C₂₃	—	4	2	no	—
183	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
199	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
200	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
201	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₂₃	C₂⁴	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	4	yes	—
206	M₁₆×C₂₃	—	4	4	no	—
207	M₁₆×C₂₃	—	4	8	no	—
208	C₂×C₈×C₂₃	—	4	8	no	—
209	C₂×C₈×C₂₃	—	4	4	no	—
210	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
211	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
212	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
213	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
214	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
215	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
216	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
217	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
218	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
219	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
220	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
221	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
222	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
223	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
224	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
225	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
226	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
227	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
228	C₂²⋊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	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
237	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
249	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₄²×C₂₃	C₂⁴	1	4	yes	—
253	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
254	#60290	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂³×C₂₃	—	2	2	no	—
256	C₂³×C₂₃	—	2	2	no	—
257	C₂³×C₂₃	—	2	4	no	—
258	C₂³×C₂₃	—	4	1	no	—
259	C₂³×C₂₃	—	4	2	no	—
260	C₂³×C₂₃	—	4	2	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	D₄×C₂₃	—	2	8	no	—
268	D₄×C₂₃	—	2	4	no	—
269	D₄×C₂₃	—	2	4	no	—
270	D₄×C₂₃	—	4	4	no	—
271	C₂×C₄×C₂₃	—	2	2	no	—
272	C₂×C₄×C₂₃	—	2	4	no	—
273	C₂×C₄×C₂₃	—	2	2	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	2	no	—
280	C₂×C₄×C₂₃	—	2	8	no	—
281	C₂×C₄×C₂₃	—	2	2	no	—
282	C₂×C₄×C₂₃	—	2	2	no	—
283	C₂×C₄×C₂₃	—	4	1	no	—
284	C₂×C₄×C₂₃	—	4	1	no	—
285	C₂×C₄×C₂₃	—	4	4	no	—
286	C₂×C₄×C₂₃	—	4	1	no	—
287	C₂×C₄×C₂₃	—	4	2	no	—
288	C₂×C₄×C₂₃	—	4	1	no	—
289	C₂×C₄×C₂₃	—	4	1	no	—
290	C₂×C₄×C₂₃	—	4	1	no	—
291	C₂×C₄×C₂₃	—	4	1	no	—
292	C₂×C₄×C₂₃	—	4	2	no	—
293	C₂×C₄×C₂₃	#131	1	4	yes	—
294	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
296	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
297	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
298	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
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	4	yes	—
304	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
305	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
306	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
308	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
309	C₈×C₂₃	—	2	4	no	—
310	C₈×C₂₃	—	2	4	no	—
311	C₈×C₂₃	—	2	4	no	—
312	C₈×C₂₃	—	2	4	no	—
313	C₂×#529	C₂×C₂₃	1	1	yes	characteristic
314	#2994	C₂×C₂₃	1	4	yes	complemented
315	#2993	C₂×C₂₃	1	4	yes	complemented
316	#2983	C₂×C₂₃	1	1	yes	characteristic, complemented
317	#2982	C₂×C₂₃	1	1	yes	characteristic, complemented
318	#2975	C₂×C₂₃	1	1	yes	characteristic, complemented
319	#2974	C₂×C₂₃	1	4	yes	complemented
320	#2972	C₂×C₂₃	1	1	yes	characteristic, complemented
321	#2969	C₂×C₂₃	1	4	yes	complemented
322	#2966	C₂×C₂₃	1	4	yes	complemented
323	#2924	C₂×C₂₃	1	4	yes	complemented
324	#2920	C₂×C₂₃	1	1	yes	characteristic, complemented
325	C₂×#431	C₂×C₂₃	1	1	yes	characteristic, complemented
326	C₂²×C₂₃	—	2	1	no	—
327	C₂²×C₂₃	—	2	1	no	—
328	C₂²×C₂₃	—	2	1	no	—
329	C₂²×C₂₃	—	2	1	no	—
330	C₂²×C₂₃	—	2	1	no	—
331	C₂²×C₂₃	—	2	4	no	—
332	C₂²×C₂₃	—	2	1	no	—
333	C₂²×C₂₃	—	2	4	no	—
334	C₂²×C₂₃	—	2	1	no	—
335	C₂²×C₂₃	—	2	4	no	—
336	C₂²×C₂₃	—	4	4	no	—
337	C₂²×C₂₃	—	8	4	no	—
338	C₂²×C₂₃	C₂×#131	1	2	yes	—
339	C₂²×C₂₃	#568	1	2	yes	—
340	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
341	C₄×C₂₃	—	2	1	no	—
342	C₄×C₂₃	—	2	1	no	—
343	C₄×C₂₃	—	2	4	no	—
344	C₄×C₂₃	—	2	1	no	—
345	C₄×C₂₃	—	2	1	no	—
346	C₄×C₂₃	—	2	1	no	—
347	C₄×C₂₃	—	2	4	no	—
348	C₄×C₂₃	—	2	1	no	—
349	C₄×C₂₃	—	2	1	no	—
350	C₄×C₂₃	—	2	1	no	—
351	C₄×C₂₃	—	2	1	no	—
352	C₄×C₂₃	—	2	4	no	—
353	C₄×C₂₃	C₂×#131	1	2	yes	—
354	C₄×C₂₃	C₂×#131	1	2	yes	—
355	C₄×C₂₃	#585	1	2	yes	—
356	#529	C₄×C₂₃	1	2	yes	—
