Subgroups — #24921332

Order 10624.

1232 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128434	C₂	1	2	yes	maximal, complemented
2	#19128433	C₂	1	2	yes	maximal, complemented
3	#19128370	C₂	1	2	yes	maximal, complemented
4	#19128369	C₂	1	2	yes	maximal, complemented
5	#19128348	C₂	1	2	yes	maximal, complemented
6	#19128346	C₂	1	2	yes	maximal, complemented
7	#19128344	C₂	1	2	yes	maximal, complemented
8	#19128339	C₂	1	2	yes	maximal, complemented
9	#19128304	C₂	1	2	yes	maximal, complemented
10	#19128302	C₂	1	2	yes	maximal, complemented
11	#19128267	C₂	1	2	yes	maximal, complemented
12	#19128256	C₂	1	1	yes	maximal, characteristic, complemented
13	#19128252	C₂	1	1	yes	maximal, characteristic, complemented
14	#19128251	C₂	1	1	yes	maximal, characteristic, complemented
15	#19128249	C₂	1	1	yes	maximal, characteristic, complemented
16	#127×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#19128173	C₂	1	2	yes	maximal, complemented
18	C₄×#13050590	C₂	1	1	yes	maximal, characteristic, complemented
19	#532×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13050591	C₂²	1	2	yes	complemented
21	C₂×#13050590	C₂²	1	1	yes	characteristic
22	C₂×#13050590	C₂²	1	2	yes	complemented
23	C₂×#13050589	C₂²	1	2	yes	complemented
24	C₂×D₄×D₈₃	C₂²	1	2	yes	—
25	C₂×D₄×D₈₃	C₂²	1	2	yes	—
26	C₂×D₄×D₈₃	C₂²	1	2	yes	—
27	#14581792	C₂²	1	1	yes	characteristic, complemented
28	#14581789	C₂²	1	1	yes	characteristic
29	#14581788	C₂²	1	2	yes	—
30	#14581788	C₂²	1	2	yes	—
31	#14581788	C₂²	1	2	yes	—
32	#14581788	C₂²	1	4	yes	complemented
33	#14581783	C₂²	1	2	yes	complemented
34	#14581781	C₂²	1	2	yes	complemented
35	#14581780	C₂²	1	2	yes	complemented
36	#14581779	C₂²	1	2	yes	complemented
37	#14581778	C₂²	1	4	yes	complemented
38	#14581776	C₂²	1	4	yes	complemented
39	#14581775	C₂²	1	4	yes	complemented
40	#14581774	C₂²	1	4	yes	complemented
41	#14581774	C₂²	1	4	yes	complemented
42	#14581772	C₂²	1	2	yes	—
43	#14581768	C₂²	1	2	yes	—
44	#14581767	C₂²	1	2	yes	complemented
45	#14581767	C₂²	1	2	yes	complemented
46	#14581766	C₂²	1	2	yes	complemented
47	#14581766	C₂²	1	4	yes	complemented
48	#14581766	C₂²	1	2	yes	complemented
49	#14581765	C₂²	1	4	yes	complemented
50	#14581764	C₂²	1	4	yes	complemented
51	#14581763	C₂²	1	2	yes	complemented
52	#14581763	C₂²	1	4	yes	complemented
53	#14581763	C₂²	1	2	yes	complemented
54	#14581762	C₂²	1	4	yes	—
55	#14581760	C₂²	1	4	yes	—
56	Q₈×Dic₈₃	C₂²	1	2	yes	complemented
57	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
58	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
59	#14581757	C₂²	1	2	yes	complemented
60	C₄×D₃₃₂	C₂²	1	1	yes	characteristic
61	C₄×D₃₃₂	C₂²	1	1	yes	characteristic
62	C₄×D₃₃₂	C₂²	1	2	yes	complemented
63	C₄×D₃₃₂	C₂²	1	2	yes	complemented
