Subgroups — #24921787

Order 10624.

1260 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128439	C₂	1	4	yes	maximal, complemented
2	#19128436	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128371	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128346	C₂	1	2	yes	maximal, complemented
5	#19128339	C₂	1	2	yes	maximal, complemented
6	D₄×D₃₃₂	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128336	C₂	1	2	yes	maximal, complemented
8	#19128335	C₂	1	2	yes	maximal, complemented
9	#19128304	C₂	1	2	yes	maximal, complemented
10	#19128302	C₂	1	2	yes	maximal, complemented
11	#19128265	C₂	1	2	yes	maximal, complemented
12	#19128264	C₂	1	2	yes	maximal, complemented
13	#19128259	C₂	1	4	yes	maximal, complemented
14	#127×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#19128238	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128233	C₂	1	1	yes	maximal, characteristic, complemented
17	#550×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13050589	C₂²	1	2	yes	complemented
19	C₂²×D₃₃₂	C₂²	1	2	yes	complemented
20	C₂×D₄×D₈₃	C₂²	1	4	yes	complemented
21	C₂×D₄×D₈₃	C₂²	1	2	yes	complemented
22	C₂×D₄×D₈₃	C₂²	1	2	yes	complemented
23	C₂×D₄×D₈₃	C₂²	1	2	yes	complemented
24	C₂×D₄×D₈₃	C₂²	1	2	yes	complemented
25	#14581789	C₂²	1	1	yes	characteristic
26	#14581788	C₂²	1	2	yes	complemented
27	#14581788	C₂²	1	2	yes	complemented
28	#14581788	C₂²	1	2	yes	complemented
29	#14581788	C₂²	1	2	yes	complemented
30	#14581787	C₂²	1	2	yes	complemented
31	#14581785	C₂²	1	2	yes	complemented
32	#14581783	C₂²	1	1	yes	characteristic, complemented
33	#14581783	C₂²	1	1	yes	characteristic, complemented
34	#14581781	C₂²	1	2	yes	complemented
35	#14581781	C₂²	1	1	yes	characteristic, complemented
36	#14581780	C₂²	1	2	yes	complemented
37	#14581779	C₂²	1	1	yes	characteristic, complemented
38	#14581777	C₂²	1	4	yes	complemented
39	#14581777	C₂²	1	2	yes	complemented
40	#14581776	C₂²	1	4	yes	complemented
41	#14581775	C₂²	1	4	yes	complemented
42	#14581774	C₂²	1	2	yes	complemented
43	#14581774	C₂²	1	4	yes	complemented
44	#14581772	C₂²	1	1	yes	characteristic, complemented
45	#14581768	C₂²	1	1	yes	characteristic, complemented
46	#14581767	C₂²	1	1	yes	characteristic
47	#14581767	C₂²	1	2	yes	complemented
48	#14581766	C₂²	1	2	yes	complemented
49	#14581766	C₂²	1	4	yes	complemented
50	#14581766	C₂²	1	4	yes	complemented
51	#14581765	C₂²	1	4	yes	complemented
52	#14581764	C₂²	1	4	yes	complemented