357	#529	C₄×C₂₃	1	2	yes	—
358	#529	C₄×C₂₃	1	2	yes	—
359	#529	C₄×C₂₃	1	2	yes	—
360	#529	C₂²×C₂₃	1	2	yes	—
361	#529	C₂²×C₂₃	1	2	yes	—
362	#529	C₂²×C₂₃	1	2	yes	—
363	#529	C₂²×C₂₃	1	2	yes	—
364	C₂×#126	C₄×C₂₃	1	2	yes	—
365	C₂×#125	C₄×C₂₃	1	1	yes	characteristic
366	C₂×#124	C₄×C₂₃	1	1	yes	characteristic
367	C₂×#123	C₄×C₂₃	1	2	yes	—
368	C₂×C₂²⋊Q₈	C₄×C₂₃	1	1	yes	characteristic
369	C₂×#121	C₄×C₂₃	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
371	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
372	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
373	C₂×#117	C₂²×C₂₃	1	2	yes	—
374	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
375	#446	C₂²×C₂₃	1	4	yes	complemented
376	#446	C₂²×C₂₃	1	4	yes	complemented
377	C₈×Q₈	C₂²×C₂₃	1	4	yes	complemented
378	C₈×Q₈	C₂²×C₂₃	1	4	yes	complemented
379	#436	C₂²×C₂₃	1	4	yes	complemented
380	#436	C₂²×C₂₃	1	8	yes	complemented
381	#436	C₂²×C₂₃	1	4	yes	complemented
382	#435	C₂²×C₂₃	1	8	yes	complemented
383	#435	C₂²×C₂₃	1	8	yes	complemented
384	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
385	C₈×D₄	C₂²×C₂₃	1	8	yes	complemented
386	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
387	#433	C₂²×C₂₃	1	8	yes	complemented
388	#433	C₂²×C₂₃	1	8	yes	complemented
389	#432	C₂²×C₂₃	1	2	yes	—
390	#432	C₂²×C₂₃	1	4	yes	—
391	#432	C₂²×C₂₃	1	2	yes	complemented
392	#431	C₂²×C₂₃	1	2	yes	—
393	#431	C₂²×C₂₃	1	1	yes	characteristic
394	#431	C₂²×C₂₃	1	1	yes	characteristic
395	#431	C₂²×C₂₃	1	1	yes	characteristic
396	#431	C₂²×C₂₃	1	1	yes	characteristic
397	#431	C₂²×C₂₃	1	4	yes	—
398	#431	C₂²×C₂₃	1	2	yes	complemented
399	#431	C₂²×C₂₃	1	2	yes	complemented
400	#431	C₂²×C₂₃	1	2	yes	complemented
401	#424	C₂²×C₂₃	1	8	yes	complemented
402	#423	C₂²×C₂₃	1	2	yes	complemented
403	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
404	#407	C₂²×C₂₃	1	2	yes	—
405	#407	C₂²×C₂₃	1	4	yes	—
406	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
407	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	—
408	#405	C₂²×C₂₃	1	8	yes	complemented
409	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
410	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
411	C₂×C₂₃	—	2	2	no	—
412	C₂×C₂₃	—	2	2	no	—
413	C₂×C₂₃	—	4	1	no	—
414	C₂×C₂₃	—	4	4	no	—
415	C₂×C₂₃	#3428	1	1	yes	characteristic
416	C₂×C₂₃	C₂²×#131	1	1	yes	characteristic
417	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
418	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
419	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
420	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
421	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
422	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
424	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
425	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
426	C₂×M₁₆	C₂³×C₂₃	1	8	yes	—
427	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
428	C₂²×C₈	C₂³×C₂₃	1	8	yes	—
429	#126	C₂×C₄×C₂₃	1	4	yes	—
430	#126	C₂×C₄×C₂₃	1	4	yes	—
431	#126	C₂×C₄×C₂₃	1	4	yes	—
432	#126	C₂×C₄×C₂₃	1	4	yes	—
433	#125	C₂×C₄×C₂₃	1	2	yes	—
434	#125	C₂×C₄×C₂₃	1	2	yes	—
435	#125	C₂×C₄×C₂₃	1	2	yes	—
436	#125	C₂×C₄×C₂₃	1	2	yes	—
437	#124	C₂×C₄×C₂₃	1	2	yes	—
438	#124	C₂×C₄×C₂₃	1	2	yes	—
439	#124	C₂×C₄×C₂₃	1	2	yes	—
440	#124	C₂×C₄×C₂₃	1	2	yes	—
441	#123	C₂×C₄×C₂₃	1	4	yes	—
442	#123	C₂×C₄×C₂₃	1	4	yes	—
443	#123	C₂×C₄×C₂₃	1	4	yes	—
444	#123	C₂×C₄×C₂₃	1	4	yes	—
445	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
446	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
447	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
448	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
449	#121	C₂×C₄×C₂₃	1	2	yes	—
450	#121	C₂×C₄×C₂₃	1	2	yes	—
451	#121	C₂×C₄×C₂₃	1	2	yes	—
452	#121	C₂×C₄×C₂₃	1	2	yes	—
453	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
454	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
455	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
456	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
457	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
458	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
459	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
460	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
461	C₄×D₄	C₂³×C₂₃	1	4	yes	—
462	C₄×D₄	C₂³×C₂₃	1	2	yes	—
463	C₄×D₄	C₂³×C₂₃	1	2	yes	—
464	C₄×D₄	C₂³×C₂₃	1	4	yes	—
465	#117	C₂×C₄×C₂₃	1	4	yes	—
466	#117	C₂×C₄×C₂₃	1	4	yes	—
467	#117	C₂³×C₂₃	1	4	yes	—
468	#117	C₂³×C₂₃	1	4	yes	—
469	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
470	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
471	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
