Subgroups — #24921306

Order 10624.

1140 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128435	C₂	1	2	yes	maximal, complemented
2	#19128434	C₂	1	2	yes	maximal, complemented
3	#19128422	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128419	C₂	1	1	yes	maximal, characteristic, complemented
5	#19128415	C₂	1	1	yes	maximal, characteristic, complemented
6	#19128414	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128400	C₂	1	2	yes	maximal, complemented
8	#19128396	C₂	1	2	yes	maximal, complemented
9	#19128370	C₂	1	1	yes	maximal, characteristic, complemented
10	#19128369	C₂	1	1	yes	maximal, characteristic, complemented
11	#19128353	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128350	C₂	1	1	yes	maximal, characteristic, complemented
13	#19128286	C₂	1	2	yes	maximal, complemented
14	#19128284	C₂	1	2	yes	maximal, complemented
15	#19128266	C₂	1	2	yes	maximal, complemented
16	#19128253	C₂	1	1	yes	maximal, characteristic, complemented
17	#19128246	C₂	1	1	yes	maximal, characteristic, complemented
18	#19128214	C₂	1	1	yes	maximal, characteristic, complemented
19	#19128212	C₂	1	1	yes	maximal, characteristic, complemented
20	#19128211	C₂	1	1	yes	maximal, characteristic, complemented
21	#19128180	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×C₂²⋊D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#525×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13050591	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13050590	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13050589	C₂²	1	2	yes	—
27	C₂×#13050589	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₈₃	C₂²	1	1	yes	characteristic
30	#14581791	C₂²	1	1	yes	characteristic, complemented
31	#14581791	C₂²	1	1	yes	characteristic, complemented
32	#14581790	C₂²	1	1	yes	characteristic, complemented
33	#14581788	C₂²	1	2	yes	—
34	#14581788	C₂²	1	2	yes	—
35	#14581788	C₂²	1	1	yes	characteristic, complemented
36	#14581787	C₂²	1	2	yes	complemented
37	#14581786	C₂²	1	2	yes	complemented
38	#14581785	C₂²	1	2	yes	complemented
39	#14581785	C₂²	1	2	yes	complemented
40	#14581782	C₂²	1	2	yes	complemented
41	#14581780	C₂²	1	2	yes	complemented
42	#14581779	C₂²	1	2	yes	complemented
43	#14581778	C₂²	1	2	yes	—
44	#14581778	C₂²	1	2	yes	—
45	#14581778	C₂²	1	2	yes	complemented
46	#14581778	C₂²	1	2	yes	complemented
47	#14581778	C₂²	1	2	yes	complemented
48	#14581777	C₂²	1	2	yes	complemented
49	#14581777	C₂²	1	2	yes	complemented
50	#14581775	C₂²	1	2	yes	complemented
51	#14581775	C₂²	1	2	yes	complemented
52	#14581774	C₂²	1	2	yes	complemented
53	#14581774	C₂²	1	2	yes	complemented
54	#14581773	C₂²	1	2	yes	complemented
55	#14581772	C₂²	1	1	yes	characteristic, complemented
56	#14581771	C₂²	1	1	yes	characteristic