53	#14581764	C₂²	1	4	yes	complemented
54	#14581764	C₂²	1	4	yes	complemented
55	#14581763	C₂²	1	1	yes	characteristic
56	#14581763	C₂²	1	2	yes	complemented
57	#14581763	C₂²	1	4	yes	complemented
58	#14581762	C₂²	1	4	yes	complemented
59	#14581762	C₂²	1	4	yes	complemented
60	#14581760	C₂²	1	4	yes	complemented
61	#14581760	C₂²	1	4	yes	complemented
62	#14581760	C₂²	1	4	yes	complemented
63	#14581760	C₂²	1	4	yes	complemented
64	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₃₃₂	C₂²	1	2	yes	complemented
66	C₄×D₃₃₂	C₂²	1	2	yes	complemented
67	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₈₃	C₂²	1	2	yes	complemented
69	#14581754	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
71	#14581751	C₂²	1	2	yes	complemented
72	#14581749	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	4	yes	complemented
74	C₄²×D₈₃	C₂²	1	1	yes	characteristic, complemented
75	C₂×#41×C₈₃	C₂²	1	2	yes	complemented
76	#127×C₈₃	C₂²	1	2	yes	complemented
77	#127×C₈₃	C₂²	1	1	yes	characteristic, complemented
78	#121×C₈₃	C₂²	1	2	yes	complemented
79	#121×C₈₃	C₂²	1	4	yes	complemented
80	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₄×C₈₃	C₂²	1	2	yes	complemented
83	C₂³×D₈₃	C₂³	1	4	yes	—
84	C₂³×D₈₃	C₂³	1	4	yes	—
85	#13050589	—	4	4	no	—
86	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
87	C₂×D₃₃₂	—	4	4	no	—
88	C₂×D₃₃₂	C₂³	1	2	yes	—
89	C₂×D₃₃₂	C₂³	1	2	yes	—
90	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
91	C₂×D₃₃₂	C₂³	1	2	yes	—
92	C₂×D₃₃₂	C₂³	1	4	yes	—
93	C₂×D₃₃₂	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₈₃	C₂³	1	4	yes	—
101	D₄×D₈₃	—	4	4	no	—
102	D₄×D₈₃	—	4	4	no	—
103	D₄×D₈₃	—	4	4	no	—
104	D₄×D₈₃	—	4	4	no	—
105	D₄×D₈₃	—	4	8	no	—
106	C₂²×Dic₈₃	C₂³	1	4	yes	—
107	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₈₃	C₂³	1	2	yes	—
109	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
110	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₈₃	C₂³	1	4	yes	—
112	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
113	C₄⋊Dic₈₃	C₂³	1	2	yes	—
114	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
115	C₄⋊Dic₈₃	C₂³	1	2	yes	—
116	C₄⋊Dic₈₃	C₂³	1	2	yes	—
117	Dic₈₃⋊C₄	C₂³	1	2	yes	—
118	Dic₈₃⋊C₄	C₂³	1	2	yes	—
119	Dic₈₃⋊C₄	C₂³	1	2	yes	—
120	Dic₈₃⋊C₄	C₂³	1	2	yes	—
121	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
122	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
123	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
124	C₂²⋊Dic₈₃	C₂³	1	4	yes	—
