Subgroups — #27184563

Order 12928.

1012 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265804	C₂	1	1	yes	maximal, characteristic, complemented
2	#20265801	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265800	C₂	1	1	yes	maximal, characteristic, complemented
4	#20265797	C₂	1	2	yes	maximal, complemented
5	#20265788	C₂	1	1	yes	maximal, characteristic, complemented
6	#20265787	C₂	1	1	yes	maximal, characteristic, complemented
7	#20265786	C₂	1	2	yes	maximal, complemented
8	#20265775	C₂	1	2	yes	maximal, complemented
9	#20265773	C₂	1	2	yes	maximal, complemented
10	#20265757	C₂	1	1	yes	maximal, characteristic
11	#20265752	C₂	1	1	yes	maximal, characteristic, complemented
12	#20265750	C₂	1	1	yes	maximal, characteristic, complemented
13	#20265731	C₂	1	1	yes	maximal, characteristic, complemented
14	#20265731	C₂	1	2	yes	maximal, complemented
15	#20265714	C₂	1	2	yes	maximal, complemented
16	#20265714	C₂	1	1	yes	maximal, characteristic, complemented
17	#20265711	C₂	1	1	yes	maximal, characteristic, complemented
18	#20265705	C₂	1	2	yes	maximal, complemented
19	#20265705	C₂	1	2	yes	maximal, complemented
20	C₄×#13108075	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13108074	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#533×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13108075	C₂²	1	1	yes	characteristic
25	C₂×#13108074	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₁₀₁	C₂²	1	1	yes	characteristic
27	#15692254	C₂²	1	2	yes	—
28	#15692254	C₂²	1	1	yes	characteristic
29	#15692253	C₂²	1	1	yes	characteristic
30	#15692253	C₂²	1	2	yes	—
31	#15692250	C₂²	1	2	yes	—
32	#15692250	C₂²	1	2	yes	—
33	#15692250	C₂²	1	2	yes	—
34	#15692250	C₂²	1	2	yes	—
35	#15692250	C₂²	1	2	yes	—
36	#15692249	C₂²	1	2	yes	—
37	#15692248	C₂²	1	2	yes	—
38	#15692248	C₂²	1	2	yes	—
39	#15692247	C₂²	1	1	yes	characteristic
40	#15692246	C₂²	1	2	yes	—
41	#15692246	C₂²	1	1	yes	characteristic
42	#15692245	C₂²	1	2	yes	—
43	#15692245	C₂²	1	2	yes	—
44	#15692245	C₂²	1	2	yes	—
45	#15692245	C₂²	1	2	yes	—
46	#15692245	C₂²	1	2	yes	—
47	#15692244	C₂²	1	1	yes	characteristic
48	#15692244	C₂²	1	2	yes	—
49	#15692243	C₂²	1	1	yes	characteristic
50	#15692241	C₂²	1	2	yes	—
51	#15692241	C₂²	1	2	yes	—
52	#15692240	C₂²	1	2	yes	—
53	#15692240	C₂²	1	2	yes	—
54	#15692240	C₂²	1	2	yes	—
55	#15692240	C₂²	1	2	yes	—
56	#15692240	C₂²	1	2	yes	—
57	#15692238	C₂²	1	2	yes	—
58	#15692237	C₂²	1	2	yes	—
59	#15692237	C₂²	1	2	yes	—
60	#15692235	C₂²	1	1	yes	characteristic
61	#15692235	C₂²	1	2	yes	—
62	#15692234	C₂²	1	1	yes	characteristic
63	#15692233	C₂²	1	2	yes	—
64	#15692233	C₂²	1	2	yes	—
65	#15692233	C₂²	1	2	yes	—
66	#15692233	C₂²	1	2	yes	—
67	#15692233	C₂²	1	2	yes	—