57	#14581771	C₂²	1	1	yes	characteristic, complemented
58	#14581769	C₂²	1	2	yes	—
59	#14581768	C₂²	1	1	yes	characteristic, complemented
60	#14581767	C₂²	1	1	yes	characteristic, complemented
61	#14581766	C₂²	1	1	yes	characteristic
62	#14581766	C₂²	1	2	yes	complemented
63	#14581766	C₂²	1	1	yes	characteristic, complemented
64	#14581765	C₂²	1	2	yes	—
65	#14581765	C₂²	1	2	yes	—
66	#14581765	C₂²	1	2	yes	complemented
67	#14581764	C₂²	1	2	yes	—
68	#14581764	C₂²	1	2	yes	—
69	#14581764	C₂²	1	2	yes	—
70	#14581764	C₂²	1	2	yes	complemented
71	#14581763	C₂²	1	2	yes	complemented
72	#14581763	C₂²	1	1	yes	characteristic, complemented
73	#14581762	C₂²	1	2	yes	—
74	#14581761	C₂²	1	2	yes	—
75	#14581760	C₂²	1	2	yes	—
76	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₁₆₆	C₂²	1	2	yes	complemented
78	#14581757	C₂²	1	1	yes	characteristic, complemented
79	#14581757	C₂²	1	2	yes	complemented
80	#14581757	C₂²	1	2	yes	complemented
81	D₄×Dic₈₃	C₂²	1	2	yes	—
82	D₄×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
83	#14581754	C₂²	1	1	yes	characteristic, complemented
84	#14581754	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
96	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	—
97	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
98	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
100	#14581751	C₂²	1	1	yes	characteristic, complemented
101	#14581750	C₂²	1	1	yes	characteristic, complemented
102	#14581750	C₂²	1	1	yes	characteristic, complemented
103	#14581749	C₂²	1	2	yes	complemented
104	#14581748	C₂²	1	2	yes	—
105	#14581748	C₂²	1	2	yes	complemented
106	C₂×Dic₈₃⋊C₄	C₂²	1	1	yes	characteristic
107	C₂×Dic₈₃⋊C₄	C₂²	1	2	yes	complemented
108	C₄⋊C₄×D₈₃	C₂²	1	2	yes	complemented
109	C₂×C₂²⋊Dic₈₃	C₂²	1	1	yes	characteristic
110	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	1	yes	characteristic
111	C₂×C₄×Dic₈₃	C₂²	1	1	yes	characteristic
112	C₂×#41×C₈₃	C₂²	1	1	yes	characteristic, complemented
113	C₂³×C₄×C₈₃	C₂²	1	1	yes	characteristic
114	#123×C₈₃	C₂²	1	2	yes	complemented
115	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
117	#121×C₈₃	C₂²	1	1	yes	characteristic
118	#121×C₈₃	C₂²	1	1	yes	characteristic, complemented
119	#120×C₈₃	C₂²	1	2	yes	—
120	C₄×D₄×C₈₃	C₂²	1	2	yes	—
121	C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
122	#117×C₈₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₈₃	C₂³	1	1	yes	characteristic
124	#13050591	—	4	2	no	—
125	#13050590	—	4	2	no	—
126	#13050589	—	2	8	no	—
127	#13050589	—	4	2	no	—
128	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₆₆	C₂³	1	2	yes	—
130	C₂×Dic₁₆₆	C₂³	1	2	yes	—
131	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
132	C₂×D₃₃₂	C₂³	1	2	yes	—
133	C₂×D₃₃₂	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₈₃	—	2	4	no	—
