Subgroups — C₂₃×#60233 #19207859

Order 5888.

2298 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2977	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2976	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2974	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2973	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2972	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2933	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2929	C₂	1	4	yes	maximal, complemented
9	C₂₃×#2924	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2880	C₂	1	2	yes	maximal, complemented
11	C₂×C₂₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#131	C₂²	1	4	yes	complemented
16	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	complemented
17	C₂³×C₈×C₂₃	C₂²	1	2	yes	complemented
18	C₂₃×#525	C₄	1	2	yes	—
19	C₂₃×#525	C₄	1	2	yes	—
20	C₂₃×#525	C₄	1	2	yes	—
21	C₂₃×#525	C₄	1	2	yes	—
22	C₂₃×#525	C₂²	1	2	yes	—
23	C₂₃×#525	C₂²	1	2	yes	—
24	C₂₃×#525	C₂²	1	2	yes	—
25	C₂₃×#525	C₂²	1	2	yes	—
26	C₂×C₂₃×#123	C₄	1	2	yes	—
27	C₂×C₂₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
29	C₂×C₂₃×#121	C₄	1	1	yes	characteristic
30	C₂×C₂₃×#121	C₄	1	1	yes	characteristic
31	C₂×C₂₃×#120	C₄	1	2	yes	—
32	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
34	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
35	C₂₃×#436	C₂²	1	8	yes	complemented
36	C₂₃×#435	C₂²	1	8	yes	complemented
37	C₂₃×#435	C₂²	1	8	yes	complemented
38	C₂₃×#435	C₂²	1	8	yes	complemented
39	C₂₃×#435	C₂²	1	8	yes	complemented
40	C₈×D₄×C₂₃	C₂²	1	8	yes	complemented
41	C₈×D₄×C₂₃	C₂²	1	8	yes	complemented
42	C₈×D₄×C₂₃	C₂²	1	8	yes	complemented
43	C₂₃×#433	C₂²	1	8	yes	complemented
44	C₂₃×#432	C₂²	1	4	yes	complemented
45	C₂₃×#431	C₂²	1	4	yes	complemented
46	C₂₃×#424	C₂²	1	4	yes	complemented
47	C₂₃×#408	C₂²	1	4	yes	complemented
48	C₂₃×#408	C₂²	1	8	yes	complemented
49	C₂₃×#407	C₂²	1	2	yes	—
50	C₂₃×#407	C₂²	1	2	yes	—
51	C₂₃×#407	C₂²	1	2	yes	complemented
52	C₂₃×#407	C₂²	1	2	yes	complemented
53	C₂₃×#407	C₂²	1	4	yes	complemented
54	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
55	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
57	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
59	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
60	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
61	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
62	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
63	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
64	C₂₃×#405	C₂²	1	4	yes	complemented
65	C₂⁵×C₂₃	C₂×C₄	1	1	yes	characteristic
66	C₂×#41×C₂₃	—	4	4	no	—
67	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
68	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
69	C₂×#41×C₂₃	C₂³	1	2	yes	—
70	C₂×#41×C₂₃	C₂³	1	2	yes	—
71	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
72	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
73	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
74	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
75	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
76	C₂³×C₄×C₂₃	—	4	4	no	—
77	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
78	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
81	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
83	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
92	C₂₃×#131	—	4	8	no	—
93	C₂×M₁₆×C₂₃	—	4	4	no	—
94	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
95	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
96	C₂×M₁₆×C₂₃	C₂³	1	8	yes	complemented
97	C₂²×C₈×C₂₃	—	4	4	no	—
98	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
99	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
100	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
101	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
102	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
103	C₂²×C₈×C₂₃	C₂³	1	8	yes	complemented
104	C₂₃×#123	C₂×C₄	1	4	yes	—
105	C₂₃×#123	C₂×C₄	1	4	yes	—
106	C₂₃×#123	C₂×C₄	1	4	yes	—
