Subgroups — #24921827

Order 10624.

1150 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128441	C₂	1	2	yes	maximal, complemented
2	#19128440	C₂	1	2	yes	maximal, complemented
3	#19128422	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128401	C₂	1	1	yes	maximal, characteristic, complemented
5	#19128397	C₂	1	1	yes	maximal, characteristic, complemented
6	#19128370	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128369	C₂	1	2	yes	maximal, complemented
8	#19128351	C₂	1	1	yes	maximal, characteristic, complemented
9	#19128344	C₂	1	1	yes	maximal, characteristic, complemented
10	#19128341	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128319	C₂	1	2	yes	maximal, complemented
13	#19128289	C₂	1	2	yes	maximal, complemented
14	#19128283	C₂	1	2	yes	maximal, complemented
15	#19128281	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128279	C₂	1	1	yes	maximal, characteristic, complemented
17	#19128268	C₂	1	1	yes	maximal, characteristic, complemented
18	#19128267	C₂	1	1	yes	maximal, characteristic, complemented
19	#19128266	C₂	1	2	yes	maximal, complemented
20	#19128248	C₂	1	1	yes	maximal, characteristic, complemented
21	#19128248	C₂	1	1	yes	maximal, characteristic, complemented
22	#19128230	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13050591	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13050590	C₂²	1	2	yes	complemented
26	C₂×#13050590	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13050590	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13050589	C₂²	1	2	yes	complemented
29	C₂²×C₂²⋊D₈₃	C₂²	1	2	yes	—
30	C₂×D₄×D₈₃	C₂²	1	1	yes	characteristic
31	#14581791	C₂²	1	1	yes	characteristic, complemented
32	#14581791	C₂²	1	1	yes	characteristic, complemented
33	#14581788	C₂²	1	1	yes	characteristic
34	#14581788	C₂²	1	1	yes	characteristic
35	#14581788	C₂²	1	2	yes	complemented
36	#14581788	C₂²	1	2	yes	complemented
37	#14581788	C₂²	1	2	yes	complemented
38	#14581787	C₂²	1	2	yes	complemented
39	#14581787	C₂²	1	2	yes	complemented
40	#14581785	C₂²	1	2	yes	complemented
41	#14581785	C₂²	1	2	yes	complemented
42	#14581785	C₂²	1	2	yes	complemented
43	#14581784	C₂²	1	1	yes	characteristic, complemented
44	#14581779	C₂²	1	2	yes	complemented
45	#14581778	C₂²	1	2	yes	—
46	#14581778	C₂²	1	2	yes	complemented
47	#14581778	C₂²	1	1	yes	characteristic, complemented
48	#14581778	C₂²	1	1	yes	characteristic, complemented
49	#14581778	C₂²	1	2	yes	complemented
50	#14581775	C₂²	1	2	yes	complemented
51	#14581774	C₂²	1	2	yes	complemented
52	#14581774	C₂²	1	2	yes	complemented
53	#14581774	C₂²	1	2	yes	complemented
54	#14581774	C₂²	1	2	yes	complemented
55	#14581773	C₂²	1	2	yes	complemented
56	#14581771	C₂²	1	2	yes	complemented
57	#14581770	C₂²	1	2	yes	complemented
58	#14581769	C₂²	1	2	yes	complemented
59	#14581768	C₂²	1	1	yes	characteristic, complemented
60	#14581768	C₂²	1	1	yes	characteristic, complemented
61	#14581767	C₂²	1	2	yes	complemented