125	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
134	(C₂×D₈₃)⋊C₄	C₂³	1	4	yes	—
135	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
136	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
137	C₄×Dic₈₃	C₂³	1	2	yes	—
138	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
139	#41×C₈₃	—	4	4	no	—
140	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
141	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
142	C₂×D₄×C₈₃	C₂³	1	2	yes	—
143	C₂×D₄×C₈₃	C₂³	1	2	yes	—
144	C₂×D₄×C₈₃	C₂³	1	4	yes	—
145	C₂×D₄×C₈₃	C₂³	1	4	yes	—
146	C₂×D₄×C₈₃	C₂³	1	2	yes	—
147	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
148	C₂²×C₄×C₈₃	C₂³	1	4	yes	—
149	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
154	C₄²×C₈₃	C₂³	1	2	yes	—
155	C₄²×C₈₃	C₂³	1	1	yes	characteristic
156	C₂³×C₈₃	C₂⁴	1	2	yes	—
157	C₂³×C₈₃	C₂⁴	1	4	yes	—
158	C₂²×D₈₃	—	2	8	no	—
159	C₂²×D₈₃	—	4	4	no	—
160	C₂²×D₈₃	—	4	4	no	—
161	C₂²×D₈₃	—	4	4	no	—
162	C₂²×D₈₃	—	4	4	no	—
163	C₂²×D₈₃	—	4	4	no	—
164	C₂²×D₈₃	C₂⁴	1	2	yes	—
165	C₂²×D₈₃	C₂⁴	1	4	yes	—
166	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
167	Q₈×C₈₃	—	2	2	no	—
168	D₄×C₈₃	—	2	4	no	—
169	D₄×C₈₃	—	2	2	no	—
170	D₄×C₈₃	—	2	4	no	—
171	D₄×C₈₃	—	4	4	no	—
172	D₄×C₈₃	—	4	2	no	—
173	D₄×C₈₃	—	4	4	no	—
174	C₂×C₄×C₈₃	—	2	4	no	—
175	C₂×C₄×C₈₃	—	4	4	no	—
176	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
178	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
179	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
180	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
182	C₂²⋊D₈₃	—	2	4	no	—
183	C₂²⋊D₈₃	—	4	4	no	—
184	C₂²⋊D₈₃	—	4	4	no	—
185	C₂²⋊D₈₃	—	4	4	no	—
186	C₂²⋊D₈₃	—	4	4	no	—
187	C₂²⋊D₈₃	—	4	4	no	—
188	C₂²⋊D₈₃	—	4	4	no	—
189	C₂×Dic₈₃	—	4	4	no	—
190	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
191	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
192	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
193	C₂×Dic₈₃	C₂⁴	1	2	yes	—
194	C₂×Dic₈₃	C₂⁴	1	2	yes	—
195	C₂×Dic₈₃	C₂⁴	1	2	yes	—
196	D₃₃₂	—	2	4	no	—
197	D₃₃₂	—	2	4	no	—
198	D₃₃₂	—	2	4	no	—
199	D₃₃₂	—	2	2	no	—
200	D₃₃₂	—	4	2	no	—
201	D₃₃₂	—	4	4	no	—
202	C₄×D₈₃	—	2	2	no	—
203	C₄×D₈₃	—	2	2	no	—
204	C₄×D₈₃	—	2	2	no	—
205	C₄×D₈₃	—	2	4	no	—
206	C₄×D₈₃	—	4	4	no	—
207	Dic₁₆₆	—	2	2	no	—
208	C₂²×C₈₃	—	2	4	no	—
209	C₂²×C₈₃	—	2	2	no	—
210	C₂²×C₈₃	—	2	2	no	—
211	C₂²×C₈₃	—	2	4	no	—
212	C₂²×C₈₃	—	2	4	no	—
213	C₂²×C₈₃	—	2	2	no	—
214	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
