Subgroups — #24921555

Order 10624.

992 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128428	C₂	1	1	yes	maximal, characteristic, complemented
2	#19128428	C₂	1	2	yes	maximal, complemented
3	#19128426	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128422	C₂	1	1	yes	maximal, characteristic, complemented
5	#19128418	C₂	1	2	yes	maximal, complemented
6	#19128389	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128387	C₂	1	2	yes	maximal, complemented
8	#19128385	C₂	1	1	yes	maximal, characteristic, complemented
9	#19128383	C₂	1	2	yes	maximal, complemented
10	#19128366	C₂	1	1	yes	maximal, characteristic, complemented
11	#19128364	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128364	C₂	1	1	yes	maximal, characteristic, complemented
13	#19128310	C₂	1	2	yes	maximal, complemented
14	#19128309	C₂	1	1	yes	maximal, characteristic, complemented
15	#19128308	C₂	1	2	yes	maximal, complemented
16	#19128257	C₂	1	2	yes	maximal, complemented
17	#19128255	C₂	1	1	yes	maximal, characteristic, complemented
18	#19128234	C₂	1	2	yes	maximal
19	#19128229	C₂	1	1	yes	maximal, characteristic
20	#19128178	C₂	1	1	yes	maximal, characteristic, complemented
21	#19128177	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#541×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×Dic₁₆₆	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₈₃	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₈₃	C₂²	1	1	yes	characteristic
27	#14581791	C₂²	1	2	yes	—
28	#14581791	C₂²	1	2	yes	—
29	#14581791	C₂²	1	2	yes	—
30	#14581791	C₂²	1	2	yes	—
31	#14581791	C₂²	1	1	yes	characteristic
32	#14581790	C₂²	1	1	yes	characteristic
33	#14581790	C₂²	1	1	yes	characteristic
34	#14581787	C₂²	1	2	yes	—
35	#14581787	C₂²	1	2	yes	—
36	#14581787	C₂²	1	2	yes	—
37	#14581787	C₂²	1	1	yes	characteristic
38	#14581786	C₂²	1	2	yes	—
39	#14581785	C₂²	1	2	yes	—
40	#14581785	C₂²	1	2	yes	—
41	#14581785	C₂²	1	1	yes	characteristic
42	#14581784	C₂²	1	2	yes	—
43	#14581783	C₂²	1	1	yes	characteristic
44	#14581783	C₂²	1	2	yes	—
45	#14581783	C₂²	1	2	yes	—
46	#14581782	C₂²	1	2	yes	—
47	#14581782	C₂²	1	2	yes	—
48	#14581782	C₂²	1	2	yes	—
49	#14581782	C₂²	1	2	yes	—
50	#14581782	C₂²	1	2	yes	—
51	#14581782	C₂²	1	2	yes	—
52	#14581782	C₂²	1	1	yes	characteristic
53	#14581782	C₂²	1	2	yes	—
54	#14581778	C₂²	1	1	yes	characteristic
55	#14581778	C₂²	1	2	yes	—
56	#14581777	C₂²	1	1	yes	characteristic
57	#14581777	C₂²	1	2	yes	—
58	#14581774	C₂²	1	2	yes	—
59	#14581774	C₂²	1	1	yes	characteristic
60	#14581772	C₂²	1	1	yes	characteristic
61	#14581772	C₂²	1	1	yes	characteristic
62	#14581770	C₂²	1	2	yes	—