135	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
146	C₂²×Dic₈₃	C₂³	1	2	yes	—
147	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
148	C₂²×Dic₈₃	C₂³	1	2	yes	—
149	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
150	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₈₃	—	4	2	no	—
152	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₈₃	C₂³	1	2	yes	—
154	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₈₃	C₂³	1	2	yes	—
156	C₂×C₄×D₈₃	C₂³	1	2	yes	—
157	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₈₃	C₂³	1	2	yes	—
160	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₈₃	C₂³	1	2	yes	—
163	Dic₈₃⋊C₄	C₂³	1	2	yes	—
164	Dic₈₃⋊C₄	C₂³	1	2	yes	—
165	Dic₈₃⋊C₄	C₂³	1	2	yes	—
166	Dic₈₃⋊C₄	C₂³	1	2	yes	—
167	Dic₈₃⋊C₄	C₂³	1	2	yes	—
168	Dic₈₃⋊C₄	C₂³	1	2	yes	—
169	Dic₈₃⋊C₄	C₂³	1	2	yes	—
170	Dic₈₃⋊C₄	C₂³	1	2	yes	—
171	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
184	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
196	C₄×Dic₈₃	C₂³	1	2	yes	—
197	C₄×Dic₈₃	C₂³	1	2	yes	—
198	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₈₃	C₂³	1	2	yes	—
200	C₄×Dic₈₃	C₂³	1	2	yes	—
201	C₄×Dic₈₃	C₂³	1	2	yes	—
202	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
203	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
204	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
205	C₂⁴×C₈₃	C₂³	1	1	yes	characteristic
206	#41×C₈₃	—	4	2	no	—
207	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₈₃	C₂³	1	2	yes	—
209	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₈₃	C₂³	1	2	yes	—
211	C₂×D₄×C₈₃	C₂³	1	2	yes	—
212	C₂²×C₄×C₈₃	—	4	2	no	—
213	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
217	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
219	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
223	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
229	C₄²×C₈₃	C₂³	1	2	yes	—
230	C₂³×C₈₃	—	2	2	no	—
231	C₂³×C₈₃	—	4	1	no	—
232	C₂³×C₈₃	—	4	1	no	—
233	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
234	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
235	C₂³×C₈₃	C₂⁴	1	2	yes	—
236	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
237	C₂²×D₈₃	—	2	2	no	—
238	C₂²×D₈₃	—	4	1	no	—
239	C₂²×D₈₃	—	4	1	no	—
240	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
241	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
242	C₂²×D₈₃	C₂⁴	1	2	yes	—
243	Q₈×C₈₃	—	2	2	no	—
244	D₄×C₈₃	—	2	4	no	—
245	D₄×C₈₃	—	2	2	no	—
246	D₄×C₈₃	—	4	2	no	—
247	D₄×C₈₃	—	4	2	no	—
248	C₂×C₄×C₈₃	—	2	2	no	—
249	C₂×C₄×C₈₃	—	2	2	no	—
250	C₂×C₄×C₈₃	—	2	2	no	—
251	C₂×C₄×C₈₃	—	4	1	no	—
252	C₂×C₄×C₈₃	—	4	1	no	—
253	C₂×C₄×C₈₃	—	4	1	no	—
254	C₂×C₄×C₈₃	—	4	2	no	—
255	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
