Subgroups — C₂₃×#60377 #19208003

Order 5888.

4756 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#577	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3013	C₂	1	3	yes	maximal, complemented
6	C₂₃×#3012	C₂	1	3	yes	maximal, complemented
7	C₂₃×#3011	C₂	1	3	yes	maximal, complemented
8	C₂₃×#3009	C₂	1	3	yes	maximal, complemented
9	C₂₃×#3007	C₂	1	3	yes	maximal, complemented
10	C₂₃×#3005	C₂	1	3	yes	maximal, complemented
11	C₂₃×#3002	C₂	1	3	yes	maximal, complemented
12	C₂×C₂₃×#452	C₂	1	3	yes	maximal, complemented
13	C₂₃×#2898	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#585	—	2	8	no	—
17	C₂₃×#585	—	2	8	no	—
18	C₂×C₂₃×2₋¹⁺⁴	—	2	1	no	—
19	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	3	yes	—
20	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂₃×H(5,𝔽₂)	—	2	3	no	—
23	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	3	yes	—
24	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₂₃	—	2	3	no	—
26	C₂²×#41×C₂₃	—	2	1	no	—
27	C₂²×#41×C₂₃	C₂²	1	3	yes	—
28	C₂²×#41×C₂₃	C₂²	1	3	yes	—
29	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
30	C₂₃×#578	—	2	8	no	—
31	C₂₃×#577	—	2	8	no	—
32	C₂×C₂₃×#137	C₂²	1	3	yes	complemented
33	C₂×C₂₃×#137	C₂²	1	3	yes	complemented
34	C₂×C₂₃×#137	C₂²	1	3	yes	complemented
35	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	3	yes	complemented
36	C₂×C₂₃×#135	C₂²	1	3	yes	complemented
37	C₂×C₂₃×#135	C₂²	1	3	yes	complemented
38	C₂²×Q₁₆×C₂₃	C₂²	1	3	yes	complemented
39	C₂²×SD₁₆×C₂₃	C₂²	1	3	yes	complemented
40	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
42	D₄×Q₈×C₂₃	—	2	1	no	—
43	C₂₃×#548	—	2	1	no	—
44	C₂₃×#547	—	2	3	no	—
45	C₂₃×#546	—	2	3	no	—
46	C₂₃×#537	C₂²	1	3	yes	complemented
47	C₂₃×#536	C₂²	1	3	yes	complemented
48	C₂₃×#525	C₂²	1	3	yes	complemented
49	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	3	yes	complemented
50	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#452	C₂²	1	3	yes	complemented
52	C₂₃×#452	C₂²	1	6	yes	complemented
53	C₂₃×#452	C₂²	1	6	yes	complemented
54	C₂₃×#452	C₂²	1	6	yes	complemented
55	C₂₃×#452	C₂²	1	3	yes	complemented
56	C₂₃×#452	C₂²	1	6	yes	complemented
57	C₂₃×#451	C₂²	1	3	yes	complemented
58	C₂₃×#451	C₂²	1	6	yes	complemented
59	C₂₃×#450	C₂²	1	3	yes	complemented
60	C₂₃×#450	C₂²	1	6	yes	complemented
61	C₂₃×#449	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#449	C₂²	1	3	yes	complemented
63	C₂₃×#449	C₂²	1	6	yes	complemented
64	C₂₃×#448	C₂²	1	3	yes	complemented
65	C₂₃×#447	C₂²	1	3	yes	complemented
66	C₂₃×#419	C₂²	1	3	yes	complemented
67	C₂₃×#418	C₂²	1	3	yes	complemented
68	C₂₃×#417	C₂²	1	3	yes	complemented
69	C₂₃×#417	C₂²	1	3	yes	complemented
70	C₂₃×#416	C₂²	1	3	yes	complemented
71	C₂₃×#416	C₂²	1	3	yes	complemented
72	C₂×C₂₃×#103	C₂²	1	3	yes	complemented
73	C₂×C₂₃×#102	C₂²	1	3	yes	complemented
74	C₂₃×#408	C₂²	1	3	yes	complemented
75	C₂₃×#408	C₂²	1	3	yes	complemented
76	C₂₃×#407	C₂²	1	3	yes	complemented
77	C₂×C₂₃×C₂²⋊C₈	C₂²	1	3	yes	complemented
78	C₂₃×2₋¹⁺⁴	—	2	16	no	—
79	C₂₃×2₋¹⁺⁴	—	2	12	no	—
80	C₂₃×2₋¹⁺⁴	—	2	4	no	—
81	C₂₃×2₋¹⁺⁴	—	2	12	no	—
82	C₂₃×2₋¹⁺⁴	—	2	4	no	—
83	C₂₃×2₋¹⁺⁴	—	2	4	no	—
84	C₂₃×2₋¹⁺⁴	D₄	1	8	yes	complemented
85	C₂₃×H(5,𝔽₂)	—	2	48	no	—
86	C₂₃×H(5,𝔽₂)	—	2	12	no	—
87	C₂₃×H(5,𝔽₂)	—	2	4	no	—
88	C₂₃×H(5,𝔽₂)	—	2	12	no	—
89	C₂₃×H(5,𝔽₂)	D₄	1	8	yes	complemented
90	C₂×#41×C₂₃	—	2	16	no	—
91	C₂×#41×C₂₃	—	2	48	no	—
92	C₂×#41×C₂₃	—	2	12	no	—
93	C₂×#41×C₂₃	—	2	12	no	—
94	C₂×#41×C₂₃	—	2	4	no	—
95	C₂×#41×C₂₃	—	2	4	no	—
96	C₂×#41×C₂₃	—	2	3	no	—
97	C₂×#41×C₂₃	—	2	1	no	—
98	C₂×#41×C₂₃	—	2	12	no	—
99	C₂×#41×C₂₃	—	2	6	no	—
100	C₂×#41×C₂₃	—	2	3	no	—
101	C₂×#41×C₂₃	—	2	3	no	—
102	C₂×#41×C₂₃	—	2	12	no	—
103	C₂×#41×C₂₃	—	2	3	no	—
104	C₂×#41×C₂₃	—	2	3	no	—
105	C₂×#41×C₂₃	—	2	3	no	—
106	C₂×#41×C₂₃	—	2	3	no	—
107	C₂×#41×C₂₃	—	2	3	no	—
108	C₂×#41×C₂₃	D₄	1	3	yes	—
109	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
110	C₂×#41×C₂₃	C₂³	1	3	yes	—