64	D₄×Dic₈₃	C₂²	1	2	yes	complemented
65	D₄×Dic₈₃	C₂²	1	2	yes	complemented
66	#14581754	C₂²	1	2	yes	complemented
67	#14581754	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic, complemented
72	C₄×C₂²⋊D₈₃	C₂²	1	4	yes	complemented
73	(C₂²⋊D₈₃)⋊C₄	C₂²	1	4	yes	complemented
74	#14581751	C₂²	1	1	yes	characteristic, complemented
75	#14581750	C₂²	1	2	yes	—
76	#14581749	C₂²	1	1	yes	characteristic
77	#14581749	C₂²	1	1	yes	characteristic, complemented
78	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	4	yes	—
79	C₂²⋊C₄×D₈₃	C₂²	1	4	yes	—
80	C₄²×D₈₃	C₂²	1	1	yes	characteristic
81	C₄²×D₈₃	C₂²	1	1	yes	characteristic, complemented
82	C₂×#41×C₈₃	C₂²	1	2	yes	complemented
83	C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
84	#127×C₈₃	C₂²	1	1	yes	characteristic
85	#124×C₈₃	C₂²	1	2	yes	complemented
86	#121×C₈₃	C₂²	1	2	yes	complemented
87	#121×C₈₃	C₂²	1	2	yes	complemented
88	C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
89	C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
90	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic, complemented
91	C₂³×D₈₃	C₂³	1	4	yes	—
92	#13050591	—	4	4	no	—
93	#13050590	—	2	4	no	—
94	#13050590	—	4	4	no	—
95	#13050589	—	4	4	no	—
96	C₂×Dic₁₆₆	C₂³	1	2	yes	—
97	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
98	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
99	C₂×D₃₃₂	C₂³	1	2	yes	—
100	C₂×D₃₃₂	C₂³	1	2	yes	—
101	C₂×D₃₃₂	C₂³	1	2	yes	—
102	C₂×D₃₃₂	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
105	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
108	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
109	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
110	D₄×D₈₃	—	2	8	no	—
111	D₄×D₈₃	—	4	4	no	—
112	D₄×D₈₃	—	4	4	no	—
113	C₂²×Dic₈₃	C₂³	1	4	yes	—
114	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
115	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
116	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
117	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
118	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
119	C₂×C₄×D₈₃	C₂³	1	4	yes	—
120	C₂×C₄×D₈₃	C₂³	1	4	yes	—
121	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
122	C₄⋊Dic₈₃	C₂³	1	2	yes	—
123	C₄⋊Dic₈₃	C₂³	1	4	yes	—
124	C₄⋊Dic₈₃	C₂³	1	2	yes	—
125	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
126	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
127	Dic₈₃⋊C₄	C₂³	1	4	yes	—
128	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
129	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
130	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
131	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
132	C₂²⋊Dic₈₃	C₂³	1	4	yes	—
133	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
