Subgroups — #24922009

Order 10624.

1056 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128453	C₂	1	2	yes	maximal, complemented
2	#19128442	C₂	1	2	yes	maximal, complemented
3	#19128400	C₂	1	2	yes	maximal, complemented
4	#19128395	C₂	1	2	yes	maximal, complemented
5	#19128375	C₂	1	2	yes	maximal, complemented
6	#19128349	C₂	1	2	yes	maximal, complemented
7	#19128346	C₂	1	2	yes	maximal, complemented
8	#19128343	C₂	1	2	yes	maximal, complemented
9	#19128323	C₂	1	2	yes	maximal, complemented
10	#19128300	C₂	1	1	yes	maximal, characteristic, complemented
11	#19128299	C₂	1	2	yes	maximal, complemented
12	#19128291	C₂	1	1	yes	maximal, characteristic, complemented
13	#19128285	C₂	1	2	yes	maximal, complemented
14	#19128284	C₂	1	2	yes	maximal, complemented
15	#19128278	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128259	C₂	1	1	yes	maximal, characteristic, complemented
17	#19128251	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14581786	C₂	1	1	yes	maximal, characteristic, complemented
19	#529×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13050590	C₂²	1	2	yes	complemented
21	C₂×#13050589	C₂²	1	2	yes	complemented
22	C₂×D₄×D₈₃	C₂²	1	2	yes	—
23	#14581792	C₂²	1	1	yes	characteristic, complemented
24	#14581791	C₂²	1	2	yes	complemented
25	#14581789	C₂²	1	1	yes	characteristic, complemented
26	#14581787	C₂²	1	2	yes	complemented
27	#14581787	C₂²	1	2	yes	complemented
28	#14581786	C₂²	1	2	yes	complemented
29	#14581786	C₂²	1	2	yes	complemented
30	#14581786	C₂²	1	2	yes	complemented
31	#14581786	C₂²	1	2	yes	complemented
32	#14581786	C₂²	1	2	yes	complemented
33	#14581785	C₂²	1	2	yes	complemented
34	#14581783	C₂²	1	2	yes	complemented
35	#14581782	C₂²	1	2	yes	complemented
36	#14581781	C₂²	1	2	yes	complemented
37	#14581780	C₂²	1	2	yes	—
38	#14581780	C₂²	1	2	yes	complemented
39	#14581778	C₂²	1	2	yes	—
40	#14581777	C₂²	1	2	yes	—
41	#14581777	C₂²	1	2	yes	—
42	#14581777	C₂²	1	2	yes	complemented
43	#14581777	C₂²	1	2	yes	complemented
44	#14581777	C₂²	1	2	yes	complemented
45	#14581777	C₂²	1	2	yes	complemented
46	#14581776	C₂²	1	2	yes	—
47	#14581776	C₂²	1	2	yes	complemented
48	#14581775	C₂²	1	2	yes	complemented
49	#14581774	C₂²	1	2	yes	—
50	#14581774	C₂²	1	2	yes	complemented
51	#14581772	C₂²	1	2	yes	complemented
52	#14581770	C₂²	1	2	yes	complemented
53	#14581770	C₂²	1	2	yes	complemented
54	#14581770	C₂²	1	2	yes	complemented
55	#14581769	C₂²	1	2	yes	complemented
56	#14581769	C₂²	1	2	yes	complemented
57	#14581768	C₂²	1	2	yes	complemented
58	#14581767	C₂²	1	2	yes	—
59	#14581767	C₂²	1	2	yes	—
60	#14581767	C₂²	1	2	yes	complemented
61	#14581766	C₂²	1	2	yes	—
62	#14581766	C₂²	1	1	yes	characteristic
63	#14581766	C₂²	1	2	yes	complemented
64	#14581766	C₂²	1	1	yes	characteristic, complemented
65	#14581765	C₂²	1	2	yes	—
66	#14581765	C₂²	1	2	yes	complemented
67	#14581765	C₂²	1	2	yes	complemented
68	#14581765	C₂²	1	2	yes	complemented
69	#14581764	C₂²	1	2	yes	—