111	C₂×#41×C₂₃	C₂³	1	3	yes	—
112	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×#41×C₂₃	C₂³	1	6	yes	—
114	C₂×#41×C₂₃	C₂³	1	3	yes	—
115	C₂×#41×C₂₃	C₂³	1	3	yes	—
116	C₂×#41×C₂₃	C₂³	1	3	yes	—
117	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
118	C₂²×Q₈×C₂₃	—	2	3	no	—
119	C₂²×Q₈×C₂₃	—	2	1	no	—
120	C₂²×Q₈×C₂₃	—	2	1	no	—
121	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
122	C₂²×Q₈×C₂₃	C₂³	1	3	yes	—
123	C₂²×Q₈×C₂₃	C₂³	1	3	yes	—
124	C₂²×Q₈×C₂₃	C₂³	1	3	yes	—
125	C₂²×D₄×C₂₃	—	2	3	no	—
126	C₂²×D₄×C₂₃	—	2	3	no	—
127	C₂²×D₄×C₂₃	—	2	6	no	—
128	C₂²×D₄×C₂₃	—	2	3	no	—
129	C₂²×D₄×C₂₃	—	2	3	no	—
130	C₂²×D₄×C₂₃	D₄	1	3	yes	—
131	C₂²×D₄×C₂₃	C₂³	1	3	yes	—
132	C₂²×D₄×C₂₃	C₂³	1	3	yes	—
133	C₂³×C₄×C₂₃	—	2	3	no	—
134	C₂³×C₄×C₂₃	—	2	3	no	—
135	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
136	C₂₃×#137	—	2	12	no	—
137	C₂₃×#137	—	2	12	no	—
138	C₂₃×#137	—	2	12	no	—
139	C₂₃×AGL(1,ℤ/8)	—	2	12	no	—
140	C₂₃×#135	—	2	12	no	—
141	C₂₃×#135	—	2	12	no	—
142	C₂×Q₁₆×C₂₃	—	2	12	no	—
143	C₂×Q₁₆×C₂₃	C₂³	1	3	yes	—
144	C₂×Q₁₆×C₂₃	C₂³	1	6	yes	—
145	C₂×Q₁₆×C₂₃	C₂³	1	3	yes	—
146	C₂×SD₁₆×C₂₃	—	2	12	no	—
147	C₂×SD₁₆×C₂₃	C₂³	1	3	yes	—
148	C₂×SD₁₆×C₂₃	C₂³	1	6	yes	—
149	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₂₃	C₂³	1	3	yes	—
151	C₂×SD₁₆×C₂₃	C₂³	1	3	yes	—
152	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₂₃	C₂³	1	3	yes	—
154	C₂₃×#131	—	2	4	no	—
155	C₂₃×#131	—	2	4	no	—
156	C₂×M₁₆×C₂₃	C₂³	1	3	yes	—
157	C₂×M₁₆×C₂₃	C₂³	1	3	yes	—
158	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
159	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
160	C₂₃×C₄⋊Q₈	—	2	3	no	—
161	C₂₃×#124	—	2	3	no	—
162	C₂₃×#123	—	2	6	no	—
163	C₂₃×#123	—	2	3	no	—
164	C₂₃×C₂²⋊Q₈	—	2	3	no	—
165	C₂₃×C₂²⋊Q₈	—	2	3	no	—
166	C₂₃×C₂²⋊Q₈	—	2	3	no	—
167	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
168	C₂₃×C₂²⋊Q₈	C₂³	1	3	yes	—
169	C₂₃×C₂²⋊Q₈	C₂³	1	3	yes	—
170	C₂₃×#121	—	2	6	no	—
171	C₂₃×#121	—	2	3	no	—
172	C₂₃×#121	C₂³	1	3	yes	—
173	C₂₃×#121	C₂³	1	1	yes	characteristic
174	C₂₃×#120	—	2	3	no	—
175	C₄×Q₈×C₂₃	—	2	1	no	—
176	C₄×D₄×C₂₃	—	2	3	no	—
177	C₄×D₄×C₂₃	—	2	3	no	—
178	C₄×D₄×C₂₃	—	2	3	no	—
179	C₂₃×#117	C₂³	1	3	yes	—
180	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
182	C₂×C₂²⋊C₄×C₂₃	—	2	3	no	—
183	C₂₃×#103	C₂³	1	3	yes	—
184	C₂₃×#103	C₂³	1	6	yes	—
185	C₂₃×#103	C₂³	1	1	yes	characteristic
186	C₂₃×#103	C₂³	1	3	yes	—
187	C₂₃×#103	C₂³	1	3	yes	—
188	C₂₃×#102	C₂³	1	3	yes	—
189	C₂₃×#102	C₂³	1	6	yes	—
190	C₂₃×#102	C₂³	1	1	yes	characteristic
191	C₂₃×#102	C₂³	1	3	yes	—
192	C₂₃×#102	C₂³	1	3	yes	—
193	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
194	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
195	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
196	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
197	C₂₃×C₂²⋊C₈	C₂³	1	6	yes	—
198	C₂⁴×C₂₃	—	2	3	no	—
199	C₂⁴×C₂₃	—	2	3	no	—
200	C₂⁴×C₂₃	C₂×D₄	1	3	yes	—
201	#41×C₂₃	—	2	24	no	—
202	#41×C₂₃	—	2	24	no	—
203	#41×C₂₃	—	2	48	no	—
204	#41×C₂₃	—	2	24	no	—
205	#41×C₂₃	—	2	24	no	—
206	#41×C₂₃	—	2	24	no	—
207	#41×C₂₃	—	2	24	no	—
208	#41×C₂₃	—	2	4	no	—
209	#41×C₂₃	—	2	8	no	—
210	#41×C₂₃	—	2	2	no	—
211	#41×C₂₃	—	2	6	no	—
212	#41×C₂₃	—	2	12	no	—
213	#41×C₂₃	—	2	12	no	—
214	#41×C₂₃	—	2	24	no	—
215	#41×C₂₃	—	2	2	no	—
216	#41×C₂₃	—	2	6	no	—
217	#41×C₂₃	—	2	12	no	—
218	#41×C₂₃	—	2	6	no	—
219	#41×C₂₃	—	2	6	no	—
220	#41×C₂₃	—	2	6	no	—
221	#41×C₂₃	—	2	6	no	—
222	#41×C₂₃	—	2	6	no	—
223	#41×C₂₃	—	2	6	no	—
224	#41×C₂₃	—	4	12	no	—
225	#41×C₂₃	C₂×D₄	1	12	yes	—
226	#41×C₂₃	C₂×D₄	1	12	yes	—
227	#41×C₂₃	C₂×D₄	1	4	yes	—
228	#41×C₂₃	C₂×D₄	1	4	yes	—
229	C₂×Q₈×C₂₃	—	2	24	no	—
230	C₂×Q₈×C₂₃	—	2	8	no	—
231	C₂×Q₈×C₂₃	—	2	4	no	—
232	C₂×Q₈×C₂₃	—	2	6	no	—
233	C₂×Q₈×C₂₃	—	2	6	no	—
234	C₂×Q₈×C₂₃	—	2	3	no	—
235	C₂×Q₈×C₂₃	—	2	3	no	—
236	C₂×Q₈×C₂₃	—	2	6	no	—
237	C₂×Q₈×C₂₃	—	2	3	no	—
238	C₂×Q₈×C₂₃	—	2	6	no	—
239	C₂×Q₈×C₂₃	—	2	6	no	—
240	C₂×Q₈×C₂₃	—	4	4	no	—
