Subgroups — #24921871

Order 10624.

1002 conjugacy classes of subgroups.

The subgroup lattice has 624 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	#19128452	C₂	1	2	yes	maximal, complemented
3	#19128434	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128433	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₈×Dic₁₆₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#19128431	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128423	C₂	1	1	yes	maximal, characteristic, complemented
8	#19128420	C₂	1	1	yes	maximal, characteristic, complemented
9	#19128418	C₂	1	2	yes	maximal, complemented
10	D₄×Dic₁₆₆	C₂	1	1	yes	maximal, characteristic, complemented
11	#19128366	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128364	C₂	1	2	yes	maximal, complemented
13	#19128324	C₂	1	1	yes	maximal, characteristic, complemented
14	#19128322	C₂	1	1	yes	maximal, characteristic, complemented
15	#19128319	C₂	1	2	yes	maximal, complemented
16	#19128318	C₂	1	1	yes	maximal, characteristic, complemented
17	#19128315	C₂	1	2	yes	maximal, complemented
18	#19128273	C₂	1	2	yes	maximal, complemented
19	#19128271	C₂	1	2	yes	maximal, complemented
20	#19128254	C₂	1	1	yes	maximal, characteristic, complemented
21	#19128253	C₂	1	1	yes	maximal, characteristic, complemented
22	#19128246	C₂	1	1	yes	maximal, characteristic
23	#542×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13050589	C₂²	1	2	yes	—
25	C₂²×Dic₁₆₆	C₂²	1	2	yes	—
26	C₂×Q₈×D₈₃	C₂²	1	2	yes	—
27	#14581792	C₂²	1	1	yes	characteristic
28	#14581792	C₂²	1	2	yes	—
29	#14581791	C₂²	1	1	yes	characteristic
30	#14581791	C₂²	1	1	yes	characteristic
31	#14581791	C₂²	1	2	yes	—
32	#14581791	C₂²	1	1	yes	characteristic
33	#14581791	C₂²	1	1	yes	characteristic
34	#14581791	C₂²	1	1	yes	characteristic
35	#14581791	C₂²	1	1	yes	characteristic
36	#14581791	C₂²	1	2	yes	—
37	#14581791	C₂²	1	2	yes	—
38	#14581790	C₂²	1	2	yes	—
39	#14581790	C₂²	1	1	yes	characteristic
40	#14581790	C₂²	1	2	yes	—
41	#14581788	C₂²	1	1	yes	characteristic
42	#14581787	C₂²	1	2	yes	—
43	#14581787	C₂²	1	2	yes	—
44	#14581787	C₂²	1	2	yes	—
45	#14581786	C₂²	1	2	yes	—
46	#14581785	C₂²	1	2	yes	—
47	#14581785	C₂²	1	2	yes	—
48	#14581785	C₂²	1	2	yes	—
49	#14581783	C₂²	1	1	yes	characteristic
50	#14581783	C₂²	1	1	yes	characteristic
51	#14581782	C₂²	1	2	yes	—
52	#14581781	C₂²	1	1	yes	characteristic
53	#14581780	C₂²	1	1	yes	characteristic
54	#14581779	C₂²	1	1	yes	characteristic
55	#14581779	C₂²	1	2	yes	—
56	#14581778	C₂²	1	2	yes	—
57	#14581778	C₂²	1	2	yes	—