62	#14581767	C₂²	1	1	yes	characteristic, complemented
63	#14581767	C₂²	1	1	yes	characteristic, complemented
64	#14581766	C₂²	1	1	yes	characteristic
65	#14581766	C₂²	1	2	yes	complemented
66	#14581766	C₂²	1	1	yes	characteristic, complemented
67	#14581766	C₂²	1	2	yes	complemented
68	#14581765	C₂²	1	1	yes	characteristic
69	#14581765	C₂²	1	2	yes	complemented
70	#14581765	C₂²	1	2	yes	complemented
71	#14581765	C₂²	1	1	yes	characteristic, complemented
72	#14581765	C₂²	1	2	yes	complemented
73	#14581765	C₂²	1	2	yes	complemented
74	#14581765	C₂²	1	2	yes	complemented
75	#14581764	C₂²	1	2	yes	—
76	#14581764	C₂²	1	2	yes	complemented
77	#14581764	C₂²	1	2	yes	complemented
78	#14581764	C₂²	1	2	yes	complemented
79	#14581763	C₂²	1	1	yes	characteristic
80	#14581763	C₂²	1	1	yes	characteristic
81	#14581763	C₂²	1	1	yes	characteristic
82	#14581763	C₂²	1	1	yes	characteristic, complemented
83	#14581763	C₂²	1	2	yes	complemented
84	#14581763	C₂²	1	1	yes	characteristic, complemented
85	#14581763	C₂²	1	1	yes	characteristic, complemented
86	#14581762	C₂²	1	2	yes	complemented
87	#14581762	C₂²	1	2	yes	complemented
88	#14581761	C₂²	1	2	yes	—
89	#14581761	C₂²	1	2	yes	complemented
90	#14581761	C₂²	1	2	yes	complemented
91	#14581760	C₂²	1	2	yes	—
92	#14581760	C₂²	1	2	yes	complemented
93	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
94	#14581757	C₂²	1	2	yes	complemented
95	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
97	D₄×Dic₈₃	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
103	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
104	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
105	#14581751	C₂²	1	1	yes	characteristic, complemented
106	#14581750	C₂²	1	1	yes	characteristic, complemented
107	#14581748	C₂²	1	2	yes	complemented
108	C₂×C₄⋊Dic₈₃	C₂²	1	1	yes	characteristic, complemented
109	C₄⋊C₄×D₈₃	C₂²	1	1	yes	characteristic, complemented
110	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
111	C₄²×D₈₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₈₃	C₂²	1	1	yes	characteristic, complemented
113	C₂²×D₄×C₈₃	C₂²	1	1	yes	characteristic
114	#124×C₈₃	C₂²	1	1	yes	characteristic
115	#123×C₈₃	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
117	#121×C₈₃	C₂²	1	1	yes	characteristic
118	#121×C₈₃	C₂²	1	2	yes	complemented
119	#120×C₈₃	C₂²	1	2	yes	complemented
120	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₈₃	C₂²	1	2	yes	complemented
123	C₂³×D₈₃	C₂³	1	2	yes	—
124	#13050591	—	4	2	no	—
125	#13050590	—	4	4	no	—
126	#13050590	—	4	2	no	—
127	#13050590	—	4	2	no	—
128	#13050589	—	4	4	no	—
129	C₂×Dic₁₆₆	C₂³	1	2	yes	—
130	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
132	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
133	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
134	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
135	C₂×D₃₃₂	C₂³	1	2	yes	—
136	C₂×D₃₃₂	C₂³	1	2	yes	—