241	C₂×Q₈×C₂₃	C₂×D₄	1	12	yes	—
242	C₂×Q₈×C₂₃	C₂×D₄	1	3	yes	—
243	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₂₃	C₂⁴	1	3	yes	—
245	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₂₃	C₂⁴	1	3	yes	—
247	C₂×D₄×C₂₃	—	2	24	no	—
248	C₂×D₄×C₂₃	—	2	48	no	—
249	C₂×D₄×C₂₃	—	2	24	no	—
250	C₂×D₄×C₂₃	—	2	24	no	—
251	C₂×D₄×C₂₃	—	2	6	no	—
252	C₂×D₄×C₂₃	—	2	3	no	—
253	C₂×D₄×C₂₃	—	2	1	no	—
254	C₂×D₄×C₂₃	—	2	3	no	—
255	C₂×D₄×C₂₃	—	2	3	no	—
256	C₂×D₄×C₂₃	—	2	24	no	—
257	C₂×D₄×C₂₃	—	2	12	no	—
258	C₂×D₄×C₂₃	—	2	6	no	—
259	C₂×D₄×C₂₃	—	2	6	no	—
260	C₂×D₄×C₂₃	—	2	1	no	—
261	C₂×D₄×C₂₃	—	2	3	no	—
262	C₂×D₄×C₂₃	—	2	3	no	—
263	C₂×D₄×C₂₃	—	2	3	no	—
264	C₂×D₄×C₂₃	—	2	3	no	—
265	C₂×D₄×C₂₃	—	2	6	no	—
266	C₂×D₄×C₂₃	C₂×D₄	1	6	yes	—
267	C₂×D₄×C₂₃	C₂×D₄	1	3	yes	—
268	C₂×D₄×C₂₃	C₂×D₄	1	12	yes	—
269	C₂×D₄×C₂₃	C₂×D₄	1	3	yes	—
270	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
271	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
272	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
273	C₂²×C₄×C₂₃	—	2	24	no	—
274	C₂²×C₄×C₂₃	—	2	24	no	—
275	C₂²×C₄×C₂₃	—	2	3	no	—
276	C₂²×C₄×C₂₃	—	2	3	no	—
277	C₂²×C₄×C₂₃	—	2	3	no	—
278	C₂²×C₄×C₂₃	—	2	1	no	—
279	C₂²×C₄×C₂₃	—	2	6	no	—
280	C₂²×C₄×C₂₃	—	2	3	no	—
281	C₂²×C₄×C₂₃	—	2	3	no	—
282	C₂²×C₄×C₂₃	—	2	6	no	—
283	C₂²×C₄×C₂₃	—	2	6	no	—
284	C₂²×C₄×C₂₃	—	2	3	no	—
285	C₂²×C₄×C₂₃	—	2	3	no	—
286	C₂²×C₄×C₂₃	—	2	3	no	—
287	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
288	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
289	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
290	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
292	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
293	Q₁₆×C₂₃	—	2	6	no	—
294	Q₁₆×C₂₃	—	2	12	no	—
295	Q₁₆×C₂₃	—	2	6	no	—
296	SD₁₆×C₂₃	—	2	2	no	—
297	SD₁₆×C₂₃	—	2	6	no	—
298	SD₁₆×C₂₃	—	2	6	no	—
299	SD₁₆×C₂₃	—	2	12	no	—
300	SD₁₆×C₂₃	—	2	6	no	—
301	D₈×C₂₃	—	2	2	no	—
302	D₈×C₂₃	—	2	6	no	—
303	M₁₆×C₂₃	—	2	6	no	—
304	M₁₆×C₂₃	—	2	6	no	—
305	C₂×C₈×C₂₃	—	2	6	no	—
306	C₂×C₈×C₂₃	—	2	6	no	—
307	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
308	C₂×C₈×C₂₃	C₂⁴	1	3	yes	—
309	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
310	C₂×C₈×C₂₃	C₂⁴	1	3	yes	—
311	C₄⋊C₄×C₂₃	—	2	3	no	—
312	C₄⋊C₄×C₂₃	—	2	6	no	—
313	C₄⋊C₄×C₂₃	—	2	3	no	—
314	C₄⋊C₄×C₂₃	—	2	3	no	—
315	C₄⋊C₄×C₂₃	C₂⁴	1	3	yes	—
316	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₂²⋊C₄×C₂₃	—	2	3	no	—
318	C₂²⋊C₄×C₂₃	—	2	6	no	—
319	C₂²⋊C₄×C₂₃	—	2	3	no	—
320	C₂²⋊C₄×C₂₃	—	2	3	no	—
321	C₂²⋊C₄×C₂₃	—	2	1	no	—
322	C₂²⋊C₄×C₂₃	—	2	3	no	—
323	C₄²×C₂₃	—	2	3	no	—
324	#60377	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₂³×C₂₃	—	2	12	no	—
326	C₂³×C₂₃	—	2	3	no	—
327	C₂³×C₂₃	—	2	1	no	—
328	C₂³×C₂₃	—	2	6	no	—
329	C₂³×C₂₃	—	2	12	no	—
330	C₂³×C₂₃	—	2	1	no	—
331	C₂³×C₂₃	—	4	3	no	—
332	C₂³×C₂₃	—	4	3	no	—
333	C₂³×C₂₃	—	8	3	no	—
334	C₂³×C₂₃	—	8	3	no	—
335	C₂³×C₂₃	—	8	3	no	—
336	C₂³×C₂₃	—	8	3	no	—
337	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
338	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
339	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
340	Q₈×C₂₃	—	2	12	no	—
341	Q₈×C₂₃	—	2	12	no	—
342	Q₈×C₂₃	—	2	6	no	—
343	Q₈×C₂₃	—	2	1	no	—
344	Q₈×C₂₃	—	2	3	no	—
345	Q₈×C₂₃	—	2	3	no	—
346	Q₈×C₂₃	—	2	3	no	—
347	Q₈×C₂₃	—	4	6	no	—
348	Q₈×C₂₃	#120	1	4	yes	—
349	Q₈×C₂₃	C₂²×D₄	1	2	yes	—
350	Q₈×C₂₃	C₂²×D₄	1	6	yes	—
351	D₄×C₂₃	—	2	24	no	—
352	D₄×C₂₃	—	2	12	no	—
353	D₄×C₂₃	—	2	4	no	—
354	D₄×C₂₃	—	2	12	no	—
355	D₄×C₂₃	—	2	12	no	—
356	D₄×C₂₃	—	2	12	no	—
357	D₄×C₂₃	—	2	12	no	—
358	D₄×C₂₃	—	2	6	no	—
359	D₄×C₂₃	—	2	12	no	—
360	D₄×C₂₃	—	2	3	no	—
361	D₄×C₂₃	—	2	1	no	—
362	D₄×C₂₃	—	2	1	no	—
363	D₄×C₂₃	—	2	1	no	—
364	D₄×C₂₃	—	4	2	no	—
365	D₄×C₂₃	—	4	6	no	—
366	D₄×C₂₃	—	8	3	no	—
367	D₄×C₂₃	#120	1	12	yes	—
368	D₄×C₂₃	C₂²×D₄	1	2	yes	—
369	D₄×C₂₃	C₂²×D₄	1	6	yes	—
370	C₂×C₄×C₂₃	—	2	12	no	—
371	C₂×C₄×C₂₃	—	2	4	no	—
372	C₂×C₄×C₂₃	—	2	12	no	—