63	#14581770	C₂²	1	2	yes	—
64	#14581770	C₂²	1	2	yes	—
65	#14581770	C₂²	1	2	yes	—
66	#14581770	C₂²	1	1	yes	characteristic
67	#14581770	C₂²	1	2	yes	—
68	#14581769	C₂²	1	2	yes	—
69	#14581769	C₂²	1	2	yes	—
70	#14581768	C₂²	1	1	yes	characteristic
71	#14581768	C₂²	1	1	yes	characteristic
72	#14581765	C₂²	1	1	yes	characteristic
73	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic
74	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic
75	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
76	C₄×Dic₁₆₆	C₂²	1	2	yes	—
77	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
78	C₄×Dic₁₆₆	C₂²	1	2	yes	—
79	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
80	C₄×Dic₁₆₆	C₂²	1	2	yes	—
81	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
82	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
83	#14581757	C₂²	1	1	yes	characteristic
84	#14581757	C₂²	1	1	yes	characteristic
85	#14581757	C₂²	1	2	yes	—
86	#14581757	C₂²	1	2	yes	—
87	#14581757	C₂²	1	2	yes	—
88	#14581757	C₂²	1	2	yes	—
89	#14581757	C₂²	1	2	yes	—
90	#14581757	C₂²	1	2	yes	—
91	#14581757	C₂²	1	2	yes	—
92	C₄×D₃₃₂	C₂²	1	1	yes	characteristic
93	#14581754	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
96	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	—
97	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	—
98	#14581751	C₂²	1	1	yes	characteristic
99	#14581750	C₂²	1	2	yes	—
100	#14581750	C₂²	1	2	yes	—
101	#14581750	C₂²	1	1	yes	characteristic
102	#14581750	C₂²	1	2	yes	—
103	#14581749	C₂²	1	2	yes	—
104	#14581749	C₂²	1	2	yes	—
105	#14581749	C₂²	1	1	yes	characteristic
106	#14581748	C₂²	1	2	yes	—
107	#14581748	C₂²	1	2	yes	—
108	C₄⋊C₄×D₈₃	C₂²	1	2	yes	—
109	C₄⋊C₄×D₈₃	C₂²	1	1	yes	characteristic
110	C₄²×D₈₃	C₂²	1	1	yes	characteristic
111	C₄²×D₈₃	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
113	#126×C₈₃	C₂²	1	2	yes	—
114	#126×C₈₃	C₂²	1	2	yes	—
115	#125×C₈₃	C₂²	1	2	yes	—
116	#125×C₈₃	C₂²	1	1	yes	characteristic
117	#125×C₈₃	C₂²	1	2	yes	—
118	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
119	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
121	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
122	#117×C₈₃	C₂²	1	1	yes	characteristic
123	C₂×Dic₁₆₆	—	2	4	no	—
124	C₂×Dic₁₆₆	C₂³	1	2	yes	—
125	C₂×Dic₁₆₆	C₂³	1	2	yes	—
126	C₂×Dic₁₆₆	C₂³	1	2	yes	—
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	1	yes	characteristic
131	Q₈×D₈₃	—	2	4	no	—
132	Q₈×D₈₃	—	2	4	no	—
133	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
136	C₂²×Dic₈₃	C₂³	1	2	yes	—
137	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₈₃	C₂³	1	2	yes	—
141	C₂×C₄×D₈₃	C₂³	1	2	yes	—
