Subgroups — #24921149

Order 10624.

1328 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128381	C₂	1	2	yes	maximal, complemented
2	#19128379	C₂	1	2	yes	maximal, complemented
3	#19128376	C₂	1	2	yes	maximal, complemented
4	#19128376	C₂	1	2	yes	maximal, complemented
5	#19128348	C₂	1	2	yes	maximal, complemented
6	#19128344	C₂	1	2	yes	maximal, complemented
7	#19128343	C₂	1	2	yes	maximal, complemented
8	#19128340	C₂	1	2	yes	maximal, complemented
9	#19128326	C₂	1	1	yes	maximal, characteristic, complemented
10	#19128289	C₂	1	1	yes	maximal, characteristic, complemented
11	#19128286	C₂	1	2	yes	maximal, complemented
12	#19128259	C₂	1	1	yes	maximal, characteristic, complemented
13	#19128214	C₂	1	1	yes	maximal, characteristic, complemented
14	#19128211	C₂	1	1	yes	maximal, characteristic, complemented
15	#19128210	C₂	1	2	yes	maximal, complemented
16	#120×D₈₃	C₂	1	2	yes	maximal, complemented
17	#19128173	C₂	1	2	yes	maximal, complemented
18	C₂×C₂²⋊C₄×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#538×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₈₃	C₂²	1	1	yes	characteristic
21	C₂×#13050591	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13050590	C₂²	1	2	yes	complemented
23	C₂×#13050589	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₄×D₈₃	C₂²	1	2	yes	—
25	C₂×D₄×D₈₃	C₂²	1	2	yes	complemented
26	C₂×D₄×D₈₃	C₂²	1	2	yes	complemented
27	C₂²×C₄×D₈₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄×D₈₃	C₂²	1	1	yes	characteristic, complemented
29	#14581785	C₂²	1	2	yes	complemented
30	#14581785	C₂²	1	2	yes	complemented
31	#14581785	C₂²	1	2	yes	complemented
32	#14581779	C₂²	1	2	yes	complemented
33	#14581778	C₂²	1	2	yes	complemented
34	#14581778	C₂²	1	2	yes	complemented
35	#14581777	C₂²	1	2	yes	complemented
36	#14581777	C₂²	1	2	yes	complemented
37	#14581777	C₂²	1	2	yes	complemented
38	#14581774	C₂²	1	2	yes	complemented
39	#14581774	C₂²	1	2	yes	complemented
40	#14581774	C₂²	1	2	yes	complemented
41	#14581774	C₂²	1	2	yes	complemented
42	#14581774	C₂²	1	2	yes	complemented
43	#14581773	C₂²	1	2	yes	complemented
44	#14581772	C₂²	1	2	yes	complemented
45	#14581772	C₂²	1	1	yes	characteristic, complemented
46	#14581771	C₂²	1	1	yes	characteristic, complemented
47	#14581770	C₂²	1	2	yes	complemented
48	#14581770	C₂²	1	2	yes	complemented
49	#14581770	C₂²	1	2	yes	complemented
50	#14581769	C₂²	1	2	yes	complemented
51	#14581768	C₂²	1	2	yes	complemented
52	#14581768	C₂²	1	1	yes	characteristic, complemented
53	#14581767	C₂²	1	1	yes	characteristic, complemented
54	#14581766	C₂²	1	1	yes	characteristic, complemented
55	#14581765	C₂²	1	2	yes	complemented
56	#14581765	C₂²	1	2	yes	complemented
57	#14581764	C₂²	1	2	yes	complemented
58	#14581764	C₂²	1	2	yes	complemented
59	#14581763	C₂²	1	2	yes	complemented
60	#14581763	C₂²	1	1	yes	characteristic, complemented
61	#14581762	C₂²	1	2	yes	—
62	#14581762	C₂²	1	2	yes	—
63	#14581762	C₂²	1	2	yes	complemented
64	#14581762	C₂²	1	2	yes	complemented
65	#14581761	C₂²	1	2	yes	complemented
