Subgroups — #24921420

Order 10624.

1142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128434	C₂	1	1	yes	maximal, characteristic, complemented
2	#19128419	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128414	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128381	C₂	1	2	yes	maximal, complemented
5	#19128375	C₂	1	2	yes	maximal, complemented
6	#19128366	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128359	C₂	1	2	yes	maximal, complemented
8	#19128348	C₂	1	1	yes	maximal, characteristic, complemented
9	#19128347	C₂	1	1	yes	maximal, characteristic, complemented
10	#19128340	C₂	1	2	yes	maximal, complemented
11	#19128335	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128325	C₂	1	1	yes	maximal, characteristic, complemented
13	#19128318	C₂	1	1	yes	maximal, characteristic, complemented
14	#19128285	C₂	1	2	yes	maximal, complemented
15	#19128283	C₂	1	2	yes	maximal, complemented
16	#19128246	C₂	1	1	yes	maximal, characteristic, complemented
17	#19128231	C₂	1	1	yes	maximal, characteristic, complemented
18	#19128229	C₂	1	2	yes	maximal, complemented
19	#124×D₈₃	C₂	1	2	yes	maximal, complemented
20	#19128175	C₂	1	1	yes	maximal, characteristic, complemented
21	#19128173	C₂	1	1	yes	maximal, characteristic, complemented
22	#19128169	C₂	1	1	yes	maximal, characteristic, complemented
23	#555×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13050590	C₂²	1	1	yes	characteristic
25	C₂×#13050589	C₂²	1	2	yes	complemented
26	C₂×Q₈×D₈₃	C₂²	1	2	yes	complemented
27	C₂²×D₃₃₂	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₈₃	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₈₃	C₂²	1	2	yes	—
30	#14581791	C₂²	1	1	yes	characteristic, complemented
31	#14581791	C₂²	1	1	yes	characteristic, complemented
32	#14581788	C₂²	1	1	yes	characteristic
33	#14581787	C₂²	1	2	yes	complemented
34	#14581787	C₂²	1	1	yes	characteristic, complemented
35	#14581786	C₂²	1	2	yes	complemented
36	#14581785	C₂²	1	1	yes	characteristic, complemented
37	#14581785	C₂²	1	2	yes	complemented
38	#14581785	C₂²	1	2	yes	complemented
39	#14581782	C₂²	1	1	yes	characteristic, complemented
40	#14581781	C₂²	1	2	yes	complemented
41	#14581780	C₂²	1	1	yes	characteristic, complemented
42	#14581780	C₂²	1	2	yes	complemented
43	#14581779	C₂²	1	1	yes	characteristic, complemented
44	#14581779	C₂²	1	2	yes	complemented
45	#14581778	C₂²	1	2	yes	—
46	#14581778	C₂²	1	1	yes	characteristic
47	#14581778	C₂²	1	2	yes	complemented
48	#14581778	C₂²	1	2	yes	complemented
49	#14581778	C₂²	1	2	yes	complemented
50	#14581777	C₂²	1	2	yes	complemented
51	#14581777	C₂²	1	2	yes	complemented
52	#14581776	C₂²	1	1	yes	characteristic, complemented
53	#14581775	C₂²	1	2	yes	complemented
54	#14581774	C₂²	1	2	yes	complemented