373	C₂×C₄×C₂₃	—	2	24	no	—
374	C₂×C₄×C₂₃	—	2	6	no	—
375	C₂×C₄×C₂₃	—	2	12	no	—
376	C₂×C₄×C₂₃	—	2	3	no	—
377	C₂×C₄×C₂₃	—	2	1	no	—
378	C₂×C₄×C₂₃	—	2	6	no	—
379	C₂×C₄×C₂₃	—	2	12	no	—
380	C₂×C₄×C₂₃	—	2	12	no	—
381	C₂×C₄×C₂₃	—	2	6	no	—
382	C₂×C₄×C₂₃	—	2	1	no	—
383	C₂×C₄×C₂₃	—	2	1	no	—
384	C₂×C₄×C₂₃	—	2	3	no	—
385	C₂×C₄×C₂₃	—	2	3	no	—
386	C₂×C₄×C₂₃	—	2	1	no	—
387	C₂×C₄×C₂₃	—	2	3	no	—
388	C₂×C₄×C₂₃	—	2	3	no	—
389	C₂×C₄×C₂₃	—	4	6	no	—
390	C₂×C₄×C₂₃	—	4	6	no	—
391	C₂×C₄×C₂₃	—	8	3	no	—
392	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
394	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
395	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
396	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
397	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
398	C₈×C₂₃	—	2	1	no	—
399	C₈×C₂₃	—	2	1	no	—
400	C₈×C₂₃	—	2	3	no	—
401	C₈×C₂₃	—	2	3	no	—
402	C₂×#585	C₂×C₂₃	1	1	yes	characteristic, complemented
403	C₂×#578	C₂×C₂₃	1	1	yes	characteristic, complemented
404	C₂×#577	C₂×C₂₃	1	1	yes	characteristic, complemented
405	#3489	C₂×C₂₃	1	1	yes	characteristic, complemented
406	#3013	C₂×C₂₃	1	3	yes	complemented
407	#3012	C₂×C₂₃	1	3	yes	complemented
408	#3011	C₂×C₂₃	1	3	yes	complemented
409	#3009	C₂×C₂₃	1	3	yes	complemented
410	#3007	C₂×C₂₃	1	3	yes	complemented
411	#3005	C₂×C₂₃	1	3	yes	complemented
412	#3002	C₂×C₂₃	1	3	yes	complemented
413	C₂×#452	C₂×C₂₃	1	3	yes	complemented
414	#2898	C₂×C₂₃	1	1	yes	characteristic, complemented
415	#2897	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#2880	C₂×C₂₃	1	1	yes	characteristic, complemented
417	C₂²×C₂₃	—	2	3	no	—
418	C₂²×C₂₃	—	2	3	no	—
419	C₂²×C₂₃	—	2	3	no	—
420	C₂²×C₂₃	—	2	1	no	—
421	C₂²×C₂₃	—	2	1	no	—
422	C₂²×C₂₃	—	2	3	no	—
423	C₂²×C₂₃	—	2	3	no	—
424	C₂²×C₂₃	—	2	1	no	—
425	C₂²×C₂₃	—	2	6	no	—
426	C₂²×C₂₃	—	2	2	no	—
427	C₂²×C₂₃	—	4	3	no	—
428	C₂²×C₂₃	—	4	1	no	—
429	C₂²×C₂₃	—	4	3	no	—
430	C₂²×C₂₃	—	4	1	no	—
431	C₂²×C₂₃	—	4	1	no	—
432	C₂²×C₂₃	—	4	1	no	—
433	C₂²×C₂₃	—	4	1	no	—
434	C₂²×C₂₃	—	8	6	no	—
435	C₂²×C₂₃	—	8	12	no	—
436	C₂²×C₂₃	—	8	12	no	—
437	C₂²×C₂₃	C₂×#120	1	6	yes	—
438	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₂₃	—	2	1	no	—
440	C₄×C₂₃	—	2	6	no	—
441	C₄×C₂₃	—	2	2	no	—
442	C₄×C₂₃	—	2	3	no	—
443	C₄×C₂₃	—	4	3	no	—
444	C₄×C₂₃	—	4	1	no	—
445	C₄×C₂₃	—	4	3	no	—
446	C₄×C₂₃	C₂×#120	1	6	yes	—
447	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
448	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
449	#585	—	2	8	no	—
450	#585	—	2	8	no	—
451	C₂×2₋¹⁺⁴	—	2	1	no	—
452	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	3	yes	—
453	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
454	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	C₂×H(5,𝔽₂)	—	2	3	no	—
456	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	3	yes	—
457	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
458	C₂²×#41	—	2	3	no	—
459	C₂²×#41	—	2	1	no	—
460	C₂²×#41	C₂²×C₂₃	1	3	yes	—
461	C₂²×#41	C₂²×C₂₃	1	3	yes	—
462	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
463	#578	—	2	8	no	—
464	#577	—	2	8	no	—
465	C₂×#137	C₂²×C₂₃	1	3	yes	complemented
466	C₂×#137	C₂²×C₂₃	1	3	yes	complemented
467	C₂×#137	C₂²×C₂₃	1	3	yes	complemented
468	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	3	yes	complemented
469	C₂×#135	C₂²×C₂₃	1	3	yes	complemented
470	C₂×#135	C₂²×C₂₃	1	3	yes	complemented
471	C₂²×Q₁₆	C₂²×C₂₃	1	3	yes	complemented
472	C₂²×SD₁₆	C₂²×C₂₃	1	3	yes	complemented
473	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
474	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
475	D₄×Q₈	—	2	1	no	—
476	#548	—	2	1	no	—
477	#547	—	2	3	no	—
478	#546	—	2	3	no	—
479	#537	C₂²×C₂₃	1	3	yes	complemented
480	#536	C₂²×C₂₃	1	3	yes	complemented
481	#525	C₂²×C₂₃	1	3	yes	complemented
482	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	3	yes	complemented
483	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