137	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₈₃	—	4	4	no	—
139	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
155	D₄×D₈₃	—	4	2	no	—
156	C₂²×Dic₈₃	C₂³	1	2	yes	—
157	C₂²×Dic₈₃	C₂³	1	2	yes	—
158	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₈₃	C₂³	1	2	yes	—
164	C₂×C₄×D₈₃	C₂³	1	2	yes	—
165	C₂×C₄×D₈₃	C₂³	1	2	yes	—
166	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
167	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
168	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₈₃	C₂³	1	2	yes	—
170	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₈₃	C₂³	1	2	yes	—
172	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₈₃⋊C₄	C₂³	1	2	yes	—
174	Dic₈₃⋊C₄	C₂³	1	2	yes	—
175	Dic₈₃⋊C₄	C₂³	1	2	yes	—
176	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
177	Dic₈₃⋊C₄	C₂³	1	2	yes	—
178	Dic₈₃⋊C₄	C₂³	1	2	yes	—
179	Dic₈₃⋊C₄	C₂³	1	2	yes	—
180	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
189	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
195	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
204	C₄×Dic₈₃	C₂³	1	2	yes	—
205	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
206	C₂⁴×C₈₃	C₂³	1	2	yes	—
207	#41×C₈₃	—	4	2	no	—
208	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₈₃	—	4	2	no	—
210	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
212	C₂×D₄×C₈₃	C₂³	1	2	yes	—
213	C₂×D₄×C₈₃	C₂³	1	2	yes	—
214	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
215	C₂×D₄×C₈₃	C₂³	1	2	yes	—
216	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
217	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
219	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
220	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
221	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
226	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
229	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
230	C₄²×C₈₃	C₂³	1	1	yes	characteristic
231	C₂³×C₈₃	—	4	2	no	—
232	C₂³×C₈₃	—	4	2	no	—
233	C₂³×C₈₃	—	4	2	no	—
234	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
235	C₂³×C₈₃	C₂⁴	1	2	yes	—
236	C₂³×C₈₃	C₂⁴	1	2	yes	—
237	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
238	C₂²×D₈₃	—	4	2	no	—
239	C₂²×D₈₃	—	4	2	no	—
240	C₂²×D₈₃	—	4	2	no	—
241	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
242	C₂²×D₈₃	C₂⁴	1	2	yes	—
243	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
244	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
245	Q₈×C₈₃	—	2	2	no	—
246	D₄×C₈₃	—	2	2	no	—
247	D₄×C₈₃	—	2	2	no	—
248	D₄×C₈₃	—	4	2	no	—
249	D₄×C₈₃	—	4	1	no	—
250	D₄×C₈₃	—	4	2	no	—
251	D₄×C₈₃	—	4	2	no	—
252	C₂×C₄×C₈₃	—	2	2	no	—
253	C₂×C₄×C₈₃	—	2	2	no	—
254	C₂×C₄×C₈₃	—	4	2	no	—
255	C₂×C₄×C₈₃	—	4	2	no	—
256	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
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	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
263	C₂²⋊D₈₃	—	2	2	no	—
264	C₂²⋊D₈₃	—	2	4	no	—
265	C₂²⋊D₈₃	—	2	2	no	—