55	#14581774	C₂²	1	2	yes	complemented
56	#14581773	C₂²	1	2	yes	complemented
57	#14581773	C₂²	1	1	yes	characteristic, complemented
58	#14581772	C₂²	1	1	yes	characteristic, complemented
59	#14581771	C₂²	1	1	yes	characteristic, complemented
60	#14581770	C₂²	1	2	yes	complemented
61	#14581770	C₂²	1	2	yes	complemented
62	#14581769	C₂²	1	1	yes	characteristic, complemented
63	#14581769	C₂²	1	2	yes	complemented
64	#14581768	C₂²	1	2	yes	complemented
65	#14581768	C₂²	1	2	yes	complemented
66	#14581767	C₂²	1	1	yes	characteristic
67	#14581766	C₂²	1	1	yes	characteristic, complemented
68	#14581765	C₂²	1	2	yes	—
69	#14581765	C₂²	1	2	yes	complemented
70	#14581765	C₂²	1	2	yes	complemented
71	#14581764	C₂²	1	1	yes	characteristic
72	#14581764	C₂²	1	2	yes	complemented
73	#14581763	C₂²	1	2	yes	complemented
74	#14581762	C₂²	1	2	yes	—
75	#14581760	C₂²	1	2	yes	—
76	#14581760	C₂²	1	2	yes	complemented
77	#14581760	C₂²	1	2	yes	complemented
78	C₄×Dic₁₆₆	C₂²	1	2	yes	complemented
79	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
80	#14581757	C₂²	1	1	yes	characteristic, complemented
81	#14581757	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₃₃₂	C₂²	1	1	yes	characteristic
83	C₄×D₃₃₂	C₂²	1	2	yes	complemented
84	C₄×D₃₃₂	C₂²	1	2	yes	complemented
85	D₄×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
86	#14581754	C₂²	1	1	yes	characteristic
87	#14581754	C₂²	1	1	yes	characteristic
88	#14581754	C₂²	1	1	yes	characteristic
89	#14581754	C₂²	1	1	yes	characteristic, complemented
90	#14581754	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
95	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
96	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
97	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
98	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
99	#14581751	C₂²	1	1	yes	characteristic, complemented
100	#14581750	C₂²	1	1	yes	characteristic, complemented
101	#14581749	C₂²	1	1	yes	characteristic, complemented
102	#14581749	C₂²	1	2	yes	complemented
103	#14581749	C₂²	1	2	yes	complemented
104	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
110	C₂×C₄×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₈₃	C₂²	1	2	yes	complemented
112	C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
113	#124×C₈₃	C₂²	1	2	yes	complemented
114	#124×C₈₃	C₂²	1	2	yes	complemented
115	#121×C₈₃	C₂²	1	1	yes	characteristic
116	#121×C₈₃	C₂²	1	2	yes	complemented
117	#121×C₈₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
120	#117×C₈₃	C₂²	1	2	yes	complemented
121	#117×C₈₃	C₂²	1	1	yes	characteristic, complemented
122	#117×C₈₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₈₃	C₂³	1	2	yes	—
124	C₂³×D₈₃	C₂³	1	2	yes	—
125	#13050590	—	2	4	no	—
126	#13050589	—	4	4	no	—