142	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₈₃	C₂³	1	2	yes	—
144	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₈₃	C₂³	1	2	yes	—
146	C₄⋊Dic₈₃	C₂³	1	2	yes	—
147	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₈₃	C₂³	1	2	yes	—
149	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₈₃	C₂³	1	2	yes	—
151	C₄⋊Dic₈₃	C₂³	1	2	yes	—
152	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
153	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
154	Dic₈₃⋊C₄	C₂³	1	2	yes	—
155	Dic₈₃⋊C₄	C₂³	1	2	yes	—
156	Dic₈₃⋊C₄	C₂³	1	2	yes	—
157	Dic₈₃⋊C₄	C₂³	1	2	yes	—
158	Dic₈₃⋊C₄	C₂³	1	2	yes	—
159	Dic₈₃⋊C₄	C₂³	1	2	yes	—
160	Dic₈₃⋊C₄	C₂³	1	2	yes	—
161	Dic₈₃⋊C₄	C₂³	1	2	yes	—
162	Dic₈₃⋊C₄	C₂³	1	2	yes	—
163	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
164	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
165	Dic₈₃⋊C₄	C₂³	1	2	yes	—
166	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₈₃⋊C₄	C₂³	1	2	yes	—
169	Dic₈₃⋊C₄	C₂³	1	2	yes	—
170	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₈₃⋊C₄	C₂³	1	2	yes	—
172	Dic₈₃⋊C₄	C₂³	1	2	yes	—
173	Dic₈₃⋊C₄	C₂³	1	2	yes	—
174	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
177	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
182	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
188	C₄×Dic₈₃	C₂³	1	2	yes	—
189	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
190	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
191	C₄×Dic₈₃	C₂³	1	2	yes	—
192	C₄×Dic₈₃	C₂³	1	2	yes	—
193	C₄×Dic₈₃	C₂³	1	2	yes	—
194	C₄×Dic₈₃	C₂³	1	2	yes	—
195	C₄×Dic₈₃	C₂³	1	2	yes	—
196	C₄×Dic₈₃	C₂³	1	2	yes	—
197	C₄×Dic₈₃	C₂³	1	2	yes	—
198	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₈₃	C₂³	1	2	yes	—
201	C₄×Dic₈₃	C₂³	1	2	yes	—
202	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
205	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
206	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
207	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
208	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
209	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
212	C₄⋊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	2	yes	—
216	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
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	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
221	C₄²×C₈₃	C₂³	1	2	yes	—
222	C₄²×C₈₃	C₂³	1	1	yes	characteristic
223	C₄²×C₈₃	C₂³	1	1	yes	characteristic
224	C₄²×C₈₃	C₂³	1	2	yes	—
225	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
226	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
228	Q₈×C₈₃	—	2	2	no	—
229	Q₈×C₈₃	—	2	2	no	—