257	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
258	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
261	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
262	C₂²⋊D₈₃	—	2	4	no	—
263	C₂²⋊D₈₃	—	2	2	no	—
264	C₂²⋊D₈₃	—	2	2	no	—
265	C₂²⋊D₈₃	—	2	2	no	—
266	C₂²⋊D₈₃	—	2	2	no	—
267	C₂²⋊D₈₃	—	2	4	no	—
268	C₂²⋊D₈₃	—	4	2	no	—
269	C₂²⋊D₈₃	—	4	2	no	—
270	C₂²⋊D₈₃	—	4	2	no	—
271	C₂²⋊D₈₃	—	4	2	no	—
272	C₂²⋊D₈₃	—	4	2	no	—
273	C₂×Dic₈₃	—	2	4	no	—
274	C₂×Dic₈₃	—	4	1	no	—
275	C₂×Dic₈₃	—	4	1	no	—
276	C₂×Dic₈₃	—	4	2	no	—
277	C₂×Dic₈₃	#41	1	4	yes	complemented
278	C₂×Dic₈₃	C₂⁴	1	2	yes	—
279	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₈₃	C₂⁴	1	2	yes	—
281	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₈₃	C₂⁴	1	2	yes	—
285	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
287	D₃₃₂	—	2	2	no	—
288	D₃₃₂	—	4	2	no	—
289	D₃₃₂	—	4	2	no	—
290	C₄×D₈₃	—	2	2	no	—
291	C₄×D₈₃	—	2	2	no	—
292	C₄×D₈₃	—	2	4	no	—
293	C₄×D₈₃	—	4	1	no	—
294	C₄×D₈₃	—	4	1	no	—
295	C₄×D₈₃	—	4	2	no	—
296	C₄×D₈₃	—	4	2	no	—
297	Dic₁₆₆	—	2	2	no	—
298	Dic₁₆₆	—	2	4	no	—
299	Dic₁₆₆	—	4	2	no	—
300	C₂²×C₈₃	—	2	1	no	—
301	C₂²×C₈₃	—	2	1	no	—
302	C₂²×C₈₃	—	2	2	no	—
303	C₂²×C₈₃	—	2	1	no	—
304	C₂²×C₈₃	—	2	1	no	—
305	C₂²×C₈₃	—	2	2	no	—
306	C₂²×C₈₃	—	2	1	no	—
307	C₂²×C₈₃	—	2	1	no	—
308	C₂²×C₈₃	—	2	2	no	—
309	C₂²×C₈₃	—	2	1	no	—
310	C₂²×C₈₃	—	2	1	no	—
311	C₂²×C₈₃	—	4	4	no	—
312	C₂²×C₈₃	C₂×#41	1	2	yes	—
313	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
314	C₂×D₈₃	—	2	2	no	—
315	C₂×D₈₃	—	2	1	no	—
316	C₂×D₈₃	—	2	1	no	—
317	C₂×D₈₃	—	2	1	no	—
318	C₂×D₈₃	—	2	1	no	—
319	C₂×D₈₃	—	2	2	no	—
320	C₂×D₈₃	—	2	1	no	—
321	C₂×D₈₃	—	2	2	no	—
322	C₂×D₈₃	—	2	1	no	—
323	C₂×D₈₃	—	4	4	no	—
324	C₄×C₈₃	—	2	2	no	—
325	C₄×C₈₃	—	2	1	no	—
326	C₄×C₈₃	—	2	1	no	—
327	C₄×C₈₃	—	2	2	no	—
328	C₄×C₈₃	—	2	1	no	—
329	C₄×C₈₃	—	2	2	no	—
330	C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
331	Dic₈₃	—	2	2	no	—
332	Dic₈₃	—	2	2	no	—
333	Dic₈₃	—	2	1	no	—
334	Dic₈₃	—	2	1	no	—
335	Dic₈₃	—	2	1	no	—
336	Dic₈₃	—	2	2	no	—
337	Dic₈₃	—	2	1	no	—
338	Dic₈₃	C₂×#41	1	2	yes	—
339	Dic₈₃	C₂×#41	1	2	yes	—
340	C₂×C₈₃	—	2	2	no	—
341	C₂×C₈₃	—	4	2	no	—
342	C₂×C₈₃	—	4	1	no	—
343	C₂×C₈₃	—	4	1	no	—
344	C₂×C₈₃	C₂²×#41	1	1	yes	characteristic
345	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₈₃	#585	1	1	yes	characteristic
347	D₈₃	—	4	2	no	—
348	D₈₃	—	4	1	no	—
349	D₈₃	—	4	1	no	—
350	#3506	—	83	1	no	maximal, Sylow
351	C₈₃	#3506	1	1	yes	characteristic, complemented, Sylow
352	#559	—	83	2	no	—
353	#559	—	83	2	no	—
354	#556	—	83	1	no	—
355	#556	—	83	1	no	—
356	#555	—	83	1	no	—
357	#555	—	83	1	no	—
358	#553	—	83	2	no	—
359	#553	—	83	2	no	—
360	#550	—	83	1	no	—
361	#550	—	83	1	no	—
362	#547	—	83	1	no	—
363	#547	—	83	1	no	—
364	#538	—	83	2	no	—
365	#538	—	83	2	no	—