127	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₆₆	C₂³	1	2	yes	—
129	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₆₆	C₂³	1	2	yes	—
131	Q₈×D₈₃	—	4	4	no	—
132	C₂×D₃₃₂	—	2	4	no	—
133	C₂×D₃₃₂	C₂³	1	2	yes	—
134	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
135	C₂×D₃₃₂	C₂³	1	2	yes	—
136	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
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	1	yes	characteristic
143	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
144	D₄×D₈₃	—	2	4	no	—
145	D₄×D₈₃	—	4	4	no	—
146	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
147	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
148	C₂²×Dic₈₃	C₂³	1	2	yes	—
149	C₂×C₄×D₈₃	C₂³	1	2	yes	—
150	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₈₃	C₂³	1	2	yes	—
152	C₂×C₄×D₈₃	C₂³	1	2	yes	—
153	C₂×C₄×D₈₃	C₂³	1	2	yes	—
154	C₂×C₄×D₈₃	C₂³	1	2	yes	—
155	C₂×C₄×D₈₃	C₂³	1	2	yes	—
156	C₂×C₄×D₈₃	C₂³	1	2	yes	—
157	C₄⋊Dic₈₃	C₂³	1	2	yes	—
158	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
162	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
163	Dic₈₃⋊C₄	C₂³	1	2	yes	—
164	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
165	Dic₈₃⋊C₄	C₂³	1	2	yes	—
166	Dic₈₃⋊C₄	C₂³	1	2	yes	—
167	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₈₃⋊C₄	C₂³	1	2	yes	—
169	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
170	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₈₃⋊C₄	C₂³	1	2	yes	—
173	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
181	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
188	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
197	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
198	C₄×Dic₈₃	C₂³	1	2	yes	—
199	C₄×Dic₈₃	C₂³	1	2	yes	—
200	C₄×Dic₈₃	C₂³	1	2	yes	—
201	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
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	C₂×Q₈×C₈₃	C₂³	1	2	yes	—
206	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₈₃	C₂³	1	2	yes	—
208	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₈₃	C₂³	1	2	yes	—
210	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
213	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
215	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
225	C₄²×C₈₃	C₂³	1	2	yes	—
226	C₄²×C₈₃	C₂³	1	1	yes	characteristic
227	C₄²×C₈₃	C₂³	1	2	yes	—
228	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
229	C₂³×C₈₃	C₂⁴	1	2	yes	—
230	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₈₃	—	2	4	no	—
232	C₂²×D₈₃	—	2	4	no	—
233	C₂²×D₈₃	—	4	2	no	—
234	C₂²×D₈₃	—	4	2	no	—
235	C₂²×D₈₃	—	4	2	no	—
236	C₂²×D₈₃	—	4	2	no	—
237	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
238	C₂²×D₈₃	C₂⁴	1	2	yes	—
239	C₂²×D₈₃	C₂⁴	1	2	yes	—
240	Q₈×C₈₃	—	4	2	no	—
241	D₄×C₈₃	—	2	2	no	—