66	#14581760	C₂²	1	2	yes	—
67	#14581760	C₂²	1	2	yes	—
68	#14581760	C₂²	1	2	yes	complemented
69	#14581760	C₂²	1	2	yes	complemented
70	C₄×D₃₃₂	C₂²	1	2	yes	complemented
71	C₄×D₃₃₂	C₂²	1	2	yes	complemented
72	D₄×Dic₈₃	C₂²	1	2	yes	complemented
73	#14581754	C₂²	1	2	yes	complemented
74	#14581754	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
78	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
79	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
80	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
81	#14581750	C₂²	1	1	yes	characteristic, complemented
82	#14581750	C₂²	1	2	yes	complemented
83	#14581750	C₂²	1	1	yes	characteristic, complemented
84	#14581749	C₂²	1	2	yes	complemented
85	#14581749	C₂²	1	2	yes	complemented
86	C₂×C₂²⋊Dic₈₃	C₂²	1	1	yes	characteristic, complemented
87	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	1	yes	characteristic
88	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	1	yes	characteristic
89	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	2	yes	complemented
90	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	—
91	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
93	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
97	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
98	#126×C₈₃	C₂²	1	2	yes	complemented
99	#124×C₈₃	C₂²	1	2	yes	complemented
100	#123×C₈₃	C₂²	1	2	yes	complemented
101	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
102	#121×C₈₃	C₂²	1	2	yes	complemented
103	#121×C₈₃	C₂²	1	1	yes	characteristic, complemented
104	#120×C₈₃	C₂²	1	2	yes	complemented
105	C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₈₃	—	2	4	no	—
108	C₂³×D₈₃	—	4	2	no	—
109	C₂³×D₈₃	—	4	2	no	—
110	C₂³×D₈₃	C₂³	1	1	yes	characteristic
111	C₂³×D₈₃	C₂³	1	2	yes	—
112	C₂³×D₈₃	C₂³	1	2	yes	—
113	C₂³×D₈₃	C₂³	1	2	yes	—
114	C₂³×D₈₃	C₂³	1	1	yes	characteristic
115	#13050591	—	4	2	no	—
116	#13050590	—	4	4	no	—
117	#13050589	—	4	2	no	—
118	C₂×Dic₁₆₆	C₂³	1	2	yes	complemented
119	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic, complemented
120	C₂×D₃₃₂	C₂³	1	2	yes	—
121	C₂×D₃₃₂	C₂³	1	2	yes	—
122	C₂×D₃₃₂	C₂³	1	2	yes	—
123	C₂×D₃₃₂	C₂³	1	1	yes	characteristic, complemented
124	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	complemented
131	D₄×D₈₃	—	2	8	no	—
132	D₄×D₈₃	—	4	4	no	—
133	D₄×D₈₃	—	4	4	no	—
134	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
135	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
136	C₂²×Dic₈₃	C₂³	1	2	yes	complemented
137	C₂×C₄×D₈₃	—	4	2	no	—
138	C₂×C₄×D₈₃	—	4	2	no	—
139	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₈₃	C₂³	1	2	yes	—
141	C₂×C₄×D₈₃	C₂³	1	2	yes	—
142	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₈₃	C₂³	1	2	yes	—
145	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₈₃	C₂³	1	2	yes	—
147	C₂×C₄×D₈₃	C₂³	1	2	yes	—
148	C₂×C₄×D₈₃	C₂³	1	2	yes	complemented
149	C₂×C₄×D₈₃	C₂³	1	2	yes	complemented
150	C₄⋊Dic₈₃	C₂³	1	2	yes	complemented
151	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic, complemented