266	C₂²⋊D₈₃	—	4	2	no	—
267	C₂²⋊D₈₃	—	4	2	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	C₂²⋊D₈₃	—	4	2	no	—
274	C₂²⋊D₈₃	—	4	2	no	—
275	C₂²⋊D₈₃	—	4	1	no	—
276	C₂²⋊D₈₃	—	4	1	no	—
277	C₂²⋊D₈₃	—	4	1	no	—
278	C₂²⋊D₈₃	—	4	1	no	—
279	C₂×Dic₈₃	—	2	4	no	—
280	C₂×Dic₈₃	—	4	2	no	—
281	C₂×Dic₈₃	C₂⁴	1	2	yes	—
282	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₈₃	C₂⁴	1	2	yes	—
286	C₂×Dic₈₃	C₂⁴	1	2	yes	—
287	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
289	D₃₃₂	—	2	2	no	—
290	D₃₃₂	—	4	1	no	—
291	D₃₃₂	—	4	2	no	—
292	D₃₃₂	—	4	1	no	—
293	D₃₃₂	—	4	1	no	—
294	D₃₃₂	—	4	2	no	—
295	C₄×D₈₃	—	2	2	no	—
296	C₄×D₈₃	—	2	2	no	—
297	C₄×D₈₃	—	2	2	no	—
298	C₄×D₈₃	—	2	2	no	—
299	C₄×D₈₃	—	4	1	no	—
300	C₄×D₈₃	—	4	2	no	—
301	C₄×D₈₃	—	4	2	no	—
302	C₄×D₈₃	—	4	2	no	—
303	Dic₁₆₆	—	2	4	no	—
304	Dic₁₆₆	—	4	1	no	—
305	Dic₁₆₆	—	4	1	no	—
306	C₂²×C₈₃	—	2	2	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	—	2	1	no	—
312	C₂²×C₈₃	—	2	2	no	—
313	C₂²×C₈₃	—	2	2	no	—
314	C₂²×C₈₃	—	2	1	no	—
315	C₂²×C₈₃	—	2	2	no	—
316	C₂²×C₈₃	—	2	2	no	—
317	C₂²×C₈₃	—	2	1	no	—
318	C₂²×C₈₃	—	8	4	no	—
319	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
320	C₂×D₈₃	—	2	1	no	—
321	C₂×D₈₃	—	2	1	no	—
322	C₂×D₈₃	—	2	1	no	—
323	C₂×D₈₃	—	2	1	no	—
324	C₂×D₈₃	—	2	1	no	—
325	C₂×D₈₃	—	2	2	no	—
326	C₂×D₈₃	—	2	2	no	—
327	C₂×D₈₃	—	2	1	no	—
328	C₂×D₈₃	—	2	1	no	—
329	C₂×D₈₃	—	2	1	no	—
330	C₂×D₈₃	—	2	1	no	—
331	C₂×D₈₃	—	2	2	no	—
332	C₂×D₈₃	—	8	4	no	—
333	C₄×C₈₃	—	2	2	no	—
334	C₄×C₈₃	—	2	1	no	—
335	C₄×C₈₃	—	2	1	no	—
336	C₄×C₈₃	—	2	1	no	—
337	C₄×C₈₃	—	2	2	no	—
338	C₄×C₈₃	—	2	1	no	—
339	C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
340	Dic₈₃	—	2	2	no	—
341	Dic₈₃	—	2	1	no	—
342	Dic₈₃	—	2	1	no	—
343	Dic₈₃	—	2	1	no	—
344	Dic₈₃	—	2	2	no	—
345	Dic₈₃	—	2	1	no	—
346	Dic₈₃	—	2	2	no	—
347	Dic₈₃	H(5,𝔽₂)	1	2	yes	—
348	C₂×C₈₃	—	4	2	no	—
349	C₂×C₈₃	—	4	1	no	—
350	C₂×C₈₃	—	4	2	no	—
351	C₂×C₈₃	—	4	1	no	—
352	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂×C₈₃	#585	1	1	yes	characteristic
355	D₈₃	—	4	1	no	—
356	D₈₃	—	4	1	no	—
357	D₈₃	—	4	2	no	—
358	D₈₃	—	4	1	no	—
359	#3546	—	83	1	no	maximal, Sylow
360	C₈₃	#3546	1	1	yes	characteristic, complemented, Sylow
361	#560	—	83	2	no	—
362	#560	—	83	2	no	—
363	#556	—	83	1	no	—
364	#553	—	83	1	no	—
365	#553	—	83	1	no	—
366	#550	—	83	1	no	—
367	#550	—	83	2	no	—
368	#547	—	83	1	no	—
369	#546	—	83	1	no	—
370	#546	—	83	2	no	—
371	#546	D₈₃	1	1	yes	characteristic, complemented
372	D₄²	—	83	1	no	—
373	#542	—	83	2	no	—
374	#538	—	83	2	no	—
375	#538	—	83	2	no	—
376	#537	—	83	1	no	—
377	#537	—	83	1	no	—
378	#535	—	83	1	no	—
379	#535	—	83	1	no	—
380	#535	—	83	2	no	—
381	#532	—	83	1	no	—
382	#532	—	83	1	no	—
383	#529	—	83	1	no	—
384	C₂×#41	—	83	1	no	—
385	C₂×#41	—	83	2	no	—
386	C₂×#41	—	83	1	no	—
387	C₂×#41	—	83	1	no	—
388	C₂×#41	—	83	2	no	—
389	C₂×#41	C₂×D₈₃	1	1	yes	characteristic, complemented
390	C₂²×D₄	—	83	2	no	—
391	C₂²×D₄	—	83	1	no	—