242	D₄×C₈₃	—	4	1	no	—
243	D₄×C₈₃	—	4	2	no	—
244	D₄×C₈₃	—	4	2	no	—
245	C₂×C₄×C₈₃	—	2	2	no	—
246	C₂×C₄×C₈₃	—	2	2	no	—
247	C₂×C₄×C₈₃	—	4	2	no	—
248	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₈₃	—	2	4	no	—
257	C₂²⋊D₈₃	—	2	4	no	—
258	C₂²⋊D₈₃	—	2	2	no	—
259	C₂²⋊D₈₃	—	2	4	no	—
260	C₂²⋊D₈₃	—	4	1	no	—
261	C₂²⋊D₈₃	—	4	2	no	—
262	C₂²⋊D₈₃	—	4	2	no	—
263	C₂×Dic₈₃	—	2	2	no	—
264	C₂×Dic₈₃	—	4	1	no	—
265	C₂×Dic₈₃	—	4	2	no	—
266	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₈₃	C₂⁴	1	2	yes	—
268	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₈₃	C₂⁴	1	2	yes	—
273	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
275	D₃₃₂	—	2	4	no	—
276	D₃₃₂	—	2	2	no	—
277	D₃₃₂	—	4	2	no	—
278	D₃₃₂	#41	1	4	yes	complemented
279	C₄×D₈₃	—	2	4	no	—
280	C₄×D₈₃	—	2	2	no	—
281	C₄×D₈₃	—	2	4	no	—
282	C₄×D₈₃	—	4	2	no	—
283	C₄×D₈₃	—	4	2	no	—
284	C₄×D₈₃	—	4	2	no	—
285	C₄×D₈₃	—	4	2	no	—
286	C₄×D₈₃	—	4	2	no	—
287	Dic₁₆₆	—	2	2	no	—
288	Dic₁₆₆	—	2	2	no	—
289	Dic₁₆₆	—	2	4	no	—
290	Dic₁₆₆	—	4	2	no	—
291	C₂²×C₈₃	—	2	1	no	—
292	C₂²×C₈₃	—	2	2	no	—
293	C₂²×C₈₃	—	2	1	no	—
294	C₂²×C₈₃	—	2	1	no	—
295	C₂²×C₈₃	—	2	2	no	—
296	C₂²×C₈₃	—	2	1	no	—
297	C₂²×C₈₃	—	2	1	no	—
298	C₂²×C₈₃	—	2	2	no	—
299	C₂²×C₈₃	—	2	1	no	—
300	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
301	C₂×D₈₃	—	2	2	no	—
302	C₂×D₈₃	—	2	2	no	—
303	C₂×D₈₃	—	2	1	no	—
304	C₂×D₈₃	—	2	2	no	—
305	C₂×D₈₃	—	2	2	no	—
306	C₂×D₈₃	—	2	1	no	—
307	C₂×D₈₃	—	2	2	no	—
308	C₂×D₈₃	—	2	1	no	—
309	C₂×D₈₃	—	8	4	no	—
310	C₂×D₈₃	—	8	4	no	—
311	C₂×D₈₃	C₂×#41	1	4	yes	—
312	C₄×C₈₃	—	2	1	no	—
313	C₄×C₈₃	—	2	1	no	—
314	C₄×C₈₃	—	2	2	no	—
315	C₄×C₈₃	—	2	1	no	—
316	C₄×C₈₃	—	2	2	no	—
317	C₄×C₈₃	—	2	2	no	—
318	C₄×C₈₃	—	2	1	no	—
319	C₄×C₈₃	C₂×#41	1	2	yes	—
320	Dic₈₃	—	2	2	no	—
321	Dic₈₃	—	2	1	no	—
322	Dic₈₃	—	2	1	no	—
323	Dic₈₃	—	2	2	no	—
324	Dic₈₃	—	2	1	no	—
325	Dic₈₃	—	2	1	no	—
326	Dic₈₃	—	2	1	no	—
327	Dic₈₃	—	2	1	no	—
328	Dic₈₃	H(5,𝔽₂)	1	2	yes	—
329	C₂×C₈₃	—	4	1	no	—
330	C₂×C₈₃	—	4	2	no	—
331	C₂×C₈₃	—	4	1	no	—
332	C₂×C₈₃	C₂²×#41	1	1	yes	characteristic
333	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₈₃	#585	1	1	yes	characteristic
335	D₈₃	—	2	4	no	—
336	D₈₃	—	4	2	no	—
337	D₈₃	—	4	1	no	—
338	#3514	—	83	1	no	maximal, Sylow
339	C₈₃	#3514	1	1	yes	characteristic, complemented, Sylow
340	#559	—	83	1	no	—
341	#556	—	83	1	no	—
342	#555	—	83	1	no	—
343	#555	D₈₃	1	1	yes	characteristic, complemented
344	#551	—	83	2	no	—
345	#551	—	83	2	no	—
346	D₄×Q₈	—	83	1	no	—
347	#548	—	83	2	no	—
348	#546	—	83	2	no	—
349	#546	—	83	1	no	—
350	#546	—	83	1	no	—
351	D₄²	—	83	1	no	—
352	#542	—	83	1	no	—
353	#542	—	83	1	no	—
354	#538	—	83	2	no	—
355	#538	—	83	2	no	—
356	#532	—	83	1	no	—
357	#529	—	83	1	no	—
358	#529	—	83	2	no	—
359	C₂×#124	—	83	2	no	—
360	#518	—	83	1	no	—