68	#15692231	C₂²	1	1	yes	characteristic
69	#15692231	C₂²	1	2	yes	—
70	#15692231	C₂²	1	1	yes	characteristic
71	#15692231	C₂²	1	2	yes	—
72	#15692230	C₂²	1	2	yes	—
73	#15692230	C₂²	1	1	yes	characteristic
74	#15692229	C₂²	1	1	yes	characteristic
75	#15692228	C₂²	1	2	yes	—
76	#15692228	C₂²	1	2	yes	—
77	Q₈×Dic₁₀₁	C₂²	1	1	yes	characteristic
78	Q₈×Dic₁₀₁	C₂²	1	1	yes	characteristic
79	C₄×Dic₂₀₂	C₂²	1	1	yes	characteristic
80	C₄×Dic₂₀₂	C₂²	1	2	yes	—
81	C₄×Dic₂₀₂	C₂²	1	2	yes	—
82	C₄×Dic₂₀₂	C₂²	1	1	yes	characteristic
83	C₄×Dic₂₀₂	C₂²	1	1	yes	characteristic
84	#15692220	C₂²	1	2	yes	—
85	#15692220	C₂²	1	1	yes	characteristic
86	C₄×D₄₀₄	C₂²	1	1	yes	characteristic
87	C₄×D₄₀₄	C₂²	1	1	yes	characteristic
88	C₄×D₄₀₄	C₂²	1	2	yes	—
89	C₄×D₄₀₄	C₂²	1	1	yes	characteristic
90	C₄×D₄₀₄	C₂²	1	2	yes	—
91	#15692217	C₂²	1	2	yes	—
92	#15692217	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
94	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
98	#15692214	C₂²	1	1	yes	characteristic
99	#15692213	C₂²	1	1	yes	characteristic
100	#15692213	C₂²	1	2	yes	—
101	#15692212	C₂²	1	2	yes	—
102	#15692212	C₂²	1	2	yes	—
103	#15692212	C₂²	1	2	yes	—
104	#15692212	C₂²	1	1	yes	characteristic
105	#15692212	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₁₀₁	C₂²	1	2	yes	—
108	C₄²×D₁₀₁	C₂²	1	1	yes	characteristic
109	C₄²×D₁₀₁	C₂²	1	2	yes	—
110	C₄²×D₁₀₁	C₂²	1	1	yes	characteristic
111	C₄²×D₁₀₁	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
113	C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
114	#125×C₁₀₁	C₂²	1	2	yes	—
115	C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₁₀₁	C₂²	1	2	yes	—
118	C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
119	C₄×Q₈×C₁₀₁	C₂²	1	2	yes	—
120	C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
121	#117×C₁₀₁	C₂²	1	2	yes	—
122	C₂×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
123	#13108075	—	2	4	no	—
124	#13108074	—	2	4	no	—
125	C₂×Dic₂₀₂	C₂³	1	2	yes	—
126	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₀₂	C₂³	1	2	yes	—
129	Q₈×D₁₀₁	—	2	4	no	—
130	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
131	C₂×D₄₀₄	C₂³	1	2	yes	—
132	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
133	C₂×D₄₀₄	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
137	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
138	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
140	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
143	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
145	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
147	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
150	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
152	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