230	C₂×C₄×C₈₃	—	2	2	no	—
231	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
235	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
237	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
238	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
241	C₂²⋊D₈₃	—	2	2	no	—
242	C₂²⋊D₈₃	—	2	2	no	—
243	C₂×Dic₈₃	—	2	4	no	—
244	C₂×Dic₈₃	C₂⁴	1	2	yes	—
245	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₈₃	C₂⁴	1	2	yes	—
247	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₈₃	C₂⁴	1	2	yes	—
249	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₈₃	C₂⁴	1	2	yes	—
253	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
254	D₃₃₂	—	2	2	no	—
255	C₄×D₈₃	—	2	2	no	—
256	C₄×D₈₃	—	2	4	no	—
257	C₄×D₈₃	—	2	2	no	—
258	C₄×D₈₃	—	2	2	no	—
259	C₄×D₈₃	—	2	4	no	—
260	C₄×D₈₃	—	2	4	no	—
261	C₄×D₈₃	—	2	2	no	—
262	Dic₁₆₆	—	2	2	no	—
263	Dic₁₆₆	—	2	4	no	—
264	Dic₁₆₆	—	2	4	no	—
265	Dic₁₆₆	—	2	4	no	—
266	Dic₁₆₆	—	2	2	no	—
267	Dic₁₆₆	—	2	4	no	—
268	Dic₁₆₆	#41	1	4	yes	—
269	C₂²×C₈₃	—	2	1	no	—
270	C₂²×C₈₃	—	2	1	no	—
271	C₂²×C₈₃	—	2	1	no	—
272	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
273	C₂×D₈₃	—	2	1	no	—
274	C₂×D₈₃	—	2	1	no	—
275	C₂×D₈₃	—	2	1	no	—
276	C₂×D₈₃	—	2	1	no	—
277	C₂×D₈₃	—	2	1	no	—
278	C₂×D₈₃	2₋¹⁺⁴	1	2	yes	—
279	C₄×C₈₃	—	2	1	no	—
280	C₄×C₈₃	—	2	2	no	—
281	C₄×C₈₃	—	2	2	no	—
282	C₄×C₈₃	—	2	1	no	—
283	C₄×C₈₃	—	2	2	no	—
284	C₄×C₈₃	—	2	1	no	—
285	C₄×C₈₃	—	2	2	no	—
286	C₄×C₈₃	—	2	1	no	—
287	C₄×C₈₃	—	2	1	no	—
288	C₄×C₈₃	C₂×#41	1	2	yes	—
289	Dic₈₃	—	2	1	no	—
290	Dic₈₃	—	2	1	no	—
291	Dic₈₃	—	2	2	no	—
292	Dic₈₃	—	2	1	no	—
293	Dic₈₃	—	2	2	no	—
294	Dic₈₃	—	2	2	no	—
295	Dic₈₃	—	2	1	no	—
296	Dic₈₃	—	2	1	no	—
297	Dic₈₃	C₂×#41	1	4	yes	—
298	Dic₈₃	2₋¹⁺⁴	1	2	yes	—
299	C₂×C₈₃	—	4	1	no	—
300	C₂×C₈₃	C₂²×#41	1	1	yes	characteristic
301	C₂×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
302	C₂×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
303	D₈₃	—	2	2	no	—
304	D₈₃	—	4	1	no	—
305	#3523	—	83	1	no	maximal, Sylow
306	C₈₃	#3523	1	1	yes	characteristic, complemented, Sylow
307	#557	—	83	1	no	—
308	#557	—	83	1	no	—
309	#557	—	83	2	no	—
310	#556	—	83	2	no	—
311	#556	—	83	1	no	—
312	#552	—	83	2	no	—
313	#552	—	83	2	no	—
314	#552	—	83	1	no	—
315	#552	—	83	1	no	—
316	D₄×Q₈	—	83	1	no	—
317	D₄×Q₈	—	83	1	no	—
318	D₄×Q₈	—	83	1	no	—
319	#541	—	83	2	no	—
320	#541	—	83	2	no	—
321	#541	—	83	1	no	—
322	#541	D₈₃	1	1	yes	characteristic, complemented
323	#533	—	83	2	no	—
324	#533	—	83	1	no	—
325	#529	—	83	2	no	—
326	#529	—	83	1	no	—
327	#519	—	83	1	no	—
328	#519	—	83	1	no	—
329	C₂×C₄×Q₈	—	83	1	no	—
330	C₂²×Q₈	—	83	1	no	—
331	C₂²×Q₈	—	83	1	no	—
332	C₂²×Q₈	—	83	1	no	—