107	C₂₃×#123	C₂×C₄	1	4	yes	—
108	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
109	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
110	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
111	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
112	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
113	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
114	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
115	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
116	C₂₃×#121	C₂×C₄	1	2	yes	—
117	C₂₃×#121	C₂×C₄	1	2	yes	—
118	C₂₃×#121	C₂×C₄	1	2	yes	—
119	C₂₃×#121	C₂×C₄	1	2	yes	—
120	C₂₃×#121	C₂×C₄	1	2	yes	—
121	C₂₃×#121	C₂×C₄	1	2	yes	—
122	C₂₃×#121	C₂×C₄	1	2	yes	—
123	C₂₃×#121	C₂×C₄	1	2	yes	—
124	C₂₃×#120	C₂×C₄	1	4	yes	—
125	C₂₃×#120	C₂×C₄	1	4	yes	—
126	C₂₃×#120	C₂×C₄	1	4	yes	—
127	C₂₃×#120	C₂×C₄	1	4	yes	—
128	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
129	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
130	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
131	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
132	C₄×D₄×C₂₃	C₂³	1	4	yes	—
133	C₄×D₄×C₂₃	C₂³	1	4	yes	—
134	C₄×D₄×C₂₃	C₂³	1	4	yes	—
135	C₄×D₄×C₂₃	C₂³	1	4	yes	—
136	C₂₃×#117	C₂×C₄	1	2	yes	—
137	C₂₃×#117	C₂×C₄	1	2	yes	—
138	C₂₃×#117	C₂³	1	2	yes	—
139	C₂₃×#117	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
144	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
145	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
146	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
147	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
148	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
149	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
150	C₂₃×C₄⋊C₈	C₂³	1	8	yes	complemented
151	C₂₃×C₄⋊C₈	C₂³	1	8	yes	complemented
152	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
153	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
154	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
155	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
156	C₂₃×C₂²⋊C₈	C₂³	1	2	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	4	yes	—
161	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
162	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
163	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
164	C₂₃×#97	C₂³	1	8	yes	complemented
165	C₄×C₈×C₂₃	C₂³	1	8	yes	complemented
166	C₂⁴×C₂₃	—	2	4	no	—
167	C₂⁴×C₂₃	—	4	2	no	—
168	C₂⁴×C₂₃	—	4	2	no	—
169	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
170	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
171	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
172	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
173	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
174	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
175	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
176	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
177	#41×C₂₃	—	2	8	no	—
178	#41×C₂₃	—	4	4	no	—
179	#41×C₂₃	—	4	4	no	—
180	#41×C₂₃	—	4	4	no	—
181	C₂×Q₈×C₂₃	—	4	2	no	—
182	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
183	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
184	C₂×D₄×C₂₃	—	2	8	no	—
185	C₂×D₄×C₂₃	—	4	2	no	—
186	C₂×D₄×C₂₃	—	4	4	no	—
187	C₂×D₄×C₂₃	—	4	4	no	—
188	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
189	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
190	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
191	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
192	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
193	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
194	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
195	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
196	C₂²×C₄×C₂₃	—	2	4	no	—
197	C₂²×C₄×C₂₃	—	2	4	no	—
198	C₂²×C₄×C₂₃	—	2	4	no	—
199	C₂²×C₄×C₂₃	—	4	2	no	—
200	C₂²×C₄×C₂₃	—	4	2	no	—
201	C₂²×C₄×C₂₃	—	4	2	no	—
202	C₂²×C₄×C₂₃	—	4	2	no	—
203	C₂²×C₄×C₂₃	—	4	2	no	—
204	C₂²×C₄×C₂₃	—	4	2	no	—
205	C₂²×C₄×C₂₃	—	4	2	no	—