152	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic, complemented
153	C₄⋊Dic₈₃	C₂³	1	2	yes	complemented
154	Dic₈₃⋊C₄	C₂³	1	2	yes	complemented
155	Dic₈₃⋊C₄	C₂³	1	2	yes	complemented
156	Dic₈₃⋊C₄	C₂³	1	2	yes	complemented
157	Dic₈₃⋊C₄	C₂³	1	2	yes	complemented
158	Dic₈₃⋊C₄	C₂³	1	2	yes	complemented
159	Dic₈₃⋊C₄	C₂³	1	2	yes	complemented
160	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
161	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
162	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
163	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
164	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
165	C₂²⋊Dic₈₃	C₂³	1	2	yes	complemented
166	C₂²⋊Dic₈₃	C₂³	1	2	yes	complemented
167	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	complemented
178	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	complemented
179	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	complemented
180	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	complemented
181	C₄×Dic₈₃	C₂³	1	2	yes	complemented
182	C₄×Dic₈₃	C₂³	1	2	yes	complemented
183	C₄×Dic₈₃	C₂³	1	2	yes	complemented
184	C₂⁴×C₈₃	C₂³	1	1	yes	characteristic
185	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic, complemented
186	C₂×D₄×C₈₃	C₂³	1	2	yes	—
187	C₂×D₄×C₈₃	C₂³	1	2	yes	—
188	C₂×D₄×C₈₃	C₂³	1	2	yes	—
189	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic, complemented
190	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
191	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
192	C₂²×C₄×C₈₃	C₂³	1	2	yes	complemented
193	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic, complemented
194	C₄⋊C₄×C₈₃	C₂³	1	2	yes	complemented
195	C₄⋊C₄×C₈₃	C₂³	1	2	yes	complemented
196	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic, complemented
197	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
201	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
202	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	complemented
203	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	complemented
204	C₄²×C₈₃	C₂³	1	2	yes	complemented
205	C₂³×C₈₃	—	2	2	no	—
206	C₂³×C₈₃	—	4	1	no	—
207	C₂³×C₈₃	—	4	1	no	—
208	C₂³×C₈₃	C₂⁴	1	2	yes	—
209	C₂³×C₈₃	C₂⁴	1	2	yes	—
210	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
211	C₂²×D₈₃	—	2	2	no	—
212	C₂²×D₈₃	—	2	2	no	—
213	C₂²×D₈₃	—	2	2	no	—
214	C₂²×D₈₃	—	2	4	no	—
215	C₂²×D₈₃	—	2	4	no	—
216	C₂²×D₈₃	—	2	4	no	—
217	C₂²×D₈₃	—	2	4	no	—
218	C₂²×D₈₃	—	2	4	no	—
219	C₂²×D₈₃	—	4	2	no	—
220	C₂²×D₈₃	—	4	2	no	—
221	C₂²×D₈₃	—	4	1	no	—
222	C₂²×D₈₃	—	4	1	no	—
223	C₂²×D₈₃	—	4	2	no	—
224	C₂²×D₈₃	—	4	2	no	—
225	C₂²×D₈₃	—	4	16	no	—
226	C₂²×D₈₃	#41	1	4	yes	complemented
227	C₂²×D₈₃	C₂⁴	1	2	yes	—
228	C₂²×D₈₃	C₂⁴	1	2	yes	—
229	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
230	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
231	Q₈×C₈₃	—	4	1	no	—
232	D₄×C₈₃	—	2	4	no	—
233	D₄×C₈₃	—	4	2	no	—
234	D₄×C₈₃	—	4	2	no	—
235	D₄×C₈₃	—	4	1	no	—
236	C₂×C₄×C₈₃	—	4	1	no	—
237	C₂×C₄×C₈₃	—	4	1	no	—
238	C₂×C₄×C₈₃	—	4	2	no	—