361	#518	—	83	1	no	—
362	C₄×#41	—	83	1	no	—
363	C₂×#41	—	83	2	no	—
364	C₂×#41	—	83	1	no	—
365	C₂²×Q₈	—	83	2	no	—
366	C₂²×D₄	—	83	2	no	—
367	C₂²×D₄	—	83	1	no	—
368	C₂²×D₄	—	83	1	no	—
369	C₄⋊Q₈	—	83	1	no	—
370	C₄⋊Q₈	—	83	1	no	—
371	C₄⋊Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
372	#127	—	83	1	no	—
373	#126	—	83	2	no	—
374	#126	—	83	1	no	—
375	#126	—	83	2	no	—
376	#126	—	83	1	no	—
377	#126	—	83	2	no	—
378	#126	—	83	2	no	—
379	#125	—	83	1	no	—
380	#124	—	83	2	no	—
381	#124	—	83	2	no	—
382	#124	—	83	1	no	—
383	#124	—	83	1	no	—
384	#124	—	83	2	no	—
385	#124	—	83	2	no	—
386	#124	—	83	2	no	—
387	#124	—	83	2	no	—
388	#124	—	83	2	no	—
389	#124	—	83	1	no	—
390	#124	C₂×D₈₃	1	2	yes	complemented
391	#124	C₂×D₈₃	1	2	yes	complemented
392	#123	—	83	1	no	—
393	#123	—	83	2	no	—
394	#123	—	83	2	no	—
395	#123	—	83	2	no	—
396	#123	—	83	2	no	—
397	#123	—	83	2	no	—
398	#123	—	83	2	no	—
399	#123	—	83	1	no	—
400	C₂²⋊Q₈	—	83	2	no	—
401	C₂²⋊Q₈	—	83	2	no	—
402	C₂²⋊Q₈	—	83	1	no	—
403	C₂²⋊Q₈	—	83	2	no	—
404	C₂²⋊Q₈	—	83	2	no	—
405	C₂²⋊Q₈	—	83	1	no	—
406	C₂²⋊Q₈	—	83	1	no	—
407	C₂²⋊Q₈	—	83	2	no	—
408	#121	—	83	2	no	—
409	#121	—	83	1	no	—
410	#121	—	83	2	no	—
411	#121	—	83	1	no	—
412	#121	—	83	1	no	—
413	#121	—	83	2	no	—
414	#121	—	83	2	no	—
415	#121	—	83	2	no	—
416	#121	C₂×D₈₃	1	1	yes	characteristic
417	#121	C₂×D₈₃	1	1	yes	characteristic, complemented
418	#121	C₂×D₈₃	1	2	yes	complemented
419	#120	—	83	2	no	—
420	#120	—	83	2	no	—
421	#120	—	83	2	no	—
422	#120	—	83	2	no	—
423	C₄×Q₈	—	83	1	no	—
424	C₄×Q₈	—	83	1	no	—
425	C₄×Q₈	—	83	2	no	—
426	C₄×Q₈	—	83	1	no	—
427	C₄×D₄	—	83	1	no	—
428	C₄×D₄	—	83	2	no	—
429	C₄×D₄	—	83	1	no	—
430	C₄×D₄	—	83	1	no	—
431	C₄×D₄	—	83	2	no	—
432	C₄×D₄	—	83	1	no	—
433	C₄×D₄	—	83	1	no	—
434	C₄×D₄	—	83	1	no	—
435	C₄×D₄	—	83	1	no	—
436	C₄×D₄	—	83	1	no	—
437	C₄×D₄	—	83	2	no	—
438	C₄×D₄	—	83	2	no	—
439	C₄×D₄	—	83	2	no	—
440	C₄×D₄	—	83	2	no	—
441	C₄×D₄	—	83	2	no	—
442	C₄×D₄	—	83	1	no	—
443	C₄×D₄	—	83	2	no	—
444	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
445	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
446	#117	—	83	1	no	—
447	#117	—	83	1	no	—
448	#117	—	83	2	no	—
449	#117	—	83	1	no	—
450	#117	—	83	2	no	—
451	#117	C₂×D₈₃	1	1	yes	characteristic, complemented
452	#117	C₂×D₈₃	1	1	yes	characteristic, complemented
453	#117	C₂×D₈₃	1	2	yes	complemented
454	C₂×C₂²⋊C₄	—	83	2	no	—
455	C₂×C₂²⋊C₄	—	83	2	no	—
456	C₂×C₂²⋊C₄	—	83	2	no	—
457	C₂×C₂²⋊C₄	—	83	2	no	—
458	C₂×C₂²⋊C₄	—	83	2	no	—
459	C₂×C₂²⋊C₄	—	83	2	no	—
460	C₂×C₄²	—	83	1	no	—
461	C₂×C₄²	—	83	2	no	—
462	C₂⁴	—	83	2	no	—
463	C₂⁴	—	83	2	no	—
464	#41	—	332	4	no	—
465	#41	—	166	4	no	—
466	C₂×Q₈	—	332	4	no	—
467	C₂×Q₈	—	83	2	no	—
468	C₂×Q₈	—	83	1	no	—
469	C₂×Q₈	—	83	1	no	—
470	C₂×Q₈	—	83	2	no	—