206	C₂²×C₄×C₂₃	—	4	2	no	—
207	C₂²×C₄×C₂₃	—	4	4	no	—
208	C₂²×C₄×C₂₃	—	4	2	no	—
209	C₂²×C₄×C₂₃	—	4	2	no	—
210	C₂²×C₄×C₂₃	—	4	2	no	—
211	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
212	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
215	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
221	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
222	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
230	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
231	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
232	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
234	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
235	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
244	M₁₆×C₂₃	—	2	8	no	—
245	M₁₆×C₂₃	—	4	4	no	—
246	M₁₆×C₂₃	—	4	8	no	—
247	C₂×C₈×C₂₃	—	2	8	no	—
248	C₂×C₈×C₂₃	—	4	2	no	—
249	C₂×C₈×C₂₃	—	4	4	no	—
250	C₂×C₈×C₂₃	—	4	2	no	—
251	C₂×C₈×C₂₃	—	4	4	no	—
252	C₂×C₈×C₂₃	—	4	8	no	—
253	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
254	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
255	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
256	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
257	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
258	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
259	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
260	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
261	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
262	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
263	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
264	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
265	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
266	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
267	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
268	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
269	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
270	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
271	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
272	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
273	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
274	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
275	C₄²×C₂₃	C₂⁴	1	4	yes	—
276	#60233	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂³×C₂₃	—	2	2	no	—
278	C₂³×C₂₃	—	2	2	no	—
279	C₂³×C₂₃	—	2	2	no	—
280	C₂³×C₂₃	—	2	2	no	—
281	C₂³×C₂₃	—	2	2	no	—
282	C₂³×C₂₃	—	2	2	no	—
283	C₂³×C₂₃	—	2	2	no	—
284	C₂³×C₂₃	—	2	2	no	—
285	C₂³×C₂₃	—	2	2	no	—
286	C₂³×C₂₃	—	2	2	no	—
287	C₂³×C₂₃	—	2	2	no	—
288	C₂³×C₂₃	—	2	2	no	—
289	C₂³×C₂₃	—	2	4	no	—
290	C₂³×C₂₃	—	4	1	no	—
291	C₂³×C₂₃	—	4	1	no	—
292	C₂³×C₂₃	—	4	1	no	—
293	C₂³×C₂₃	—	4	1	no	—
294	C₂³×C₂₃	—	4	1	no	—
295	C₂³×C₂₃	—	4	1	no	—
296	C₂³×C₂₃	—	4	1	no	—
297	C₂³×C₂₃	—	4	1	no	—
298	C₂³×C₂₃	—	4	2	no	—
299	C₂³×C₂₃	—	4	2	no	—
300	C₂³×C₂₃	—	4	16	no	—
301	C₂³×C₂₃	#131	1	4	yes	complemented
302	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
303	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
304	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
305	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
306	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
307	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
308	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
309	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
310	Q₈×C₂₃	—	2	4	no	—
311	Q₈×C₂₃	—	4	2	no	—
312	D₄×C₂₃	—	2	8	no	—
313	D₄×C₂₃	—	2	8	no	—
314	D₄×C₂₃	—	2	8	no	—
315	D₄×C₂₃	—	2	8	no	—
316	D₄×C₂₃	—	2	4	no	—
317	D₄×C₂₃	—	4	4	no	—
318	D₄×C₂₃	—	4	2	no	—
319	D₄×C₂₃	—	4	4	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	4	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	8	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	4	1	no	—
338	C₂×C₄×C₂₃	—	4	1	no	—
339	C₂×C₄×C₂₃	—	4	1	no	—
340	C₂×C₄×C₂₃	—	4	1	no	—
341	C₂×C₄×C₂₃	—	4	1	no	—
342	C₂×C₄×C₂₃	—	4	1	no	—
343	C₂×C₄×C₂₃	—	4	1	no	—
344	C₂×C₄×C₂₃	—	4	1	no	—