155	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
156	#13108053	C₂³	1	2	yes	—
157	#13108053	C₂³	1	2	yes	—
158	#13108053	C₂³	1	2	yes	—
159	#13108053	C₂³	1	1	yes	characteristic
160	#13108053	C₂³	1	1	yes	characteristic
161	#13108053	C₂³	1	1	yes	characteristic
162	#13108053	C₂³	1	1	yes	characteristic
163	#13108053	C₂³	1	2	yes	—
164	#13108053	C₂³	1	2	yes	—
165	#13108053	C₂³	1	2	yes	—
166	#13108053	C₂³	1	2	yes	—
167	#13108053	C₂³	1	2	yes	—
168	#13108053	C₂³	1	2	yes	—
169	#13108053	C₂³	1	2	yes	—
170	#13108053	C₂³	1	2	yes	—
171	#13108053	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
175	#13108051	C₂³	1	1	yes	characteristic
176	#13108051	C₂³	1	1	yes	characteristic
177	#13108051	C₂³	1	1	yes	characteristic
178	#13108051	C₂³	1	1	yes	characteristic
179	#13108051	C₂³	1	2	yes	—
180	#13108051	C₂³	1	2	yes	—
181	#13108051	C₂³	1	2	yes	—
182	#13108051	C₂³	1	2	yes	—
183	#13108051	C₂³	1	2	yes	—
184	#13108051	C₂³	1	2	yes	—
185	#13108051	C₂³	1	2	yes	—
186	#13108051	C₂³	1	2	yes	—
187	#13108051	C₂³	1	2	yes	—
188	#13108051	C₂³	1	2	yes	—
189	#13108051	C₂³	1	2	yes	—
190	#13108051	C₂³	1	2	yes	—
191	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₀₁	C₂³	1	2	yes	—
194	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₀₁	C₂³	1	2	yes	—
198	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₀₁	C₂³	1	2	yes	—
200	C₄×Dic₁₀₁	C₂³	1	2	yes	—
201	C₄×Dic₁₀₁	C₂³	1	2	yes	—
202	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
204	C₂×Q₈×C₁₀₁	C₂³	1	2	yes	—
205	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
209	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
210	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
211	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
219	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
220	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
221	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
222	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
223	C₄²×C₁₀₁	C₂³	1	2	yes	—
224	C₄²×C₁₀₁	C₂³	1	2	yes	—
225	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
226	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
227	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
228	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
229	Q₈×C₁₀₁	—	2	2	no	—
230	Q₈×C₁₀₁	—	2	2	no	—
231	Q₈×C₁₀₁	—	4	2	no	—
232	C₂×C₄×C₁₀₁	—	2	2	no	—
233	C₂×C₄×C₁₀₁	—	2	2	no	—
234	C₂×C₄×C₁₀₁	—	4	1	no	—
235	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
240	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
241	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₁₀₁	—	2	2	no	—
246	C₂²⋊D₁₀₁	—	2	2	no	—
247	C₂²⋊D₁₀₁	—	4	2	no	—
248	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
252	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