70	#14581764	C₂²	1	2	yes	complemented
71	#14581764	C₂²	1	2	yes	complemented
72	#14581762	C₂²	1	2	yes	—
73	#14581762	C₂²	1	2	yes	—
74	#14581762	C₂²	1	2	yes	complemented
75	#14581762	C₂²	1	2	yes	complemented
76	#14581760	C₂²	1	2	yes	—
77	C₄×D₃₃₂	C₂²	1	2	yes	complemented
78	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₃₃₂	C₂²	1	2	yes	complemented
81	#14581754	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
83	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
84	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
85	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	complemented
86	#14581749	C₂²	1	2	yes	complemented
87	C₂×Dic₈₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
88	C₂×Dic₈₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
89	C₂×Dic₈₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
90	C₄⋊C₄×D₈₃	C₂²	1	2	yes	complemented
91	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	1	yes	characteristic
92	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	1	yes	characteristic
93	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	1	yes	characteristic
94	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₈₃	C₂²	1	2	yes	complemented
96	#126×C₈₃	C₂²	1	2	yes	complemented
97	#125×C₈₃	C₂²	1	1	yes	characteristic, complemented
98	#124×C₈₃	C₂²	1	1	yes	characteristic, complemented
99	#123×C₈₃	C₂²	1	2	yes	complemented
100	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
101	#121×C₈₃	C₂²	1	1	yes	characteristic
102	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
103	C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
104	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
105	#117×C₈₃	C₂²	1	2	yes	complemented
106	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₈₃	C₂³	1	1	yes	characteristic
108	C₂³×D₈₃	C₂³	1	2	yes	—
109	#13050590	—	4	4	no	—
110	#13050589	—	4	4	no	—
111	C₂×Dic₁₆₆	C₂³	1	2	yes	—
112	C₂×Dic₁₆₆	C₂³	1	2	yes	—
113	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
114	C₂×D₃₃₂	C₂³	1	2	yes	—
115	C₂×D₃₃₂	C₂³	1	2	yes	—
116	C₂×D₃₃₂	C₂³	1	2	yes	—
117	C₂×D₃₃₂	C₂³	1	2	yes	—
118	C₂×D₃₃₂	C₂³	1	2	yes	—
119	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
126	D₄×D₈₃	—	4	4	no	—
127	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
128	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
129	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
130	C₂²×Dic₈₃	C₂³	1	2	yes	—
131	C₂×C₄×D₈₃	C₂³	1	2	yes	—
132	C₂×C₄×D₈₃	C₂³	1	2	yes	—
133	C₂×C₄×D₈₃	C₂³	1	2	yes	—
134	C₂×C₄×D₈₃	C₂³	1	2	yes	—
135	C₂×C₄×D₈₃	C₂³	1	2	yes	—
136	C₂×C₄×D₈₃	C₂³	1	2	yes	—
137	C₄⋊Dic₈₃	C₂³	1	2	yes	—
138	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₈₃	C₂³	1	2	yes	—
141	C₄⋊Dic₈₃	C₂³	1	2	yes	—
142	Dic₈₃⋊C₄	C₂³	1	2	yes	—
143	Dic₈₃⋊C₄	C₂³	1	2	yes	—
144	Dic₈₃⋊C₄	C₂³	1	2	yes	—
145	Dic₈₃⋊C₄	C₂³	1	2	yes	—
146	Dic₈₃⋊C₄	C₂³	1	2	yes	—
147	Dic₈₃⋊C₄	C₂³	1	2	yes	—
148	Dic₈₃⋊C₄	C₂³	1	2	yes	—
149	Dic₈₃⋊C₄	C₂³	1	2	yes	—