58	#14581778	C₂²	1	2	yes	—
59	#14581778	C₂²	1	2	yes	—
60	#14581778	C₂²	1	2	yes	—
61	#14581776	C₂²	1	2	yes	—
62	#14581775	C₂²	1	2	yes	—
63	#14581774	C₂²	1	2	yes	—
64	#14581774	C₂²	1	2	yes	—
65	#14581774	C₂²	1	2	yes	—
66	#14581774	C₂²	1	2	yes	—
67	#14581773	C₂²	1	2	yes	—
68	#14581772	C₂²	1	2	yes	—
69	#14581771	C₂²	1	1	yes	characteristic
70	#14581771	C₂²	1	2	yes	—
71	#14581770	C₂²	1	2	yes	—
72	#14581770	C₂²	1	2	yes	—
73	#14581770	C₂²	1	2	yes	—
74	#14581770	C₂²	1	2	yes	—
75	#14581769	C₂²	1	2	yes	—
76	#14581769	C₂²	1	2	yes	—
77	#14581769	C₂²	1	2	yes	—
78	#14581769	C₂²	1	2	yes	—
79	#14581769	C₂²	1	2	yes	—
80	#14581769	C₂²	1	1	yes	characteristic
81	#14581769	C₂²	1	1	yes	characteristic
82	#14581769	C₂²	1	1	yes	characteristic
83	#14581769	C₂²	1	1	yes	characteristic
84	#14581768	C₂²	1	2	yes	—
85	#14581766	C₂²	1	1	yes	characteristic
86	#14581764	C₂²	1	2	yes	—
87	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic
88	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic
89	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
90	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
91	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
92	C₄×Dic₁₆₆	C₂²	1	2	yes	—
93	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
94	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
95	#14581757	C₂²	1	2	yes	—
96	#14581757	C₂²	1	2	yes	—
97	#14581757	C₂²	1	1	yes	characteristic
98	#14581757	C₂²	1	1	yes	characteristic
99	C₄×D₃₃₂	C₂²	1	1	yes	characteristic
100	D₄×Dic₈₃	C₂²	1	1	yes	characteristic
101	D₄×Dic₈₃	C₂²	1	1	yes	characteristic
102	#14581754	C₂²	1	1	yes	characteristic
103	#14581754	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	—
105	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	—
106	(C₂²⋊D₈₃)⋊C₄	C₂²	1	2	yes	—
107	#14581751	C₂²	1	1	yes	characteristic
108	#14581749	C₂²	1	2	yes	—
109	#14581748	C₂²	1	2	yes	—
110	#14581748	C₂²	1	2	yes	—
111	C₂×C₄×Dic₈₃	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
113	#126×C₈₃	C₂²	1	2	yes	—
114	#124×C₈₃	C₂²	1	1	yes	characteristic
115	#124×C₈₃	C₂²	1	2	yes	—
116	#123×C₈₃	C₂²	1	2	yes	—
117	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
118	C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	—
119	#121×C₈₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
122	#117×C₈₃	C₂²	1	1	yes	characteristic
123	#13050589	—	4	4	no	—
124	C₂×Dic₁₆₆	—	4	4	no	—
125	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
126	C₂×Dic₁₆₆	C₂³	1	2	yes	—
127	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₆₆	C₂³	1	2	yes	—