345	C₂×C₄×C₂₃	—	4	1	no	—
346	C₂×C₄×C₂₃	—	4	1	no	—
347	C₂×C₄×C₂₃	—	4	1	no	—
348	C₂×C₄×C₂₃	—	4	1	no	—
349	C₂×C₄×C₂₃	—	4	2	no	—
350	C₂×C₄×C₂₃	—	4	4	no	—
351	C₂×C₄×C₂₃	—	4	2	no	—
352	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
353	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
354	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
355	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
356	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
357	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
358	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
359	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
360	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
361	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
362	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
363	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
364	C₈×C₂₃	—	2	4	no	—
365	C₈×C₂₃	—	2	4	no	—
366	C₈×C₂₃	—	2	8	no	—
367	C₂×#525	C₂×C₂₃	1	1	yes	characteristic
368	#2977	C₂×C₂₃	1	4	yes	complemented
369	#2976	C₂×C₂₃	1	4	yes	complemented
370	#2974	C₂×C₂₃	1	4	yes	complemented
371	#2973	C₂×C₂₃	1	2	yes	complemented
372	#2972	C₂×C₂₃	1	2	yes	complemented
373	#2933	C₂×C₂₃	1	4	yes	complemented
374	#2929	C₂×C₂₃	1	4	yes	complemented
375	#2924	C₂×C₂₃	1	2	yes	complemented
376	#2880	C₂×C₂₃	1	2	yes	complemented
377	C₂×#407	C₂×C₂₃	1	1	yes	characteristic, complemented
378	C₂²×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
379	C₂²×C₂₃	—	2	8	no	—
380	C₂²×C₂₃	—	2	1	no	—
381	C₂²×C₂₃	—	2	1	no	—
382	C₂²×C₂₃	—	2	1	no	—
383	C₂²×C₂₃	—	2	1	no	—
384	C₂²×C₂₃	—	2	1	no	—
385	C₂²×C₂₃	—	2	1	no	—
386	C₂²×C₂₃	—	2	1	no	—
387	C₂²×C₂₃	—	2	1	no	—
388	C₂²×C₂₃	—	2	1	no	—
389	C₂²×C₂₃	—	2	1	no	—
390	C₂²×C₂₃	—	2	1	no	—
391	C₂²×C₂₃	—	2	1	no	—
392	C₂²×C₂₃	—	2	4	no	—
393	C₂²×C₂₃	—	2	4	no	—
394	C₂²×C₂₃	—	2	1	no	—
395	C₂²×C₂₃	—	2	1	no	—
396	C₂²×C₂₃	—	2	4	no	—
397	C₂²×C₂₃	—	2	1	no	—
398	C₂²×C₂₃	—	2	1	no	—
399	C₂²×C₂₃	—	4	4	no	—
400	C₂²×C₂₃	—	4	4	no	—
401	C₂²×C₂₃	—	4	4	no	—
402	C₂²×C₂₃	—	4	4	no	—
403	C₂²×C₂₃	—	4	4	no	—
404	C₂²×C₂₃	—	4	4	no	—
405	C₂²×C₂₃	—	8	4	no	—
406	C₂²×C₂₃	#518	1	2	yes	—
407	C₂²×C₂₃	C₂×#131	1	2	yes	—
408	C₂²×C₂₃	C₂×#131	1	2	yes	—
409	C₂²×C₂₃	C₂×#131	1	2	yes	—
410	C₂²×C₂₃	#568	1	2	yes	—
411	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
412	C₄×C₂₃	—	2	1	no	—
413	C₄×C₂₃	—	2	1	no	—
414	C₄×C₂₃	—	2	1	no	—
415	C₄×C₂₃	—	2	1	no	—
416	C₄×C₂₃	—	2	1	no	—
417	C₄×C₂₃	—	2	1	no	—
418	C₄×C₂₃	—	2	4	no	—
419	C₄×C₂₃	—	2	4	no	—
420	C₄×C₂₃	—	2	4	no	—
421	C₄×C₂₃	#518	1	2	yes	—
422	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
423	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
424	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×#131	C₂²×C₂₃	1	4	yes	complemented
426	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	complemented
427	C₂³×C₈	C₂²×C₂₃	1	2	yes	complemented
428	#525	C₄×C₂₃	1	2	yes	—
429	#525	C₄×C₂₃	1	2	yes	—
430	#525	C₄×C₂₃	1	2	yes	—
431	#525	C₄×C₂₃	1	2	yes	—
432	#525	C₂²×C₂₃	1	2	yes	—
433	#525	C₂²×C₂₃	1	2	yes	—
434	#525	C₂²×C₂₃	1	2	yes	—
435	#525	C₂²×C₂₃	1	2	yes	—
436	C₂×#123	C₄×C₂₃	1	2	yes	—
437	C₂×C₂²⋊Q₈	C₄×C₂₃	1	1	yes	characteristic
438	C₂×C₂²⋊Q₈	C₄×C₂₃	1	1	yes	characteristic
439	C₂×#121	C₄×C₂₃	1	1	yes	characteristic
440	C₂×#121	C₄×C₂₃	1	1	yes	characteristic
441	C₂×#120	C₄×C₂₃	1	2	yes	—
442	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
443	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
444	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
445	#436	C₂²×C₂₃	1	8	yes	complemented
446	#435	C₂²×C₂₃	1	8	yes	complemented
447	#435	C₂²×C₂₃	1	8	yes	complemented
448	#435	C₂²×C₂₃	1	8	yes	complemented
449	#435	C₂²×C₂₃	1	8	yes	complemented
450	C₈×D₄	C₂²×C₂₃	1	8	yes	complemented
451	C₈×D₄	C₂²×C₂₃	1	8	yes	complemented
452	C₈×D₄	C₂²×C₂₃	1	8	yes	complemented
453	#433	C₂²×C₂₃	1	8	yes	complemented
454	#432	C₂²×C₂₃	1	4	yes	complemented
455	#431	C₂²×C₂₃	1	4	yes	complemented
456	#424	C₂²×C₂₃	1	4	yes	complemented