215	C₂×D₈₃	—	2	1	no	—
216	C₂×D₈₃	—	2	1	no	—
217	C₂×D₈₃	—	2	2	no	—
218	C₂×D₈₃	—	2	4	no	—
219	C₂×D₈₃	—	2	2	no	—
220	C₂×D₈₃	—	2	4	no	—
221	C₂×D₈₃	—	2	2	no	—
222	C₂×D₈₃	—	2	4	no	—
223	C₂×D₈₃	—	8	8	no	—
224	C₂×D₈₃	—	8	8	no	—
225	C₂×D₈₃	H(5,𝔽₂)	1	2	yes	—
226	C₄×C₈₃	—	2	1	no	—
227	C₄×C₈₃	—	2	2	no	—
228	C₄×C₈₃	—	2	2	no	—
229	C₄×C₈₃	—	2	2	no	—
230	C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
231	C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
232	Dic₈₃	—	2	2	no	—
233	Dic₈₃	—	2	2	no	—
234	Dic₈₃	—	2	1	no	—
235	Dic₈₃	—	2	1	no	—
236	Dic₈₃	—	2	1	no	—
237	Dic₈₃	—	2	2	no	—
238	C₂×C₈₃	—	4	2	no	—
239	C₂×C₈₃	—	4	4	no	—
240	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
243	D₈₃	—	2	2	no	—
244	D₈₃	—	4	2	no	—
245	D₈₃	—	4	4	no	—
246	#3543	—	83	1	no	maximal, Sylow
247	C₈₃	#3543	1	1	yes	characteristic, complemented, Sylow
248	#560	—	83	4	no	—
249	#559	—	83	1	no	—
250	#550	—	83	1	no	—
251	#550	D₈₃	1	1	yes	characteristic, complemented
252	#546	—	83	2	no	—
253	#546	—	83	2	no	—
254	D₄²	—	83	2	no	—
255	D₄²	—	83	2	no	—
256	D₄²	—	83	1	no	—
257	#540	—	83	2	no	—
258	#540	—	83	2	no	—
259	#535	—	83	2	no	—
260	#535	—	83	2	no	—
261	#534	—	83	4	no	—
262	C₂×#127	—	83	1	no	—
263	#529	—	83	1	no	—
264	#529	—	83	1	no	—
265	C₂×#41	—	83	2	no	—
266	C₂×#41	C₂×D₈₃	1	2	yes	complemented
267	C₂²×D₄	—	83	2	no	—
268	C₂²×D₄	—	83	2	no	—
269	C₂²×D₄	—	83	2	no	—
270	C₂²×D₄	—	83	4	no	—
271	C₂²×D₄	—	83	2	no	—
272	C₂²×D₄	—	83	2	no	—
273	#127	—	83	2	no	—
274	#127	—	83	2	no	—
275	#127	—	83	2	no	—
276	#127	—	83	2	no	—
277	#127	—	83	1	no	—
278	#127	C₂×D₈₃	1	1	yes	characteristic, complemented
279	#127	C₂×D₈₃	1	2	yes	complemented
280	#126	—	83	2	no	—
281	#126	—	83	2	no	—
282	#125	—	83	1	no	—
283	#125	—	83	1	no	—
284	#124	—	83	1	no	—
285	#124	—	83	2	no	—
286	#124	—	83	1	no	—
287	#124	—	83	2	no	—
288	#123	—	83	4	no	—
289	#123	—	83	2	no	—
290	#123	—	83	4	no	—
291	#123	—	83	2	no	—
292	#123	—	83	4	no	—
293	#123	—	83	4	no	—
294	C₂²⋊Q₈	—	83	1	no	—
295	C₂²⋊Q₈	—	83	1	no	—
296	#121	—	83	1	no	—
297	#121	—	83	2	no	—
298	#121	—	83	4	no	—
299	#121	—	83	4	no	—
300	#121	—	83	4	no	—
301	#121	—	83	4	no	—
302	#121	—	83	4	no	—
303	#121	—	83	4	no	—
304	#121	—	83	2	no	—
305	#121	—	83	1	no	—
306	#121	—	83	2	no	—
307	#121	—	83	4	no	—
308	#121	C₂×D₈₃	1	4	yes	complemented
309	#121	C₂×D₈₃	1	2	yes	complemented
310	#120	—	83	4	no	—
311	#120	—	83	4	no	—
312	#120	—	83	4	no	—
313	#120	—	83	4	no	—
314	#120	—	83	4	no	—
