Subgroups — C₂₃×#60265 #19207891

Order 5888.

1918 conjugacy classes of subgroups.

The subgroup lattice has 718 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×#2994	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2992	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2990	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2989	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2988	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2962	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2935	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2929	C₂	1	4	yes	maximal, complemented
10	C₂₃×#2925	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2906	C₂	1	2	yes	maximal, complemented
13	C₂²×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#131	C₂²	1	4	yes	—
15	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
16	C₂₃×#533	C₄	1	1	yes	characteristic
17	C₂₃×#533	C₄	1	1	yes	characteristic
18	C₂₃×#533	C₂²	1	1	yes	characteristic
19	C₂₃×#532	C₄	1	1	yes	characteristic
20	C₂₃×#532	C₄	1	1	yes	characteristic
21	C₂₃×#532	C₂²	1	1	yes	characteristic
22	C₂₃×#529	C₄	1	2	yes	—
23	C₂₃×#529	C₄	1	2	yes	—
24	C₂₃×#529	C₄	1	2	yes	—
25	C₂₃×#529	C₄	1	2	yes	—
26	C₂₃×#529	C₂²	1	2	yes	—
27	C₂₃×#529	C₂²	1	2	yes	—
28	C₂₃×#525	C₄	1	2	yes	—
29	C₂₃×#525	C₄	1	2	yes	—
30	C₂₃×#525	C₂²	1	2	yes	—
31	C₄×#41×C₂₃	C₂²	1	2	yes	—
32	C₄×#41×C₂₃	C₂²	1	2	yes	—
33	C₄×#41×C₂₃	C₂²	1	2	yes	—
34	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#446	C₂²	1	4	yes	complemented
36	C₂₃×#446	C₂²	1	8	yes	complemented
37	C₈×Q₈×C₂₃	C₂²	1	4	yes	complemented
38	C₂₃×#436	C₂²	1	4	yes	complemented
39	C₂₃×#435	C₂²	1	8	yes	—
40	C₂₃×#435	C₂²	1	8	yes	—
41	C₂₃×#435	C₂²	1	8	yes	complemented
42	C₈×D₄×C₂₃	C₂²	1	8	yes	—
43	C₈×D₄×C₂₃	C₂²	1	8	yes	—
44	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
45	C₂₃×#433	C₂²	1	8	yes	complemented
46	C₂₃×#432	C₂²	1	2	yes	—
47	C₂₃×#432	C₂²	1	2	yes	—
48	C₂₃×#432	C₂²	1	4	yes	complemented
49	C₂₃×#431	C₂²	1	2	yes	—
50	C₂₃×#431	C₂²	1	2	yes	—
51	C₂₃×#431	C₂²	1	4	yes	complemented
52	C₂₃×#424	C₂²	1	4	yes	—
53	C₂₃×#424	C₂²	1	8	yes	complemented
54	C₂₃×#423	C₂²	1	1	yes	characteristic
55	C₂₃×#423	C₂²	1	1	yes	characteristic
56	C₂₃×#423	C₂²	1	4	yes	complemented
57	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
58	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
59	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
62	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
63	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
64	C₂×C₂₃×C₄⋊C₈	C₂²	1	4	yes	complemented
65	C₂₃×#408	C₂²	1	4	yes	—
66	C₂₃×#407	C₂²	1	2	yes	—
67	C₂₃×#405	C₂²	1	4	yes	—
68	C₄×M₁₆×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	C₂₃×#131	—	4	8	no	—
76	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
77	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
78	C₂×M₁₆×C₂₃	C₂³	1	8	yes	—
79	C₂²×C₈×C₂₃	—	4	4	no	—
80	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
81	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
82	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
83	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
84	C₂²×C₈×C₂₃	C₂³	1	8	yes	—
85	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
86	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
87	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
88	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
89	C₂₃×#126	C₂×C₄	1	4	yes	—
90	C₂₃×#126	C₂×C₄	1	4	yes	—
91	C₂₃×#125	C₂×C₄	1	2	yes	—
92	C₂₃×#125	C₂×C₄	1	2	yes	—
93	C₂₃×#125	C₂×C₄	1	2	yes	—
94	C₂₃×#124	C₂×C₄	1	2	yes	—
95	C₂₃×#124	C₂×C₄	1	2	yes	—
96	C₂₃×#124	C₂×C₄	1	2	yes	—
97	C₂₃×#123	C₂×C₄	1	4	yes	—
98	C₂₃×#123	C₂×C₄	1	4	yes	—
99	C₂₃×#123	C₂×C₄	1	4	yes	—
100	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
101	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
102	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
103	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
104	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
105	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
106	C₂₃×#121	C₂×C₄	1	2	yes	—
107	C₂₃×#121	C₂×C₄	1	2	yes	—
108	C₂₃×#121	C₂×C₄	1	2	yes	—
109	C₂₃×#121	C₂×C₄	1	2	yes	—
110	C₂₃×#121	C₂×C₄	1	2	yes	—
111	C₂₃×#121	C₂×C₄	1	2	yes	—
112	C₂₃×#120	C₂×C₄	1	4	yes	—
113	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
114	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
115	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
116	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