457	#408	C₂²×C₂₃	1	8	yes	complemented
458	#408	C₂²×C₂₃	1	4	yes	complemented
459	#407	C₂²×C₂₃	1	2	yes	—
460	#407	C₂²×C₂₃	1	2	yes	—
461	#407	C₂²×C₂₃	1	2	yes	complemented
462	#407	C₂²×C₂₃	1	2	yes	complemented
463	#407	C₂²×C₂₃	1	4	yes	complemented
464	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
465	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
466	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
467	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
468	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
469	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
470	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
471	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
472	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
473	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
474	#405	C₂²×C₂₃	1	4	yes	complemented
475	C₂×C₂₃	—	2	2	no	—
476	C₂×C₂₃	—	2	2	no	—
477	C₂×C₂₃	—	2	2	no	—
478	C₂×C₂₃	—	2	2	no	—
479	C₂×C₂₃	—	2	2	no	—
480	C₂×C₂₃	—	4	1	no	—
481	C₂×C₂₃	—	4	1	no	—
482	C₂×C₂₃	—	4	4	no	—
483	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
484	C₂×C₂₃	C₂²×#131	1	1	yes	characteristic
485	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
486	C₂⁵	C₂×C₄×C₂₃	1	1	yes	characteristic
487	C₂×#41	—	4	4	no	—
488	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
489	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
490	C₂×#41	C₂³×C₂₃	1	2	yes	—
491	C₂×#41	C₂³×C₂₃	1	2	yes	—
492	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
493	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
494	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
495	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
496	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
497	C₂³×C₄	—	4	4	no	—
498	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
499	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
500	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
501	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
502	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
503	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
504	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
511	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
513	#131	—	4	8	no	—
514	C₂×M₁₆	—	4	4	no	—
515	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
516	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
517	C₂×M₁₆	C₂³×C₂₃	1	8	yes	complemented
518	C₂²×C₈	—	4	4	no	—
519	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
520	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
521	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
522	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
523	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
524	C₂²×C₈	C₂³×C₂₃	1	8	yes	complemented
525	#123	C₂×C₄×C₂₃	1	4	yes	—
526	#123	C₂×C₄×C₂₃	1	4	yes	—
527	#123	C₂×C₄×C₂₃	1	4	yes	—
528	#123	C₂×C₄×C₂₃	1	4	yes	—
529	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
530	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
531	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
532	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
533	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
534	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
535	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
536	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
537	#121	C₂×C₄×C₂₃	1	2	yes	—
538	#121	C₂×C₄×C₂₃	1	2	yes	—
539	#121	C₂×C₄×C₂₃	1	2	yes	—
540	#121	C₂×C₄×C₂₃	1	2	yes	—
541	#121	C₂×C₄×C₂₃	1	2	yes	—
542	#121	C₂×C₄×C₂₃	1	2	yes	—
543	#121	C₂×C₄×C₂₃	1	2	yes	—
544	#121	C₂×C₄×C₂₃	1	2	yes	—
545	#120	C₂×C₄×C₂₃	1	4	yes	—
546	#120	C₂×C₄×C₂₃	1	4	yes	—
547	#120	C₂×C₄×C₂₃	1	4	yes	—
548	#120	C₂×C₄×C₂₃	1	4	yes	—
549	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
550	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
551	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
552	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