333	C₄⋊Q₈	—	83	1	no	—
334	C₄⋊Q₈	—	83	1	no	—
335	C₄⋊Q₈	—	83	2	no	—
336	C₄⋊Q₈	—	83	2	no	—
337	C₄⋊Q₈	—	83	1	no	—
338	C₄⋊Q₈	—	83	2	no	—
339	C₄⋊Q₈	—	83	2	no	—
340	C₄⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
341	#126	—	83	1	no	—
342	#126	—	83	2	no	—
343	#126	—	83	2	no	—
344	#126	—	83	2	no	—
345	#126	—	83	1	no	—
346	#126	—	83	2	no	—
347	#126	—	83	2	no	—
348	#126	—	83	2	no	—
349	#126	C₂×D₈₃	1	2	yes	—
350	#126	C₂×D₈₃	1	2	yes	—
351	#125	—	83	2	no	—
352	#125	—	83	1	no	—
353	#125	—	83	2	no	—
354	#125	—	83	2	no	—
355	#125	—	83	2	no	—
356	#125	—	83	2	no	—
357	#125	—	83	2	no	—
358	#125	—	83	2	no	—
359	#125	—	83	2	no	—
360	#125	—	83	2	no	—
361	#125	—	83	1	no	—
362	#125	—	83	2	no	—
363	#125	C₂×D₈₃	1	2	yes	—
364	#125	C₂×D₈₃	1	2	yes	—
365	#125	C₂×D₈₃	1	1	yes	characteristic
366	#124	—	83	2	no	—
367	#124	—	83	1	no	—
368	#123	—	83	2	no	—
369	#123	—	83	1	no	—
370	#123	—	83	2	no	—
371	#123	—	83	1	no	—
372	C₂²⋊Q₈	—	83	1	no	—
373	C₂²⋊Q₈	—	83	1	no	—
374	C₂²⋊Q₈	—	83	2	no	—
375	C₂²⋊Q₈	—	83	1	no	—
376	C₂²⋊Q₈	—	83	2	no	—
377	C₂²⋊Q₈	—	83	2	no	—
378	C₂²⋊Q₈	—	83	2	no	—
379	C₂²⋊Q₈	—	83	2	no	—
380	C₂²⋊Q₈	—	83	1	no	—
381	C₂²⋊Q₈	—	83	1	no	—
382	C₂²⋊Q₈	—	83	2	no	—
383	C₂²⋊Q₈	—	83	2	no	—
384	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
385	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
386	#121	—	83	1	no	—
387	C₄×Q₈	—	83	1	no	—
388	C₄×Q₈	—	83	1	no	—
389	C₄×Q₈	—	83	1	no	—
390	C₄×Q₈	—	83	2	no	—
391	C₄×Q₈	—	83	2	no	—
392	C₄×Q₈	—	83	2	no	—
393	C₄×Q₈	—	83	1	no	—
394	C₄×Q₈	—	83	2	no	—
395	C₄×Q₈	—	83	2	no	—
396	C₄×Q₈	—	83	2	no	—
397	C₄×Q₈	—	83	2	no	—
398	C₄×Q₈	—	83	1	no	—
399	C₄×Q₈	—	83	2	no	—
400	C₄×Q₈	—	83	1	no	—
401	C₄×Q₈	—	83	1	no	—
402	C₄×Q₈	—	83	1	no	—
403	C₄×Q₈	—	83	2	no	—
404	C₄×Q₈	—	83	1	no	—
405	C₄×Q₈	—	83	2	no	—
406	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
407	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
408	C₄×D₄	—	83	1	no	—
409	C₄×D₄	—	83	1	no	—
410	C₄×D₄	—	83	2	no	—
411	C₄×D₄	—	83	2	no	—
412	C₄×D₄	—	83	2	no	—
413	C₄×D₄	—	83	1	no	—
414	#117	—	83	1	no	—
415	#117	—	83	2	no	—
416	#117	—	83	1	no	—
417	#117	—	83	2	no	—
418	#117	—	83	2	no	—
419	#117	—	83	2	no	—
420	#117	—	83	2	no	—
421	#117	—	83	1	no	—
422	#117	—	83	2	no	—
423	#117	—	83	2	no	—
424	#117	C₂×D₈₃	1	1	yes	characteristic
425	C₂×C₄⋊C₄	—	83	2	no	—
426	C₂×C₄⋊C₄	—	83	1	no	—
427	C₂×C₄²	—	83	2	no	—
428	C₂×C₄²	—	83	1	no	—
429	C₂×Q₈	—	83	1	no	—
430	C₂×Q₈	—	83	2	no	—
431	C₂×Q₈	—	83	1	no	—
432	C₂×Q₈	—	83	2	no	—
433	C₂×Q₈	—	83	2	no	—
434	C₂×Q₈	—	83	2	no	—
435	C₂×Q₈	—	83	1	no	—
436	C₂×Q₈	—	166	4	no	—
437	C₂×Q₈	—	166	4	no	—
438	C₂×Q₈	—	166	4	no	—