315	#120	—	83	4	no	—
316	C₄×Q₈	—	83	1	no	—
317	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
318	C₄×D₄	—	83	2	no	—
319	C₄×D₄	—	83	2	no	—
320	C₄×D₄	—	83	2	no	—
321	C₄×D₄	—	83	2	no	—
322	C₄×D₄	—	83	1	no	—
323	C₄×D₄	—	83	2	no	—
324	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
325	C₄×D₄	C₂×D₈₃	1	2	yes	complemented
326	#117	—	83	2	no	—
327	#117	—	83	2	no	—
328	C₂×C₂²⋊C₄	—	83	4	no	—
329	C₂×C₄²	—	83	1	no	—
330	C₂⁴	—	83	4	no	—
331	C₂⁴	—	83	4	no	—
332	#41	—	4	4	no	—
333	#41	—	332	4	no	—
334	C₂×Q₈	—	83	1	no	—
335	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
336	C₂×D₄	—	332	4	no	—
337	C₂×D₄	—	332	8	no	—
338	C₂×D₄	—	332	4	no	—
339	C₂×D₄	—	332	4	no	—
340	C₂×D₄	—	332	4	no	—
341	C₂×D₄	—	332	4	no	—
342	C₂×D₄	—	83	4	no	—
343	C₂×D₄	—	83	4	no	—
344	C₂×D₄	—	83	4	no	—
345	C₂×D₄	—	83	4	no	—
346	C₂×D₄	—	83	4	no	—
347	C₂×D₄	—	83	4	no	—
348	C₂×D₄	—	83	2	no	—
349	C₂×D₄	—	83	4	no	—
350	C₂×D₄	—	83	2	no	—
351	C₂×D₄	—	83	2	no	—
352	C₂×D₄	—	83	2	no	—
353	C₂×D₄	—	83	1	no	—
354	C₂×D₄	—	83	2	no	—
355	C₂×D₄	C₂²×D₈₃	1	2	yes	—
356	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
357	C₂×D₄	C₂²×D₈₃	1	2	yes	—
358	C₂×D₄	C₂²×D₈₃	1	4	yes	—
359	C₂×D₄	C₂²×D₈₃	1	4	yes	—
360	C₂×D₄	C₂²×D₈₃	1	2	yes	—
361	C₂²×C₄	—	83	4	no	—
362	C₂²×C₄	—	83	4	no	—
363	C₂²×C₄	—	83	1	no	—
364	C₂²×C₄	—	83	1	no	—
365	C₂²×C₄	—	83	1	no	—
366	C₂²×C₄	—	83	2	no	—
367	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
368	C₂²×C₄	C₂²×D₈₃	1	4	yes	—
369	C₄⋊C₄	—	83	2	no	—
370	C₄⋊C₄	—	83	2	no	—
371	C₄⋊C₄	—	83	2	no	—
372	C₄⋊C₄	—	83	2	no	—
373	C₄⋊C₄	—	83	1	no	—
374	C₄⋊C₄	—	83	1	no	—
375	C₄⋊C₄	—	83	2	no	—
376	C₄⋊C₄	—	83	2	no	—
377	C₄⋊C₄	—	83	2	no	—
378	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
379	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
381	C₂²⋊C₄	—	83	2	no	—
382	C₂²⋊C₄	—	83	2	no	—
383	C₂²⋊C₄	—	83	2	no	—
384	C₂²⋊C₄	—	83	4	no	—
385	C₂²⋊C₄	—	83	2	no	—
386	C₂²⋊C₄	—	83	2	no	—
387	C₂²⋊C₄	—	83	4	no	—
388	C₂²⋊C₄	—	83	4	no	—
389	C₂²⋊C₄	—	83	2	no	—
390	C₂²⋊C₄	—	83	2	no	—
391	C₂²⋊C₄	—	83	2	no	—
392	C₂²⋊C₄	—	83	2	no	—
393	C₂²⋊C₄	—	83	4	no	—
394	C₂²⋊C₄	—	83	4	no	—
395	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
396	C₂²⋊C₄	C₂²×D₈₃	1	4	yes	—
397	C₄²	—	83	1	no	—
398	C₄²	—	83	1	no	—
399	C₄²	—	83	1	no	—
400	C₄²	—	83	2	no	—
401	C₄²	C₂²×D₈₃	1	1	yes	characteristic
402	C₄²	C₂²×D₈₃	1	2	yes	—
403	C₂³	—	332	4	no	—
404	C₂³	—	332	4	no	—
405	C₂³	—	332	4	no	—
406	C₂³	—	332	4	no	—