553	C₄×D₄	C₂³×C₂₃	1	4	yes	—
554	C₄×D₄	C₂³×C₂₃	1	4	yes	—
555	C₄×D₄	C₂³×C₂₃	1	4	yes	—
556	C₄×D₄	C₂³×C₂₃	1	4	yes	—
557	#117	C₂×C₄×C₂₃	1	2	yes	—
558	#117	C₂×C₄×C₂₃	1	2	yes	—
559	#117	C₂³×C₂₃	1	2	yes	—
560	#117	C₂³×C₂₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
570	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
571	C₄⋊C₈	C₂³×C₂₃	1	8	yes	complemented
572	C₄⋊C₈	C₂³×C₂₃	1	8	yes	complemented
573	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
574	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
575	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
576	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
577	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
578	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
579	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
580	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
581	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
582	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
583	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	complemented
584	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	complemented
585	#97	C₂³×C₂₃	1	8	yes	complemented
586	C₄×C₈	C₂³×C₂₃	1	8	yes	complemented
587	C₂₃	#60233	1	1	yes	characteristic, direct product factor, Sylow
588	C₂⁴	—	2	4	no	—
589	C₂⁴	—	4	2	no	—
590	C₂⁴	—	4	2	no	—
591	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
592	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
593	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
594	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
595	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
596	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
597	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
598	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
599	#41	—	2	8	no	—
600	#41	—	4	4	no	—
601	#41	—	4	4	no	—
602	#41	—	4	4	no	—
603	C₂×Q₈	—	4	2	no	—
604	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
605	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
606	C₂×D₄	—	2	8	no	—
607	C₂×D₄	—	4	2	no	—
608	C₂×D₄	—	4	4	no	—
609	C₂×D₄	—	4	4	no	—
610	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
611	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
612	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
613	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
614	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
615	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
616	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
617	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	4	2	no	—
622	C₂²×C₄	—	4	2	no	—
623	C₂²×C₄	—	4	2	no	—
624	C₂²×C₄	—	4	2	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	4	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
634	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
635	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
636	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
637	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
638	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
639	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
640	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
641	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
642	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
643	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
644	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
645	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
646	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
647	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
648	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
649	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
650	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
651	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
652	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
653	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