239	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
240	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
241	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
242	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
245	C₂²⋊D₈₃	—	2	4	no	—
246	C₂²⋊D₈₃	—	2	4	no	—
247	C₂²⋊D₈₃	—	2	4	no	—
248	C₂²⋊D₈₃	—	2	4	no	—
249	C₂²⋊D₈₃	—	4	2	no	—
250	C₂²⋊D₈₃	—	4	2	no	—
251	C₂²⋊D₈₃	—	4	2	no	—
252	C₂×Dic₈₃	—	4	1	no	—
253	C₂×Dic₈₃	—	4	1	no	—
254	C₂×Dic₈₃	—	4	2	no	—
255	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₈₃	C₂⁴	1	2	yes	—
257	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₈₃	C₂⁴	1	2	yes	—
259	C₂×Dic₈₃	C₂⁴	1	2	yes	—
260	C₂×Dic₈₃	C₂⁴	1	2	yes	—
261	D₃₃₂	—	2	4	no	—
262	D₃₃₂	—	2	4	no	—
263	D₃₃₂	—	2	4	no	—
264	D₃₃₂	—	4	1	no	—
265	C₄×D₈₃	—	2	4	no	—
266	C₄×D₈₃	—	2	2	no	—
267	C₄×D₈₃	—	2	4	no	—
268	C₄×D₈₃	—	2	2	no	—
269	C₄×D₈₃	—	4	2	no	—
270	C₄×D₈₃	—	4	1	no	—
271	C₄×D₈₃	—	4	1	no	—
272	C₄×D₈₃	—	4	2	no	—
273	C₄×D₈₃	—	4	2	no	—
274	C₄×D₈₃	—	4	2	no	—
275	C₄×D₈₃	—	4	2	no	—
276	Dic₁₆₆	—	4	1	no	—
277	Dic₁₆₆	—	4	2	no	—
278	C₂²×C₈₃	—	2	1	no	—
279	C₂²×C₈₃	—	2	1	no	—
280	C₂²×C₈₃	—	2	2	no	—
281	C₂²×C₈₃	—	2	2	no	—
282	C₂²×C₈₃	—	2	2	no	—
283	C₂²×C₈₃	—	2	2	no	—
284	C₂²×C₈₃	—	2	2	no	—
285	C₂²×C₈₃	—	2	2	no	—
286	C₂²×C₈₃	—	4	4	no	—
287	C₂²×C₈₃	C₂×#41	1	2	yes	—
288	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
289	C₂×D₈₃	—	2	8	no	—
290	C₂×D₈₃	—	2	1	no	—
291	C₂×D₈₃	—	2	1	no	—
292	C₂×D₈₃	—	2	1	no	—
293	C₂×D₈₃	—	2	1	no	—
294	C₂×D₈₃	—	2	2	no	—
295	C₂×D₈₃	—	2	2	no	—
296	C₂×D₈₃	—	2	2	no	—
297	C₂×D₈₃	—	2	2	no	—
298	C₂×D₈₃	—	2	2	no	—
299	C₂×D₈₃	—	4	4	no	—
300	C₂×D₈₃	—	4	8	no	—
301	C₂×D₈₃	—	4	8	no	—
302	C₂×D₈₃	—	8	4	no	—
303	C₂×D₈₃	C₂×#41	1	4	yes	—
304	C₂×D₈₃	H(5,𝔽₂)	1	2	yes	—
305	C₂×D₈₃	H(5,𝔽₂)	1	2	yes	—
306	C₄×C₈₃	—	2	2	no	—
307	C₄×C₈₃	—	2	1	no	—
308	C₄×C₈₃	—	2	2	no	—
309	C₄×C₈₃	—	2	2	no	—
310	C₄×C₈₃	—	2	1	no	—
311	C₄×C₈₃	—	2	2	no	—
312	Dic₈₃	—	2	2	no	—
313	Dic₈₃	—	2	2	no	—
314	Dic₈₃	—	2	2	no	—
315	Dic₈₃	—	2	2	no	—
316	Dic₈₃	—	2	1	no	—
317	Dic₈₃	—	2	1	no	—
318	C₂×C₈₃	—	2	2	no	—
319	C₂×C₈₃	—	4	2	no	—
320	C₂×C₈₃	—	4	2	no	—
321	C₂×C₈₃	C₂²×#41	1	1	yes	characteristic
322	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	D₈₃	—	2	2	no	—
325	D₈₃	—	2	2	no	—
326	D₈₃	—	2	4	no	—
327	D₈₃	—	4	2	no	—
328	#3490	—	83	1	no	maximal, Sylow
329	C₈₃	#3490	1	1	yes	characteristic, complemented, Sylow
330	#551	—	83	2	no	—
331	#551	—	83	2	no	—
332	#551	—	83	2	no	—
333	#551	—	83	2	no	—
334	#546	—	83	2	no	—
335	#546	—	83	2	no	—
336	#546	—	83	2	no	—
337	#546	—	83	2	no	—
338	#543	—	83	1	no	—
339	#538	—	83	2	no	—
340	#538	—	83	1	no	—
341	#538	D₈₃	1	1	yes	characteristic, complemented
342	#534	—	83	1	no	—
343	#525	—	83	1	no	—
344	#525	—	83	1	no	—
345	#525	—	83	2	no	—
346	C₂×#120	—	83	2	no	—
347	#518	—	83	2	no	—
348	C₂²×C₂²⋊C₄	—	83	1	no	—
349	C₂⁵	—	83	1	no	—
350	C₂×#41	—	83	1	no	—
351	C₂×#41	—	83	1	no	—
352	C₂×#41	—	83	2	no	—
353	C₂²×D₄	—	83	2	no	—
354	C₂²×D₄	—	83	2	no	—
355	C₂²×D₄	—	83	2	no	—
356	C₂³×C₄	—	83	1	no	—
357	C₂³×C₄	—	83	1	no	—