407	C₂³	—	332	4	no	—
408	C₂³	—	83	1	no	—
409	C₂³	—	83	4	no	—
410	C₂³	—	83	2	no	—
411	C₂³	—	166	8	no	—
412	C₂³	C₂³×D₈₃	1	2	yes	—
413	C₂³	C₂³×D₈₃	1	4	yes	—
414	Q₈	—	2	2	no	—
415	Q₈	—	166	2	no	—
416	D₄	—	2	4	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	4	no	—
419	D₄	—	4	4	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	4	no	—
422	D₄	—	332	2	no	—
423	D₄	—	332	4	no	—
424	D₄	—	332	4	no	—
425	D₄	—	332	4	no	—
426	D₄	—	332	4	no	—
427	D₄	—	332	4	no	—
428	D₄	—	332	4	no	—
429	D₄	—	332	4	no	—
430	D₄	—	166	4	no	—
431	D₄	—	166	4	no	—
432	D₄	—	166	2	no	—
433	D₄	—	166	4	no	—
434	D₄	—	166	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	332	4	no	—
438	C₂×C₄	—	332	4	no	—
439	C₂×C₄	—	83	1	no	—
440	C₂×C₄	—	83	1	no	—
441	C₂×C₄	—	83	1	no	—
442	C₂×C₄	—	83	2	no	—
443	C₂×C₄	—	83	2	no	—
444	C₂×C₄	—	83	2	no	—
445	C₂×C₄	—	166	2	no	—
446	C₂×C₄	—	166	2	no	—
447	C₂×C₄	—	166	2	no	—
448	C₂×C₄	—	166	4	no	—
449	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₈₃	1	2	yes	—
451	C₂×C₄	C₂³×D₈₃	1	2	yes	—
452	C₂×C₄	C₂³×D₈₃	1	2	yes	—
453	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
454	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
455	C₂²	—	2	4	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	83	2	no	—
462	C₂²	—	664	8	no	—
463	C₂²	—	664	8	no	—
464	C₂²	—	166	4	no	—
465	C₂²	—	166	2	no	—
466	C₂²	—	166	2	no	—
467	C₂²	—	166	4	no	—
468	C₂²	—	166	2	no	—
469	C₂²	—	166	4	no	—
470	C₂²	—	166	1	no	—
471	C₂²	—	166	1	no	—
472	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	166	2	no	—
478	C₄	—	166	1	no	—
479	C₄	—	166	1	no	—
480	C₄	—	166	2	no	—
481	C₄	—	166	2	no	—
482	C₄	—	166	1	no	—
483	C₄	#14581837	1	2	yes	—
484	C₄	#14581838	1	2	yes	—
485	C₂	—	4	2	no	—
486	C₂	—	4	4	no	—
487	C₂	—	332	2	no	—
488	C₂	—	332	4	no	—
489	C₂	—	166	2	no	—
490	C₂	H(5,𝔽₂)×D₈₃	1	1	yes	characteristic
491	C₂	C₂×#14581837	1	1	yes	characteristic
492	C₂	C₂×#14581838	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#550×C₈₃	C₂
hypercenter	#550	D₈₃
hypocenter	C₈₃	#3543
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. #19128439	C₂	semidirect
2. #19128436	C₂	semidirect
3. #19128371	C₂	semidirect
4. #19128346	C₂	semidirect
5. #19128339	C₂	semidirect
6. D₄×D₃₃₂	C₂	semidirect
7. #19128336	C₂	semidirect
8. #19128335	C₂	semidirect
9. #19128304	C₂	semidirect
10. #19128302	C₂	semidirect
11. #19128265	C₂	semidirect
12. #19128264	C₂	semidirect
13. #19128259	C₂	semidirect
14. #127×D₈₃	C₂	semidirect