134	C₂²⋊Dic₈₃	C₂³	1	4	yes	—
135	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
136	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
137	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
138	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
139	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
140	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
141	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
142	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
143	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
144	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
145	C₄×Dic₈₃	C₂³	1	4	yes	—
146	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
147	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
148	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
149	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
150	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
151	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
152	#41×C₈₃	—	4	4	no	—
153	C₂×Q₈×C₈₃	C₂³	1	2	yes	—
154	C₂×D₄×C₈₃	C₂³	1	2	yes	—
155	C₂×D₄×C₈₃	C₂³	1	2	yes	—
156	C₂×D₄×C₈₃	C₂³	1	2	yes	—
157	C₂×D₄×C₈₃	C₂³	1	4	yes	—
158	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
159	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
160	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
161	C₂²×C₄×C₈₃	C₂³	1	4	yes	—
162	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
163	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
165	C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
166	C₄²×C₈₃	C₂³	1	1	yes	characteristic
167	C₄²×C₈₃	C₂³	1	1	yes	characteristic
168	C₄²×C₈₃	C₂³	1	1	yes	characteristic
169	C₄²×C₈₃	C₂³	1	1	yes	characteristic
170	C₂³×C₈₃	C₂⁴	1	4	yes	—
171	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
172	C₂²×D₈₃	—	2	8	no	—
173	C₂²×D₈₃	—	4	4	no	—
174	C₂²×D₈₃	—	4	4	no	—
175	C₂²×D₈₃	C₂⁴	1	4	yes	—
176	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
177	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
178	Q₈×C₈₃	—	2	4	no	—
179	D₄×C₈₃	—	2	4	no	—
180	D₄×C₈₃	—	2	4	no	—
181	D₄×C₈₃	—	2	4	no	—
182	D₄×C₈₃	—	4	4	no	—
183	C₂×C₄×C₈₃	—	2	2	no	—
184	C₂×C₄×C₈₃	—	2	2	no	—
185	C₂×C₄×C₈₃	—	2	2	no	—
186	C₂×C₄×C₈₃	—	4	4	no	—
187	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
188	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
189	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₈₃	C₂⁴	1	4	yes	—
191	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
194	C₂²⋊D₈₃	—	2	2	no	—
195	C₂²⋊D₈₃	—	2	8	no	—
196	C₂²⋊D₈₃	—	2	2	no	—
197	C₂²⋊D₈₃	—	4	4	no	—
198	C₂²⋊D₈₃	—	4	4	no	—
199	C₂²⋊D₈₃	—	4	4	no	—
200	C₂²⋊D₈₃	—	4	4	no	—
201	C₂×Dic₈₃	—	4	4	no	—
202	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