439	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
440	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
441	C₂×D₄	—	83	1	no	—
442	C₂×D₄	—	83	1	no	—
443	C₂×D₄	—	83	1	no	—
444	C₂²×C₄	—	83	2	no	—
445	C₂²×C₄	—	83	1	no	—
446	C₂²×C₄	—	83	2	no	—
447	C₂²×C₄	—	83	1	no	—
448	C₂²×C₄	—	83	2	no	—
449	C₂²×C₄	—	83	1	no	—
450	C₂²×C₄	—	83	2	no	—
451	C₂²×C₄	—	83	1	no	—
452	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
453	C₄⋊C₄	—	83	2	no	—
454	C₄⋊C₄	—	83	1	no	—
455	C₄⋊C₄	—	83	2	no	—
456	C₄⋊C₄	—	83	2	no	—
457	C₄⋊C₄	—	83	2	no	—
458	C₄⋊C₄	—	83	2	no	—
459	C₄⋊C₄	—	83	2	no	—
460	C₄⋊C₄	—	83	1	no	—
461	C₄⋊C₄	—	83	2	no	—
462	C₄⋊C₄	—	83	1	no	—
463	C₄⋊C₄	—	83	2	no	—
464	C₄⋊C₄	—	83	1	no	—
465	C₄⋊C₄	—	83	2	no	—
466	C₄⋊C₄	—	83	2	no	—
467	C₄⋊C₄	—	83	2	no	—
468	C₄⋊C₄	—	83	2	no	—
469	C₄⋊C₄	—	83	2	no	—
470	C₄⋊C₄	—	83	1	no	—
471	C₄⋊C₄	—	83	2	no	—
472	C₄⋊C₄	—	83	1	no	—
473	C₄⋊C₄	—	83	2	no	—
474	C₄⋊C₄	—	83	1	no	—
475	C₄⋊C₄	—	83	1	no	—
476	C₄⋊C₄	—	83	2	no	—
477	C₄⋊C₄	—	83	2	no	—
478	C₄⋊C₄	—	83	2	no	—
479	C₄⋊C₄	—	83	2	no	—
480	C₄⋊C₄	—	83	2	no	—
481	C₄⋊C₄	—	83	1	no	—
482	C₄⋊C₄	—	83	1	no	—
483	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
485	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
487	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
488	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
489	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
492	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
493	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
494	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
495	C₂²⋊C₄	—	83	2	no	—
496	C₂²⋊C₄	—	83	1	no	—
497	C₂²⋊C₄	—	83	1	no	—
498	C₂²⋊C₄	—	83	1	no	—
499	C₂²⋊C₄	—	83	2	no	—
500	C₂²⋊C₄	—	83	1	no	—
501	C₂²⋊C₄	—	83	1	no	—
502	C₂²⋊C₄	—	83	2	no	—
503	C₂²⋊C₄	—	83	1	no	—
504	C₂²⋊C₄	—	83	2	no	—
505	C₂²⋊C₄	—	83	1	no	—
506	C₂²⋊C₄	—	83	2	no	—
507	C₂²⋊C₄	—	83	2	no	—
508	C₂²⋊C₄	—	83	1	no	—
509	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
510	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
511	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
513	C₄²	—	83	2	no	—
514	C₄²	—	83	2	no	—
515	C₄²	—	83	1	no	—
516	C₄²	—	83	2	no	—
517	C₄²	—	83	1	no	—
518	C₄²	—	83	1	no	—
519	C₄²	—	83	2	no	—
520	C₄²	—	83	2	no	—
521	C₄²	—	83	2	no	—
522	C₄²	—	83	2	no	—
523	C₄²	—	83	2	no	—
524	C₄²	—	83	2	no	—
525	C₄²	—	83	2	no	—
526	C₄²	—	83	1	no	—
527	C₄²	C₂²×D₈₃	1	1	yes	characteristic
528	C₄²	C₂²×D₈₃	1	2	yes	—
529	C₄²	C₂²×D₈₃	1	2	yes	—
530	C₄²	C₂²×D₈₃	1	1	yes	characteristic
531	C₂³	—	83	1	no	—
532	C₂³	—	83	1	no	—
533	C₂³	C₂³×D₈₃	1	1	yes	characteristic