484	#452	C₂²×C₂₃	1	3	yes	complemented
485	#452	C₂²×C₂₃	1	6	yes	complemented
486	#452	C₂²×C₂₃	1	6	yes	complemented
487	#452	C₂²×C₂₃	1	6	yes	complemented
488	#452	C₂²×C₂₃	1	3	yes	complemented
489	#452	C₂²×C₂₃	1	6	yes	complemented
490	#451	C₂²×C₂₃	1	3	yes	complemented
491	#451	C₂²×C₂₃	1	6	yes	complemented
492	#450	C₂²×C₂₃	1	3	yes	complemented
493	#450	C₂²×C₂₃	1	6	yes	complemented
494	#449	C₂²×C₂₃	1	1	yes	characteristic, complemented
495	#449	C₂²×C₂₃	1	3	yes	complemented
496	#449	C₂²×C₂₃	1	6	yes	complemented
497	#448	C₂²×C₂₃	1	3	yes	complemented
498	#447	C₂²×C₂₃	1	3	yes	complemented
499	#419	C₂²×C₂₃	1	3	yes	complemented
500	#418	C₂²×C₂₃	1	3	yes	complemented
501	#417	C₂²×C₂₃	1	3	yes	complemented
502	#417	C₂²×C₂₃	1	3	yes	complemented
503	#416	C₂²×C₂₃	1	3	yes	complemented
504	#416	C₂²×C₂₃	1	3	yes	complemented
505	C₂×#103	C₂²×C₂₃	1	3	yes	complemented
506	C₂×#102	C₂²×C₂₃	1	3	yes	complemented
507	#408	C₂²×C₂₃	1	3	yes	complemented
508	#408	C₂²×C₂₃	1	3	yes	complemented
509	#407	C₂²×C₂₃	1	3	yes	complemented
510	C₂×C₂²⋊C₈	C₂²×C₂₃	1	3	yes	complemented
511	C₂×C₂₃	—	2	6	no	—
512	C₂×C₂₃	—	4	3	no	—
513	C₂×C₂₃	—	4	1	no	—
514	C₂×C₂₃	—	4	6	no	—
515	C₂×C₂₃	—	4	2	no	—
516	C₂×C₂₃	—	8	1	no	—
517	C₂×C₂₃	C₂²×#120	1	1	yes	characteristic
518	C₂×C₂₃	#3584	1	1	yes	characteristic
519	C₂×C₂₃	#3586	1	1	yes	characteristic
520	2₋¹⁺⁴	—	2	16	no	—
521	2₋¹⁺⁴	—	2	12	no	—
522	2₋¹⁺⁴	—	2	4	no	—
523	2₋¹⁺⁴	—	2	12	no	—
524	2₋¹⁺⁴	—	2	4	no	—
525	2₋¹⁺⁴	—	2	4	no	—
526	2₋¹⁺⁴	D₄×C₂₃	1	8	yes	complemented
527	H(5,𝔽₂)	—	2	48	no	—
528	H(5,𝔽₂)	—	2	12	no	—
529	H(5,𝔽₂)	—	2	4	no	—
530	H(5,𝔽₂)	—	2	12	no	—
531	H(5,𝔽₂)	D₄×C₂₃	1	8	yes	complemented
532	C₂×#41	—	2	16	no	—
533	C₂×#41	—	2	48	no	—
534	C₂×#41	—	2	12	no	—
535	C₂×#41	—	2	12	no	—
536	C₂×#41	—	2	4	no	—
537	C₂×#41	—	2	4	no	—
538	C₂×#41	—	2	3	no	—
539	C₂×#41	—	2	1	no	—
540	C₂×#41	—	2	12	no	—
541	C₂×#41	—	2	6	no	—
542	C₂×#41	—	2	3	no	—
543	C₂×#41	—	2	3	no	—
544	C₂×#41	—	2	12	no	—
545	C₂×#41	—	2	3	no	—
546	C₂×#41	—	2	3	no	—
547	C₂×#41	—	2	3	no	—
548	C₂×#41	—	2	3	no	—
549	C₂×#41	—	2	3	no	—
550	C₂×#41	D₄×C₂₃	1	3	yes	—
551	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
552	C₂×#41	C₂³×C₂₃	1	3	yes	—
553	C₂×#41	C₂³×C₂₃	1	3	yes	—
554	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
555	C₂×#41	C₂³×C₂₃	1	6	yes	—
556	C₂×#41	C₂³×C₂₃	1	3	yes	—
557	C₂×#41	C₂³×C₂₃	1	3	yes	—
558	C₂×#41	C₂³×C₂₃	1	3	yes	—
559	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
560	C₂²×Q₈	—	2	3	no	—
561	C₂²×Q₈	—	2	1	no	—
562	C₂²×Q₈	—	2	1	no	—
563	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
564	C₂²×Q₈	C₂³×C₂₃	1	3	yes	—
565	C₂²×Q₈	C₂³×C₂₃	1	3	yes	—
566	C₂²×Q₈	C₂³×C₂₃	1	3	yes	—
567	C₂²×D₄	—	2	3	no	—
568	C₂²×D₄	—	2	3	no	—
569	C₂²×D₄	—	2	6	no	—
570	C₂²×D₄	—	2	3	no	—
571	C₂²×D₄	—	2	3	no	—
572	C₂²×D₄	D₄×C₂₃	1	3	yes	—
573	C₂²×D₄	C₂³×C₂₃	1	3	yes	—
574	C₂²×D₄	C₂³×C₂₃	1	3	yes	—
575	C₂³×C₄	—	2	3	no	—
576	C₂³×C₄	—	2	3	no	—
577	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
578	#137	—	2	12	no	—
579	#137	—	2	12	no	—
580	#137	—	2	12	no	—
581	AGL(1,ℤ/8)	—	2	12	no	—
582	#135	—	2	12	no	—
583	#135	—	2	12	no	—
584	C₂×Q₁₆	—	2	12	no	—
585	C₂×Q₁₆	C₂³×C₂₃	1	3	yes	—
586	C₂×Q₁₆	C₂³×C₂₃	1	6	yes	—
587	C₂×Q₁₆	C₂³×C₂₃	1	3	yes	—
588	C₂×SD₁₆	—	2	12	no	—
589	C₂×SD₁₆	C₂³×C₂₃	1	3	yes	—
590	C₂×SD₁₆	C₂³×C₂₃	1	6	yes	—
591	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
592	C₂×SD₁₆	C₂³×C₂₃	1	3	yes	—
593	C₂×SD₁₆	C₂³×C₂₃	1	3	yes	—
594	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
595	C₂×D₈	C₂³×C₂₃	1	3	yes	—
596	#131	—	2	4	no	—
597	#131	—	2	4	no	—
598	C₂×M₁₆	C₂³×C₂₃	1	3	yes	—
599	C₂×M₁₆	C₂³×C₂₃	1	3	yes	—
600	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
601	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
602	C₄⋊Q₈	—	2	3	no	—
603	#124	—	2	3	no	—
604	#123	—	2	6	no	—
605	#123	—	2	3	no	—
606	C₂²⋊Q₈	—	2	3	no	—
607	C₂²⋊Q₈	—	2	3	no	—
608	C₂²⋊Q₈	—	2	3	no	—
609	C₂²⋊Q₈	C₂³×C₂₃	1	3	yes	—