203	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
204	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
205	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
206	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
207	C₂×Dic₈₃	C₂⁴	1	4	yes	—
208	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
209	D₃₃₂	—	2	2	no	—
210	D₃₃₂	—	2	4	no	—
211	D₃₃₂	—	2	4	no	—
212	D₃₃₂	—	2	4	no	—
213	D₃₃₂	—	4	4	no	—
214	C₄×D₈₃	—	2	2	no	—
215	C₄×D₈₃	—	2	2	no	—
216	C₄×D₈₃	—	2	2	no	—
217	C₄×D₈₃	—	2	2	no	—
218	C₄×D₈₃	—	2	2	no	—
219	C₄×D₈₃	—	4	4	no	—
220	C₄×D₈₃	—	4	4	no	—
221	C₄×D₈₃	#41	1	4	yes	complemented
222	Dic₁₆₆	—	2	4	no	—
223	Dic₁₆₆	—	2	2	no	—
224	C₂²×C₈₃	—	2	1	no	—
225	C₂²×C₈₃	—	2	4	no	—
226	C₂²×C₈₃	—	2	4	no	—
227	C₂²×C₈₃	—	2	1	no	—
228	C₂²×C₈₃	—	2	4	no	—
229	C₂²×C₈₃	—	2	1	no	—
230	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
231	C₂×D₈₃	—	2	1	no	—
232	C₂×D₈₃	—	2	1	no	—
233	C₂×D₈₃	—	2	1	no	—
234	C₂×D₈₃	—	2	4	no	—
235	C₂×D₈₃	—	2	1	no	—
236	C₂×D₈₃	—	2	1	no	—
237	C₂×D₈₃	—	2	4	no	—
238	C₂×D₈₃	—	2	4	no	—
239	C₂×D₈₃	—	8	8	no	—
240	C₂×D₈₃	C₂×#41	1	2	yes	—
241	C₄×C₈₃	—	2	1	no	—
242	C₄×C₈₃	—	2	1	no	—
243	C₄×C₈₃	—	2	4	no	—
244	C₄×C₈₃	—	2	1	no	—
245	C₄×C₈₃	C₂×#41	1	2	yes	—
246	C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
247	C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
248	Dic₈₃	—	2	1	no	—
249	Dic₈₃	—	2	4	no	—
250	Dic₈₃	—	2	1	no	—
251	Dic₈₃	—	2	1	no	—
252	Dic₈₃	—	2	1	no	—
253	Dic₈₃	—	2	1	no	—
254	Dic₈₃	C₂×#41	1	2	yes	—
255	C₂×C₈₃	—	4	4	no	—
256	C₂×C₈₃	—	4	1	no	—
257	C₂×C₈₃	C₂²×#41	1	1	yes	characteristic
258	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
260	D₈₃	—	2	2	no	—
261	D₈₃	—	4	1	no	—
262	D₈₃	—	4	4	no	—
263	#3508	—	83	1	no	maximal, Sylow
264	C₈₃	#3508	1	1	yes	characteristic, complemented, Sylow
265	#559	—	83	2	no	—
266	#559	—	83	2	no	—
267	#550	—	83	2	no	—
268	#550	—	83	2	no	—
269	#546	—	83	2	no	—
270	#546	—	83	2	no	—
271	#546	—	83	2	no	—
272	#546	—	83	2	no	—
273	#540	—	83	2	no	—
274	#540	—	83	2	no	—
275	#535	—	83	2	no	—
276	#533	—	83	1	no	—
277	#532	—	83	1	no	—
278	#532	—	83	1	no	—
279	#532	—	83	1	no	—
280	#532	D₈₃	1	1	yes	characteristic, complemented
281	C₂×#127	—	83	1	no	—
282	#518	—	83	2	no	—
283	C₄×#41	—	83	1	no	—
284	C₂×#41	—	83	2	no	—
285	C₂×#41	—	83	2	no	—
286	C₂×#41	—	83	2	no	—
287	C₂×#41	—	83	1	no	—
288	C₂×#41	C₂×D₈₃	1	2	yes	complemented
289	C₂²×D₄	—	83	2	no	—
290	C₂²×D₄	—	83	2	no	—
291	C₂²×D₄	—	83	2	no	—
292	C₄⋊Q₈	—	83	1	no	—
293	C₄⋊Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
294	#127	—	83	2	no	—
295	#127	—	83	2	no	—
296	#127	—	83	2	no	—
297	#127	—	83	4	no	—
298	#127	—	83	1	no	—
299	#127	C₂×D₈₃	1	1	yes	characteristic
300	#125	—	83	2	no	—
301	#124	—	83	2	no	—
302	#124	—	83	2	no	—
303	#124	—	83	4	no	—