132	C₂×Dic₁₆₆	C₂³	1	2	yes	—
133	C₂×Dic₁₆₆	C₂³	1	2	yes	—
134	C₂×Dic₁₆₆	C₂³	1	2	yes	—
135	Q₈×D₈₃	—	4	4	no	—
136	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
140	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
141	C₂²×Dic₈₃	C₂³	1	1	yes	characteristic
142	C₂²×Dic₈₃	C₂³	1	2	yes	—
143	C₂²×Dic₈₃	C₂³	1	2	yes	—
144	C₂×C₄×D₈₃	C₂³	1	2	yes	—
145	C₂×C₄×D₈₃	C₂³	1	2	yes	—
146	C₂×C₄×D₈₃	C₂³	1	2	yes	—
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	2	yes	—
151	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₈₃	C₂³	1	2	yes	—
153	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₈₃	C₂³	1	2	yes	—
155	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
162	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
163	Dic₈₃⋊C₄	C₂³	1	2	yes	—
164	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
165	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₈₃⋊C₄	C₂³	1	2	yes	—
167	Dic₈₃⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
173	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
175	Dic₈₃⋊C₄	C₂³	1	2	yes	—
176	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
183	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
191	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
198	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
202	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₈₃	C₂³	1	2	yes	—
204	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₈₃	C₂³	1	2	yes	—
206	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
208	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
210	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
211	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
212	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
216	C₂²⋊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	2	yes	—
221	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
222	C₄²×C₈₃	C₂³	1	1	yes	characteristic
223	C₄²×C₈₃	C₂³	1	2	yes	—
224	C₄²×C₈₃	C₂³	1	1	yes	characteristic
225	C₂³×C₈₃	C₂⁴	1	2	yes	—
226	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₈₃	C₂⁴	1	2	yes	—
228	Q₈×C₈₃	—	2	2	no	—
229	Q₈×C₈₃	—	4	2	no	—
230	D₄×C₈₃	—	2	2	no	—
231	D₄×C₈₃	—	4	2	no	—
232	C₂×C₄×C₈₃	—	2	2	no	—
233	C₂×C₄×C₈₃	—	4	2	no	—
234	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
237	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
240	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
242	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
243	C₂²⋊D₈₃	—	2	4	no	—
244	C₂²⋊D₈₃	—	4	2	no	—