610	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
611	C₂²⋊Q₈	C₂³×C₂₃	1	3	yes	—
612	#121	—	2	6	no	—
613	#121	—	2	3	no	—
614	#121	C₂³×C₂₃	1	1	yes	characteristic
615	#121	C₂³×C₂₃	1	3	yes	—
616	#120	—	2	3	no	—
617	C₄×Q₈	—	2	1	no	—
618	C₄×D₄	—	2	3	no	—
619	C₄×D₄	—	2	3	no	—
620	C₄×D₄	—	2	3	no	—
621	#117	C₂³×C₂₃	1	3	yes	—
622	C₂×C₄⋊C₄	—	2	3	no	—
623	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
624	C₂×C₂²⋊C₄	—	2	3	no	—
625	#103	C₂³×C₂₃	1	3	yes	—
626	#103	C₂³×C₂₃	1	6	yes	—
627	#103	C₂³×C₂₃	1	1	yes	characteristic
628	#103	C₂³×C₂₃	1	3	yes	—
629	#103	C₂³×C₂₃	1	3	yes	—
630	#102	C₂³×C₂₃	1	3	yes	—
631	#102	C₂³×C₂₃	1	6	yes	—
632	#102	C₂³×C₂₃	1	1	yes	characteristic
633	#102	C₂³×C₂₃	1	3	yes	—
634	#102	C₂³×C₂₃	1	3	yes	—
635	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
636	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
637	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
638	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
639	C₂²⋊C₈	C₂³×C₂₃	1	6	yes	—
640	C₂₃	#60377	1	1	yes	characteristic, direct product factor, Sylow
641	C₂⁴	—	2	3	no	—
642	C₂⁴	—	2	3	no	—
643	C₂⁴	C₂×D₄×C₂₃	1	3	yes	—
644	#41	—	2	24	no	—
645	#41	—	2	24	no	—
646	#41	—	2	48	no	—
647	#41	—	2	24	no	—
648	#41	—	2	24	no	—
649	#41	—	2	24	no	—
650	#41	—	2	24	no	—
651	#41	—	2	4	no	—
652	#41	—	2	8	no	—
653	#41	—	2	2	no	—
654	#41	—	2	6	no	—
655	#41	—	2	12	no	—
656	#41	—	2	12	no	—
657	#41	—	2	24	no	—
658	#41	—	2	2	no	—
659	#41	—	2	6	no	—
660	#41	—	2	12	no	—
661	#41	—	2	6	no	—
662	#41	—	2	6	no	—
663	#41	—	2	6	no	—
664	#41	—	2	6	no	—
665	#41	—	2	6	no	—
666	#41	—	2	6	no	—
667	#41	—	4	12	no	—
668	#41	C₂×D₄×C₂₃	1	12	yes	—
669	#41	C₂×D₄×C₂₃	1	12	yes	—
670	#41	C₂×D₄×C₂₃	1	4	yes	—
671	#41	C₂×D₄×C₂₃	1	4	yes	—
672	C₂×Q₈	—	2	24	no	—
673	C₂×Q₈	—	2	8	no	—
674	C₂×Q₈	—	2	4	no	—
675	C₂×Q₈	—	2	6	no	—
676	C₂×Q₈	—	2	6	no	—
677	C₂×Q₈	—	2	3	no	—
678	C₂×Q₈	—	2	3	no	—
679	C₂×Q₈	—	2	6	no	—
680	C₂×Q₈	—	2	3	no	—
681	C₂×Q₈	—	2	6	no	—
682	C₂×Q₈	—	2	6	no	—
683	C₂×Q₈	—	4	4	no	—
684	C₂×Q₈	C₂×D₄×C₂₃	1	12	yes	—
685	C₂×Q₈	C₂×D₄×C₂₃	1	3	yes	—
686	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
687	C₂×Q₈	C₂⁴×C₂₃	1	3	yes	—
688	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
689	C₂×Q₈	C₂⁴×C₂₃	1	3	yes	—
690	C₂×D₄	—	2	24	no	—
691	C₂×D₄	—	2	48	no	—
692	C₂×D₄	—	2	24	no	—
693	C₂×D₄	—	2	24	no	—
694	C₂×D₄	—	2	6	no	—
695	C₂×D₄	—	2	3	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	3	no	—
698	C₂×D₄	—	2	3	no	—
699	C₂×D₄	—	2	24	no	—
700	C₂×D₄	—	2	12	no	—
701	C₂×D₄	—	2	6	no	—
702	C₂×D₄	—	2	6	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	3	no	—
705	C₂×D₄	—	2	3	no	—
706	C₂×D₄	—	2	3	no	—
707	C₂×D₄	—	2	3	no	—
708	C₂×D₄	—	2	6	no	—
709	C₂×D₄	C₂×D₄×C₂₃	1	6	yes	—
710	C₂×D₄	C₂×D₄×C₂₃	1	3	yes	—
711	C₂×D₄	C₂×D₄×C₂₃	1	12	yes	—
712	C₂×D₄	C₂×D₄×C₂₃	1	3	yes	—
713	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
714	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
715	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
716	C₂²×C₄	—	2	24	no	—
717	C₂²×C₄	—	2	24	no	—
718	C₂²×C₄	—	2	3	no	—
719	C₂²×C₄	—	2	3	no	—
720	C₂²×C₄	—	2	3	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	6	no	—
723	C₂²×C₄	—	2	3	no	—
724	C₂²×C₄	—	2	3	no	—
725	C₂²×C₄	—	2	6	no	—
726	C₂²×C₄	—	2	6	no	—
727	C₂²×C₄	—	2	3	no	—
728	C₂²×C₄	—	2	3	no	—
729	C₂²×C₄	—	2	3	no	—
730	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
731	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
732	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
733	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
735	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
736	Q₁₆	—	2	6	no	—
737	Q₁₆	—	2	12	no	—
738	Q₁₆	—	2	6	no	—
739	SD₁₆	—	2	2	no	—
740	SD₁₆	—	2	6	no	—
741	SD₁₆	—	2	6	no	—
742	SD₁₆	—	2	12	no	—
743	SD₁₆	—	2	6	no	—
744	D₈	—	2	2	no	—
745	D₈	—	2	6	no	—
746	M₁₆	—	2	6	no	—
747	M₁₆	—	2	6	no	—
748	C₂×C₈	—	2	6	no	—
749	C₂×C₈	—	2	6	no	—