534	Q₈	—	2	2	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	83	4	no	—
537	Q₈	—	166	4	no	—
538	Q₈	—	166	4	no	—
539	Q₈	—	166	4	no	—
540	Q₈	—	166	4	no	—
541	Q₈	—	166	2	no	—
542	Q₈	—	166	2	no	—
543	D₄	—	166	2	no	—
544	D₄	—	166	2	no	—
545	D₄	—	166	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	83	1	no	—
548	C₂×C₄	—	83	2	no	—
549	C₂×C₄	—	83	2	no	—
550	C₂×C₄	—	83	2	no	—
551	C₂×C₄	—	83	1	no	—
552	C₂×C₄	—	83	1	no	—
553	C₂×C₄	—	83	1	no	—
554	C₂×C₄	—	83	1	no	—
555	C₂×C₄	—	83	1	no	—
556	C₂×C₄	—	83	2	no	—
557	C₂×C₄	—	166	4	no	—
558	C₂×C₄	—	166	4	no	—
559	C₂×C₄	—	166	2	no	—
560	C₂×C₄	—	166	2	no	—
561	C₂×C₄	—	166	4	no	—
562	C₂×C₄	—	166	4	no	—
563	C₂×C₄	—	166	2	no	—
564	C₂×C₄	—	166	2	no	—
565	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₈₃	1	2	yes	—
569	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₈₃	1	2	yes	—
572	C₂×C₄	C₂³×D₈₃	1	2	yes	—
573	C₂×C₄	C₂³×D₈₃	1	2	yes	—
574	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	83	2	no	—
579	C₂²	—	166	1	no	—
580	C₂²	—	166	1	no	—
581	C₂²	—	166	1	no	—
582	C₂²	—	166	1	no	—
583	C₂²	—	166	1	no	—
584	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	83	4	no	—
595	C₄	—	83	2	no	—
596	C₄	—	166	2	no	—
597	C₄	—	166	1	no	—
598	C₄	—	166	1	no	—
599	C₄	—	166	2	no	—
600	C₄	—	166	1	no	—
601	C₄	—	166	1	no	—
602	C₄	—	166	2	no	—
603	C₄	—	166	1	no	—
604	C₄	#41×D₈₃	1	2	yes	—
605	C₂	—	4	1	no	—
606	C₂	—	332	1	no	—
607	C₂	—	166	2	no	—
608	C₂	C₂×#41×D₈₃	1	1	yes	characteristic
609	C₂	2₋¹⁺⁴×D₈₃	1	1	yes	characteristic
610	C₂	2₋¹⁺⁴×D₈₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#541×C₈₃	C₂
prime radical	#14581765	C₂²
hypercenter	#541	D₈₃
hypocenter	C₈₃	#3523
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. #19128428	C₂	semidirect
2. #19128428	C₂	semidirect
3. #19128426	C₂	semidirect
4. #19128422	C₂	semidirect
5. #19128418	C₂	semidirect
6. #19128389	C₂	semidirect
7. #19128387	C₂	semidirect
8. #19128385	C₂	semidirect
9. #19128383	C₂	semidirect
10. #19128366	C₂	semidirect
11. #19128364	C₂	semidirect
12. #19128364	C₂	semidirect
13. #19128310	C₂	semidirect
14. #19128309	C₂	semidirect
15. #19128308	C₂	semidirect
16. #19128257	C₂	semidirect
17. #19128255	C₂	semidirect
20. #19128178	C₂	semidirect
21. #19128177	C₂	semidirect
22. C₄×Q₈×D₈₃	C₂	semidirect
23. #541×C₈₃	C₂	semidirect
306. C₈₃	#3523	semidirect
322. #541	D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128428	2
#19128426	2
#19128422	2
#19128418	2
#19128389	2
#19128387	2
#19128385	2
#19128383	2
#19128366	2
#19128364	2
#19128310	2
#19128309	2
#19128308	2
#19128257	2
#19128255	2
#19128234	2
#19128229	2
#19128178	2
#19128177	2
C₄×Q₈×D₈₃	2
#541×C₈₃	2
#3523	83