117	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
118	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
119	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
120	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
121	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
122	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
123	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
124	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
125	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
126	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
127	C₄×D₄×C₂₃	C₂³	1	4	yes	—
128	C₄×D₄×C₂₃	C₂³	1	4	yes	—
129	C₄×D₄×C₂₃	C₂³	1	2	yes	—
130	C₄×D₄×C₂₃	C₂³	1	2	yes	—
131	C₂₃×#117	C₂×C₄	1	2	yes	—
132	C₂₃×#117	C₂×C₄	1	2	yes	—
133	C₂₃×#117	C₂×C₄	1	4	yes	—
134	C₂₃×#117	C₂×C₄	1	4	yes	—
135	C₂₃×#117	C₂³	1	2	yes	—
136	C₂₃×#117	C₂³	1	4	yes	—
137	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
138	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
139	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
140	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
141	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
142	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
150	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
151	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
152	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
153	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
154	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
155	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
156	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
157	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
158	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
159	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
160	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
161	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
162	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
163	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
164	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
165	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
166	C₂₃×#97	C₂³	1	4	yes	—
167	C₂₃×#97	C₂³	1	8	yes	—
168	C₄×C₈×C₂₃	C₂³	1	4	yes	—
169	C₄×C₈×C₂₃	C₂³	1	8	yes	—
170	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
171	#41×C₂₃	—	2	8	no	—
172	#41×C₂₃	—	2	4	no	—
173	#41×C₂₃	—	2	4	no	—
174	#41×C₂₃	—	4	4	no	—
175	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
176	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
177	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
178	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
179	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
180	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
181	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
182	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
183	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
184	C₂²×C₄×C₂₃	—	2	4	no	—
185	C₂²×C₄×C₂₃	—	2	2	no	—
186	C₂²×C₄×C₂₃	—	2	2	no	—
187	C₂²×C₄×C₂₃	—	4	2	no	—
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	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	4	yes	—
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	1	yes	characteristic
202	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
204	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
209	M₁₆×C₂₃	—	2	4	no	—
210	M₁₆×C₂₃	—	2	4	no	—
211	M₁₆×C₂₃	—	4	8	no	—
212	C₂×C₈×C₂₃	—	2	8	no	—
213	C₂×C₈×C₂₃	—	4	2	no	—
214	C₂×C₈×C₂₃	—	4	4	no	—
215	C₂×C₈×C₂₃	—	4	2	no	—
216	C₂×C₈×C₂₃	—	4	8	no	—
217	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
218	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
219	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
220	C₂×C₈×C₂₃	C₂⁴	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	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
230	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
231	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
232	C₄⋊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	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
239	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
240	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
241	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
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	1	yes	characteristic
251	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