245	C₂²⋊D₈₃	—	4	2	no	—
246	C₂×Dic₈₃	—	2	4	no	—
247	C₂×Dic₈₃	—	2	2	no	—
248	C₂×Dic₈₃	—	2	2	no	—
249	C₂×Dic₈₃	—	4	2	no	—
250	C₂×Dic₈₃	C₂⁴	1	2	yes	—
251	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₈₃	C₂⁴	1	2	yes	—
255	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₈₃	C₂⁴	1	2	yes	—
258	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
261	D₃₃₂	—	2	2	no	—
262	C₄×D₈₃	—	2	4	no	—
263	C₄×D₈₃	—	4	2	no	—
264	C₄×D₈₃	—	4	2	no	—
265	Dic₁₆₆	—	2	2	no	—
266	Dic₁₆₆	—	2	2	no	—
267	Dic₁₆₆	—	2	4	no	—
268	Dic₁₆₆	—	2	2	no	—
269	Dic₁₆₆	—	2	2	no	—
270	Dic₁₆₆	—	2	2	no	—
271	Dic₁₆₆	—	4	2	no	—
272	Dic₁₆₆	—	4	2	no	—
273	Dic₁₆₆	—	4	2	no	—
274	Dic₁₆₆	—	4	2	no	—
275	C₂²×C₈₃	—	2	2	no	—
276	C₂²×C₈₃	—	2	1	no	—
277	C₂²×C₈₃	—	2	1	no	—
278	C₂²×C₈₃	—	2	2	no	—
279	C₂²×C₈₃	—	2	1	no	—
280	C₂²×C₈₃	—	2	2	no	—
281	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
282	C₂×D₈₃	—	2	2	no	—
283	C₂×D₈₃	—	2	2	no	—
284	C₂×D₈₃	—	2	2	no	—
285	C₄×C₈₃	—	2	1	no	—
286	C₄×C₈₃	—	2	2	no	—
287	C₄×C₈₃	—	2	1	no	—
288	C₄×C₈₃	—	2	2	no	—
289	C₄×C₈₃	—	2	1	no	—
290	C₄×C₈₃	—	2	1	no	—
291	C₄×C₈₃	—	2	1	no	—
292	C₄×C₈₃	—	2	2	no	—
293	C₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
294	Dic₈₃	—	2	1	no	—
295	Dic₈₃	—	2	2	no	—
296	Dic₈₃	—	2	1	no	—
297	Dic₈₃	—	2	2	no	—
298	Dic₈₃	—	2	1	no	—
299	Dic₈₃	—	2	1	no	—
300	Dic₈₃	—	2	1	no	—
301	Dic₈₃	—	2	2	no	—
302	Dic₈₃	—	2	1	no	—
303	Dic₈₃	H(5,𝔽₂)	1	2	yes	—
304	Dic₈₃	2₋¹⁺⁴	1	2	yes	—
305	C₂×C₈₃	—	4	2	no	—
306	C₂×C₈₃	—	4	1	no	—
307	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
309	C₂×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	D₈₃	—	4	2	no	—
311	#3550	—	83	1	no	maximal, Sylow
312	C₈₃	#3550	1	1	yes	characteristic, complemented, Sylow
313	#563	—	83	2	no	—
314	#563	—	83	2	no	—
315	#559	—	83	1	no	—
316	#559	—	83	1	no	—
317	Q₈²	—	83	1	no	—
318	Q₈²	—	83	1	no	—
319	#556	—	83	2	no	—
320	#556	—	83	1	no	—
321	#556	—	83	1	no	—
322	D₄×Q₈	—	83	1	no	—
323	D₄×Q₈	—	83	2	no	—
324	D₄×Q₈	—	83	1	no	—
325	#542	—	83	2	no	—
326	#542	—	83	2	no	—
327	#542	—	83	1	no	—
328	#542	—	83	1	no	—
329	#542	—	83	1	no	—
330	#542	D₈₃	1	1	yes	characteristic, complemented
331	#536	—	83	2	no	—
332	#536	—	83	2	no	—
333	#533	—	83	1	no	—
334	#533	—	83	1	no	—
335	#532	—	83	1	no	—
336	C₂×#41	—	83	2	no	—
337	C₂²×Q₈	—	83	2	no	—
338	C₂²×Q₈	—	83	2	no	—
339	C₄⋊Q₈	—	83	1	no	—
340	C₄⋊Q₈	—	83	2	no	—
341	C₄⋊Q₈	—	83	2	no	—
342	C₄⋊Q₈	—	83	1	no	—
343	C₄⋊Q₈	—	83	1	no	—
344	C₄⋊Q₈	—	83	1	no	—
345	C₄⋊Q₈	—	83	1	no	—
346	C₄⋊Q₈	—	83	2	no	—
347	C₄⋊Q₈	—	83	2	no	—
348	C₄⋊Q₈	—	83	2	no	—