304	#124	—	83	2	no	—
305	#124	C₂×D₈₃	1	2	yes	complemented
306	#123	—	83	4	no	—
307	#123	—	83	4	no	—
308	#123	—	83	4	no	—
309	#123	—	83	4	no	—
310	C₂²⋊Q₈	—	83	2	no	—
311	C₂²⋊Q₈	—	83	2	no	—
312	#121	—	83	2	no	—
313	#121	—	83	2	no	—
314	#121	—	83	4	no	—
315	#121	—	83	4	no	—
316	#121	—	83	2	no	—
317	#121	—	83	2	no	—
318	#121	—	83	4	no	—
319	#121	—	83	2	no	—
320	#121	—	83	2	no	—
321	#121	—	83	4	no	—
322	#121	C₂×D₈₃	1	2	yes	complemented
323	#121	C₂×D₈₃	1	2	yes	complemented
324	#120	—	83	4	no	—
325	#120	—	83	4	no	—
326	C₄×Q₈	—	83	2	no	—
327	C₄×Q₈	—	83	2	no	—
328	C₄×Q₈	—	83	1	no	—
329	C₄×Q₈	—	83	1	no	—
330	C₄×D₄	—	83	2	no	—
331	C₄×D₄	—	83	2	no	—
332	C₄×D₄	—	83	1	no	—
333	C₄×D₄	—	83	1	no	—
334	C₄×D₄	—	83	1	no	—
335	C₄×D₄	—	83	1	no	—
336	C₄×D₄	—	83	4	no	—
337	C₄×D₄	—	83	2	no	—
338	C₄×D₄	—	83	2	no	—
339	C₄×D₄	—	83	4	no	—
340	C₄×D₄	—	83	1	no	—
341	C₄×D₄	—	83	1	no	—
342	C₄×D₄	—	83	2	no	—
343	C₄×D₄	—	83	2	no	—
344	C₄×D₄	C₂×D₈₃	1	2	yes	complemented
345	C₄×D₄	C₂×D₈₃	1	2	yes	complemented
346	#117	—	83	1	no	—
347	#117	—	83	2	no	—
348	#117	—	83	1	no	—
349	#117	—	83	1	no	—
350	C₂×C₂²⋊C₄	—	83	4	no	—
351	C₂×C₂²⋊C₄	—	83	4	no	—
352	C₂×C₄²	—	83	1	no	—
353	C₂×C₄²	—	83	1	no	—
354	C₂×C₄²	C₂×D₈₃	1	1	yes	characteristic, complemented
355	C₂⁴	—	83	4	no	—
356	#41	—	4	4	no	—
357	#41	—	332	4	no	—
358	#41	—	332	4	no	—
359	#41	—	332	4	no	—
360	#41	—	166	4	no	—
361	C₂×Q₈	—	83	1	no	—
362	C₂×Q₈	—	83	2	no	—
363	C₂×Q₈	C₂²×D₈₃	1	2	yes	—
364	C₂×D₄	—	332	4	no	—
365	C₂×D₄	—	332	4	no	—
366	C₂×D₄	—	83	4	no	—
367	C₂×D₄	—	83	4	no	—
368	C₂×D₄	—	83	4	no	—
369	C₂×D₄	—	83	4	no	—
370	C₂×D₄	—	83	1	no	—
371	C₂×D₄	—	83	4	no	—
372	C₂×D₄	—	83	1	no	—
373	C₂×D₄	—	83	4	no	—
374	C₂×D₄	—	83	1	no	—
375	C₂×D₄	—	83	2	no	—
376	C₂×D₄	—	83	2	no	—
377	C₂×D₄	—	83	2	no	—
378	C₂×D₄	—	166	8	no	—
379	C₂×D₄	C₂²×D₈₃	1	2	yes	—
380	C₂×D₄	C₂²×D₈₃	1	2	yes	—
381	C₂×D₄	C₂²×D₈₃	1	2	yes	—
382	C₂×D₄	C₂²×D₈₃	1	4	yes	—
383	C₂²×C₄	—	83	4	no	—
384	C₂²×C₄	—	83	4	no	—
385	C₂²×C₄	—	83	4	no	—
386	C₂²×C₄	—	83	1	no	—
387	C₂²×C₄	—	83	1	no	—
388	C₂²×C₄	—	83	1	no	—
389	C₂²×C₄	—	83	1	no	—
390	C₂²×C₄	—	83	1	no	—
391	C₂²×C₄	—	83	1	no	—
392	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
393	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
394	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
395	C₂²×C₄	C₂²×D₈₃	1	4	yes	—
396	C₄⋊C₄	—	83	1	no	—
397	C₄⋊C₄	—	83	1	no	—
398	C₄⋊C₄	—	83	2	no	—
399	C₄⋊C₄	—	83	1	no	—
400	C₄⋊C₄	—	83	1	no	—
401	C₄⋊C₄	—	83	1	no	—
402	C₄⋊C₄	—	83	1	no	—
403	C₄⋊C₄	—	83	2	no	—
404	C₄⋊C₄	—	83	4	no	—
405	C₄⋊C₄	—	83	4	no	—
406	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
407	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
408	C₂²⋊C₄	—	83	4	no	—
409	C₂²⋊C₄	—	83	1	no	—
410	C₂²⋊C₄	—	83	1	no	—