392	C₂²×D₄	C₂×D₈₃	1	1	yes	characteristic
393	C₄⋊Q₈	—	83	1	no	—
394	C₄⋊Q₈	—	83	1	no	—
395	#127	—	83	1	no	—
396	#127	—	83	1	no	—
397	#127	—	83	2	no	—
398	#127	—	83	2	no	—
399	#127	—	83	2	no	—
400	#126	—	83	2	no	—
401	#126	—	83	2	no	—
402	#126	—	83	2	no	—
403	#126	—	83	2	no	—
404	#126	—	83	2	no	—
405	#125	—	83	1	no	—
406	#124	—	83	2	no	—
407	#124	—	83	2	no	—
408	#124	—	83	2	no	—
409	#124	—	83	1	no	—
410	#124	—	83	1	no	—
411	#124	—	83	2	no	—
412	#124	C₂×D₈₃	1	1	yes	characteristic
413	#123	—	83	2	no	—
414	#123	—	83	2	no	—
415	#123	—	83	2	no	—
416	#123	—	83	2	no	—
417	#123	—	83	2	no	—
418	#123	—	83	2	no	—
419	#123	C₂×D₈₃	1	2	yes	complemented
420	C₂²⋊Q₈	—	83	1	no	—
421	C₂²⋊Q₈	—	83	1	no	—
422	C₂²⋊Q₈	—	83	2	no	—
423	C₂²⋊Q₈	—	83	2	no	—
424	C₂²⋊Q₈	—	83	2	no	—
425	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
426	#121	—	83	1	no	—
427	#121	—	83	1	no	—
428	#121	—	83	1	no	—
429	#121	—	83	1	no	—
430	#121	—	83	1	no	—
431	#121	—	83	1	no	—
432	#121	—	83	2	no	—
433	#121	—	83	2	no	—
434	#121	—	83	2	no	—
435	#121	—	83	2	no	—
436	#121	—	83	2	no	—
437	#121	—	83	1	no	—
438	#121	—	83	1	no	—
439	#121	—	83	2	no	—
440	#121	—	83	2	no	—
441	#121	—	83	1	no	—
442	#121	—	83	1	no	—
443	#121	—	83	2	no	—
444	#121	—	83	1	no	—
445	#121	—	83	1	no	—
446	#121	—	83	2	no	—
447	#121	—	83	2	no	—
448	#121	—	83	2	no	—
449	#121	—	83	2	no	—
450	#121	—	83	2	no	—
451	#121	C₂×D₈₃	1	1	yes	characteristic
452	#121	C₂×D₈₃	1	2	yes	complemented
453	#120	—	83	2	no	—
454	#120	—	83	2	no	—
455	#120	—	83	2	no	—
456	#120	—	83	2	no	—
457	#120	—	83	2	no	—
458	#120	—	83	2	no	—
459	#120	—	83	2	no	—
460	#120	C₂×D₈₃	1	2	yes	complemented
461	C₄×Q₈	—	83	1	no	—
462	C₄×Q₈	—	83	2	no	—
463	C₄×D₄	—	83	1	no	—
464	C₄×D₄	—	83	2	no	—
465	C₄×D₄	—	83	1	no	—
466	C₄×D₄	—	83	1	no	—
467	C₄×D₄	—	83	2	no	—
468	C₄×D₄	—	83	2	no	—
469	C₄×D₄	—	83	2	no	—
470	C₄×D₄	—	83	2	no	—
471	C₄×D₄	—	83	1	no	—
472	C₄×D₄	—	83	1	no	—
473	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
474	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
475	#117	—	83	1	no	—
476	#117	—	83	1	no	—
477	#117	—	83	2	no	—
478	C₂×C₄⋊C₄	—	83	1	no	—
479	C₂×C₄⋊C₄	—	83	1	no	—
480	C₂×C₂²⋊C₄	—	83	2	no	—
481	C₂×C₂²⋊C₄	C₂×D₈₃	1	2	yes	complemented
482	C₂×C₄²	—	83	1	no	—
483	C₂⁴	—	83	2	no	—
484	C₂⁴	C₂²×D₈₃	1	2	yes	—
485	#41	—	4	2	no	—
486	#41	—	332	2	no	—
487	#41	—	332	2	no	—
488	#41	—	332	4	no	—
489	#41	—	332	4	no	—
490	#41	—	332	2	no	—
491	C₂×Q₈	—	83	1	no	—
492	C₂×Q₈	—	83	1	no	—
493	C₂×Q₈	—	83	2	no	—
494	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	332	2	no	—
497	C₂×D₄	—	332	4	no	—
498	C₂×D₄	—	83	2	no	—
499	C₂×D₄	—	83	2	no	—
500	C₂×D₄	—	83	2	no	—
501	C₂×D₄	—	83	2	no	—
502	C₂×D₄	—	83	1	no	—
503	C₂×D₄	—	83	2	no	—
504	C₂×D₄	—	83	1	no	—
505	C₂×D₄	—	83	1	no	—
506	C₂×D₄	—	83	2	no	—
507	C₂×D₄	—	83	2	no	—
508	C₂×D₄	—	83	2	no	—
509	C₂×D₄	—	83	2	no	—
510	C₂×D₄	—	83	1	no	—
511	C₂×D₄	—	83	1	no	—
512	C₂×D₄	—	83	2	no	—
513	C₂×D₄	—	83	1	no	—
514	C₂×D₄	—	83	1	no	—