252	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
253	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
254	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
255	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
256	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
257	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
258	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
259	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
260	C₄²×C₂₃	C₂⁴	1	4	yes	—
261	#60265	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂³×C₂₃	—	2	2	no	—
263	C₂³×C₂₃	—	2	2	no	—
264	C₂³×C₂₃	—	2	2	no	—
265	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
266	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
267	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
268	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
269	Q₈×C₂₃	—	2	4	no	—
270	Q₈×C₂₃	—	2	4	no	—
271	Q₈×C₂₃	—	4	2	no	—
272	D₄×C₂₃	—	2	8	no	—
273	D₄×C₂₃	—	2	8	no	—
274	D₄×C₂₃	—	2	8	no	—
275	D₄×C₂₃	—	2	4	no	—
276	D₄×C₂₃	—	2	4	no	—
277	D₄×C₂₃	—	4	2	no	—
278	C₂×C₄×C₂₃	—	2	2	no	—
279	C₂×C₄×C₂₃	—	2	2	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	2	no	—
284	C₂×C₄×C₂₃	—	2	2	no	—
285	C₂×C₄×C₂₃	—	2	2	no	—
286	C₂×C₄×C₂₃	—	2	2	no	—
287	C₂×C₄×C₂₃	—	2	2	no	—
288	C₂×C₄×C₂₃	—	2	8	no	—
289	C₂×C₄×C₂₃	—	2	1	no	—
290	C₂×C₄×C₂₃	—	2	1	no	—
291	C₂×C₄×C₂₃	—	2	4	no	—
292	C₂×C₄×C₂₃	—	2	1	no	—
293	C₂×C₄×C₂₃	—	2	1	no	—
294	C₂×C₄×C₂₃	—	2	4	no	—
295	C₂×C₄×C₂₃	—	4	1	no	—
296	C₂×C₄×C₂₃	—	4	1	no	—
297	C₂×C₄×C₂₃	—	4	1	no	—
298	C₂×C₄×C₂₃	—	4	1	no	—
299	C₂×C₄×C₂₃	—	4	4	no	—
300	C₂×C₄×C₂₃	#131	1	4	yes	complemented
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	1	yes	characteristic
308	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
309	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
310	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
311	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
312	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
313	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
314	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
315	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
316	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
317	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
318	C₈×C₂₃	—	2	4	no	—
319	C₈×C₂₃	—	2	4	no	—
320	C₈×C₂₃	—	2	4	no	—
321	C₈×C₂₃	—	2	4	no	—
322	#3444	C₂×C₂₃	1	1	yes	characteristic
323	#2994	C₂×C₂₃	1	4	yes	complemented
324	#2992	C₂×C₂₃	1	4	yes	complemented
325	#2990	C₂×C₂₃	1	4	yes	complemented
326	#2989	C₂×C₂₃	1	2	yes	complemented
327	#2988	C₂×C₂₃	1	2	yes	complemented
328	#2962	C₂×C₂₃	1	2	yes	complemented
329	#2935	C₂×C₂₃	1	2	yes	complemented
330	#2929	C₂×C₂₃	1	4	yes	complemented
331	#2925	C₂×C₂₃	1	2	yes	complemented
332	#2920	C₂×C₂₃	1	1	yes	characteristic, complemented
333	#2906	C₂×C₂₃	1	2	yes	complemented
334	C₂²×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
335	C₂²×C₂₃	—	2	8	no	—
336	C₂²×C₂₃	—	2	1	no	—
337	C₂²×C₂₃	—	2	1	no	—
338	C₂²×C₂₃	—	2	1	no	—
339	C₂²×C₂₃	—	2	1	no	—
340	C₂²×C₂₃	—	2	1	no	—
341	C₂²×C₂₃	—	2	1	no	—
342	C₂²×C₂₃	—	2	4	no	—
343	C₂²×C₂₃	—	2	4	no	—
344	C₂²×C₂₃	—	2	4	no	—
345	C₂²×C₂₃	#520	1	2	yes	—
346	C₂²×C₂₃	C₂×#131	1	2	yes	—
347	C₂²×C₂₃	#568	1	2	yes	—
348	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
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	4	no	—
355	C₄×C₂₃	—	2	1	no	—
356	C₄×C₂₃	—	2	1	no	—
357	C₄×C₂₃	—	2	1	no	—
358	C₄×C₂₃	—	2	1	no	—
359	C₄×C₂₃	—	2	4	no	—
360	C₄×C₂₃	#520	1	2	yes	—
361	C₄×C₂₃	C₂×#131	1	2	yes	—
362	C₄×C₂₃	C₂×#131	1	2	yes	—
363	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
365	C₂×#131	C₂²×C₂₃	1	4	yes	—
366	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
367	#533	C₄×C₂₃	1	1	yes	characteristic
368	#533	C₄×C₂₃	1	1	yes	characteristic
369	#533	C₂²×C₂₃	1	1	yes	characteristic
370	#532	C₄×C₂₃	1	1	yes	characteristic
371	#532	C₄×C₂₃	1	1	yes	characteristic
372	#532	C₂²×C₂₃	1	1	yes	characteristic
373	#529	C₄×C₂₃	1	2	yes	—
374	#529	C₄×C₂₃	1	2	yes	—
375	#529	C₄×C₂₃	1	2	yes	—
376	#529	C₄×C₂₃	1	2	yes	—
377	#529	C₂²×C₂₃	1	2	yes	—
378	#529	C₂²×C₂₃	1	2	yes	—
379	#525	C₄×C₂₃	1	2	yes	—
380	#525	C₄×C₂₃	1	2	yes	—
381	#525	C₂²×C₂₃	1	2	yes	—
382	C₄×#41	C₂²×C₂₃	1	2	yes	—
383	C₄×#41	C₂²×C₂₃	1	2	yes	—
384	C₄×#41	C₂²×C₂₃	1	2	yes	—
385	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
386	#446	C₂²×C₂₃	1	4	yes	complemented
387	#446	C₂²×C₂₃	1	8	yes	complemented
388	C₈×Q₈	C₂²×C₂₃	1	4	yes	complemented
389	#436	C₂²×C₂₃	1	4	yes	complemented