253	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
256	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
257	D₄₀₄	—	2	2	no	—
258	D₄₀₄	—	2	4	no	—
259	D₄₀₄	—	2	2	no	—
260	D₄₀₄	—	4	2	no	—
261	C₄×D₁₀₁	—	2	4	no	—
262	C₄×D₁₀₁	—	2	2	no	—
263	C₄×D₁₀₁	—	2	2	no	—
264	C₄×D₁₀₁	—	2	2	no	—
265	C₄×D₁₀₁	—	2	4	no	—
266	C₄×D₁₀₁	—	2	4	no	—
267	C₄×D₁₀₁	—	4	1	no	—
268	C₄×D₁₀₁	—	4	2	no	—
269	C₄×D₁₀₁	—	4	2	no	—
270	C₄×D₁₀₁	—	4	1	no	—
271	C₄×D₁₀₁	#41	1	4	yes	—
272	Dic₂₀₂	—	2	2	no	—
273	Dic₂₀₂	—	2	4	no	—
274	Dic₂₀₂	—	2	2	no	—
275	Dic₂₀₂	—	4	2	no	—
276	C₂²×C₁₀₁	—	2	1	no	—
277	C₂²×C₁₀₁	—	2	1	no	—
278	C₂²×C₁₀₁	—	2	1	no	—
279	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
280	C₂×D₁₀₁	—	2	1	no	—
281	C₂×D₁₀₁	—	2	1	no	—
282	C₂×D₁₀₁	—	2	2	no	—
283	C₂×D₁₀₁	—	2	1	no	—
284	C₂×D₁₀₁	—	2	2	no	—
285	C₂×D₁₀₁	—	2	1	no	—
286	C₂×D₁₀₁	—	2	1	no	—
287	C₂×D₁₀₁	—	2	2	no	—
288	C₂×D₁₀₁	C₂×#41	1	2	yes	—
289	C₄×C₁₀₁	—	2	2	no	—
290	C₄×C₁₀₁	—	2	1	no	—
291	C₄×C₁₀₁	—	2	2	no	—
292	C₄×C₁₀₁	—	2	1	no	—
293	C₄×C₁₀₁	—	2	2	no	—
294	C₄×C₁₀₁	—	2	1	no	—
295	C₄×C₁₀₁	—	2	2	no	—
296	C₄×C₁₀₁	—	2	1	no	—
297	C₄×C₁₀₁	C₂×#41	1	2	yes	—
298	C₄×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
299	Dic₁₀₁	—	2	2	no	—
300	Dic₁₀₁	—	2	1	no	—
301	Dic₁₀₁	—	2	1	no	—
302	Dic₁₀₁	—	2	1	no	—
303	Dic₁₀₁	—	2	2	no	—
304	Dic₁₀₁	—	2	1	no	—
305	Dic₁₀₁	—	2	2	no	—
306	Dic₁₀₁	—	2	1	no	—
307	Dic₁₀₁	C₂×#41	1	2	yes	—
308	C₂×C₁₀₁	—	4	1	no	—
309	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
310	C₂×C₁₀₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
311	C₂×C₁₀₁	#585	1	1	yes	characteristic
312	D₁₀₁	—	2	2	no	—
313	D₁₀₁	—	4	2	no	—
314	D₁₀₁	—	4	1	no	—
315	#3461	—	101	1	no	maximal, Sylow
316	C₁₀₁	#3461	1	1	yes	characteristic, complemented, Sylow
317	#544	—	101	1	no	—
318	#542	—	101	1	no	—
319	#542	—	101	2	no	—
320	#542	—	101	1	no	—
321	#541	—	101	1	no	—
322	#541	—	101	2	no	—
323	#541	—	101	1	no	—
324	#539	—	101	2	no	—
325	#539	—	101	2	no	—
326	#537	—	101	1	no	—
327	#536	—	101	1	no	—
328	#536	—	101	1	no	—
329	#533	—	101	2	no	—
330	#533	—	101	1	no	—
331	#533	D₁₀₁	1	1	yes	characteristic, complemented
332	#529	—	101	2	no	—
333	#529	—	101	1	no	—
334	#529	—	101	2	no	—
335	#529	—	101	2	no	—
336	#529	—	101	1	no	—
337	C₄×#41	—	101	1	no	—
338	C₄×#41	—	101	1	no	—
339	C₂×C₄×Q₈	—	101	1	no	—
340	C₂×#41	—	101	1	no	—
341	C₂×#41	—	101	1	no	—
342	C₂²×Q₈	—	101	1	no	—
343	C₄⋊Q₈	—	101	1	no	—
344	C₄⋊Q₈	—	101	2	no	—
345	C₄⋊Q₈	—	101	2	no	—
346	C₄⋊Q₈	—	101	1	no	—
347	C₄⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic
348	C₄⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic
349	#126	—	101	2	no	—
350	#126	—	101	2	no	—
351	#126	—	101	2	no	—
352	#126	—	101	2	no	—
353	#126	—	101	2	no	—