366	#535	—	83	2	no	—
367	#533	—	83	1	no	—
368	#532	—	83	1	no	—
369	#525	—	83	1	no	—
370	#525	—	83	1	no	—
371	#525	—	83	1	no	—
372	#525	D₈₃	1	1	yes	characteristic, complemented
373	#520	—	83	2	no	—
374	C₂×C₄×D₄	—	83	1	no	—
375	C₂×#41	—	83	1	no	—
376	C₂×#41	—	83	1	no	—
377	C₂×#41	—	83	2	no	—
378	C₂×#41	—	83	1	no	—
379	C₂×#41	C₂×D₈₃	1	1	yes	characteristic, complemented
380	C₂²×D₄	—	83	1	no	—
381	C₂³×C₄	—	83	1	no	—
382	C₂³×C₄	C₂×D₈₃	1	1	yes	characteristic
383	C₄⋊Q₈	—	83	1	no	—
384	C₄⋊Q₈	—	83	1	no	—
385	C₄⋊Q₈	—	83	1	no	—
386	#127	—	83	1	no	—
387	#127	—	83	2	no	—
388	#127	—	83	2	no	—
389	#126	—	83	2	no	—
390	#126	—	83	2	no	—
391	#126	—	83	2	no	—
392	#126	—	83	2	no	—
393	#125	—	83	2	no	—
394	#124	—	83	2	no	—
395	#124	—	83	2	no	—
396	#124	—	83	2	no	—
397	#124	—	83	2	no	—
398	#124	—	83	2	no	—
399	#124	—	83	2	no	—
400	#124	—	83	2	no	—
401	#123	—	83	2	no	—
402	#123	—	83	2	no	—
403	#123	—	83	2	no	—
404	#123	—	83	2	no	—
405	#123	—	83	2	no	—
406	#123	—	83	2	no	—
407	#123	—	83	2	no	—
408	#123	C₂×D₈₃	1	2	yes	complemented
409	C₂²⋊Q₈	—	83	1	no	—
410	C₂²⋊Q₈	—	83	1	no	—
411	C₂²⋊Q₈	—	83	1	no	—
412	C₂²⋊Q₈	—	83	1	no	—
413	C₂²⋊Q₈	—	83	2	no	—
414	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
415	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
416	#121	—	83	1	no	—
417	#121	—	83	2	no	—
418	#121	—	83	2	no	—
419	#121	—	83	2	no	—
420	#121	—	83	2	no	—
421	#121	—	83	2	no	—
422	#121	—	83	1	no	—
423	#121	—	83	1	no	—
424	#121	—	83	2	no	—
425	#121	—	83	1	no	—
426	#121	—	83	2	no	—
427	#121	—	83	2	no	—
428	#121	—	83	2	no	—
429	#121	C₂×D₈₃	1	1	yes	characteristic
430	#121	C₂×D₈₃	1	1	yes	characteristic, complemented
431	#120	—	83	2	no	—
432	#120	—	83	2	no	—
433	#120	—	83	2	no	—
434	#120	C₂×D₈₃	1	2	yes	—
435	C₄×Q₈	—	83	1	no	—
436	C₄×Q₈	—	83	2	no	—
437	C₄×Q₈	—	83	1	no	—
438	C₄×Q₈	—	83	2	no	—
439	C₄×Q₈	—	83	2	no	—
440	C₄×D₄	—	83	2	no	—
441	C₄×D₄	—	83	1	no	—
442	C₄×D₄	—	83	1	no	—
443	C₄×D₄	—	83	1	no	—
444	C₄×D₄	—	83	1	no	—
445	C₄×D₄	—	83	1	no	—
446	C₄×D₄	—	83	1	no	—
447	C₄×D₄	—	83	1	no	—
448	C₄×D₄	—	83	1	no	—
449	C₄×D₄	—	83	1	no	—
450	C₄×D₄	—	83	2	no	—
451	C₄×D₄	—	83	2	no	—
452	C₄×D₄	—	83	2	no	—
453	C₄×D₄	—	83	2	no	—
454	C₄×D₄	—	83	1	no	—
455	C₄×D₄	—	83	2	no	—
456	C₄×D₄	—	83	2	no	—
457	C₄×D₄	—	83	2	no	—
458	C₄×D₄	—	83	2	no	—
459	C₄×D₄	C₂×D₈₃	1	2	yes	—
460	C₄×D₄	C₂×D₈₃	1	2	yes	complemented
461	#117	—	83	1	no	—
462	#117	—	83	1	no	—
463	#117	—	83	1	no	—
464	#117	—	83	2	no	—
465	#117	—	83	2	no	—
466	#117	—	83	2	no	—
467	#117	C₂×D₈₃	1	1	yes	characteristic, complemented
468	C₂×C₄⋊C₄	—	83	1	no	—
469	C₂×C₄⋊C₄	—	83	2	no	—
470	C₂×C₄⋊C₄	—	83	2	no	—
471	C₂×C₂²⋊C₄	—	83	1	no	—
472	C₂×C₂²⋊C₄	—	83	1	no	—
473	C₂×C₄²	—	83	1	no	—
474	C₂⁴	—	83	1	no	—
475	C₂⁴	C₂²×D₈₃	1	1	yes	characteristic
476	#41	—	4	2	no	—