349	C₄⋊Q₈	—	83	1	no	—
350	C₄⋊Q₈	—	83	1	no	—
351	C₄⋊Q₈	—	83	2	no	—
352	C₄⋊Q₈	—	83	1	no	—
353	C₄⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
354	#127	—	83	1	no	—
355	#126	—	83	2	no	—
356	#126	—	83	2	no	—
357	#126	—	83	2	no	—
358	#126	—	83	2	no	—
359	#126	—	83	2	no	—
360	#126	—	83	2	no	—
361	#126	—	83	2	no	—
362	#126	C₂×D₈₃	1	2	yes	—
363	#125	—	83	2	no	—
364	#125	—	83	1	no	—
365	#125	—	83	1	no	—
366	#124	—	83	1	no	—
367	#124	—	83	2	no	—
368	#124	—	83	1	no	—
369	#124	—	83	2	no	—
370	#124	—	83	2	no	—
371	#124	—	83	2	no	—
372	#124	—	83	2	no	—
373	#124	—	83	2	no	—
374	#124	—	83	1	no	—
375	#124	C₂×D₈₃	1	2	yes	—
376	#124	C₂×D₈₃	1	1	yes	characteristic
377	#123	—	83	2	no	—
378	#123	—	83	2	no	—
379	#123	—	83	2	no	—
380	#123	—	83	2	no	—
381	#123	—	83	2	no	—
382	#123	—	83	2	no	—
383	#123	—	83	2	no	—
384	#123	C₂×D₈₃	1	2	yes	—
385	C₂²⋊Q₈	—	83	2	no	—
386	C₂²⋊Q₈	—	83	1	no	—
387	C₂²⋊Q₈	—	83	2	no	—
388	C₂²⋊Q₈	—	83	2	no	—
389	C₂²⋊Q₈	—	83	2	no	—
390	C₂²⋊Q₈	—	83	2	no	—
391	C₂²⋊Q₈	—	83	2	no	—
392	C₂²⋊Q₈	—	83	2	no	—
393	C₂²⋊Q₈	—	83	2	no	—
394	C₂²⋊Q₈	—	83	1	no	—
395	C₂²⋊Q₈	—	83	1	no	—
396	C₂²⋊Q₈	—	83	1	no	—
397	C₂²⋊Q₈	—	83	1	no	—
398	C₂²⋊Q₈	—	83	2	no	—
399	C₂²⋊Q₈	—	83	2	no	—
400	C₂²⋊Q₈	—	83	2	no	—
401	C₂²⋊Q₈	—	83	2	no	—
402	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
403	C₂²⋊Q₈	C₂×D₈₃	1	2	yes	—
404	#121	—	83	2	no	—
405	#121	—	83	1	no	—
406	#121	C₂×D₈₃	1	1	yes	characteristic
407	C₄×Q₈	—	83	1	no	—
408	C₄×Q₈	—	83	1	no	—
409	C₄×Q₈	—	83	2	no	—
410	C₄×Q₈	—	83	1	no	—
411	C₄×Q₈	—	83	2	no	—
412	C₄×Q₈	—	83	1	no	—
413	C₄×Q₈	—	83	1	no	—
414	C₄×Q₈	—	83	1	no	—
415	C₄×Q₈	—	83	1	no	—
416	C₄×Q₈	—	83	1	no	—
417	C₄×Q₈	—	83	2	no	—
418	C₄×Q₈	—	83	1	no	—
419	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
420	C₄×D₄	—	83	1	no	—
421	C₄×D₄	—	83	1	no	—
422	C₄×D₄	—	83	2	no	—
423	C₄×D₄	—	83	1	no	—
424	C₄×D₄	—	83	1	no	—
425	C₄×D₄	—	83	2	no	—
426	C₄×D₄	—	83	2	no	—
427	C₄×D₄	—	83	1	no	—
428	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic
429	#117	—	83	1	no	—
430	#117	—	83	2	no	—
431	#117	—	83	2	no	—
432	#117	—	83	2	no	—
433	#117	C₂×D₈₃	1	1	yes	characteristic
434	C₂×C₄²	—	83	1	no	—
435	#41	—	332	4	no	—
436	C₂×Q₈	—	332	4	no	—
437	C₂×Q₈	—	332	4	no	—
438	C₂×Q₈	—	83	2	no	—
439	C₂×Q₈	—	83	2	no	—
440	C₂×Q₈	—	83	2	no	—
441	C₂×Q₈	—	83	2	no	—
442	C₂×Q₈	—	83	1	no	—
443	C₂×Q₈	—	83	1	no	—
444	C₂×Q₈	—	83	1	no	—
445	C₂×Q₈	—	83	2	no	—
446	C₂×Q₈	—	83	1	no	—
447	C₂×Q₈	—	83	1	no	—
448	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
449	C₂×Q₈	C₂²×D₈₃	1	2	yes	—
450	C₂×D₄	—	83	2	no	—