358	#126	—	83	2	no	—
359	#126	—	83	2	no	—
360	#126	—	83	2	no	—
361	#126	C₂×D₈₃	1	2	yes	complemented
362	#124	—	83	2	no	—
363	#124	—	83	2	no	—
364	#124	—	83	2	no	—
365	#124	C₂×D₈₃	1	2	yes	complemented
366	#123	—	83	2	no	—
367	#123	—	83	2	no	—
368	#123	—	83	2	no	—
369	#123	—	83	2	no	—
370	#123	—	83	2	no	—
371	#123	—	83	2	no	—
372	#123	—	83	2	no	—
373	#123	—	83	2	no	—
374	#123	—	83	2	no	—
375	#123	C₂×D₈₃	1	2	yes	complemented
376	C₂²⋊Q₈	—	83	1	no	—
377	C₂²⋊Q₈	—	83	2	no	—
378	C₂²⋊Q₈	—	83	1	no	—
379	C₂²⋊Q₈	—	83	2	no	—
380	C₂²⋊Q₈	—	83	2	no	—
381	C₂²⋊Q₈	—	83	2	no	—
382	C₂²⋊Q₈	—	83	1	no	—
383	C₂²⋊Q₈	—	83	2	no	—
384	C₂²⋊Q₈	—	83	2	no	—
385	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
386	#121	—	83	2	no	—
387	#121	—	83	2	no	—
388	#121	—	83	2	no	—
389	#121	—	83	1	no	—
390	#121	—	83	1	no	—
391	#121	—	83	1	no	—
392	#121	—	83	2	no	—
393	#121	—	83	2	no	—
394	#121	C₂×D₈₃	1	2	yes	complemented
395	#121	C₂×D₈₃	1	1	yes	characteristic, complemented
396	#120	—	83	2	no	—
397	#120	—	83	2	no	—
398	#120	—	83	2	no	—
399	#120	—	83	2	no	—
400	#120	—	83	2	no	—
401	#120	—	83	2	no	—
402	#120	—	83	2	no	—
403	#120	—	83	2	no	—
404	#120	—	83	2	no	—
405	#120	C₂×D₈₃	1	2	yes	complemented
406	C₄×D₄	—	83	2	no	—
407	C₄×D₄	—	83	2	no	—
408	C₄×D₄	—	83	2	no	—
409	C₄×D₄	—	83	2	no	—
410	C₄×D₄	—	83	2	no	—
411	C₄×D₄	—	83	2	no	—
412	C₄×D₄	—	83	2	no	—
413	C₄×D₄	—	83	2	no	—
414	C₄×D₄	—	83	2	no	—
415	C₄×D₄	—	83	2	no	—
416	C₄×D₄	—	83	2	no	—
417	C₄×D₄	C₂×D₈₃	1	2	yes	complemented
418	#117	—	83	2	no	—
419	#117	—	83	1	no	—
420	#117	—	83	1	no	—
421	#117	—	83	2	no	—
422	#117	—	83	2	no	—
423	C₂×C₂²⋊C₄	—	83	1	no	—
424	C₂×C₂²⋊C₄	—	83	1	no	—
425	C₂×C₂²⋊C₄	—	83	1	no	—
426	C₂×C₂²⋊C₄	—	83	2	no	—
427	C₂×C₂²⋊C₄	—	83	2	no	—
428	C₂×C₂²⋊C₄	—	83	2	no	—
429	C₂×C₂²⋊C₄	—	83	2	no	—
430	C₂×C₂²⋊C₄	—	83	2	no	—
431	C₂×C₂²⋊C₄	—	83	2	no	—
432	C₂×C₂²⋊C₄	—	83	2	no	—
433	C₂×C₂²⋊C₄	—	83	2	no	—
434	C₂×C₂²⋊C₄	—	83	2	no	—
435	C₂×C₂²⋊C₄	C₂×D₈₃	1	1	yes	characteristic, complemented
436	C₂⁴	—	332	2	no	—
437	C₂⁴	—	332	2	no	—
438	C₂⁴	—	83	1	no	—
439	C₂⁴	—	83	2	no	—
440	C₂⁴	—	83	2	no	—
441	C₂⁴	—	83	2	no	—
442	C₂⁴	—	83	1	no	—
443	C₂⁴	—	166	4	no	—
444	C₂⁴	C₂²×D₈₃	1	1	yes	characteristic
445	#41	—	332	4	no	—
446	#41	—	332	2	no	—
447	#41	—	332	2	no	—
448	C₂×Q₈	—	83	1	no	—
449	C₂×Q₈	—	83	2	no	—
450	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic, complemented
451	C₂×D₄	—	332	4	no	—
452	C₂×D₄	—	332	4	no	—
453	C₂×D₄	—	83	2	no	—
454	C₂×D₄	—	83	2	no	—
455	C₂×D₄	—	83	2	no	—
456	C₂×D₄	—	83	2	no	—
457	C₂×D₄	—	83	2	no	—
458	C₂×D₄	—	83	2	no	—
459	C₂×D₄	—	83	2	no	—
460	C₂×D₄	—	83	1	no	—
461	C₂×D₄	—	83	2	no	—
462	C₂×D₄	—	83	2	no	—
463	C₂×D₄	—	83	2	no	—
464	C₂×D₄	—	166	8	no	—
465	C₂×D₄	C₂²×D₈₃	1	2	yes	—
466	C₂×D₄	C₂²×D₈₃	1	2	yes	—
467	C₂×D₄	C₂²×D₈₃	1	2	yes	—
468	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic, complemented
469	C₂²×C₄	—	332	2	no	—
470	C₂²×C₄	—	332	2	no	—
471	C₂²×C₄	—	83	1	no	—
472	C₂²×C₄	—	83	1	no	—
473	C₂²×C₄	—	83	2	no	—
474	C₂²×C₄	—	83	1	no	—
475	C₂²×C₄	—	83	1	no	—