477	#41	—	332	2	no	—
478	#41	—	332	2	no	—
479	#41	—	332	2	no	—
480	#41	—	166	8	no	—
481	C₂×Q₈	—	83	2	no	—
482	C₂×Q₈	—	83	2	no	—
483	C₂×Q₈	—	83	1	no	—
484	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
485	C₂×D₄	—	83	2	no	—
486	C₂×D₄	—	83	2	no	—
487	C₂×D₄	—	83	2	no	—
488	C₂×D₄	—	83	2	no	—
489	C₂×D₄	—	83	2	no	—
490	C₂×D₄	—	83	2	no	—
491	C₂×D₄	—	83	1	no	—
492	C₂×D₄	—	83	1	no	—
493	C₂×D₄	—	83	1	no	—
494	C₂×D₄	—	83	1	no	—
495	C₂×D₄	—	83	2	no	—
496	C₂×D₄	—	83	2	no	—
497	C₂×D₄	—	83	2	no	—
498	C₂×D₄	—	83	1	no	—
499	C₂×D₄	—	166	4	no	—
500	C₂×D₄	C₂²×D₈₃	1	2	yes	—
501	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
502	C₂×D₄	C₂²×D₈₃	1	2	yes	—
503	C₂×D₄	C₂²×D₈₃	1	2	yes	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	332	2	no	—
506	C₂²×C₄	—	83	1	no	—
507	C₂²×C₄	—	83	1	no	—
508	C₂²×C₄	—	83	2	no	—
509	C₂²×C₄	—	83	2	no	—
510	C₂²×C₄	—	83	2	no	—
511	C₂²×C₄	—	83	1	no	—
512	C₂²×C₄	—	83	1	no	—
513	C₂²×C₄	—	83	1	no	—
514	C₂²×C₄	—	83	2	no	—
515	C₂²×C₄	—	83	2	no	—
516	C₂²×C₄	—	83	1	no	—
517	C₂²×C₄	—	83	1	no	—
518	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
519	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
520	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
521	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
522	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
523	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
525	C₄⋊C₄	—	83	1	no	—
526	C₄⋊C₄	—	83	1	no	—
527	C₄⋊C₄	—	83	2	no	—
528	C₄⋊C₄	—	83	1	no	—
529	C₄⋊C₄	—	83	1	no	—
530	C₄⋊C₄	—	83	2	no	—
531	C₄⋊C₄	—	83	2	no	—
532	C₄⋊C₄	—	83	2	no	—
533	C₄⋊C₄	—	83	2	no	—
534	C₄⋊C₄	—	83	1	no	—
535	C₄⋊C₄	—	83	1	no	—
536	C₄⋊C₄	—	83	2	no	—
537	C₄⋊C₄	—	83	2	no	—
538	C₄⋊C₄	—	83	2	no	—
539	C₄⋊C₄	—	83	2	no	—
540	C₄⋊C₄	—	83	2	no	—
541	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
542	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
545	C₂²⋊C₄	—	83	1	no	—
546	C₂²⋊C₄	—	83	1	no	—
547	C₂²⋊C₄	—	83	1	no	—
548	C₂²⋊C₄	—	83	1	no	—
549	C₂²⋊C₄	—	83	2	no	—
550	C₂²⋊C₄	—	83	2	no	—
551	C₂²⋊C₄	—	83	2	no	—
552	C₂²⋊C₄	—	83	2	no	—
553	C₂²⋊C₄	—	83	2	no	—
554	C₂²⋊C₄	—	83	1	no	—
555	C₂²⋊C₄	—	83	1	no	—
556	C₂²⋊C₄	—	83	1	no	—
557	C₂²⋊C₄	—	83	1	no	—
558	C₂²⋊C₄	—	83	2	no	—
559	C₂²⋊C₄	—	83	2	no	—
560	C₂²⋊C₄	—	83	2	no	—
561	C₂²⋊C₄	—	83	2	no	—
562	C₂²⋊C₄	—	83	2	no	—
563	C₂²⋊C₄	—	83	2	no	—
564	C₂²⋊C₄	—	83	2	no	—
565	C₂²⋊C₄	—	83	2	no	—
566	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
567	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
568	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
569	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
571	C₄²	—	83	1	no	—
572	C₄²	—	83	1	no	—
573	C₄²	—	83	1	no	—
574	C₄²	—	83	1	no	—
575	C₄²	—	83	2	no	—
576	C₄²	—	83	2	no	—
577	C₄²	—	83	2	no	—
578	C₄²	—	83	2	no	—