390	#435	C₂²×C₂₃	1	8	yes	—
391	#435	C₂²×C₂₃	1	8	yes	—
392	#435	C₂²×C₂₃	1	8	yes	complemented
393	C₈×D₄	C₂²×C₂₃	1	8	yes	—
394	C₈×D₄	C₂²×C₂₃	1	8	yes	—
395	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
396	#433	C₂²×C₂₃	1	8	yes	complemented
397	#432	C₂²×C₂₃	1	2	yes	—
398	#432	C₂²×C₂₃	1	2	yes	—
399	#432	C₂²×C₂₃	1	4	yes	complemented
400	#431	C₂²×C₂₃	1	2	yes	—
401	#431	C₂²×C₂₃	1	2	yes	—
402	#431	C₂²×C₂₃	1	4	yes	complemented
403	#424	C₂²×C₂₃	1	4	yes	—
404	#424	C₂²×C₂₃	1	8	yes	complemented
405	#423	C₂²×C₂₃	1	1	yes	characteristic
406	#423	C₂²×C₂₃	1	1	yes	characteristic
407	#423	C₂²×C₂₃	1	4	yes	complemented
408	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
409	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
410	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
413	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
414	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
415	C₂×C₄⋊C₈	C₂²×C₂₃	1	4	yes	complemented
416	#408	C₂²×C₂₃	1	4	yes	—
417	#407	C₂²×C₂₃	1	2	yes	—
418	#405	C₂²×C₂₃	1	4	yes	—
419	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
420	C₂×C₂₃	—	2	2	no	—
421	C₂×C₂₃	—	2	2	no	—
422	C₂×C₂₃	—	2	2	no	—
423	C₂×C₂₃	—	4	4	no	—
424	C₂×C₂₃	C₂×#520	1	1	yes	characteristic
425	C₂×C₂₃	C₂²×#131	1	1	yes	characteristic
426	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
427	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
428	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
429	C₂×#41	C₂³×C₂₃	1	2	yes	—
430	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
431	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
433	#131	—	4	8	no	—
434	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
435	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
436	C₂×M₁₆	C₂³×C₂₃	1	8	yes	—
437	C₂²×C₈	—	4	4	no	—
438	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
439	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
440	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
441	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
442	C₂²×C₈	C₂³×C₂₃	1	8	yes	—
443	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
444	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
445	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
446	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
447	#126	C₂×C₄×C₂₃	1	4	yes	—
448	#126	C₂×C₄×C₂₃	1	4	yes	—
449	#125	C₂×C₄×C₂₃	1	2	yes	—
450	#125	C₂×C₄×C₂₃	1	2	yes	—
451	#125	C₂×C₄×C₂₃	1	2	yes	—
452	#124	C₂×C₄×C₂₃	1	2	yes	—
453	#124	C₂×C₄×C₂₃	1	2	yes	—
454	#124	C₂×C₄×C₂₃	1	2	yes	—
455	#123	C₂×C₄×C₂₃	1	4	yes	—
456	#123	C₂×C₄×C₂₃	1	4	yes	—
457	#123	C₂×C₄×C₂₃	1	4	yes	—
458	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
459	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
460	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
461	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
462	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
463	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
464	#121	C₂×C₄×C₂₃	1	2	yes	—
465	#121	C₂×C₄×C₂₃	1	2	yes	—
466	#121	C₂×C₄×C₂₃	1	2	yes	—
467	#121	C₂×C₄×C₂₃	1	2	yes	—
468	#121	C₂×C₄×C₂₃	1	2	yes	—
469	#121	C₂×C₄×C₂₃	1	2	yes	—
470	#120	C₂×C₄×C₂₃	1	4	yes	—
471	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
472	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
473	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
474	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
475	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
476	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
477	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
478	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
479	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
480	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
481	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
482	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
483	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
484	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
485	C₄×D₄	C₂³×C₂₃	1	4	yes	—
486	C₄×D₄	C₂³×C₂₃	1	4	yes	—
487	C₄×D₄	C₂³×C₂₃	1	2	yes	—
488	C₄×D₄	C₂³×C₂₃	1	2	yes	—
489	#117	C₂×C₄×C₂₃	1	2	yes	—
490	#117	C₂×C₄×C₂₃	1	2	yes	—
491	#117	C₂×C₄×C₂₃	1	4	yes	—
492	#117	C₂×C₄×C₂₃	1	4	yes	—
493	#117	C₂³×C₂₃	1	2	yes	—
494	#117	C₂³×C₂₃	1	4	yes	—
495	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
496	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
497	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