354	#126	—	101	2	no	—
355	#126	—	101	2	no	—
356	#126	—	101	2	no	—
357	#125	—	101	2	no	—
358	#125	—	101	2	no	—
359	#125	—	101	2	no	—
360	#125	—	101	1	no	—
361	#125	—	101	2	no	—
362	#125	—	101	2	no	—
363	#125	—	101	2	no	—
364	#125	—	101	1	no	—
365	#125	C₂×D₁₀₁	1	2	yes	—
366	#124	—	101	1	no	—
367	#124	—	101	2	no	—
368	#124	—	101	2	no	—
369	#124	—	101	2	no	—
370	#124	—	101	1	no	—
371	#123	—	101	2	no	—
372	#123	—	101	2	no	—
373	#123	—	101	2	no	—
374	#123	—	101	2	no	—
375	#123	—	101	2	no	—
376	#123	—	101	2	no	—
377	#123	—	101	2	no	—
378	#123	—	101	2	no	—
379	C₂²⋊Q₈	—	101	1	no	—
380	C₂²⋊Q₈	—	101	2	no	—
381	C₂²⋊Q₈	—	101	1	no	—
382	C₂²⋊Q₈	—	101	2	no	—
383	C₂²⋊Q₈	—	101	1	no	—
384	C₂²⋊Q₈	—	101	2	no	—
385	C₂²⋊Q₈	—	101	2	no	—
386	C₂²⋊Q₈	—	101	2	no	—
387	C₂²⋊Q₈	—	101	1	no	—
388	C₂²⋊Q₈	—	101	2	no	—
389	C₂²⋊Q₈	—	101	2	no	—
390	C₂²⋊Q₈	—	101	2	no	—
391	C₂²⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic
392	C₂²⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic
393	C₂²⋊Q₈	C₂×D₁₀₁	1	2	yes	—
394	#121	—	101	1	no	—
395	#121	—	101	2	no	—
396	#121	—	101	1	no	—
397	#121	—	101	2	no	—
398	#121	—	101	2	no	—
399	C₄×Q₈	—	101	1	no	—
400	C₄×Q₈	—	101	1	no	—
401	C₄×Q₈	—	101	2	no	—
402	C₄×Q₈	—	101	1	no	—
403	C₄×Q₈	—	101	2	no	—
404	C₄×Q₈	—	101	1	no	—
405	C₄×Q₈	—	101	1	no	—
406	C₄×Q₈	—	101	1	no	—
407	C₄×Q₈	—	101	2	no	—
408	C₄×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
409	C₄×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
410	C₄×Q₈	C₂×D₁₀₁	1	2	yes	—
411	C₄×D₄	—	101	1	no	—
412	C₄×D₄	—	101	1	no	—
413	C₄×D₄	—	101	1	no	—
414	C₄×D₄	—	101	1	no	—
415	C₄×D₄	—	101	2	no	—
416	C₄×D₄	—	101	2	no	—
417	C₄×D₄	—	101	1	no	—
418	C₄×D₄	—	101	1	no	—
419	C₄×D₄	—	101	2	no	—
420	C₄×D₄	—	101	1	no	—
421	C₄×D₄	—	101	1	no	—
422	C₄×D₄	—	101	2	no	—
423	#117	—	101	1	no	—
424	#117	—	101	1	no	—
425	#117	—	101	2	no	—
426	#117	—	101	1	no	—
427	#117	—	101	1	no	—
428	#117	—	101	2	no	—
429	#117	—	101	2	no	—
430	#117	—	101	2	no	—
431	#117	C₂×D₁₀₁	1	2	yes	—
432	C₂×C₄⋊C₄	—	101	1	no	—
433	C₂×C₄⋊C₄	—	101	2	no	—
434	C₂×C₄²	—	101	1	no	—
435	C₂×C₄²	—	101	2	no	—
436	C₂×C₄²	—	101	2	no	—
437	C₂×C₄²	—	101	1	no	—
438	C₂×C₄²	C₂×D₁₀₁	1	1	yes	characteristic
439	#41	—	202	4	no	—
440	#41	—	202	4	no	—
441	C₂×Q₈	—	101	2	no	—
442	C₂×Q₈	—	101	2	no	—
443	C₂×Q₈	—	101	1	no	—
444	C₂×Q₈	—	101	1	no	—
445	C₂×Q₈	—	202	4	no	—
446	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
447	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
448	C₂×Q₈	C₂²×D₁₀₁	1	2	yes	—
449	C₂×D₄	—	101	2	no	—
450	C₂×D₄	—	101	1	no	—
451	C₂×D₄	—	101	1	no	—
452	C₂×D₄	—	101	2	no	—
453	C₂×D₄	—	101	2	no	—
454	C₂×D₄	—	101	1	no	—
455	C₂×D₄	—	101	1	no	—
456	C₂²×C₄	—	101	1	no	—
457	C₂²×C₄	—	101	1	no	—
458	C₂²×C₄	—	101	2	no	—