150	Dic₈₃⋊C₄	C₂³	1	2	yes	—
151	Dic₈₃⋊C₄	C₂³	1	2	yes	—
152	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
153	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
154	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
155	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
156	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
157	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
158	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
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	C₄×Dic₈₃	C₂³	1	2	yes	—
173	C₄×Dic₈₃	C₂³	1	2	yes	—
174	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
175	C₂×D₄×C₈₃	C₂³	1	2	yes	—
176	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
177	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
178	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
179	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
180	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
182	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
183	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
184	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
185	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
186	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
187	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
192	C₄²×C₈₃	C₂³	1	2	yes	—
193	C₄²×C₈₃	C₂³	1	1	yes	characteristic
194	C₄²×C₈₃	C₂³	1	1	yes	characteristic
195	C₄²×C₈₃	C₂³	1	1	yes	characteristic
196	C₄²×C₈₃	C₂³	1	1	yes	characteristic
197	C₂³×C₈₃	C₂⁴	1	2	yes	—
198	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
199	C₂²×D₈₃	—	2	2	no	—
200	C₂²×D₈₃	—	4	2	no	—
201	C₂²×D₈₃	—	4	2	no	—
202	C₂²×D₈₃	—	4	2	no	—
203	C₂²×D₈₃	—	4	1	no	—
204	C₂²×D₈₃	—	4	1	no	—
205	C₂²×D₈₃	C₂⁴	1	2	yes	—
206	C₂²×D₈₃	C₂⁴	1	2	yes	—
207	C₂²×D₈₃	C₂⁴	1	2	yes	—
208	Q₈×C₈₃	—	4	1	no	—
209	D₄×C₈₃	—	2	4	no	—
210	D₄×C₈₃	—	4	1	no	—
211	C₂×C₄×C₈₃	—	2	2	no	—
212	C₂×C₄×C₈₃	—	4	2	no	—
213	C₂×C₄×C₈₃	—	4	1	no	—
214	C₂×C₄×C₈₃	—	4	1	no	—
215	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
217	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
218	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
219	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
220	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
221	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
222	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
223	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
224	C₂²⋊D₈₃	—	2	4	no	—
225	C₂²⋊D₈₃	—	2	4	no	—
226	C₂²⋊D₈₃	—	4	2	no	—
227	C₂²⋊D₈₃	—	4	2	no	—
228	C₂²⋊D₈₃	—	4	2	no	—
229	C₂²⋊D₈₃	—	4	2	no	—
230	C₂×Dic₈₃	—	2	2	no	—
231	C₂×Dic₈₃	—	4	1	no	—
232	C₂×Dic₈₃	—	4	1	no	—
233	C₂×Dic₈₃	—	4	2	no	—
234	C₂×Dic₈₃	C₂⁴	1	2	yes	—
235	C₂×Dic₈₃	C₂⁴	1	2	yes	—
236	C₂×Dic₈₃	C₂⁴	1	2	yes	—
237	C₂×Dic₈₃	C₂⁴	1	2	yes	—
238	C₂×Dic₈₃	C₂⁴	1	2	yes	—
239	D₃₃₂	—	4	2	no	—
240	D₃₃₂	—	4	2	no	—
241	D₃₃₂	—	4	2	no	—
242	D₃₃₂	—	4	2	no	—
243	D₃₃₂	—	4	1	no	—
244	D₃₃₂	—	4	1	no	—