579	C₄²	—	83	2	no	—
580	C₄²	C₂²×D₈₃	1	2	yes	—
581	C₂³	—	2	2	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	332	1	no	—
585	C₂³	—	332	1	no	—
586	C₂³	—	83	1	no	—
587	C₂³	—	83	1	no	—
588	C₂³	—	83	2	no	—
589	C₂³	—	166	2	no	—
590	C₂³	C₂³×D₈₃	1	1	yes	characteristic
591	C₂³	C₂³×D₈₃	1	1	yes	characteristic
592	C₂³	C₂³×D₈₃	1	2	yes	—
593	C₂³	C₂³×D₈₃	1	1	yes	characteristic
594	Q₈	—	2	2	no	—
595	Q₈	—	332	2	no	—
596	Q₈	—	166	4	no	—
597	Q₈	—	166	2	no	—
598	D₄	—	2	4	no	—
599	D₄	—	2	2	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	2	no	—
602	D₄	—	332	2	no	—
603	D₄	—	332	2	no	—
604	D₄	—	332	2	no	—
605	D₄	—	332	2	no	—
606	D₄	—	332	2	no	—
607	D₄	—	332	2	no	—
608	D₄	—	332	2	no	—
609	D₄	—	166	2	no	—
610	D₄	—	166	2	no	—
611	D₄	—	166	2	no	—
612	D₄	—	166	2	no	—
613	D₄	—	166	4	no	—
614	D₄	—	166	4	no	—
615	D₄	—	166	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	332	1	no	—
624	C₂×C₄	—	332	1	no	—
625	C₂×C₄	—	332	2	no	—
626	C₂×C₄	—	332	2	no	—
627	C₂×C₄	—	332	1	no	—
628	C₂×C₄	—	332	2	no	—
629	C₂×C₄	—	332	1	no	—
630	C₂×C₄	—	83	4	no	—
631	C₂×C₄	—	83	1	no	—
632	C₂×C₄	—	83	1	no	—
633	C₂×C₄	—	83	2	no	—
634	C₂×C₄	—	83	1	no	—
635	C₂×C₄	—	83	2	no	—
636	C₂×C₄	—	83	1	no	—
637	C₂×C₄	—	83	1	no	—
638	C₂×C₄	—	83	1	no	—
639	C₂×C₄	—	83	2	no	—
640	C₂×C₄	—	166	4	no	—
641	C₂×C₄	—	166	4	no	—
642	C₂×C₄	—	166	2	no	—
643	C₂×C₄	—	166	2	no	—
644	C₂×C₄	C₂³×D₈₃	1	2	yes	—
645	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₈₃	1	2	yes	—
648	C₂×C₄	C₂³×D₈₃	1	2	yes	—
649	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	332	4	no	—
664	C₂²	—	166	2	no	—
665	C₂²	—	166	1	no	—
666	C₂²	—	166	1	no	—
667	C₂²	—	166	2	no	—
668	C₂²	—	166	1	no	—
669	C₂²	—	166	1	no	—
670	C₂²	—	166	2	no	—
671	C₂²	—	166	1	no	—
672	C₂²	—	166	1	no	—
673	C₂²	#41×D₈₃	1	2	yes	—
674	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
675	C₄	—	2	2	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	83	2	no	—
682	C₄	—	83	2	no	—
683	C₄	—	166	2	no	—
684	C₄	—	166	1	no	—
685	C₄	—	166	1	no	—
686	C₄	—	166	2	no	—
687	C₄	—	166	1	no	—
688	C₄	—	166	1	no	—
689	C₄	—	166	2	no	—
690	C₄	#14581837	1	2	yes	—
691	C₂	—	2	2	no	—
692	C₂	—	4	1	no	—
693	C₂	—	4	1	no	—
694	C₂	—	4	2	no	—
695	C₂	—	332	1	no	—
696	C₂	—	332	1	no	—
697	C₂	—	332	2	no	—
698	C₂	C₂×#41×D₈₃	1	1	yes	characteristic
699	C₂	C₂×#14581837	1	1	yes	characteristic
700	C₂	#19128537	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#525×C₈₃	C₂
hypercenter	#525	D₈₃
hypocenter	C₈₃	#3506
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #19128435	C₂	semidirect
2. #19128434	C₂	semidirect
3. #19128422	C₂	semidirect
4. #19128419	C₂	semidirect
5. #19128415	C₂	semidirect
6. #19128414	C₂	semidirect
7. #19128400	C₂	semidirect
8. #19128396	C₂	semidirect
9. #19128370	C₂	semidirect