498	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
499	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
500	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
502	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
508	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
509	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
510	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
511	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
512	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
513	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
514	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
515	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
516	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
517	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
518	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
519	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
520	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
521	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
522	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
523	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
524	#97	C₂³×C₂₃	1	4	yes	—
525	#97	C₂³×C₂₃	1	8	yes	—
526	C₄×C₈	C₂³×C₂₃	1	4	yes	—
527	C₄×C₈	C₂³×C₂₃	1	8	yes	—
528	C₂₃	#60265	1	1	yes	characteristic, direct product factor, Sylow
529	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
530	#41	—	2	8	no	—
531	#41	—	2	4	no	—
532	#41	—	2	4	no	—
533	#41	—	4	4	no	—
534	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
535	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
536	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
537	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
538	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
539	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
540	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
541	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
542	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	4	2	no	—
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	1	yes	characteristic
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	1	yes	characteristic
557	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
558	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
559	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
560	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
561	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
562	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
563	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
567	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
568	M₁₆	—	2	4	no	—
569	M₁₆	—	2	4	no	—
570	M₁₆	—	4	8	no	—
571	C₂×C₈	—	2	8	no	—
572	C₂×C₈	—	4	2	no	—
573	C₂×C₈	—	4	4	no	—
574	C₂×C₈	—	4	2	no	—
575	C₂×C₈	—	4	8	no	—
576	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
577	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
578	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
579	C₂×C₈	C₂⁴×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	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
585	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
586	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
587	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
588	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
589	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
590	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
591	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
592	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
593	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
594	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
595	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
596	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
597	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
598	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
599	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
600	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
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	1	yes	characteristic
606	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
607	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
608	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
609	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
610	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