750	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
751	C₂×C₈	C₂⁴×C₂₃	1	3	yes	—
752	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
753	C₂×C₈	C₂⁴×C₂₃	1	3	yes	—
754	C₄⋊C₄	—	2	3	no	—
755	C₄⋊C₄	—	2	6	no	—
756	C₄⋊C₄	—	2	3	no	—
757	C₄⋊C₄	—	2	3	no	—
758	C₄⋊C₄	C₂⁴×C₂₃	1	3	yes	—
759	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
760	C₂²⋊C₄	—	2	3	no	—
761	C₂²⋊C₄	—	2	6	no	—
762	C₂²⋊C₄	—	2	3	no	—
763	C₂²⋊C₄	—	2	3	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	3	no	—
766	C₄²	—	2	3	no	—
767	C₂³	—	2	12	no	—
768	C₂³	—	2	3	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	6	no	—
771	C₂³	—	2	12	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	4	3	no	—
774	C₂³	—	4	3	no	—
775	C₂³	—	8	3	no	—
776	C₂³	—	8	3	no	—
777	C₂³	—	8	3	no	—
778	C₂³	—	8	3	no	—
779	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
780	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
781	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
782	Q₈	—	2	12	no	—
783	Q₈	—	2	1	no	—
784	Q₈	—	2	3	no	—
785	Q₈	—	2	12	no	—
786	Q₈	—	2	6	no	—
787	Q₈	—	2	3	no	—
788	Q₈	—	2	3	no	—
789	Q₈	—	4	6	no	—
790	Q₈	C₂₃×#120	1	4	yes	—
791	Q₈	C₂²×D₄×C₂₃	1	2	yes	—
792	Q₈	C₂²×D₄×C₂₃	1	6	yes	—
793	D₄	—	2	24	no	—
794	D₄	—	2	12	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	12	no	—
797	D₄	—	2	12	no	—
798	D₄	—	2	12	no	—
799	D₄	—	2	12	no	—
800	D₄	—	2	3	no	—
801	D₄	—	2	1	no	—
802	D₄	—	2	1	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	6	no	—
805	D₄	—	2	12	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	6	no	—
808	D₄	—	8	3	no	—
809	D₄	C₂₃×#120	1	12	yes	—
810	D₄	C₂²×D₄×C₂₃	1	2	yes	—
811	D₄	C₂²×D₄×C₂₃	1	6	yes	—
812	C₂×C₄	—	2	12	no	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	12	no	—
815	C₂×C₄	—	2	24	no	—
816	C₂×C₄	—	2	3	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	6	no	—
819	C₂×C₄	—	2	12	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	3	no	—
823	C₂×C₄	—	2	3	no	—
824	C₂×C₄	—	2	6	no	—
825	C₂×C₄	—	2	12	no	—
826	C₂×C₄	—	2	12	no	—
827	C₂×C₄	—	2	6	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	3	no	—
830	C₂×C₄	—	2	3	no	—
831	C₂×C₄	—	4	6	no	—
832	C₂×C₄	—	4	6	no	—
833	C₂×C₄	—	8	3	no	—
834	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
836	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
837	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
838	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
839	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
840	C₈	—	2	1	no	—
841	C₈	—	2	1	no	—
842	C₈	—	2	3	no	—
843	C₈	—	2	3	no	—
844	C₂²	—	2	3	no	—
845	C₂²	—	2	3	no	—
846	C₂²	—	2	3	no	—
847	C₂²	—	2	1	no	—
848	C₂²	—	2	6	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	3	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	3	no	—
854	C₂²	—	4	3	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	3	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	8	6	no	—
862	C₂²	—	8	12	no	—
863	C₂²	—	8	12	no	—
864	C₂²	C₂×C₂₃×#120	1	6	yes	—
865	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
866	C₄	—	2	1	no	—
867	C₄	—	2	6	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	3	no	—
870	C₄	—	4	3	no	—
871	C₄	—	4	3	no	—
872	C₄	—	4	1	no	—
873	C₄	C₂×C₂₃×#120	1	6	yes	—
874	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
875	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
876	C₂	—	2	6	no	—
877	C₂	—	4	3	no	—
878	C₂	—	4	1	no	—
879	C₂	—	4	6	no	—
880	C₂	—	4	2	no	—
881	C₂	—	8	1	no	—
882	C₂	C₂²×C₂₃×#120	1	1	yes	characteristic
883	C₂	C₂₃×#3584	1	1	yes	characteristic
884	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#585	C₂	semidirect
2. C₂×C₂₃×#578	C₂	semidirect
3. C₂×C₂₃×#577	C₂	semidirect
4. C₂₃×#3489	C₂	semidirect
5. C₂₃×#3013	C₂	semidirect
6. C₂₃×#3012	C₂	semidirect
7. C₂₃×#3011	C₂	semidirect
8. C₂₃×#3009	C₂	semidirect
9. C₂₃×#3007	C₂	semidirect
10. C₂₃×#3005	C₂	semidirect
11. C₂₃×#3002	C₂	semidirect