476	C₂²×C₄	—	83	2	no	—
477	C₂²×C₄	—	83	2	no	—
478	C₂²×C₄	—	83	2	no	—
479	C₂²×C₄	—	83	2	no	—
480	C₂²×C₄	—	83	2	no	—
481	C₂²×C₄	—	83	2	no	—
482	C₂²×C₄	—	83	1	no	—
483	C₂²×C₄	—	83	1	no	—
484	C₂²×C₄	—	83	2	no	—
485	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₈₃	1	2	yes	complemented
488	C₄⋊C₄	—	83	2	no	—
489	C₄⋊C₄	—	83	2	no	—
490	C₄⋊C₄	—	83	2	no	—
491	C₄⋊C₄	—	83	2	no	—
492	C₄⋊C₄	—	83	1	no	—
493	C₄⋊C₄	—	83	2	no	—
494	C₄⋊C₄	—	83	1	no	—
495	C₄⋊C₄	—	83	2	no	—
496	C₄⋊C₄	—	83	2	no	—
497	C₄⋊C₄	—	83	2	no	—
498	C₄⋊C₄	C₂²×D₈₃	1	2	yes	complemented
499	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic, complemented
500	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic, complemented
501	C₄⋊C₄	C₂²×D₈₃	1	2	yes	complemented
502	C₂²⋊C₄	—	83	2	no	—
503	C₂²⋊C₄	—	83	2	no	—
504	C₂²⋊C₄	—	83	2	no	—
505	C₂²⋊C₄	—	83	2	no	—
506	C₂²⋊C₄	—	83	2	no	—
507	C₂²⋊C₄	—	83	2	no	—
508	C₂²⋊C₄	—	83	2	no	—
509	C₂²⋊C₄	—	83	2	no	—
510	C₂²⋊C₄	—	83	2	no	—
511	C₂²⋊C₄	—	83	2	no	—
512	C₂²⋊C₄	—	83	2	no	—
513	C₂²⋊C₄	—	83	2	no	—
514	C₂²⋊C₄	—	83	2	no	—
515	C₂²⋊C₄	—	83	2	no	—
516	C₂²⋊C₄	—	83	2	no	—
517	C₂²⋊C₄	—	83	2	no	—
518	C₂²⋊C₄	—	83	2	no	—
519	C₂²⋊C₄	—	83	2	no	—
520	C₂²⋊C₄	—	83	2	no	—
521	C₂²⋊C₄	—	83	2	no	—
522	C₂²⋊C₄	—	83	2	no	—
523	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	complemented
529	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	complemented
530	C₄²	—	83	2	no	—
531	C₄²	—	83	2	no	—
532	C₄²	—	83	2	no	—
533	C₄²	C₂²×D₈₃	1	2	yes	complemented
534	C₂³	—	2	2	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	332	1	no	—
538	C₂³	—	332	1	no	—
539	C₂³	—	332	2	no	—
540	C₂³	—	332	2	no	—
541	C₂³	—	332	2	no	—
542	C₂³	—	332	2	no	—
543	C₂³	—	332	16	no	—
544	C₂³	—	83	4	no	—
545	C₂³	—	83	2	no	—
546	C₂³	—	83	1	no	—
547	C₂³	—	83	1	no	—
548	C₂³	—	83	2	no	—
549	C₂³	—	166	4	no	—
550	C₂³	—	166	4	no	—
551	C₂³	—	166	4	no	—
552	C₂³	—	166	4	no	—
553	C₂³	—	166	4	no	—
554	C₂³	—	166	2	no	—
555	C₂³	—	166	2	no	—
556	C₂³	—	166	2	no	—
557	C₂³	C₂³×D₈₃	1	2	yes	—
558	C₂³	C₂³×D₈₃	1	2	yes	—
559	C₂³	C₂³×D₈₃	1	1	yes	characteristic
560	Q₈	—	4	1	no	—
561	Q₈	—	332	1	no	—
562	Q₈	—	332	2	no	—
563	D₄	—	2	4	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	2	no	—
566	D₄	—	4	1	no	—
567	D₄	—	332	1	no	—
568	D₄	—	332	2	no	—
569	D₄	—	332	2	no	—
570	D₄	—	332	2	no	—
571	D₄	—	166	4	no	—
572	D₄	—	166	4	no	—
573	D₄	—	166	4	no	—
574	D₄	—	166	4	no	—
575	D₄	—	166	4	no	—
576	D₄	—	166	4	no	—
577	D₄	—	166	4	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	332	2	no	—
582	C₂×C₄	—	332	1	no	—
583	C₂×C₄	—	332	1	no	—
584	C₂×C₄	—	332	2	no	—
585	C₂×C₄	—	332	2	no	—
586	C₂×C₄	—	332	2	no	—
587	C₂×C₄	—	332	2	no	—
588	C₂×C₄	—	332	1	no	—
589	C₂×C₄	—	332	1	no	—
590	C₂×C₄	—	332	2	no	—
591	C₂×C₄	—	83	2	no	—
592	C₂×C₄	—	83	1	no	—
593	C₂×C₄	—	83	1	no	—
594	C₂×C₄	—	83	2	no	—
595	C₂×C₄	—	83	2	no	—
596	C₂×C₄	—	83	2	no	—
597	C₂×C₄	—	166	4	no	—
598	C₂×C₄	—	166	2	no	—
599	C₂×C₄	—	166	2	no	—
600	C₂×C₄	—	166	4	no	—
601	C₂×C₄	C₂³×D₈₃	1	2	yes	—
602	C₂×C₄	C₂³×D₈₃	1	2	yes	—
603	C₂×C₄	C₂³×D₈₃	1	2	yes	—