451	C₂×D₄	—	83	2	no	—
452	C₂×D₄	—	83	2	no	—
453	C₂×D₄	—	83	1	no	—
454	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
455	C₂×D₄	C₂²×D₈₃	1	2	yes	—
456	C₂²×C₄	—	83	2	no	—
457	C₂²×C₄	—	83	2	no	—
458	C₂²×C₄	—	83	2	no	—
459	C₂²×C₄	—	83	1	no	—
460	C₂²×C₄	—	83	1	no	—
461	C₂²×C₄	—	83	2	no	—
462	C₂²×C₄	—	83	2	no	—
463	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
464	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
465	C₄⋊C₄	—	83	2	no	—
466	C₄⋊C₄	—	83	1	no	—
467	C₄⋊C₄	—	83	1	no	—
468	C₄⋊C₄	—	83	2	no	—
469	C₄⋊C₄	—	83	1	no	—
470	C₄⋊C₄	—	83	2	no	—
471	C₄⋊C₄	—	83	1	no	—
472	C₄⋊C₄	—	83	1	no	—
473	C₄⋊C₄	—	83	1	no	—
474	C₄⋊C₄	—	83	1	no	—
475	C₄⋊C₄	—	83	2	no	—
476	C₄⋊C₄	—	83	1	no	—
477	C₄⋊C₄	—	83	2	no	—
478	C₄⋊C₄	—	83	1	no	—
479	C₄⋊C₄	—	83	1	no	—
480	C₄⋊C₄	—	83	1	no	—
481	C₄⋊C₄	—	83	1	no	—
482	C₄⋊C₄	—	83	2	no	—
483	C₄⋊C₄	—	83	2	no	—
484	C₄⋊C₄	—	83	2	no	—
485	C₄⋊C₄	—	83	2	no	—
486	C₄⋊C₄	—	83	2	no	—
487	C₄⋊C₄	—	83	2	no	—
488	C₄⋊C₄	—	83	2	no	—
489	C₄⋊C₄	—	83	1	no	—
490	C₄⋊C₄	—	83	1	no	—
491	C₄⋊C₄	—	83	2	no	—
492	C₄⋊C₄	—	83	1	no	—
493	C₄⋊C₄	—	83	1	no	—
494	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
499	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
500	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
501	C₂²⋊C₄	—	83	1	no	—
502	C₂²⋊C₄	—	83	1	no	—
503	C₂²⋊C₄	—	83	2	no	—
504	C₂²⋊C₄	—	83	2	no	—
505	C₂²⋊C₄	—	83	2	no	—
506	C₂²⋊C₄	—	83	2	no	—
507	C₂²⋊C₄	—	83	2	no	—
508	C₂²⋊C₄	—	83	2	no	—
509	C₂²⋊C₄	—	83	2	no	—
510	C₂²⋊C₄	—	83	2	no	—
511	C₂²⋊C₄	—	83	2	no	—
512	C₂²⋊C₄	—	83	2	no	—
513	C₂²⋊C₄	—	83	2	no	—
514	C₂²⋊C₄	—	83	2	no	—
515	C₂²⋊C₄	—	83	2	no	—
516	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
519	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
520	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
523	C₄²	—	83	1	no	—
524	C₄²	—	83	1	no	—
525	C₄²	—	83	1	no	—
526	C₄²	—	83	1	no	—
527	C₄²	—	83	2	no	—
528	C₄²	—	83	2	no	—
529	C₄²	—	83	1	no	—
530	C₄²	—	83	1	no	—
531	C₄²	—	83	2	no	—
532	C₄²	—	83	2	no	—
533	C₄²	—	83	2	no	—
534	C₄²	C₂²×D₈₃	1	2	yes	—
535	C₄²	C₂²×D₈₃	1	1	yes	characteristic
536	C₄²	C₂²×D₈₃	1	1	yes	characteristic
537	C₂³	—	83	2	no	—
538	C₂³	C₂³×D₈₃	1	2	yes	—
539	C₂³	C₂³×D₈₃	1	1	yes	characteristic
540	Q₈	—	2	2	no	—
541	Q₈	—	4	2	no	—
542	Q₈	—	332	2	no	—
543	Q₈	—	332	2	no	—
544	Q₈	—	332	2	no	—
545	Q₈	—	332	2	no	—
546	Q₈	—	166	2	no	—
547	Q₈	—	166	4	no	—
548	Q₈	—	166	2	no	—
549	Q₈	—	166	2	no	—
550	Q₈	—	166	2	no	—
551	Q₈	—	166	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	332	2	no	—
555	D₄	—	332	2	no	—