245	D₃₃₂	—	4	2	no	—
246	C₄×D₈₃	—	4	2	no	—
247	C₄×D₈₃	—	4	2	no	—
248	C₄×D₈₃	—	4	2	no	—
249	C₄×D₈₃	—	4	2	no	—
250	C₄×D₈₃	—	4	2	no	—
251	C₄×D₈₃	—	4	2	no	—
252	Dic₁₆₆	—	4	2	no	—
253	Dic₁₆₆	—	4	2	no	—
254	C₂²×C₈₃	—	2	1	no	—
255	C₂²×C₈₃	—	2	1	no	—
256	C₂²×C₈₃	—	2	2	no	—
257	C₂²×C₈₃	—	2	2	no	—
258	C₂²×C₈₃	—	2	2	no	—
259	C₂²×C₈₃	H(5,𝔽₂)	1	2	yes	—
260	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
261	C₂×D₈₃	—	2	2	no	—
262	C₂×D₈₃	—	2	2	no	—
263	C₂×D₈₃	—	2	2	no	—
264	C₂×D₈₃	—	2	2	no	—
265	C₂×D₈₃	—	2	2	no	—
266	C₂×D₈₃	—	2	2	no	—
267	C₂×D₈₃	—	2	2	no	—
268	C₂×D₈₃	—	2	2	no	—
269	C₂×D₈₃	—	2	2	no	—
270	C₂×D₈₃	—	8	2	no	—
271	C₂×D₈₃	—	8	4	no	—
272	C₄×C₈₃	—	2	1	no	—
273	C₄×C₈₃	—	2	2	no	—
274	C₄×C₈₃	—	2	1	no	—
275	C₄×C₈₃	—	2	2	no	—
276	C₄×C₈₃	—	2	2	no	—
277	C₄×C₈₃	—	2	1	no	—
278	C₄×C₈₃	—	2	1	no	—
279	C₄×C₈₃	—	2	1	no	—
280	C₄×C₈₃	—	2	1	no	—
281	Dic₈₃	—	2	2	no	—
282	Dic₈₃	—	2	2	no	—
283	Dic₈₃	—	2	2	no	—
284	Dic₈₃	—	2	2	no	—
285	Dic₈₃	—	2	2	no	—
286	C₂×C₈₃	—	2	2	no	—
287	C₂×C₈₃	—	4	2	no	—
288	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
289	C₂×C₈₃	#585	1	1	yes	characteristic
290	C₂×C₈₃	#585	1	1	yes	characteristic
291	D₈₃	—	4	2	no	—
292	D₈₃	—	4	2	no	—
293	D₈₃	—	4	2	no	—
294	#3560	—	83	1	no	maximal, Sylow
295	C₈₃	#3560	1	1	yes	characteristic, complemented, Sylow
296	#563	—	83	2	no	—
297	#560	—	83	2	no	—
298	#553	—	83	2	no	—
299	#553	—	83	2	no	—
300	#551	—	83	2	no	—
301	#547	—	83	2	no	—
302	#546	—	83	2	no	—
303	#546	—	83	2	no	—
304	#542	—	83	2	no	—
305	#539	—	83	2	no	—
306	#539	—	83	1	no	—
307	#538	—	83	2	no	—
308	#538	—	83	1	no	—
309	#538	—	83	2	no	—
310	#537	—	83	1	no	—
311	#534	—	83	1	no	—
312	#532	—	83	1	no	—
313	#529	D₈₃	1	1	yes	characteristic, complemented
314	C₂×#126	—	83	1	no	—
315	C₂×#41	—	83	2	no	—
316	C₂×#41	—	83	2	no	—
317	C₂²×D₄	—	83	2	no	—
318	C₄⋊Q₈	—	83	2	no	—
319	C₄⋊Q₈	—	83	1	no	—
320	#127	—	83	1	no	—
321	#126	—	83	2	no	—
322	#126	—	83	2	no	—
323	#126	—	83	2	no	—
324	#126	—	83	2	no	—
325	#126	—	83	2	no	—
326	#126	—	83	2	no	—
327	#126	—	83	2	no	—
328	#126	—	83	2	no	—
329	#126	C₂×D₈₃	1	2	yes	complemented
330	#125	—	83	2	no	—
331	#125	—	83	2	no	—
332	#125	C₂×D₈₃	1	1	yes	characteristic, complemented
333	#124	—	83	2	no	—
334	#124	—	83	2	no	—
335	#124	—	83	2	no	—
336	#124	—	83	2	no	—
337	#124	C₂×D₈₃	1	1	yes	characteristic, complemented
338	#123	—	83	2	no	—
339	#123	—	83	2	no	—
340	#123	—	83	2	no	—
341	#123	—	83	2	no	—
342	#123	—	83	2	no	—
343	#123	—	83	2	no	—
344	#123	—	83	2	no	—
345	#123	—	83	2	no	—
346	#123	—	83	2	no	—
347	#123	—	83	2	no	—
348	#123	—	83	2	no	—
349	#123	C₂×D₈₃	1	2	yes	complemented
350	C₂²⋊Q₈	—	83	2	no	—
351	C₂²⋊Q₈	—	83	2	no	—
352	C₂²⋊Q₈	—	83	2	no	—
353	C₂²⋊Q₈	—	83	2	no	—
354	C₂²⋊Q₈	—	83	2	no	—
355	C₂²⋊Q₈	—	83	2	no	—
356	C₂²⋊Q₈	—	83	2	no	—
357	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
358	#121	—	83	2	no	—
359	#121	—	83	2	no	—
360	#121	—	83	2	no	—
361	#121	—	83	1	no	—
362	#121	—	83	2	no	—
363	#121	—	83	1	no	—