471	C₂×Q₈	C₂²×D₈₃	1	2	yes	—
472	C₂×D₄	—	332	4	no	—
473	C₂×D₄	—	83	1	no	—
474	C₂×D₄	—	83	2	no	—
475	C₂×D₄	—	83	2	no	—
476	C₂×D₄	—	83	2	no	—
477	C₂×D₄	—	83	2	no	—
478	C₂×D₄	—	83	1	no	—
479	C₂×D₄	—	83	2	no	—
480	C₂×D₄	—	83	2	no	—
481	C₂×D₄	—	83	1	no	—
482	C₂×D₄	—	83	2	no	—
483	C₂×D₄	—	83	1	no	—
484	C₂×D₄	—	166	4	no	—
485	C₂×D₄	—	166	4	no	—
486	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
488	C₂×D₄	C₂²×D₈₃	1	2	yes	—
489	C₂×D₄	C₂²×D₈₃	1	2	yes	—
490	C₂²×C₄	—	83	1	no	—
491	C₂²×C₄	—	83	2	no	—
492	C₂²×C₄	—	83	2	no	—
493	C₂²×C₄	—	83	2	no	—
494	C₂²×C₄	—	83	2	no	—
495	C₂²×C₄	—	83	2	no	—
496	C₂²×C₄	—	83	2	no	—
497	C₂²×C₄	—	83	1	no	—
498	C₂²×C₄	—	83	2	no	—
499	C₂²×C₄	—	83	2	no	—
500	C₂²×C₄	—	83	1	no	—
501	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
504	C₄⋊C₄	—	83	1	no	—
505	C₄⋊C₄	—	83	1	no	—
506	C₄⋊C₄	—	83	1	no	—
507	C₄⋊C₄	—	83	1	no	—
508	C₄⋊C₄	—	83	1	no	—
509	C₄⋊C₄	—	83	1	no	—
510	C₄⋊C₄	—	83	2	no	—
511	C₄⋊C₄	—	83	2	no	—
512	C₄⋊C₄	—	83	2	no	—
513	C₄⋊C₄	—	83	1	no	—
514	C₄⋊C₄	—	83	1	no	—
515	C₄⋊C₄	—	83	2	no	—
516	C₄⋊C₄	—	83	2	no	—
517	C₄⋊C₄	—	83	2	no	—
518	C₄⋊C₄	—	83	1	no	—
519	C₄⋊C₄	—	83	1	no	—
520	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
525	C₂²⋊C₄	—	83	1	no	—
526	C₂²⋊C₄	—	83	1	no	—
527	C₂²⋊C₄	—	83	2	no	—
528	C₂²⋊C₄	—	83	2	no	—
529	C₂²⋊C₄	—	83	2	no	—
530	C₂²⋊C₄	—	83	1	no	—
531	C₂²⋊C₄	—	83	2	no	—
532	C₂²⋊C₄	—	83	1	no	—
533	C₂²⋊C₄	—	83	2	no	—
534	C₂²⋊C₄	—	83	1	no	—
535	C₂²⋊C₄	—	83	2	no	—
536	C₂²⋊C₄	—	83	1	no	—
537	C₂²⋊C₄	—	83	1	no	—
538	C₂²⋊C₄	—	83	2	no	—
539	C₂²⋊C₄	—	83	2	no	—
540	C₂²⋊C₄	—	83	2	no	—
541	C₂²⋊C₄	—	83	2	no	—
542	C₂²⋊C₄	—	83	2	no	—
543	C₂²⋊C₄	—	83	2	no	—
544	C₂²⋊C₄	—	83	2	no	—
545	C₂²⋊C₄	—	83	2	no	—
546	C₂²⋊C₄	—	83	2	no	—
547	C₂²⋊C₄	—	83	1	no	—
548	C₂²⋊C₄	—	83	2	no	—
549	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
556	C₄²	—	83	1	no	—
557	C₄²	—	83	1	no	—
558	C₄²	—	83	1	no	—
559	C₄²	—	83	2	no	—
560	C₄²	—	83	1	no	—
561	C₄²	—	83	2	no	—
562	C₄²	—	83	2	no	—
563	C₄²	—	83	1	no	—
564	C₄²	C₂²×D₈₃	1	2	yes	—
565	C₄²	C₂²×D₈₃	1	1	yes	characteristic
566	C₄²	C₂²×D₈₃	1	2	yes	—
567	C₂³	—	332	2	no	—
568	C₂³	—	332	2	no	—
569	C₂³	—	332	2	no	—
570	C₂³	—	332	2	no	—
571	C₂³	—	83	2	no	—
572	C₂³	—	83	1	no	—
573	C₂³	—	83	2	no	—
574	C₂³	—	166	4	no	—
575	C₂³	—	166	4	no	—
576	C₂³	C₂³×D₈₃	1	1	yes	characteristic
577	C₂³	C₂³×D₈₃	1	2	yes	—
578	C₂³	C₂³×D₈₃	1	1	yes	characteristic
579	Q₈	—	4	2	no	—
580	Q₈	—	332	2	no	—
581	Q₈	—	166	2	no	—
582	Q₈	—	166	4	no	—
583	Q₈	—	166	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	1	no	—
588	D₄	—	332	2	no	—
589	D₄	—	332	2	no	—
590	D₄	—	332	1	no	—
591	D₄	—	332	2	no	—
592	D₄	—	83	4	no	—
593	D₄	—	166	4	no	—
594	D₄	—	166	2	no	—
595	D₄	—	166	4	no	—
596	D₄	—	166	4	no	—
597	D₄	—	166	4	no	—