654	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
655	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
656	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
657	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
666	M₁₆	—	2	8	no	—
667	M₁₆	—	4	4	no	—
668	M₁₆	—	4	8	no	—
669	C₂×C₈	—	2	8	no	—
670	C₂×C₈	—	4	2	no	—
671	C₂×C₈	—	4	4	no	—
672	C₂×C₈	—	4	2	no	—
673	C₂×C₈	—	4	4	no	—
674	C₂×C₈	—	4	8	no	—
675	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
676	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
677	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
678	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
679	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
680	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
681	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
682	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
683	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
684	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
685	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
686	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
687	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
688	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
689	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
690	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
691	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
692	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
693	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
694	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
695	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
696	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
697	C₄²	C₂⁴×C₂₃	1	4	yes	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	4	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	1	no	—
717	C₂³	—	4	1	no	—
718	C₂³	—	4	1	no	—
719	C₂³	—	4	2	no	—
720	C₂³	—	4	2	no	—
721	C₂³	—	4	16	no	—
722	C₂³	C₂₃×#131	1	4	yes	complemented
723	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
724	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
725	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
726	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
727	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
728	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
729	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
730	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
731	Q₈	—	2	4	no	—
732	Q₈	—	4	2	no	—
733	D₄	—	2	8	no	—
734	D₄	—	2	8	no	—
735	D₄	—	2	8	no	—
736	D₄	—	2	8	no	—
737	D₄	—	2	4	no	—
738	D₄	—	4	2	no	—
739	D₄	—	4	4	no	—
740	D₄	—	4	4	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	8	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	4	4	no	—
772	C₂×C₄	—	4	2	no	—
773	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
774	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
775	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
776	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
777	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
778	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
779	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
780	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
781	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
782	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
783	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
784	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
785	C₈	—	2	4	no	—
786	C₈	—	2	4	no	—
787	C₈	—	2	8	no	—
788	C₂²	—	2	8	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	4	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	4	4	no	—
809	C₂²	—	4	4	no	—
810	C₂²	—	4	4	no	—
811	C₂²	—	4	4	no	—
812	C₂²	—	4	4	no	—
813	C₂²	—	4	4	no	—
814	C₂²	—	8	4	no	—
815	C₂²	C₂₃×#518	1	2	yes	—
816	C₂²	C₂×C₂₃×#131	1	2	yes	—
817	C₂²	C₂×C₂₃×#131	1	2	yes	—
818	C₂²	C₂×C₂₃×#131	1	2	yes	—
819	C₂²	C₂₃×#568	1	2	yes	—
820	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