515	C₂×D₄	—	83	1	no	—
516	C₂×D₄	—	83	2	no	—
517	C₂×D₄	—	83	2	no	—
518	C₂×D₄	—	83	1	no	—
519	C₂×D₄	—	83	1	no	—
520	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
521	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
522	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
523	C₂×D₄	C₂²×D₈₃	1	2	yes	—
524	C₂×D₄	C₂²×D₈₃	1	2	yes	—
525	C₂×D₄	C₂²×D₈₃	1	2	yes	—
526	C₂²×C₄	—	83	2	no	—
527	C₂²×C₄	—	83	1	no	—
528	C₂²×C₄	—	83	2	no	—
529	C₂²×C₄	—	83	2	no	—
530	C₂²×C₄	—	83	2	no	—
531	C₂²×C₄	—	83	2	no	—
532	C₂²×C₄	—	83	1	no	—
533	C₂²×C₄	—	83	1	no	—
534	C₂²×C₄	—	83	1	no	—
535	C₂²×C₄	—	83	1	no	—
536	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
538	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
539	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
540	C₄⋊C₄	—	83	1	no	—
541	C₄⋊C₄	—	83	1	no	—
542	C₄⋊C₄	—	83	2	no	—
543	C₄⋊C₄	—	83	2	no	—
544	C₄⋊C₄	—	83	1	no	—
545	C₄⋊C₄	—	83	2	no	—
546	C₄⋊C₄	—	83	2	no	—
547	C₄⋊C₄	—	83	1	no	—
548	C₄⋊C₄	—	83	2	no	—
549	C₄⋊C₄	—	83	1	no	—
550	C₄⋊C₄	—	83	2	no	—
551	C₄⋊C₄	—	83	1	no	—
552	C₄⋊C₄	—	83	2	no	—
553	C₄⋊C₄	—	83	2	no	—
554	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
556	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
557	C₂²⋊C₄	—	83	2	no	—
558	C₂²⋊C₄	—	83	2	no	—
559	C₂²⋊C₄	—	83	2	no	—
560	C₂²⋊C₄	—	83	1	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	1	no	—
566	C₂²⋊C₄	—	83	1	no	—
567	C₂²⋊C₄	—	83	2	no	—
568	C₂²⋊C₄	—	83	2	no	—
569	C₂²⋊C₄	—	83	1	no	—
570	C₂²⋊C₄	—	83	1	no	—
571	C₂²⋊C₄	—	83	2	no	—
572	C₂²⋊C₄	—	83	2	no	—
573	C₂²⋊C₄	—	83	2	no	—
574	C₂²⋊C₄	—	83	2	no	—
575	C₂²⋊C₄	—	83	2	no	—
576	C₂²⋊C₄	—	83	1	no	—
577	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
578	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
579	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
580	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
581	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
582	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
583	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
584	C₄²	—	83	1	no	—
585	C₄²	—	83	1	no	—
586	C₄²	—	83	1	no	—
587	C₄²	—	83	2	no	—
588	C₄²	—	83	2	no	—
589	C₄²	—	83	2	no	—
590	C₄²	C₂²×D₈₃	1	1	yes	characteristic
591	C₂³	—	4	2	no	—
592	C₂³	—	4	2	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	332	2	no	—
595	C₂³	—	332	2	no	—
596	C₂³	—	332	2	no	—
597	C₂³	—	83	1	no	—
598	C₂³	—	83	2	no	—
599	C₂³	—	83	1	no	—
600	C₂³	—	83	1	no	—
601	C₂³	C₂³×D₈₃	1	2	yes	—
602	C₂³	C₂³×D₈₃	1	1	yes	characteristic
603	C₂³	C₂³×D₈₃	1	2	yes	—
604	C₂³	C₂³×D₈₃	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	332	1	no	—
607	Q₈	—	332	1	no	—
608	Q₈	—	166	4	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	2	no	—
611	D₄	—	4	2	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	1	no	—
615	D₄	—	332	2	no	—
616	D₄	—	332	1	no	—
617	D₄	—	332	1	no	—
618	D₄	—	332	2	no	—
619	D₄	—	332	1	no	—
620	D₄	—	332	2	no	—
621	D₄	—	332	2	no	—