459	C₂²×C₄	—	101	2	no	—
460	C₂²×C₄	—	101	1	no	—
461	C₂²×C₄	—	101	2	no	—
462	C₂²×C₄	—	101	2	no	—
463	C₂²×C₄	—	101	1	no	—
464	C₂²×C₄	—	101	1	no	—
465	C₂²×C₄	—	101	1	no	—
466	C₂²×C₄	—	101	2	no	—
467	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
468	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
469	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
470	C₄⋊C₄	—	101	2	no	—
471	C₄⋊C₄	—	101	2	no	—
472	C₄⋊C₄	—	101	2	no	—
473	C₄⋊C₄	—	101	1	no	—
474	C₄⋊C₄	—	101	1	no	—
475	C₄⋊C₄	—	101	1	no	—
476	C₄⋊C₄	—	101	1	no	—
477	C₄⋊C₄	—	101	2	no	—
478	C₄⋊C₄	—	101	2	no	—
479	C₄⋊C₄	—	101	2	no	—
480	C₄⋊C₄	—	101	2	no	—
481	C₄⋊C₄	—	101	2	no	—
482	C₄⋊C₄	—	101	2	no	—
483	C₄⋊C₄	—	101	2	no	—
484	C₄⋊C₄	—	101	2	no	—
485	C₄⋊C₄	—	101	2	no	—
486	C₄⋊C₄	—	101	1	no	—
487	C₄⋊C₄	—	101	2	no	—
488	C₄⋊C₄	—	101	1	no	—
489	C₄⋊C₄	—	101	1	no	—
490	C₄⋊C₄	—	101	2	no	—
491	C₄⋊C₄	—	101	1	no	—
492	C₄⋊C₄	—	101	2	no	—
493	C₄⋊C₄	—	101	2	no	—
494	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
496	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
497	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
499	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
500	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
503	C₂²⋊C₄	—	101	1	no	—
504	C₂²⋊C₄	—	101	1	no	—
505	C₂²⋊C₄	—	101	2	no	—
506	C₂²⋊C₄	—	101	2	no	—
507	C₂²⋊C₄	—	101	1	no	—
508	C₂²⋊C₄	—	101	1	no	—
509	C₂²⋊C₄	—	101	1	no	—
510	C₂²⋊C₄	—	101	2	no	—
511	C₂²⋊C₄	—	101	2	no	—
512	C₂²⋊C₄	—	101	1	no	—
513	C₂²⋊C₄	—	101	2	no	—
514	C₂²⋊C₄	—	101	2	no	—
515	C₂²⋊C₄	—	101	2	no	—
516	C₂²⋊C₄	—	101	2	no	—
517	C₂²⋊C₄	—	101	2	no	—
518	C₂²⋊C₄	—	101	2	no	—
519	C₂²⋊C₄	—	101	2	no	—
520	C₂²⋊C₄	—	101	2	no	—
521	C₂²⋊C₄	—	101	2	no	—
522	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
524	C₄²	—	101	1	no	—
525	C₄²	—	101	1	no	—
526	C₄²	—	101	2	no	—
527	C₄²	—	101	1	no	—
528	C₄²	—	101	2	no	—
529	C₄²	—	101	1	no	—
530	C₄²	—	101	2	no	—
531	C₄²	—	101	2	no	—
532	C₄²	—	101	1	no	—
533	C₄²	—	101	2	no	—
534	C₄²	—	101	1	no	—
535	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
536	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
537	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
538	C₄²	C₂²×D₁₀₁	1	2	yes	—
539	C₄²	C₂²×D₁₀₁	1	2	yes	—
540	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
541	C₂³	—	101	1	no	—
542	C₂³	—	101	2	no	—
543	C₂³	—	101	1	no	—
544	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
545	Q₈	—	2	2	no	—
546	Q₈	—	2	2	no	—
547	Q₈	—	4	2	no	—
548	Q₈	—	404	2	no	—
549	Q₈	—	202	4	no	—
550	Q₈	—	202	2	no	—
551	Q₈	—	202	2	no	—
552	D₄	—	404	2	no	—
553	D₄	—	404	2	no	—
554	D₄	—	202	2	no	—
555	D₄	—	202	4	no	—
556	D₄	—	202	2	no	—
557	D₄	—	202	2	no	—
558	D₄	—	202	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	101	1	no	—