604	C₂×C₄	C₂³×D₈₃	1	2	yes	—
605	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	332	4	no	—
617	C₂²	—	332	8	no	—
618	C₂²	—	332	8	no	—
619	C₂²	—	83	4	no	—
620	C₂²	—	83	2	no	—
621	C₂²	—	83	2	no	—
622	C₂²	—	664	4	no	—
623	C₂²	—	166	8	no	—
624	C₂²	—	166	2	no	—
625	C₂²	—	166	2	no	—
626	C₂²	—	166	2	no	—
627	C₂²	—	166	1	no	—
628	C₂²	—	166	1	no	—
629	C₂²	—	166	1	no	—
630	C₂²	—	166	1	no	—
631	C₂²	—	166	2	no	—
632	C₂²	—	166	2	no	—
633	C₂²	#41×D₈₃	1	2	yes	—
634	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	166	2	no	—
642	C₄	—	166	1	no	—
643	C₄	—	166	1	no	—
644	C₄	—	166	2	no	—
645	C₄	—	166	2	no	—
646	C₄	—	166	2	no	—
647	C₂	—	2	2	no	—
648	C₂	—	4	2	no	—
649	C₂	—	4	2	no	—
650	C₂	—	332	2	no	—
651	C₂	—	166	4	no	—
652	C₂	—	166	2	no	—
653	C₂	—	166	2	no	—
654	C₂	C₂×#41×D₈₃	1	1	yes	characteristic
655	C₂	H(5,𝔽₂)×D₈₃	1	1	yes	characteristic
656	C₂	H(5,𝔽₂)×D₈₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#538×C₈₃	C₂
hypercenter	#538	D₈₃
hypocenter	C₈₃	#3490
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #19128381	C₂	semidirect
2. #19128379	C₂	semidirect
3. #19128376	C₂	semidirect
4. #19128376	C₂	semidirect
5. #19128348	C₂	semidirect
6. #19128344	C₂	semidirect
7. #19128343	C₂	semidirect
8. #19128340	C₂	semidirect
9. #19128326	C₂	semidirect
10. #19128289	C₂	semidirect
11. #19128286	C₂	semidirect
12. #19128259	C₂	semidirect
13. #19128214	C₂	semidirect
14. #19128211	C₂	semidirect
15. #19128210	C₂	semidirect
16. #120×D₈₃	C₂	semidirect
17. #19128173	C₂	semidirect
18. C₂×C₂²⋊C₄×D₈₃	C₂	semidirect
19. #538×C₈₃	C₂	semidirect
21. C₂×#13050591	C₂²	semidirect
22. C₂×#13050590	C₂²	semidirect
23. C₂×#13050589	C₂²	semidirect
25. C₂×D₄×D₈₃	C₂²	semidirect
26. C₂×D₄×D₈₃	C₂²	semidirect
27. C₂²×C₄×D₈₃	C₂²	semidirect
28. C₂²×C₄×D₈₃	C₂²	semidirect
29. #14581785	C₂²	semidirect
30. #14581785	C₂²	semidirect
31. #14581785	C₂²	semidirect
32. #14581779	C₂²	semidirect
33. #14581778	C₂²	semidirect
34. #14581778	C₂²	semidirect
35. #14581777	C₂²	semidirect
36. #14581777	C₂²	semidirect
37. #14581777	C₂²	semidirect
38. #14581774	C₂²	semidirect
39. #14581774	C₂²	semidirect
40. #14581774	C₂²	semidirect
41. #14581774	C₂²	semidirect
42. #14581774	C₂²	semidirect
43. #14581773	C₂²	semidirect
44. #14581772	C₂²	semidirect
45. #14581772	C₂²	semidirect
46. #14581771	C₂²	semidirect
47. #14581770	C₂²	semidirect
48. #14581770	C₂²	semidirect
49. #14581770	C₂²	semidirect
50. #14581769	C₂²	semidirect
51. #14581768	C₂²	semidirect
52. #14581768	C₂²	semidirect
53. #14581767	C₂²	semidirect
54. #14581766	C₂²	semidirect
55. #14581765	C₂²	semidirect
56. #14581765	C₂²	semidirect
57. #14581764	C₂²	semidirect
58. #14581764	C₂²	semidirect
59. #14581763	C₂²	semidirect
60. #14581763	C₂²	semidirect
63. #14581762	C₂²	semidirect
64. #14581762	C₂²	semidirect
65. #14581761	C₂²	semidirect
68. #14581760	C₂²	semidirect
69. #14581760	C₂²	semidirect
70. C₄×D₃₃₂	C₂²	semidirect
71. C₄×D₃₃₂	C₂²	semidirect
72. D₄×Dic₈₃	C₂²	semidirect
73. #14581754	C₂²	semidirect
74. #14581754	C₂²	semidirect