411	C₂²⋊C₄	—	83	4	no	—
412	C₂²⋊C₄	—	83	1	no	—
413	C₂²⋊C₄	—	83	1	no	—
414	C₂²⋊C₄	—	83	4	no	—
415	C₂²⋊C₄	—	83	4	no	—
416	C₂²⋊C₄	—	83	4	no	—
417	C₂²⋊C₄	—	83	1	no	—
418	C₂²⋊C₄	—	83	1	no	—
419	C₂²⋊C₄	—	83	4	no	—
420	C₂²⋊C₄	—	83	4	no	—
421	C₂²⋊C₄	C₂²×D₈₃	1	4	yes	—
422	C₂²⋊C₄	C₂²×D₈₃	1	4	yes	—
423	C₄²	—	83	1	no	—
424	C₄²	—	83	1	no	—
425	C₄²	—	83	1	no	—
426	C₄²	—	83	1	no	—
427	C₄²	—	83	1	no	—
428	C₄²	—	83	1	no	—
429	C₄²	—	83	4	no	—
430	C₄²	C₂²×D₈₃	1	1	yes	characteristic
431	C₄²	C₂²×D₈₃	1	1	yes	characteristic
432	C₄²	C₂²×D₈₃	1	1	yes	characteristic
433	C₄²	C₂²×D₈₃	1	1	yes	characteristic
434	C₂³	—	332	4	no	—
435	C₂³	—	332	4	no	—
436	C₂³	—	83	1	no	—
437	C₂³	—	83	4	no	—
438	C₂³	—	83	1	no	—
439	C₂³	—	166	8	no	—
440	C₂³	C₂³×D₈₃	1	4	yes	—
441	C₂³	C₂³×D₈₃	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	166	2	no	—
444	Q₈	—	166	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	4	no	—
448	D₄	—	4	4	no	—
449	D₄	—	332	4	no	—
450	D₄	—	332	4	no	—
451	D₄	—	332	4	no	—
452	D₄	—	332	4	no	—
453	D₄	—	332	4	no	—
454	D₄	—	166	2	no	—
455	D₄	—	166	8	no	—
456	D₄	—	166	2	no	—
457	D₄	—	166	2	no	—
458	D₄	—	166	4	no	—
459	D₄	—	166	4	no	—
460	D₄	—	166	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	332	4	no	—
466	C₂×C₄	—	332	4	no	—
467	C₂×C₄	—	332	4	no	—
468	C₂×C₄	—	83	1	no	—
469	C₂×C₄	—	83	4	no	—
470	C₂×C₄	—	83	1	no	—
471	C₂×C₄	—	83	1	no	—
472	C₂×C₄	—	83	1	no	—
473	C₂×C₄	—	83	1	no	—
474	C₂×C₄	—	83	1	no	—
475	C₂×C₄	—	83	4	no	—
476	C₂×C₄	—	166	2	no	—
477	C₂×C₄	—	166	2	no	—
478	C₂×C₄	—	166	2	no	—
479	C₂×C₄	—	166	2	no	—
480	C₂×C₄	—	166	2	no	—
481	C₂×C₄	C₂³×D₈₃	1	4	yes	—
482	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
483	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
484	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
485	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
486	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
487	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
488	C₂²	—	2	1	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	83	2	no	—
495	C₂²	—	664	8	no	—
496	C₂²	—	166	1	no	—
497	C₂²	—	166	4	no	—
498	C₂²	—	166	4	no	—
499	C₂²	—	166	1	no	—
500	C₂²	—	166	4	no	—
501	C₂²	—	166	1	no	—
502	C₂²	—	166	1	no	—
503	C₂²	—	166	1	no	—
504	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	1	no	—
509	C₄	—	83	2	no	—
510	C₄	—	166	1	no	—
511	C₄	—	166	1	no	—
512	C₄	—	166	1	no	—
513	C₄	—	166	1	no	—
514	C₄	—	166	4	no	—
515	C₄	—	166	1	no	—
516	C₄	#41×D₈₃	1	2	yes	—
517	C₄	#14581837	1	2	yes	—
518	C₄	#14581838	1	2	yes	—
519	C₂	—	4	4	no	—
520	C₂	—	4	1	no	—
521	C₂	—	332	4	no	—
522	C₂	—	332	1	no	—
523	C₂	—	166	2	no	—
524	C₂	C₂×#41×D₈₃	1	1	yes	characteristic
525	C₂	C₂×#14581837	1	1	yes	characteristic
526	C₂	C₂×#14581838	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#532×C₈₃	C₂