473	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
480	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
481	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
482	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
483	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
484	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
485	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
487	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
488	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
493	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
494	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
495	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
496	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
497	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
498	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
499	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
500	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
501	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
502	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
503	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
504	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
505	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
506	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
507	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
508	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
509	#97	C₂³×C₂₃	1	4	yes	—
510	#97	C₂³×C₂₃	1	8	yes	—
511	C₄×C₈	C₂³×C₂₃	1	4	yes	—
512	C₄×C₈	C₂³×C₂₃	1	2	yes	—
513	C₄×C₈	C₂³×C₂₃	1	2	yes	—
514	C₄×C₈	C₂³×C₂₃	1	2	yes	—
515	C₄×C₈	C₂³×C₂₃	1	2	yes	—
516	C₄×C₈	C₂³×C₂₃	1	8	yes	—
517	C₂₃	#60290	1	1	yes	characteristic, direct product factor, Sylow
518	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
519	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
522	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	4	4	no	—
525	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
526	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
527	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
528	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
534	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
535	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
536	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
537	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
538	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
539	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
540	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
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	2	yes	—
549	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
550	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
551	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
556	M₁₆	—	4	4	no	—
557	M₁₆	—	4	8	no	—
558	C₂×C₈	—	4	8	no	—
559	C₂×C₈	—	4	4	no	—
560	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
561	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
562	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
563	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
564	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
565	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
566	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
567	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
568	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
569	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
570	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
571	C₄⋊C₄	C₂²×C₄×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	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
578	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
579	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
580	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
581	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
582	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
583	C₂²⋊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	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
587	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
588	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
589	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
590	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
591	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
592	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
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	4	yes	—
599	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
600	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