15. #19128238	C₂	semidirect
16. #19128233	C₂	semidirect
17. #550×C₈₃	C₂	semidirect
18. C₂×#13050589	C₂²	semidirect
19. C₂²×D₃₃₂	C₂²	semidirect
20. C₂×D₄×D₈₃	C₂²	semidirect
21. C₂×D₄×D₈₃	C₂²	semidirect
22. C₂×D₄×D₈₃	C₂²	semidirect
23. C₂×D₄×D₈₃	C₂²	semidirect
24. C₂×D₄×D₈₃	C₂²	semidirect
26. #14581788	C₂²	semidirect
27. #14581788	C₂²	semidirect
28. #14581788	C₂²	semidirect
29. #14581788	C₂²	semidirect
30. #14581787	C₂²	semidirect
31. #14581785	C₂²	semidirect
32. #14581783	C₂²	semidirect
33. #14581783	C₂²	semidirect
34. #14581781	C₂²	semidirect
35. #14581781	C₂²	semidirect
36. #14581780	C₂²	semidirect
37. #14581779	C₂²	semidirect
38. #14581777	C₂²	semidirect
39. #14581777	C₂²	semidirect
40. #14581776	C₂²	semidirect
41. #14581775	C₂²	semidirect
42. #14581774	C₂²	semidirect
43. #14581774	C₂²	semidirect
44. #14581772	C₂²	semidirect
45. #14581768	C₂²	semidirect
47. #14581767	C₂²	semidirect
48. #14581766	C₂²	semidirect
49. #14581766	C₂²	semidirect
50. #14581766	C₂²	semidirect
51. #14581765	C₂²	semidirect
52. #14581764	C₂²	semidirect
53. #14581764	C₂²	semidirect
54. #14581764	C₂²	semidirect
56. #14581763	C₂²	semidirect
57. #14581763	C₂²	semidirect
58. #14581762	C₂²	semidirect
59. #14581762	C₂²	semidirect
60. #14581760	C₂²	semidirect
61. #14581760	C₂²	semidirect
62. #14581760	C₂²	semidirect
63. #14581760	C₂²	semidirect
64. C₄×Dic₁₆₆	C₂²	semidirect
65. C₄×D₃₃₂	C₂²	semidirect
66. C₄×D₃₃₂	C₂²	semidirect
67. C₄×D₃₃₂	C₂²	semidirect
68. D₄×Dic₈₃	C₂²	semidirect
69. #14581754	C₂²	semidirect
70. C₄×C₂²⋊D₈₃	C₂²	semidirect
71. #14581751	C₂²	semidirect
72. #14581749	C₂²	semidirect
73. C₂×(C₂×D₈₃)⋊C₄	C₂²	semidirect
74. C₄²×D₈₃	C₂²	semidirect
75. C₂×#41×C₈₃	C₂²	semidirect
76. #127×C₈₃	C₂²	semidirect
77. #127×C₈₃	C₂²	semidirect
78. #121×C₈₃	C₂²	semidirect
79. #121×C₈₃	C₂²	semidirect
80. C₄×Q₈×C₈₃	C₂²	semidirect
81. C₄×D₄×C₈₃	C₂²	semidirect
82. C₄×D₄×C₈₃	C₂²	semidirect
247. C₈₃	#3543	semidirect
251. #550	D₈₃	semidirect
266. C₂×#41	C₂×D₈₃	semidirect
278. #127	C₂×D₈₃	semidirect
279. #127	C₂×D₈₃	semidirect
308. #121	C₂×D₈₃	semidirect
309. #121	C₂×D₈₃	semidirect
317. C₄×Q₈	C₂×D₈₃	semidirect
324. C₄×D₄	C₂×D₈₃	semidirect
325. C₄×D₄	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128439	2
#19128436	2
#19128371	2
#19128346	2
#19128339	2
D₄×D₃₃₂	2
#19128336	2
#19128335	2
#19128304	2
#19128302	2
#19128265	2
#19128264	2
#19128259	2
#127×D₈₃	2
#19128238	2
#19128233	2
#550×C₈₃	2
#3543	83