556	D₄	—	166	4	no	—
557	D₄	—	166	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	332	2	no	—
561	C₂×C₄	—	332	2	no	—
562	C₂×C₄	—	332	2	no	—
563	C₂×C₄	—	83	1	no	—
564	C₂×C₄	—	83	1	no	—
565	C₂×C₄	—	83	1	no	—
566	C₂×C₄	—	83	1	no	—
567	C₂×C₄	—	83	2	no	—
568	C₂×C₄	—	83	1	no	—
569	C₂×C₄	—	83	2	no	—
570	C₂×C₄	—	83	1	no	—
571	C₂×C₄	—	83	1	no	—
572	C₂×C₄	—	83	2	no	—
573	C₂×C₄	—	83	1	no	—
574	C₂×C₄	—	166	4	no	—
575	C₂×C₄	—	166	4	no	—
576	C₂×C₄	—	166	2	no	—
577	C₂×C₄	—	166	2	no	—
578	C₂×C₄	C₂³×D₈₃	1	2	yes	—
579	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₈₃	1	2	yes	—
582	C₂×C₄	C₂³×D₈₃	1	2	yes	—
583	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
587	C₂²	—	2	2	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	166	2	no	—
594	C₂²	—	166	2	no	—
595	C₂²	—	166	2	no	—
596	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
597	C₄	—	2	1	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	2	no	—
605	C₄	—	83	2	no	—
606	C₄	—	83	2	no	—
607	C₄	—	166	1	no	—
608	C₄	—	166	2	no	—
609	C₄	—	166	1	no	—
610	C₄	—	166	1	no	—
611	C₄	—	166	2	no	—
612	C₄	—	166	1	no	—
613	C₄	—	166	1	no	—
614	C₄	—	166	1	no	—
615	C₄	—	166	2	no	—
616	C₄	#14581839	1	2	yes	—
617	C₂	—	4	2	no	—
618	C₂	—	4	1	no	—
619	C₂	—	332	2	no	—
620	C₂	H(5,𝔽₂)×D₈₃	1	1	yes	characteristic
621	C₂	2₋¹⁺⁴×D₈₃	1	1	yes	characteristic
622	C₂	C₂×#14581839	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#542×C₈₃	C₂
prime radical	#19128246	C₂
hypercenter	#542	D₈₃
hypocenter	C₈₃	#3550
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #19128453	C₂	semidirect
2. #19128452	C₂	semidirect
3. #19128434	C₂	semidirect
4. #19128433	C₂	semidirect
5. Q₈×Dic₁₆₆	C₂	semidirect
6. #19128431	C₂	semidirect
7. #19128423	C₂	semidirect
8. #19128420	C₂	semidirect
9. #19128418	C₂	semidirect
10. D₄×Dic₁₆₆	C₂	semidirect
11. #19128366	C₂	semidirect
12. #19128364	C₂	semidirect
13. #19128324	C₂	semidirect
14. #19128322	C₂	semidirect
15. #19128319	C₂	semidirect
16. #19128318	C₂	semidirect
17. #19128315	C₂	semidirect
18. #19128273	C₂	semidirect
19. #19128271	C₂	semidirect
20. #19128254	C₂	semidirect
21. #19128253	C₂	semidirect
23. #542×C₈₃	C₂	semidirect
312. C₈₃	#3550	semidirect
330. #542	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
#19128452	2
#19128434	2
#19128433	2
Q₈×Dic₁₆₆	2
#19128431	2
#19128423	2
#19128420	2
#19128418	2
D₄×Dic₁₆₆	2
#19128366	2
#19128364	2
#19128324	2
#19128322	2
#19128319	2
#19128318	2
#19128315	2
#19128273	2
#19128271	2
#19128254	2
#19128253	2
#19128246	2
#542×C₈₃	2
#3550	83