364	#121	—	83	2	no	—
365	#121	—	83	2	no	—
366	#121	—	83	2	no	—
367	#121	—	83	2	no	—
368	#121	—	83	2	no	—
369	#121	—	83	2	no	—
370	#121	—	83	2	no	—
371	#121	—	83	2	no	—
372	#121	C₂×D₈₃	1	1	yes	characteristic
373	#120	—	83	2	no	—
374	#120	—	83	2	no	—
375	#120	—	83	2	no	—
376	#120	—	83	2	no	—
377	#120	—	83	2	no	—
378	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
379	C₄×D₄	—	83	2	no	—
380	C₄×D₄	—	83	2	no	—
381	C₄×D₄	—	83	2	no	—
382	C₄×D₄	—	83	2	no	—
383	C₄×D₄	—	83	2	no	—
384	C₄×D₄	—	83	2	no	—
385	C₄×D₄	—	83	1	no	—
386	C₄×D₄	—	83	1	no	—
387	C₄×D₄	—	83	2	no	—
388	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
389	C₄×D₄	C₂×D₈₃	1	2	yes	complemented
390	#117	—	83	2	no	—
391	#117	C₂×D₈₃	1	2	yes	complemented
392	C₂×C₄⋊C₄	—	83	1	no	—
393	C₂×C₄⋊C₄	—	83	1	no	—
394	C₂×C₄⋊C₄	—	83	1	no	—
395	C₂×C₄⋊C₄	—	83	2	no	—
396	C₂×C₂²⋊C₄	—	83	1	no	—
397	C₂×C₂²⋊C₄	—	83	1	no	—
398	C₂×C₂²⋊C₄	—	83	1	no	—
399	C₂×C₂²⋊C₄	—	83	2	no	—
400	C₂×C₂²⋊C₄	—	83	2	no	—
401	C₂×C₄²	C₂×D₈₃	1	1	yes	characteristic, complemented
402	C₂⁴	—	83	2	no	—
403	C₂⁴	—	83	1	no	—
404	#41	—	332	4	no	—
405	#41	—	332	4	no	—
406	C₂×Q₈	—	83	2	no	—
407	C₂×Q₈	—	83	2	no	—
408	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
409	C₂×D₄	—	332	4	no	—
410	C₂×D₄	—	83	2	no	—
411	C₂×D₄	—	83	2	no	—
412	C₂×D₄	—	83	2	no	—
413	C₂×D₄	—	83	2	no	—
414	C₂×D₄	—	83	2	no	—
415	C₂×D₄	—	83	2	no	—
416	C₂×D₄	—	83	2	no	—
417	C₂×D₄	—	83	2	no	—
418	C₂×D₄	—	83	1	no	—
419	C₂×D₄	—	83	2	no	—
420	C₂×D₄	—	83	1	no	—
421	C₂×D₄	—	83	2	no	—
422	C₂×D₄	—	83	2	no	—
423	C₂×D₄	C₂²×D₈₃	1	2	yes	—
424	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
425	C₂²×C₄	—	83	1	no	—
426	C₂²×C₄	—	83	1	no	—
427	C₂²×C₄	—	83	2	no	—
428	C₂²×C₄	—	83	2	no	—
429	C₂²×C₄	—	83	2	no	—
430	C₂²×C₄	—	83	2	no	—
431	C₂²×C₄	—	83	2	no	—
432	C₂²×C₄	—	83	2	no	—
433	C₂²×C₄	—	83	2	no	—
434	C₂²×C₄	—	83	1	no	—
435	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
436	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
437	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
438	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
439	C₄⋊C₄	—	83	2	no	—
440	C₄⋊C₄	—	83	2	no	—
441	C₄⋊C₄	—	83	2	no	—
442	C₄⋊C₄	—	83	2	no	—
443	C₄⋊C₄	—	83	2	no	—
444	C₄⋊C₄	—	83	2	no	—
445	C₄⋊C₄	—	83	2	no	—
446	C₄⋊C₄	—	83	2	no	—
447	C₄⋊C₄	—	83	2	no	—
448	C₄⋊C₄	—	83	2	no	—
449	C₄⋊C₄	—	83	1	no	—
450	C₄⋊C₄	—	83	2	no	—
451	C₄⋊C₄	—	83	1	no	—
452	C₄⋊C₄	—	83	2	no	—
453	C₄⋊C₄	—	83	2	no	—
454	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
455	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
456	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
457	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
458	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
459	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
460	C₂²⋊C₄	—	83	2	no	—
461	C₂²⋊C₄	—	83	2	no	—
462	C₂²⋊C₄	—	83	2	no	—
463	C₂²⋊C₄	—	83	2	no	—
464	C₂²⋊C₄	—	83	2	no	—
465	C₂²⋊C₄	—	83	2	no	—
466	C₂²⋊C₄	—	83	2	no	—