622	D₄	—	332	2	no	—
623	D₄	—	332	2	no	—
624	D₄	—	332	2	no	—
625	D₄	—	332	1	no	—
626	D₄	—	332	1	no	—
627	D₄	—	332	1	no	—
628	D₄	—	332	1	no	—
629	D₄	—	332	2	no	—
630	D₄	—	332	2	no	—
631	D₄	—	332	2	no	—
632	D₄	—	332	2	no	—
633	D₄	—	166	2	no	—
634	D₄	—	166	4	no	—
635	D₄	—	166	2	no	—
636	D₄	—	166	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	332	2	no	—
642	C₂×C₄	—	332	2	no	—
643	C₂×C₄	—	332	2	no	—
644	C₂×C₄	—	332	1	no	—
645	C₂×C₄	—	332	2	no	—
646	C₂×C₄	—	83	1	no	—
647	C₂×C₄	—	83	2	no	—
648	C₂×C₄	—	83	1	no	—
649	C₂×C₄	—	83	1	no	—
650	C₂×C₄	—	83	1	no	—
651	C₂×C₄	—	83	2	no	—
652	C₂×C₄	—	83	1	no	—
653	C₂×C₄	—	83	2	no	—
654	C₂×C₄	—	166	2	no	—
655	C₂×C₄	—	166	4	no	—
656	C₂×C₄	—	166	2	no	—
657	C₂×C₄	—	166	2	no	—
658	C₂×C₄	—	166	2	no	—
659	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
660	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₈₃	1	2	yes	—
663	C₂×C₄	C₂³×D₈₃	1	2	yes	—
664	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
666	C₂²	—	2	2	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	8	4	no	—
679	C₂²	—	664	4	no	—
680	C₂²	—	166	1	no	—
681	C₂²	—	166	2	no	—
682	C₂²	—	166	1	no	—
683	C₂²	—	166	1	no	—
684	C₂²	—	166	2	no	—
685	C₂²	—	166	1	no	—
686	C₂²	—	166	1	no	—
687	C₂²	—	166	1	no	—
688	C₂²	—	166	1	no	—
689	C₂²	—	166	1	no	—
690	C₂²	—	166	2	no	—
691	C₂²	—	166	1	no	—
692	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
693	C₄	—	2	1	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	1	no	—
699	C₄	—	83	2	no	—
700	C₄	—	166	2	no	—
701	C₄	—	166	2	no	—
702	C₄	—	166	1	no	—
703	C₄	—	166	1	no	—
704	C₄	—	166	1	no	—
705	C₄	—	166	1	no	—
706	C₄	—	166	2	no	—
707	C₄	#14581837	1	2	yes	—
708	C₂	—	4	1	no	—
709	C₂	—	4	2	no	—
710	C₂	—	4	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	332	1	no	—
713	C₂	—	332	2	no	—
714	C₂	—	332	1	no	—
715	C₂	—	332	1	no	—
716	C₂	H(5,𝔽₂)×D₈₃	1	1	yes	characteristic
717	C₂	C₂×#14581837	1	1	yes	characteristic
718	C₂	#19128537	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#546×C₈₃	C₂
hypercenter	#546	D₈₃
hypocenter	C₈₃	#3546
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #19128441	C₂	semidirect
2. #19128440	C₂	semidirect
3. #19128422	C₂	semidirect
4. #19128401	C₂	semidirect
5. #19128397	C₂	semidirect
6. #19128370	C₂	semidirect
7. #19128369	C₂	semidirect
8. #19128351	C₂	semidirect
9. #19128344	C₂	semidirect
10. #19128341	C₂	semidirect
11. D₄×C₂²⋊D₈₃	C₂	semidirect
12. #19128319	C₂	semidirect
13. #19128289	C₂	semidirect
14. #19128283	C₂	semidirect
15. #19128281	C₂	semidirect
16. #19128279	C₂	semidirect
17. #19128268	C₂	semidirect
18. #19128267	C₂	semidirect
19. #19128266	C₂	semidirect
20. #19128248	C₂	semidirect
21. #19128248	C₂	semidirect
22. #19128230	C₂	semidirect
23. #546×C₈₃	C₂	semidirect
24. C₂×#13050591	C₂²	semidirect
25. C₂×#13050590	C₂²	semidirect
26. C₂×#13050590	C₂²	semidirect
27. C₂×#13050590	C₂²	semidirect
28. C₂×#13050589	C₂²	semidirect
31. #14581791	C₂²	semidirect