10. #19128369	C₂	semidirect
11. #19128353	C₂	semidirect
12. #19128350	C₂	semidirect
13. #19128286	C₂	semidirect
14. #19128284	C₂	semidirect
15. #19128266	C₂	semidirect
16. #19128253	C₂	semidirect
17. #19128246	C₂	semidirect
18. #19128214	C₂	semidirect
19. #19128212	C₂	semidirect
20. #19128211	C₂	semidirect
21. #19128180	C₂	semidirect
22. C₂×C₄×C₂²⋊D₈₃	C₂	semidirect
23. #525×C₈₃	C₂	semidirect
24. C₂×#13050591	C₂²	semidirect
25. C₂×#13050590	C₂²	semidirect
27. C₂×#13050589	C₂²	semidirect
30. #14581791	C₂²	semidirect
31. #14581791	C₂²	semidirect
32. #14581790	C₂²	semidirect
35. #14581788	C₂²	semidirect
36. #14581787	C₂²	semidirect
37. #14581786	C₂²	semidirect
38. #14581785	C₂²	semidirect
39. #14581785	C₂²	semidirect
40. #14581782	C₂²	semidirect
41. #14581780	C₂²	semidirect
42. #14581779	C₂²	semidirect
45. #14581778	C₂²	semidirect
46. #14581778	C₂²	semidirect
47. #14581778	C₂²	semidirect
48. #14581777	C₂²	semidirect
49. #14581777	C₂²	semidirect
50. #14581775	C₂²	semidirect
51. #14581775	C₂²	semidirect
52. #14581774	C₂²	semidirect
53. #14581774	C₂²	semidirect
54. #14581773	C₂²	semidirect
55. #14581772	C₂²	semidirect
57. #14581771	C₂²	semidirect
59. #14581768	C₂²	semidirect
60. #14581767	C₂²	semidirect
62. #14581766	C₂²	semidirect
63. #14581766	C₂²	semidirect
66. #14581765	C₂²	semidirect
70. #14581764	C₂²	semidirect
71. #14581763	C₂²	semidirect
72. #14581763	C₂²	semidirect
76. Q₈×Dic₈₃	C₂²	semidirect
77. C₄×Dic₁₆₆	C₂²	semidirect
78. #14581757	C₂²	semidirect
79. #14581757	C₂²	semidirect
80. #14581757	C₂²	semidirect
82. D₄×Dic₈₃	C₂²	semidirect
83. #14581754	C₂²	semidirect
84. #14581754	C₂²	semidirect
94. C₄×C₂²⋊D₈₃	C₂²	semidirect
95. C₄×C₂²⋊D₈₃	C₂²	semidirect
97. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
100. #14581751	C₂²	semidirect
101. #14581750	C₂²	semidirect
102. #14581750	C₂²	semidirect
103. #14581749	C₂²	semidirect
105. #14581748	C₂²	semidirect
107. C₂×Dic₈₃⋊C₄	C₂²	semidirect
108. C₄⋊C₄×D₈₃	C₂²	semidirect
112. C₂×#41×C₈₃	C₂²	semidirect
114. #123×C₈₃	C₂²	semidirect
116. C₂²⋊Q₈×C₈₃	C₂²	semidirect
118. #121×C₈₃	C₂²	semidirect
121. C₄×D₄×C₈₃	C₂²	semidirect
122. #117×C₈₃	C₂²	semidirect
277. C₂×Dic₈₃	#41	semidirect
351. C₈₃	#3506	semidirect
372. #525	D₈₃	semidirect
379. C₂×#41	C₂×D₈₃	semidirect
408. #123	C₂×D₈₃	semidirect
415. C₂²⋊Q₈	C₂×D₈₃	semidirect
430. #121	C₂×D₈₃	semidirect
460. C₄×D₄	C₂×D₈₃	semidirect
467. #117	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128435	2
#19128434	2
#19128422	2
#19128419	2
#19128415	2
#19128414	2
#19128400	2
#19128396	2
#19128370	2
#19128369	2
#19128353	2
#19128350	2
#19128286	2
#19128284	2
#19128266	2
#19128253	2
#19128246	2
#19128214	2
#19128212	2
#19128211	2
#19128180	2
C₂×C₄×C₂²⋊D₈₃	2
#525×C₈₃	2
#3506	83