563	C₂×C₄	—	101	4	no	—
564	C₂×C₄	—	101	1	no	—
565	C₂×C₄	—	101	1	no	—
566	C₂×C₄	—	101	1	no	—
567	C₂×C₄	—	101	2	no	—
568	C₂×C₄	—	101	2	no	—
569	C₂×C₄	—	101	1	no	—
570	C₂×C₄	—	101	1	no	—
571	C₂×C₄	—	101	2	no	—
572	C₂×C₄	—	404	1	no	—
573	C₂×C₄	—	404	1	no	—
574	C₂×C₄	—	404	2	no	—
575	C₂×C₄	—	404	2	no	—
576	C₂×C₄	—	202	4	no	—
577	C₂×C₄	—	202	4	no	—
578	C₂×C₄	—	202	2	no	—
579	C₂×C₄	—	202	2	no	—
580	C₂×C₄	—	202	4	no	—
581	C₂×C₄	—	202	2	no	—
582	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
584	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
585	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
586	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
587	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	101	2	no	—
596	C₂²	—	202	2	no	—
597	C₂²	—	202	1	no	—
598	C₂²	—	202	2	no	—
599	C₂²	—	202	1	no	—
600	C₂²	—	202	1	no	—
601	C₂²	—	202	2	no	—
602	C₂²	—	202	1	no	—
603	C₂²	—	202	1	no	—
604	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	2	no	—
613	C₄	—	101	2	no	—
614	C₄	—	202	1	no	—
615	C₄	—	202	2	no	—
616	C₄	—	202	1	no	—
617	C₄	—	202	1	no	—
618	C₄	—	202	2	no	—
619	C₄	—	202	1	no	—
620	C₄	—	202	2	no	—
621	C₄	—	202	1	no	—
622	C₄	#41×D₁₀₁	1	2	yes	—
623	C₄	#15692303	1	2	yes	—
624	C₂	—	4	1	no	—
625	C₂	—	404	2	no	—
626	C₂	—	404	1	no	—
627	C₂	—	202	2	no	—
628	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
629	C₂	C₂×#15692303	1	1	yes	characteristic
630	C₂	#20266013	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₁
Fitting	#533×C₁₀₁	C₂
prime radical	#20265757	C₂
hypercenter	#533	D₁₀₁
hypocenter	C₁₀₁	#3461
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ #533

Complements

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

N	H ≅ G/N	type
1. #20265804	C₂	semidirect
2. #20265801	C₂	semidirect
3. #20265800	C₂	semidirect
4. #20265797	C₂	semidirect
5. #20265788	C₂	semidirect
6. #20265787	C₂	semidirect
7. #20265786	C₂	semidirect
8. #20265775	C₂	semidirect
9. #20265773	C₂	semidirect
11. #20265752	C₂	semidirect
12. #20265750	C₂	semidirect
13. #20265731	C₂	semidirect
14. #20265731	C₂	semidirect
15. #20265714	C₂	semidirect
16. #20265714	C₂	semidirect
17. #20265711	C₂	semidirect
18. #20265705	C₂	semidirect
19. #20265705	C₂	semidirect
20. C₄×#13108075	C₂	semidirect
21. C₄×#13108074	C₂	semidirect
22. C₄×Q₈×D₁₀₁	C₂	semidirect
23. #533×C₁₀₁	C₂	semidirect
316. C₁₀₁	#3461	semidirect
331. #533	D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265804	2
#20265801	2
#20265800	2
#20265797	2
#20265788	2
#20265787	2
#20265786	2
#20265775	2
#20265773	2
#20265757	2
#20265752	2
#20265750	2
#20265731	2
#20265714	2
#20265711	2
#20265705	2
C₄×#13108075	2
C₄×#13108074	2
C₄×Q₈×D₁₀₁	2
#533×C₁₀₁	2
#3461	101