32. #14581791	C₂²	semidirect
35. #14581788	C₂²	semidirect
36. #14581788	C₂²	semidirect
37. #14581788	C₂²	semidirect
38. #14581787	C₂²	semidirect
39. #14581787	C₂²	semidirect
40. #14581785	C₂²	semidirect
41. #14581785	C₂²	semidirect
42. #14581785	C₂²	semidirect
43. #14581784	C₂²	semidirect
44. #14581779	C₂²	semidirect
46. #14581778	C₂²	semidirect
47. #14581778	C₂²	semidirect
48. #14581778	C₂²	semidirect
49. #14581778	C₂²	semidirect
50. #14581775	C₂²	semidirect
51. #14581774	C₂²	semidirect
52. #14581774	C₂²	semidirect
53. #14581774	C₂²	semidirect
54. #14581774	C₂²	semidirect
55. #14581773	C₂²	semidirect
56. #14581771	C₂²	semidirect
57. #14581770	C₂²	semidirect
58. #14581769	C₂²	semidirect
59. #14581768	C₂²	semidirect
60. #14581768	C₂²	semidirect
61. #14581767	C₂²	semidirect
62. #14581767	C₂²	semidirect
63. #14581767	C₂²	semidirect
65. #14581766	C₂²	semidirect
66. #14581766	C₂²	semidirect
67. #14581766	C₂²	semidirect
69. #14581765	C₂²	semidirect
70. #14581765	C₂²	semidirect
71. #14581765	C₂²	semidirect
72. #14581765	C₂²	semidirect
73. #14581765	C₂²	semidirect
74. #14581765	C₂²	semidirect
76. #14581764	C₂²	semidirect
77. #14581764	C₂²	semidirect
78. #14581764	C₂²	semidirect
82. #14581763	C₂²	semidirect
83. #14581763	C₂²	semidirect
84. #14581763	C₂²	semidirect
85. #14581763	C₂²	semidirect
86. #14581762	C₂²	semidirect
87. #14581762	C₂²	semidirect
89. #14581761	C₂²	semidirect
90. #14581761	C₂²	semidirect
92. #14581760	C₂²	semidirect
93. Q₈×Dic₈₃	C₂²	semidirect
94. #14581757	C₂²	semidirect
95. C₄×D₃₃₂	C₂²	semidirect
96. C₄×D₃₃₂	C₂²	semidirect
99. C₄×C₂²⋊D₈₃	C₂²	semidirect
100. C₄×C₂²⋊D₈₃	C₂²	semidirect
101. C₄×C₂²⋊D₈₃	C₂²	semidirect
102. C₄×C₂²⋊D₈₃	C₂²	semidirect
103. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
104. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
105. #14581751	C₂²	semidirect
106. #14581750	C₂²	semidirect
107. #14581748	C₂²	semidirect
108. C₂×C₄⋊Dic₈₃	C₂²	semidirect
109. C₄⋊C₄×D₈₃	C₂²	semidirect
110. C₂²⋊C₄×D₈₃	C₂²	semidirect
111. C₄²×D₈₃	C₂²	semidirect
112. C₂×#41×C₈₃	C₂²	semidirect
115. #123×C₈₃	C₂²	semidirect
116. C₂²⋊Q₈×C₈₃	C₂²	semidirect
118. #121×C₈₃	C₂²	semidirect
119. #120×C₈₃	C₂²	semidirect
120. C₄×D₄×C₈₃	C₂²	semidirect
121. C₄×D₄×C₈₃	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₈₃	C₂²	semidirect
360. C₈₃	#3546	semidirect
371. #546	D₈₃	semidirect
389. C₂×#41	C₂×D₈₃	semidirect
419. #123	C₂×D₈₃	semidirect
425. C₂²⋊Q₈	C₂×D₈₃	semidirect
452. #121	C₂×D₈₃	semidirect
460. #120	C₂×D₈₃	semidirect
473. C₄×D₄	C₂×D₈₃	semidirect
474. C₄×D₄	C₂×D₈₃	semidirect
481. C₂×C₂²⋊C₄	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128441	2
#19128440	2
#19128422	2
#19128401	2
#19128397	2
#19128370	2
#19128369	2
#19128351	2
#19128344	2
#19128341	2
D₄×C₂²⋊D₈₃	2
#19128319	2
#19128289	2
#19128283	2
#19128281	2
#19128279	2
#19128268	2
#19128267	2
#19128266	2
#19128248	2
#19128230	2
#546×C₈₃	2
#3546	83