467	C₂²⋊C₄	—	83	2	no	—
468	C₂²⋊C₄	—	83	2	no	—
469	C₂²⋊C₄	—	83	2	no	—
470	C₂²⋊C₄	—	83	2	no	—
471	C₂²⋊C₄	—	83	2	no	—
472	C₂²⋊C₄	—	83	2	no	—
473	C₂²⋊C₄	—	83	2	no	—
474	C₂²⋊C₄	—	83	2	no	—
475	C₂²⋊C₄	—	83	2	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	C₂²×D₈₃	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
484	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
485	C₄²	—	83	2	no	—
486	C₄²	—	83	2	no	—
487	C₄²	C₂²×D₈₃	1	1	yes	characteristic
488	C₄²	C₂²×D₈₃	1	1	yes	characteristic
489	C₄²	C₂²×D₈₃	1	1	yes	characteristic
490	C₄²	C₂²×D₈₃	1	1	yes	characteristic
491	C₄²	C₂²×D₈₃	1	2	yes	—
492	C₂³	—	332	2	no	—
493	C₂³	—	332	1	no	—
494	C₂³	—	332	1	no	—
495	C₂³	—	332	2	no	—
496	C₂³	—	332	2	no	—
497	C₂³	—	83	2	no	—
498	C₂³	—	83	2	no	—
499	C₂³	—	83	2	no	—
500	C₂³	—	166	2	no	—
501	C₂³	C₂³×D₈₃	1	2	yes	—
502	C₂³	C₂³×D₈₃	1	1	yes	characteristic
503	Q₈	—	4	1	no	—
504	Q₈	—	332	2	no	—
505	Q₈	—	332	2	no	—
506	D₄	—	2	4	no	—
507	D₄	—	4	1	no	—
508	D₄	—	332	2	no	—
509	D₄	—	332	2	no	—
510	D₄	—	332	2	no	—
511	D₄	—	332	2	no	—
512	D₄	—	332	1	no	—
513	D₄	—	332	1	no	—
514	D₄	—	332	2	no	—
515	D₄	—	332	2	no	—
516	D₄	—	332	2	no	—
517	D₄	—	332	2	no	—
518	D₄	—	332	2	no	—
519	D₄	—	166	4	no	—
520	D₄	—	166	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	332	2	no	—
526	C₂×C₄	—	332	2	no	—
527	C₂×C₄	—	332	2	no	—
528	C₂×C₄	—	332	2	no	—
529	C₂×C₄	—	332	2	no	—
530	C₂×C₄	—	332	2	no	—
531	C₂×C₄	—	332	2	no	—
532	C₂×C₄	—	332	1	no	—
533	C₂×C₄	—	332	1	no	—
534	C₂×C₄	—	83	2	no	—
535	C₂×C₄	—	83	2	no	—
536	C₂×C₄	—	83	2	no	—
537	C₂×C₄	—	83	2	no	—
538	C₂×C₄	—	83	2	no	—
539	C₂×C₄	—	166	2	no	—
540	C₂×C₄	C₂³×D₈₃	1	2	yes	—
541	C₂×C₄	C₂³×D₈₃	1	2	yes	—
542	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
543	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
547	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
548	C₂×C₄	C₂³×D₈₃	1	2	yes	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	664	2	no	—
555	C₂²	—	664	4	no	—
556	C₂²	—	166	2	no	—
557	C₂²	—	166	2	no	—
558	C₂²	—	166	2	no	—
559	C₂²	—	166	2	no	—
560	C₂²	—	166	2	no	—
561	C₂²	—	166	2	no	—
562	C₂²	—	166	2	no	—
563	C₂²	—	166	2	no	—
564	C₂²	—	166	2	no	—
565	C₂²	#14581838	1	2	yes	—
566	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	2	no	—
576	C₄	—	166	2	no	—
577	C₄	—	166	2	no	—
578	C₄	—	166	2	no	—
579	C₄	—	166	2	no	—
580	C₄	—	166	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	332	2	no	—
584	C₂	—	332	2	no	—
585	C₂	—	332	2	no	—
586	C₂	C₂×#14581838	1	1	yes	characteristic
587	C₂	#19128537	1	1	yes	characteristic
588	C₂	#19128537	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#529×C₈₃	C₂
hypercenter	#529	D₈₃
hypocenter	C₈₃	#3560
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #19128453	C₂	semidirect
2. #19128442	C₂	semidirect
3. #19128400	C₂	semidirect
4. #19128395	C₂	semidirect
5. #19128375	C₂	semidirect
6. #19128349	C₂	semidirect
7. #19128346	C₂	semidirect
8. #19128343	C₂	semidirect
9. #19128323	C₂	semidirect