598	D₄	—	166	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	332	2	no	—
603	C₂×C₄	—	332	2	no	—
604	C₂×C₄	—	332	2	no	—
605	C₂×C₄	—	332	2	no	—
606	C₂×C₄	—	332	2	no	—
607	C₂×C₄	—	332	2	no	—
608	C₂×C₄	—	332	1	no	—
609	C₂×C₄	—	83	1	no	—
610	C₂×C₄	—	83	1	no	—
611	C₂×C₄	—	83	2	no	—
612	C₂×C₄	—	83	1	no	—
613	C₂×C₄	—	83	1	no	—
614	C₂×C₄	—	83	1	no	—
615	C₂×C₄	—	83	1	no	—
616	C₂×C₄	—	83	1	no	—
617	C₂×C₄	—	83	2	no	—
618	C₂×C₄	—	166	4	no	—
619	C₂×C₄	—	166	4	no	—
620	C₂×C₄	—	166	2	no	—
621	C₂×C₄	—	166	2	no	—
622	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₈₃	1	2	yes	—
624	C₂×C₄	C₂³×D₈₃	1	2	yes	—
625	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₈₃	1	2	yes	—
629	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	83	4	no	—
640	C₂²	—	664	4	no	—
641	C₂²	—	664	4	no	—
642	C₂²	—	166	1	no	—
643	C₂²	—	166	2	no	—
644	C₂²	—	166	2	no	—
645	C₂²	—	166	1	no	—
646	C₂²	—	166	2	no	—
647	C₂²	—	166	1	no	—
648	C₂²	—	166	2	no	—
649	C₂²	—	166	2	no	—
650	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	83	2	no	—
659	C₄	—	166	1	no	—
660	C₄	—	166	2	no	—
661	C₄	—	166	1	no	—
662	C₄	—	166	2	no	—
663	C₄	—	166	1	no	—
664	C₄	—	166	1	no	—
665	C₄	—	166	1	no	—
666	C₄	—	166	1	no	—
667	C₄	#41×D₈₃	1	2	yes	—
668	C₂	—	4	1	no	—
669	C₂	—	4	2	no	—
670	C₂	—	4	1	no	—
671	C₂	—	332	1	no	—
672	C₂	—	332	2	no	—
673	C₂	—	166	4	no	—
674	C₂	C₂×#41×D₈₃	1	1	yes	characteristic
675	C₂	H(5,𝔽₂)×D₈₃	1	1	yes	characteristic
676	C₂	#19128537	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#555×C₈₃	C₂
hypercenter	#555	D₈₃
hypocenter	C₈₃	#3514
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #555

Complements

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

N	H ≅ G/N	type
1. #19128434	C₂	semidirect
2. #19128419	C₂	semidirect
3. #19128414	C₂	semidirect
4. #19128381	C₂	semidirect
5. #19128375	C₂	semidirect
6. #19128366	C₂	semidirect
7. #19128359	C₂	semidirect
8. #19128348	C₂	semidirect
9. #19128347	C₂	semidirect
10. #19128340	C₂	semidirect
11. #19128335	C₂	semidirect
12. #19128325	C₂	semidirect
13. #19128318	C₂	semidirect
14. #19128285	C₂	semidirect
15. #19128283	C₂	semidirect
16. #19128246	C₂	semidirect
17. #19128231	C₂	semidirect
18. #19128229	C₂	semidirect
19. #124×D₈₃	C₂	semidirect
20. #19128175	C₂	semidirect
21. #19128173	C₂	semidirect
22. #19128169	C₂	semidirect
23. #555×C₈₃	C₂	semidirect
25. C₂×#13050589	C₂²	semidirect
26. C₂×Q₈×D₈₃	C₂²	semidirect
30. #14581791	C₂²	semidirect
31. #14581791	C₂²	semidirect
33. #14581787	C₂²	semidirect
34. #14581787	C₂²	semidirect
35. #14581786	C₂²	semidirect
36. #14581785	C₂²	semidirect
37. #14581785	C₂²	semidirect
38. #14581785	C₂²	semidirect
39. #14581782	C₂²	semidirect
40. #14581781	C₂²	semidirect
41. #14581780	C₂²	semidirect
42. #14581780	C₂²	semidirect