75. C₄×C₂²⋊D₈₃	C₂²	semidirect
76. C₄×C₂²⋊D₈₃	C₂²	semidirect
77. C₄×C₂²⋊D₈₃	C₂²	semidirect
78. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
79. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
80. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
81. #14581750	C₂²	semidirect
82. #14581750	C₂²	semidirect
83. #14581750	C₂²	semidirect
84. #14581749	C₂²	semidirect
85. #14581749	C₂²	semidirect
86. C₂×C₂²⋊Dic₈₃	C₂²	semidirect
89. C₂×(C₂×D₈₃)⋊C₄	C₂²	semidirect
91. C₂²⋊C₄×D₈₃	C₂²	semidirect
92. C₂²⋊C₄×D₈₃	C₂²	semidirect
93. C₂²⋊C₄×D₈₃	C₂²	semidirect
94. C₂²⋊C₄×D₈₃	C₂²	semidirect
95. C₂²⋊C₄×D₈₃	C₂²	semidirect
96. C₂²⋊C₄×D₈₃	C₂²	semidirect
97. C₂²⋊C₄×D₈₃	C₂²	semidirect
98. #126×C₈₃	C₂²	semidirect
99. #124×C₈₃	C₂²	semidirect
100. #123×C₈₃	C₂²	semidirect
101. C₂²⋊Q₈×C₈₃	C₂²	semidirect
102. #121×C₈₃	C₂²	semidirect
103. #121×C₈₃	C₂²	semidirect
104. #120×C₈₃	C₂²	semidirect
105. C₄×D₄×C₈₃	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₈₃	C₂²	semidirect
118. C₂×Dic₁₆₆	C₂³	semidirect
119. C₂×Dic₁₆₆	C₂³	semidirect
123. C₂×D₃₃₂	C₂³	semidirect
130. C₂×C₂²⋊D₈₃	C₂³	semidirect
136. C₂²×Dic₈₃	C₂³	semidirect
148. C₂×C₄×D₈₃	C₂³	semidirect
149. C₂×C₄×D₈₃	C₂³	semidirect
150. C₄⋊Dic₈₃	C₂³	semidirect
151. C₄⋊Dic₈₃	C₂³	semidirect
152. C₄⋊Dic₈₃	C₂³	semidirect
153. C₄⋊Dic₈₃	C₂³	semidirect
154. Dic₈₃⋊C₄	C₂³	semidirect
155. Dic₈₃⋊C₄	C₂³	semidirect
156. Dic₈₃⋊C₄	C₂³	semidirect
157. Dic₈₃⋊C₄	C₂³	semidirect
158. Dic₈₃⋊C₄	C₂³	semidirect
159. Dic₈₃⋊C₄	C₂³	semidirect
165. C₂²⋊Dic₈₃	C₂³	semidirect
166. C₂²⋊Dic₈₃	C₂³	semidirect
177. (C₂×D₈₃)⋊C₄	C₂³	semidirect
178. (C₂×D₈₃)⋊C₄	C₂³	semidirect
179. (C₂×D₈₃)⋊C₄	C₂³	semidirect
180. (C₂×D₈₃)⋊C₄	C₂³	semidirect
181. C₄×Dic₈₃	C₂³	semidirect
182. C₄×Dic₈₃	C₂³	semidirect
183. C₄×Dic₈₃	C₂³	semidirect
185. C₂×Q₈×C₈₃	C₂³	semidirect
189. C₂×D₄×C₈₃	C₂³	semidirect
192. C₂²×C₄×C₈₃	C₂³	semidirect
193. C₄⋊C₄×C₈₃	C₂³	semidirect
194. C₄⋊C₄×C₈₃	C₂³	semidirect
195. C₄⋊C₄×C₈₃	C₂³	semidirect
196. C₄⋊C₄×C₈₃	C₂³	semidirect
202. C₂²⋊C₄×C₈₃	C₂³	semidirect
203. C₂²⋊C₄×C₈₃	C₂³	semidirect
204. C₄²×C₈₃	C₂³	semidirect
226. C₂²×D₈₃	#41	semidirect
329. C₈₃	#3490	semidirect
341. #538	D₈₃	semidirect
361. #126	C₂×D₈₃	semidirect
365. #124	C₂×D₈₃	semidirect
375. #123	C₂×D₈₃	semidirect
385. C₂²⋊Q₈	C₂×D₈₃	semidirect
394. #121	C₂×D₈₃	semidirect
395. #121	C₂×D₈₃	semidirect
405. #120	C₂×D₈₃	semidirect
417. C₄×D₄	C₂×D₈₃	semidirect
435. C₂×C₂²⋊C₄	C₂×D₈₃	semidirect
450. C₂×Q₈	C₂²×D₈₃	semidirect
468. C₂×D₄	C₂²×D₈₃	semidirect
487. C₂²×C₄	C₂²×D₈₃	semidirect
498. C₄⋊C₄	C₂²×D₈₃	semidirect
499. C₄⋊C₄	C₂²×D₈₃	semidirect
500. C₄⋊C₄	C₂²×D₈₃	semidirect
501. C₄⋊C₄	C₂²×D₈₃	semidirect
528. C₂²⋊C₄	C₂²×D₈₃	semidirect
529. C₂²⋊C₄	C₂²×D₈₃	semidirect
533. C₄²	C₂²×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128381	2
#19128379	2
#19128376	2
#19128348	2
#19128344	2
#19128343	2
#19128340	2
#19128326	2
#19128289	2
#19128286	2
#19128259	2
#19128214	2
#19128211	2
#19128210	2
#120×D₈₃	2
#19128173	2
C₂×C₂²⋊C₄×D₈₃	2
#538×C₈₃	2
#3490	83