821	C₄	—	2	1	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	2	1	no	—
827	C₄	—	2	4	no	—
828	C₄	—	2	4	no	—
829	C₄	—	2	4	no	—
830	C₄	C₂₃×#518	1	2	yes	—
831	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
832	C₂	—	2	2	no	—
833	C₂	—	2	2	no	—
834	C₂	—	2	2	no	—
835	C₂	—	2	2	no	—
836	C₂	—	2	2	no	—
837	C₂	—	4	1	no	—
838	C₂	—	4	1	no	—
839	C₂	—	4	4	no	—
840	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
841	C₂	C₂²×C₂₃×#131	1	1	yes	characteristic
842	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×#525	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×#2977	C₂	semidirect
3. C₂₃×#2976	C₂	semidirect
4. C₂₃×#2974	C₂	semidirect
5. C₂₃×#2973	C₂	semidirect
6. C₂₃×#2972	C₂	semidirect
7. C₂₃×#2933	C₂	semidirect
8. C₂₃×#2929	C₂	semidirect
9. C₂₃×#2924	C₂	semidirect
10. C₂₃×#2880	C₂	semidirect
11. C₂×C₂₃×#407	C₂	semidirect
12. C₂²×C₂₃×C₂²⋊C₈	C₂	semidirect
15. C₂×C₂₃×#131	C₂²	semidirect
16. C₂²×M₁₆×C₂₃	C₂²	semidirect
17. C₂³×C₈×C₂₃	C₂²	semidirect
35. C₂₃×#436	C₂²	semidirect
36. C₂₃×#435	C₂²	semidirect
37. C₂₃×#435	C₂²	semidirect
38. C₂₃×#435	C₂²	semidirect
39. C₂₃×#435	C₂²	semidirect
40. C₈×D₄×C₂₃	C₂²	semidirect
41. C₈×D₄×C₂₃	C₂²	semidirect
42. C₈×D₄×C₂₃	C₂²	semidirect
43. C₂₃×#433	C₂²	semidirect
44. C₂₃×#432	C₂²	semidirect
45. C₂₃×#431	C₂²	semidirect
46. C₂₃×#424	C₂²	semidirect
47. C₂₃×#408	C₂²	semidirect
48. C₂₃×#408	C₂²	semidirect
51. C₂₃×#407	C₂²	semidirect
52. C₂₃×#407	C₂²	semidirect
53. C₂₃×#407	C₂²	semidirect
59. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
60. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
61. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
62. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
63. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
64. C₂₃×#405	C₂²	semidirect
96. C₂×M₁₆×C₂₃	C₂³	semidirect
103. C₂²×C₈×C₂₃	C₂³	semidirect
150. C₂₃×C₄⋊C₈	C₂³	semidirect
151. C₂₃×C₄⋊C₈	C₂³	semidirect
162. C₂₃×C₂²⋊C₈	C₂³	semidirect
163. C₂₃×C₂²⋊C₈	C₂³	semidirect
164. C₂₃×#97	C₂³	semidirect
165. C₄×C₈×C₂₃	C₂³	semidirect
276. #60233	C₂₃	direct (N × H)
301. C₂³×C₂₃	#131	semidirect
368. #2977	C₂×C₂₃	semidirect
369. #2976	C₂×C₂₃	semidirect
370. #2974	C₂×C₂₃	semidirect
371. #2973	C₂×C₂₃	semidirect
372. #2972	C₂×C₂₃	semidirect
373. #2933	C₂×C₂₃	semidirect
374. #2929	C₂×C₂₃	semidirect
375. #2924	C₂×C₂₃	semidirect
376. #2880	C₂×C₂₃	semidirect
377. C₂×#407	C₂×C₂₃	semidirect
378. C₂²×C₂²⋊C₈	C₂×C₂₃	semidirect
425. C₂×#131	C₂²×C₂₃	semidirect
426. C₂²×M₁₆	C₂²×C₂₃	semidirect
427. C₂³×C₈	C₂²×C₂₃	semidirect
445. #436	C₂²×C₂₃	semidirect
446. #435	C₂²×C₂₃	semidirect
447. #435	C₂²×C₂₃	semidirect
448. #435	C₂²×C₂₃	semidirect
449. #435	C₂²×C₂₃	semidirect
450. C₈×D₄	C₂²×C₂₃	semidirect
451. C₈×D₄	C₂²×C₂₃	semidirect
452. C₈×D₄	C₂²×C₂₃	semidirect
453. #433	C₂²×C₂₃	semidirect
454. #432	C₂²×C₂₃	semidirect
455. #431	C₂²×C₂₃	semidirect
456. #424	C₂²×C₂₃	semidirect
457. #408	C₂²×C₂₃	semidirect
458. #408	C₂²×C₂₃	semidirect
461. #407	C₂²×C₂₃	semidirect
462. #407	C₂²×C₂₃	semidirect
463. #407	C₂²×C₂₃	semidirect
469. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
470. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
471. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
472. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
473. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
474. #405	C₂²×C₂₃	semidirect
517. C₂×M₁₆	C₂³×C₂₃	semidirect
524. C₂²×C₈	C₂³×C₂₃	semidirect
571. C₄⋊C₈	C₂³×C₂₃	semidirect
572. C₄⋊C₈	C₂³×C₂₃	semidirect
583. C₂²⋊C₈	C₂³×C₂₃	semidirect
584. C₂²⋊C₈	C₂³×C₂₃	semidirect
585. #97	C₂³×C₂₃	semidirect
586. C₄×C₈	C₂³×C₂₃	semidirect
587. C₂₃	#60233	direct (N × H)
722. C₂³	C₂₃×#131	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#525	2
C₂₃×#2977	2
C₂₃×#2976	2
C₂₃×#2974	2
C₂₃×#2973	2
C₂₃×#2972	2
C₂₃×#2933	2
C₂₃×#2929	2
C₂₃×#2924	2
C₂₃×#2880	2
C₂×C₂₃×#407	2
C₂²×C₂₃×C₂²⋊C₈	2
#60233	23

Subgroups — C23×#60233 #19207859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60233 #19207859