43. #14581779	C₂²	semidirect
44. #14581779	C₂²	semidirect
47. #14581778	C₂²	semidirect
48. #14581778	C₂²	semidirect
49. #14581778	C₂²	semidirect
50. #14581777	C₂²	semidirect
51. #14581777	C₂²	semidirect
52. #14581776	C₂²	semidirect
53. #14581775	C₂²	semidirect
54. #14581774	C₂²	semidirect
55. #14581774	C₂²	semidirect
56. #14581773	C₂²	semidirect
57. #14581773	C₂²	semidirect
58. #14581772	C₂²	semidirect
59. #14581771	C₂²	semidirect
60. #14581770	C₂²	semidirect
61. #14581770	C₂²	semidirect
62. #14581769	C₂²	semidirect
63. #14581769	C₂²	semidirect
64. #14581768	C₂²	semidirect
65. #14581768	C₂²	semidirect
67. #14581766	C₂²	semidirect
69. #14581765	C₂²	semidirect
70. #14581765	C₂²	semidirect
72. #14581764	C₂²	semidirect
73. #14581763	C₂²	semidirect
76. #14581760	C₂²	semidirect
77. #14581760	C₂²	semidirect
78. C₄×Dic₁₆₆	C₂²	semidirect
79. C₄×Dic₁₆₆	C₂²	semidirect
80. #14581757	C₂²	semidirect
81. #14581757	C₂²	semidirect
83. C₄×D₃₃₂	C₂²	semidirect
84. C₄×D₃₃₂	C₂²	semidirect
85. D₄×Dic₈₃	C₂²	semidirect
89. #14581754	C₂²	semidirect
90. #14581754	C₂²	semidirect
92. C₄×C₂²⋊D₈₃	C₂²	semidirect
93. C₄×C₂²⋊D₈₃	C₂²	semidirect
94. C₄×C₂²⋊D₈₃	C₂²	semidirect
95. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
96. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
97. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
99. #14581751	C₂²	semidirect
100. #14581750	C₂²	semidirect
101. #14581749	C₂²	semidirect
102. #14581749	C₂²	semidirect
103. #14581749	C₂²	semidirect
104. C₂×(C₂×D₈₃)⋊C₄	C₂²	semidirect
105. C₂²⋊C₄×D₈₃	C₂²	semidirect
106. C₂²⋊C₄×D₈₃	C₂²	semidirect
107. C₂²⋊C₄×D₈₃	C₂²	semidirect
108. C₂²⋊C₄×D₈₃	C₂²	semidirect
109. C₂²⋊C₄×D₈₃	C₂²	semidirect
110. C₂×C₄×Dic₈₃	C₂²	semidirect
111. C₄²×D₈₃	C₂²	semidirect
112. C₄⋊Q₈×C₈₃	C₂²	semidirect
113. #124×C₈₃	C₂²	semidirect
114. #124×C₈₃	C₂²	semidirect
116. #121×C₈₃	C₂²	semidirect
117. #121×C₈₃	C₂²	semidirect
118. C₄×D₄×C₈₃	C₂²	semidirect
119. C₄×D₄×C₈₃	C₂²	semidirect
120. #117×C₈₃	C₂²	semidirect
121. #117×C₈₃	C₂²	semidirect
122. #117×C₈₃	C₂²	semidirect
278. D₃₃₂	#41	semidirect
339. C₈₃	#3514	semidirect
343. #555	D₈₃	semidirect
371. C₄⋊Q₈	C₂×D₈₃	semidirect
390. #124	C₂×D₈₃	semidirect
391. #124	C₂×D₈₃	semidirect
417. #121	C₂×D₈₃	semidirect
418. #121	C₂×D₈₃	semidirect
444. C₄×D₄	C₂×D₈₃	semidirect
445. C₄×D₄	C₂×D₈₃	semidirect
451. #117	C₂×D₈₃	semidirect
452. #117	C₂×D₈₃	semidirect
453. #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
#19128434	2
#19128419	2
#19128414	2
#19128381	2
#19128375	2
#19128366	2
#19128359	2
#19128348	2
#19128347	2
#19128340	2
#19128335	2
#19128325	2
#19128318	2
#19128285	2
#19128283	2
#19128246	2
#19128231	2
#19128229	2
#124×D₈₃	2
#19128175	2
#19128173	2
#19128169	2
#555×C₈₃	2
#3514	83