601	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
602	C₄²	C₂⁴×C₂₃	1	4	yes	—
603	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	4	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
611	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
612	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
613	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
614	Q₈	—	2	4	no	—
615	Q₈	—	2	4	no	—
616	D₄	—	2	8	no	—
617	D₄	—	2	4	no	—
618	D₄	—	2	4	no	—
619	D₄	—	4	4	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	8	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	4	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	C₂₃×#131	1	4	yes	—
643	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
644	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
645	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
646	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
647	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
648	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
649	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
650	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
652	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
653	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
654	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
655	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
656	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
657	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
658	C₈	—	2	4	no	—
659	C₈	—	2	4	no	—
660	C₈	—	2	4	no	—
661	C₈	—	2	4	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	8	4	no	—
674	C₂²	C₂×C₂₃×#131	1	2	yes	—
675	C₂²	C₂₃×#568	1	2	yes	—
676	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	4	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	4	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	4	no	—
689	C₄	C₂×C₂₃×#131	1	2	yes	—
690	C₄	C₂×C₂₃×#131	1	2	yes	—
691	C₄	C₂₃×#585	1	2	yes	—
692	C₂	—	2	2	no	—
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	4	4	no	—
696	C₂	C₂₃×#3428	1	1	yes	characteristic
697	C₂	C₂²×C₂₃×#131	1	1	yes	characteristic
698	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	C₂×C₂₃×#121	C₄
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×#2994	C₂	semidirect
3. C₂₃×#2993	C₂	semidirect
4. C₂₃×#2983	C₂	semidirect
5. C₂₃×#2982	C₂	semidirect
6. C₂₃×#2975	C₂	semidirect
7. C₂₃×#2974	C₂	semidirect
8. C₂₃×#2972	C₂	semidirect
9. C₂₃×#2969	C₂	semidirect
10. C₂₃×#2966	C₂	semidirect
11. C₂₃×#2924	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
37. C₂₃×#436	C₂²	semidirect
38. C₂₃×#436	C₂²	semidirect
39. C₂₃×#436	C₂²	semidirect
40. C₂₃×#435	C₂²	semidirect
41. C₂₃×#435	C₂²	semidirect
42. C₈×D₄×C₂₃	C₂²	semidirect
43. C₈×D₄×C₂₃	C₂²	semidirect
44. C₈×D₄×C₂₃	C₂²	semidirect
45. C₂₃×#433	C₂²	semidirect
46. C₂₃×#433	C₂²	semidirect
49. C₂₃×#432	C₂²	semidirect
56. C₂₃×#431	C₂²	semidirect
57. C₂₃×#431	C₂²	semidirect
58. C₂₃×#431	C₂²	semidirect
59. C₂₃×#424	C₂²	semidirect
60. C₂₃×#423	C₂²	semidirect
61. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
66. C₂₃×#405	C₂²	semidirect
67. C₄×M₁₆×C₂₃	C₂²	semidirect
68. C₂×C₄×C₈×C₂₃	C₂²	semidirect
254. #60290	C₂₃	direct (N × H)
314. #2994	C₂×C₂₃	semidirect
315. #2993	C₂×C₂₃	semidirect
316. #2983	C₂×C₂₃	semidirect
317. #2982	C₂×C₂₃	semidirect
318. #2975	C₂×C₂₃	semidirect
319. #2974	C₂×C₂₃	semidirect
320. #2972	C₂×C₂₃	semidirect
321. #2969	C₂×C₂₃	semidirect
322. #2966	C₂×C₂₃	semidirect
323. #2924	C₂×C₂₃	semidirect
324. #2920	C₂×C₂₃	semidirect
325. C₂×#431	C₂×C₂₃	semidirect
375. #446	C₂²×C₂₃	semidirect
376. #446	C₂²×C₂₃	semidirect
377. C₈×Q₈	C₂²×C₂₃	semidirect
378. C₈×Q₈	C₂²×C₂₃	semidirect
379. #436	C₂²×C₂₃	semidirect
380. #436	C₂²×C₂₃	semidirect
381. #436	C₂²×C₂₃	semidirect
382. #435	C₂²×C₂₃	semidirect
383. #435	C₂²×C₂₃	semidirect
384. C₈×D₄	C₂²×C₂₃	semidirect
385. C₈×D₄	C₂²×C₂₃	semidirect
386. C₈×D₄	C₂²×C₂₃	semidirect
387. #433	C₂²×C₂₃	semidirect
388. #433	C₂²×C₂₃	semidirect
391. #432	C₂²×C₂₃	semidirect
398. #431	C₂²×C₂₃	semidirect
399. #431	C₂²×C₂₃	semidirect
400. #431	C₂²×C₂₃	semidirect
401. #424	C₂²×C₂₃	semidirect
402. #423	C₂²×C₂₃	semidirect
403. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
408. #405	C₂²×C₂₃	semidirect
409. C₄×M₁₆	C₂²×C₂₃	semidirect
410. C₂×C₄×C₈	C₂²×C₂₃	semidirect
517. C₂₃	#60290	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#529	2
C₂₃×#2994	2
C₂₃×#2993	2
C₂₃×#2983	2
C₂₃×#2982	2
C₂₃×#2975	2
C₂₃×#2974	2
C₂₃×#2972	2
C₂₃×#2969	2
C₂₃×#2966	2
C₂₃×#2924	2
C₂₃×#2920	2
C₂×C₂₃×#431	2
#60290	23

Subgroups — C23×#60290 #19207916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60290 #19207916