12. C₂×C₂₃×#452	C₂	semidirect
13. C₂₃×#2898	C₂	semidirect
14. C₂₃×#2897	C₂	semidirect
15. C₂₃×#2880	C₂	semidirect
21. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
32. C₂×C₂₃×#137	C₂²	semidirect
33. C₂×C₂₃×#137	C₂²	semidirect
34. C₂×C₂₃×#137	C₂²	semidirect
35. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
36. C₂×C₂₃×#135	C₂²	semidirect
37. C₂×C₂₃×#135	C₂²	semidirect
38. C₂²×Q₁₆×C₂₃	C₂²	semidirect
39. C₂²×SD₁₆×C₂₃	C₂²	semidirect
40. C₂×C₂₃×#131	C₂²	semidirect
41. C₂×C₂₃×#131	C₂²	semidirect
46. C₂₃×#537	C₂²	semidirect
47. C₂₃×#536	C₂²	semidirect
48. C₂₃×#525	C₂²	semidirect
49. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
50. C₂₃×#520	C₂²	semidirect
51. C₂₃×#452	C₂²	semidirect
52. C₂₃×#452	C₂²	semidirect
53. C₂₃×#452	C₂²	semidirect
54. C₂₃×#452	C₂²	semidirect
55. C₂₃×#452	C₂²	semidirect
56. C₂₃×#452	C₂²	semidirect
57. C₂₃×#451	C₂²	semidirect
58. C₂₃×#451	C₂²	semidirect
59. C₂₃×#450	C₂²	semidirect
60. C₂₃×#450	C₂²	semidirect
61. C₂₃×#449	C₂²	semidirect
62. C₂₃×#449	C₂²	semidirect
63. C₂₃×#449	C₂²	semidirect
64. C₂₃×#448	C₂²	semidirect
65. C₂₃×#447	C₂²	semidirect
66. C₂₃×#419	C₂²	semidirect
67. C₂₃×#418	C₂²	semidirect
68. C₂₃×#417	C₂²	semidirect
69. C₂₃×#417	C₂²	semidirect
70. C₂₃×#416	C₂²	semidirect
71. C₂₃×#416	C₂²	semidirect
72. C₂×C₂₃×#103	C₂²	semidirect
73. C₂×C₂₃×#102	C₂²	semidirect
74. C₂₃×#408	C₂²	semidirect
75. C₂₃×#408	C₂²	semidirect
76. C₂₃×#407	C₂²	semidirect
77. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
84. C₂₃×2₋¹⁺⁴	D₄	semidirect
89. C₂₃×H(5,𝔽₂)	D₄	semidirect
324. #60377	C₂₃	direct (N × H)
402. C₂×#585	C₂×C₂₃	semidirect
403. C₂×#578	C₂×C₂₃	semidirect
404. C₂×#577	C₂×C₂₃	semidirect
405. #3489	C₂×C₂₃	semidirect
406. #3013	C₂×C₂₃	semidirect
407. #3012	C₂×C₂₃	semidirect
408. #3011	C₂×C₂₃	semidirect
409. #3009	C₂×C₂₃	semidirect
410. #3007	C₂×C₂₃	semidirect
411. #3005	C₂×C₂₃	semidirect
412. #3002	C₂×C₂₃	semidirect
413. C₂×#452	C₂×C₂₃	semidirect
414. #2898	C₂×C₂₃	semidirect
415. #2897	C₂×C₂₃	semidirect
416. #2880	C₂×C₂₃	semidirect
454. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
465. C₂×#137	C₂²×C₂₃	semidirect
466. C₂×#137	C₂²×C₂₃	semidirect
467. C₂×#137	C₂²×C₂₃	semidirect
468. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
469. C₂×#135	C₂²×C₂₃	semidirect
470. C₂×#135	C₂²×C₂₃	semidirect
471. C₂²×Q₁₆	C₂²×C₂₃	semidirect
472. C₂²×SD₁₆	C₂²×C₂₃	semidirect
473. C₂×#131	C₂²×C₂₃	semidirect
474. C₂×#131	C₂²×C₂₃	semidirect
479. #537	C₂²×C₂₃	semidirect
480. #536	C₂²×C₂₃	semidirect
481. #525	C₂²×C₂₃	semidirect
482. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
483. #520	C₂²×C₂₃	semidirect
484. #452	C₂²×C₂₃	semidirect
485. #452	C₂²×C₂₃	semidirect
486. #452	C₂²×C₂₃	semidirect
487. #452	C₂²×C₂₃	semidirect
488. #452	C₂²×C₂₃	semidirect
489. #452	C₂²×C₂₃	semidirect
490. #451	C₂²×C₂₃	semidirect
491. #451	C₂²×C₂₃	semidirect
492. #450	C₂²×C₂₃	semidirect
493. #450	C₂²×C₂₃	semidirect
494. #449	C₂²×C₂₃	semidirect
495. #449	C₂²×C₂₃	semidirect
496. #449	C₂²×C₂₃	semidirect
497. #448	C₂²×C₂₃	semidirect
498. #447	C₂²×C₂₃	semidirect
499. #419	C₂²×C₂₃	semidirect
500. #418	C₂²×C₂₃	semidirect
501. #417	C₂²×C₂₃	semidirect
502. #417	C₂²×C₂₃	semidirect
503. #416	C₂²×C₂₃	semidirect
504. #416	C₂²×C₂₃	semidirect
505. C₂×#103	C₂²×C₂₃	semidirect
506. C₂×#102	C₂²×C₂₃	semidirect
507. #408	C₂²×C₂₃	semidirect
508. #408	C₂²×C₂₃	semidirect
509. #407	C₂²×C₂₃	semidirect
510. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
526. 2₋¹⁺⁴	D₄×C₂₃	semidirect
531. H(5,𝔽₂)	D₄×C₂₃	semidirect
640. C₂₃	#60377	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×#585	2
C₂×C₂₃×#578	2
C₂×C₂₃×#577	2
C₂₃×#3489	2
C₂₃×#3013	2
C₂₃×#3012	2
C₂₃×#3011	2
C₂₃×#3009	2
C₂₃×#3007	2
C₂₃×#3005	2
C₂₃×#3002	2
C₂×C₂₃×#452	2
C₂₃×#2898	2
C₂₃×#2897	2
C₂₃×#2880	2
#60377	23

Subgroups — C23×#60377 #19208003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60377 #19208003