611	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
612	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
613	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
614	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
615	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
616	C₄²	C₂⁴×C₂₃	1	4	yes	—
617	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
618	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
619	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
624	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
625	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
626	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
627	Q₈	—	2	4	no	—
628	Q₈	—	2	4	no	—
629	Q₈	—	4	2	no	—
630	D₄	—	2	8	no	—
631	D₄	—	2	8	no	—
632	D₄	—	2	8	no	—
633	D₄	—	2	4	no	—
634	D₄	—	2	4	no	—
635	D₄	—	4	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	8	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	C₂₃×#131	1	4	yes	complemented
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	1	yes	characteristic
662	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
663	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
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	C₂³×C₄×C₂₃	1	4	yes	—
668	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
669	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
670	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
671	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
672	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
673	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
674	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
675	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
676	C₈	—	2	4	no	—
677	C₈	—	2	4	no	—
678	C₈	—	2	4	no	—
679	C₈	—	2	4	no	—
680	C₂²	—	2	8	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	C₂₃×#520	1	2	yes	—
691	C₂²	C₂×C₂₃×#131	1	2	yes	—
692	C₂²	C₂₃×#568	1	2	yes	—
693	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	4	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	4	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	1	no	—
702	C₄	—	2	1	no	—
703	C₄	—	2	1	no	—
704	C₄	—	2	4	no	—
705	C₄	C₂₃×#520	1	2	yes	—
706	C₄	C₂×C₂₃×#131	1	2	yes	—
707	C₄	C₂×C₂₃×#131	1	2	yes	—
708	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
709	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
710	C₂	—	2	2	no	—
711	C₂	—	2	2	no	—
712	C₂	—	2	2	no	—
713	C₂	—	4	4	no	—
714	C₂	C₂×C₂₃×#520	1	1	yes	characteristic
715	C₂	C₂²×C₂₃×#131	1	1	yes	characteristic
716	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×#2994	C₂	semidirect
3. C₂₃×#2992	C₂	semidirect
4. C₂₃×#2990	C₂	semidirect
5. C₂₃×#2989	C₂	semidirect
6. C₂₃×#2988	C₂	semidirect
7. C₂₃×#2962	C₂	semidirect
8. C₂₃×#2935	C₂	semidirect
9. C₂₃×#2929	C₂	semidirect
10. C₂₃×#2925	C₂	semidirect
11. C₂₃×#2920	C₂	semidirect
12. C₂₃×#2906	C₂	semidirect
13. C₂²×C₂₃×C₄⋊C₈	C₂	semidirect
35. C₂₃×#446	C₂²	semidirect
36. C₂₃×#446	C₂²	semidirect
37. C₈×Q₈×C₂₃	C₂²	semidirect
38. C₂₃×#436	C₂²	semidirect
41. C₂₃×#435	C₂²	semidirect
44. C₈×D₄×C₂₃	C₂²	semidirect
45. C₂₃×#433	C₂²	semidirect
48. C₂₃×#432	C₂²	semidirect
51. C₂₃×#431	C₂²	semidirect
53. C₂₃×#424	C₂²	semidirect
56. C₂₃×#423	C₂²	semidirect
64. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
261. #60265	C₂₃	direct (N × H)
300. C₂×C₄×C₂₃	#131	semidirect
323. #2994	C₂×C₂₃	semidirect
324. #2992	C₂×C₂₃	semidirect
325. #2990	C₂×C₂₃	semidirect
326. #2989	C₂×C₂₃	semidirect
327. #2988	C₂×C₂₃	semidirect
328. #2962	C₂×C₂₃	semidirect
329. #2935	C₂×C₂₃	semidirect
330. #2929	C₂×C₂₃	semidirect
331. #2925	C₂×C₂₃	semidirect
332. #2920	C₂×C₂₃	semidirect
333. #2906	C₂×C₂₃	semidirect
334. C₂²×C₄⋊C₈	C₂×C₂₃	semidirect
386. #446	C₂²×C₂₃	semidirect
387. #446	C₂²×C₂₃	semidirect
388. C₈×Q₈	C₂²×C₂₃	semidirect
389. #436	C₂²×C₂₃	semidirect
392. #435	C₂²×C₂₃	semidirect
395. C₈×D₄	C₂²×C₂₃	semidirect
396. #433	C₂²×C₂₃	semidirect
399. #432	C₂²×C₂₃	semidirect
402. #431	C₂²×C₂₃	semidirect
404. #424	C₂²×C₂₃	semidirect
407. #423	C₂²×C₂₃	semidirect
415. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
528. C₂₃	#60265	direct (N × H)
658. C₂×C₄	C₂₃×#131	semidirect

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×#2994	2
C₂₃×#2992	2
C₂₃×#2990	2
C₂₃×#2989	2
C₂₃×#2988	2
C₂₃×#2962	2
C₂₃×#2935	2
C₂₃×#2929	2
C₂₃×#2925	2
C₂₃×#2920	2
C₂₃×#2906	2
C₂²×C₂₃×C₄⋊C₈	2
#60265	23

Subgroups — C23×#60265 #19207891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60265 #19207891