10. #19128300	C₂	semidirect
11. #19128299	C₂	semidirect
12. #19128291	C₂	semidirect
13. #19128285	C₂	semidirect
14. #19128284	C₂	semidirect
15. #19128278	C₂	semidirect
16. #19128259	C₂	semidirect
17. #19128251	C₂	semidirect
18. C₂×#14581786	C₂	semidirect
19. #529×C₈₃	C₂	semidirect
20. C₂×#13050590	C₂²	semidirect
21. C₂×#13050589	C₂²	semidirect
23. #14581792	C₂²	semidirect
24. #14581791	C₂²	semidirect
25. #14581789	C₂²	semidirect
26. #14581787	C₂²	semidirect
27. #14581787	C₂²	semidirect
28. #14581786	C₂²	semidirect
29. #14581786	C₂²	semidirect
30. #14581786	C₂²	semidirect
31. #14581786	C₂²	semidirect
32. #14581786	C₂²	semidirect
33. #14581785	C₂²	semidirect
34. #14581783	C₂²	semidirect
35. #14581782	C₂²	semidirect
36. #14581781	C₂²	semidirect
38. #14581780	C₂²	semidirect
42. #14581777	C₂²	semidirect
43. #14581777	C₂²	semidirect
44. #14581777	C₂²	semidirect
45. #14581777	C₂²	semidirect
47. #14581776	C₂²	semidirect
48. #14581775	C₂²	semidirect
50. #14581774	C₂²	semidirect
51. #14581772	C₂²	semidirect
52. #14581770	C₂²	semidirect
53. #14581770	C₂²	semidirect
54. #14581770	C₂²	semidirect
55. #14581769	C₂²	semidirect
56. #14581769	C₂²	semidirect
57. #14581768	C₂²	semidirect
60. #14581767	C₂²	semidirect
63. #14581766	C₂²	semidirect
64. #14581766	C₂²	semidirect
66. #14581765	C₂²	semidirect
67. #14581765	C₂²	semidirect
68. #14581765	C₂²	semidirect
70. #14581764	C₂²	semidirect
71. #14581764	C₂²	semidirect
74. #14581762	C₂²	semidirect
75. #14581762	C₂²	semidirect
77. C₄×D₃₃₂	C₂²	semidirect
78. C₄×D₃₃₂	C₂²	semidirect
79. C₄×D₃₃₂	C₂²	semidirect
80. C₄×D₃₃₂	C₂²	semidirect
81. #14581754	C₂²	semidirect
82. C₄×C₂²⋊D₈₃	C₂²	semidirect
83. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
84. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
85. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
86. #14581749	C₂²	semidirect
87. C₂×Dic₈₃⋊C₄	C₂²	semidirect
88. C₂×Dic₈₃⋊C₄	C₂²	semidirect
89. C₂×Dic₈₃⋊C₄	C₂²	semidirect
90. C₄⋊C₄×D₈₃	C₂²	semidirect
94. C₂×(C₂×D₈₃)⋊C₄	C₂²	semidirect
95. C₂²⋊C₄×D₈₃	C₂²	semidirect
96. #126×C₈₃	C₂²	semidirect
97. #125×C₈₃	C₂²	semidirect
98. #124×C₈₃	C₂²	semidirect
99. #123×C₈₃	C₂²	semidirect
100. C₂²⋊Q₈×C₈₃	C₂²	semidirect
102. C₄×Q₈×C₈₃	C₂²	semidirect
103. C₄×D₄×C₈₃	C₂²	semidirect
104. C₄×D₄×C₈₃	C₂²	semidirect
105. #117×C₈₃	C₂²	semidirect
106. C₂×C₄²×C₈₃	C₂²	semidirect
295. C₈₃	#3560	semidirect
313. #529	D₈₃	semidirect
329. #126	C₂×D₈₃	semidirect
332. #125	C₂×D₈₃	semidirect
337. #124	C₂×D₈₃	semidirect
349. #123	C₂×D₈₃	semidirect
357. C₂²⋊Q₈	C₂×D₈₃	semidirect
378. C₄×Q₈	C₂×D₈₃	semidirect
388. C₄×D₄	C₂×D₈₃	semidirect
389. C₄×D₄	C₂×D₈₃	semidirect
391. #117	C₂×D₈₃	semidirect
401. C₂×C₄²	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128453	2
#19128442	2
#19128400	2
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#19128285	2
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C₂×#14581786	2
#529×C₈₃	2
#3560	83