hypercenter	#532	D₈₃
hypocenter	C₈₃	#3508
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. #19128434	C₂	semidirect
2. #19128433	C₂	semidirect
3. #19128370	C₂	semidirect
4. #19128369	C₂	semidirect
5. #19128348	C₂	semidirect
6. #19128346	C₂	semidirect
7. #19128344	C₂	semidirect
8. #19128339	C₂	semidirect
9. #19128304	C₂	semidirect
10. #19128302	C₂	semidirect
11. #19128267	C₂	semidirect
12. #19128256	C₂	semidirect
13. #19128252	C₂	semidirect
14. #19128251	C₂	semidirect
15. #19128249	C₂	semidirect
16. #127×D₈₃	C₂	semidirect
17. #19128173	C₂	semidirect
18. C₄×#13050590	C₂	semidirect
19. #532×C₈₃	C₂	semidirect
20. C₂×#13050591	C₂²	semidirect
22. C₂×#13050590	C₂²	semidirect
23. C₂×#13050589	C₂²	semidirect
27. #14581792	C₂²	semidirect
32. #14581788	C₂²	semidirect
33. #14581783	C₂²	semidirect
34. #14581781	C₂²	semidirect
35. #14581780	C₂²	semidirect
36. #14581779	C₂²	semidirect
37. #14581778	C₂²	semidirect
38. #14581776	C₂²	semidirect
39. #14581775	C₂²	semidirect
40. #14581774	C₂²	semidirect
41. #14581774	C₂²	semidirect
44. #14581767	C₂²	semidirect
45. #14581767	C₂²	semidirect
46. #14581766	C₂²	semidirect
47. #14581766	C₂²	semidirect
48. #14581766	C₂²	semidirect
49. #14581765	C₂²	semidirect
50. #14581764	C₂²	semidirect
51. #14581763	C₂²	semidirect
52. #14581763	C₂²	semidirect
53. #14581763	C₂²	semidirect
56. Q₈×Dic₈₃	C₂²	semidirect
57. C₄×Dic₁₆₆	C₂²	semidirect
58. C₄×Dic₁₆₆	C₂²	semidirect
59. #14581757	C₂²	semidirect
62. C₄×D₃₃₂	C₂²	semidirect
63. C₄×D₃₃₂	C₂²	semidirect
64. D₄×Dic₈₃	C₂²	semidirect
65. D₄×Dic₈₃	C₂²	semidirect
66. #14581754	C₂²	semidirect
67. #14581754	C₂²	semidirect
70. C₄×C₂²⋊D₈₃	C₂²	semidirect
71. C₄×C₂²⋊D₈₃	C₂²	semidirect
72. C₄×C₂²⋊D₈₃	C₂²	semidirect
73. (C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
74. #14581751	C₂²	semidirect
77. #14581749	C₂²	semidirect
81. C₄²×D₈₃	C₂²	semidirect
82. C₂×#41×C₈₃	C₂²	semidirect
83. C₄⋊Q₈×C₈₃	C₂²	semidirect
85. #124×C₈₃	C₂²	semidirect
86. #121×C₈₃	C₂²	semidirect
87. #121×C₈₃	C₂²	semidirect
88. C₄×D₄×C₈₃	C₂²	semidirect
89. C₄×D₄×C₈₃	C₂²	semidirect
90. C₂×C₄²×C₈₃	C₂²	semidirect
221. C₄×D₈₃	#41	semidirect
264. C₈₃	#3508	semidirect
280. #532	D₈₃	semidirect
288. C₂×#41	C₂×D₈₃	semidirect
293. C₄⋊Q₈	C₂×D₈₃	semidirect
305. #124	C₂×D₈₃	semidirect
322. #121	C₂×D₈₃	semidirect
323. #121	C₂×D₈₃	semidirect
344. C₄×D₄	C₂×D₈₃	semidirect
345. C₄×D₄	C₂×D₈₃	semidirect
354. 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
#19128434	2
#19128433	2
#19128370	2
#19128369	2
#19128348	2
#19128346	2
#19128344	2
#19128339	2
#19128304	2
#19128302	2
#19128267	2
#19128256	2
#19128252	2
#19128251	2
#19128249	2
#127×D₈₃	2
#19128173	2
C₄×#13050590	2
#532×C₈₃	2
#3508	83