Subgroups — #27184518

Order 12928.

1040 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265797	C₂	1	2	yes	maximal, complemented
2	#20265793	C₂	1	2	yes	maximal, complemented
3	#20265786	C₂	1	2	yes	maximal, complemented
4	#20265779	C₂	1	2	yes	maximal, complemented
5	#20265774	C₂	1	1	yes	maximal, characteristic, complemented
6	#20265771	C₂	1	2	yes	maximal, complemented
7	#20265767	C₂	1	1	yes	maximal, characteristic, complemented
8	#20265764	C₂	1	1	yes	maximal, characteristic, complemented
9	#20265760	C₂	1	2	yes	maximal, complemented
10	#20265729	C₂	1	1	yes	maximal, characteristic, complemented
11	#20265722	C₂	1	1	yes	maximal, characteristic, complemented
12	#20265713	C₂	1	2	yes	maximal, complemented
13	#20265712	C₂	1	2	yes	maximal, complemented
14	#20265710	C₂	1	2	yes	maximal, complemented
15	#20265704	C₂	1	2	yes	maximal, complemented
16	#20265685	C₂	1	2	yes	maximal, complemented
17	C₄×#13108073	C₂	1	2	yes	maximal, complemented
18	C₂×#15692213	C₂	1	1	yes	maximal, characteristic, complemented
19	#539×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13108073	C₂²	1	2	yes	—
21	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
22	#15692254	C₂²	1	1	yes	characteristic, complemented
23	#15692254	C₂²	1	1	yes	characteristic, complemented
24	#15692253	C₂²	1	1	yes	characteristic, complemented
25	#15692251	C₂²	1	1	yes	characteristic, complemented
26	#15692250	C₂²	1	2	yes	—
27	#15692250	C₂²	1	2	yes	—
28	#15692250	C₂²	1	2	yes	—
29	#15692250	C₂²	1	2	yes	complemented
30	#15692250	C₂²	1	2	yes	complemented
31	#15692249	C₂²	1	2	yes	—
32	#15692248	C₂²	1	2	yes	complemented
33	#15692246	C₂²	1	2	yes	complemented
34	#15692245	C₂²	1	2	yes	complemented
35	#15692245	C₂²	1	2	yes	complemented
36	#15692245	C₂²	1	2	yes	complemented
37	#15692244	C₂²	1	2	yes	—
38	#15692243	C₂²	1	2	yes	—
39	#15692241	C₂²	1	2	yes	—
40	#15692241	C₂²	1	2	yes	—
41	#15692241	C₂²	1	2	yes	complemented
42	#15692240	C₂²	1	2	yes	—
43	#15692240	C₂²	1	2	yes	—
44	#15692240	C₂²	1	2	yes	complemented
45	#15692239	C₂²	1	2	yes	—
46	#15692239	C₂²	1	2	yes	complemented
47	#15692238	C₂²	1	2	yes	—
48	#15692238	C₂²	1	2	yes	—
49	#15692237	C₂²	1	2	yes	complemented
50	#15692235	C₂²	1	2	yes	complemented
51	#15692234	C₂²	1	1	yes	characteristic
52	#15692233	C₂²	1	2	yes	—
53	#15692233	C₂²	1	2	yes	—
54	#15692233	C₂²	1	2	yes	complemented
55	#15692232	C₂²	1	2	yes	—
56	#15692232	C₂²	1	2	yes	complemented
57	#15692230	C₂²	1	2	yes	—
58	#15692229	C₂²	1	2	yes	—
59	#15692229	C₂²	1	1	yes	characteristic
60	#15692228	C₂²	1	2	yes	—
61	#15692228	C₂²	1	2	yes	—
62	#15692228	C₂²	1	2	yes	—
63	#15692227	C₂²	1	2	yes	—
64	#15692227	C₂²	1	2	yes	—
65	#15692225	C₂²	1	2	yes	—
66	#15692223	C₂²	1	2	yes	—
67	Q₈×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
68	C₄×Dic₂₀₂	C₂²	1	2	yes	complemented
69	#15692220	C₂²	1	2	yes	complemented
70	#15692220	C₂²	1	1	yes	characteristic, complemented
71	#15692220	C₂²	1	2	yes	complemented
72	D₄×Dic₁₀₁	C₂²	1	2	yes	—
73	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
74	#15692217	C₂²	1	2	yes	—
75	#15692217	C₂²	1	2	yes	—
76	#15692217	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
78	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
79	#15692215	C₂²	1	2	yes	—
80	#15692215	C₂²	1	2	yes	—
81	#15692215	C₂²	1	2	yes	—
82	#15692215	C₂²	1	2	yes	complemented
83	#15692215	C₂²	1	2	yes	complemented
84	#15692213	C₂²	1	2	yes	—
85	#15692213	C₂²	1	2	yes	—
86	#15692213	C₂²	1	2	yes	—
87	#15692213	C₂²	1	2	yes	—
88	#15692213	C₂²	1	2	yes	complemented
89	#15692211	C₂²	1	2	yes	—
90	#15692211	C₂²	1	2	yes	complemented
91	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
92	C₂×#13108051	C₂²	1	1	yes	characteristic
93	C₂×#13108051	C₂²	1	1	yes	characteristic
94	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
95	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
96	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	complemented
97	C₄²×D₁₀₁	C₂²	1	2	yes	complemented
98	#126×C₁₀₁	C₂²	1	2	yes	complemented
99	#125×C₁₀₁	C₂²	1	2	yes	complemented
100	#123×C₁₀₁	C₂²	1	2	yes	—
101	#123×C₁₀₁	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
103	C₂²⋊Q₈×C₁₀₁	C₂²	1	2	yes	complemented
104	#121×C₁₀₁	C₂²	1	1	yes	characteristic
105	C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
107	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
108	#13108073	—	2	8	no	—
109	C₂×Dic₂₀₂	C₂³	1	2	yes	—
110	C₂×Dic₂₀₂	C₂³	1	2	yes	—
111	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
112	C₂×D₄₀₄	C₂³	1	2	yes	—
113	C₂×D₄₀₄	C₂³	1	2	yes	—
114	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
120	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
121	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
122	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
123	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
124	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
125	C₂×C₄×D₁₀₁	—	2	4	no	—
126	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
127	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
128	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
129	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
130	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
131	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
132	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
133	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
134	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
136	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
137	#13108053	C₂³	1	2	yes	—
138	#13108053	C₂³	1	2	yes	—
139	#13108053	C₂³	1	2	yes	—
140	#13108053	C₂³	1	2	yes	—
141	#13108053	C₂³	1	2	yes	—
142	#13108053	C₂³	1	2	yes	—
143	#13108053	C₂³	1	2	yes	—
144	#13108053	C₂³	1	2	yes	—
145	#13108053	C₂³	1	2	yes	—
146	#13108053	C₂³	1	2	yes	—
147	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
148	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
149	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
150	#13108051	C₂³	1	2	yes	—
151	#13108051	C₂³	1	2	yes	—
152	#13108051	C₂³	1	2	yes	—
153	#13108051	C₂³	1	2	yes	—
154	#13108051	C₂³	1	2	yes	—
155	#13108051	C₂³	1	2	yes	—
156	#13108051	C₂³	1	2	yes	—
157	#13108051	C₂³	1	2	yes	—
158	#13108051	C₂³	1	2	yes	—
159	#13108051	C₂³	1	2	yes	—
160	#13108051	C₂³	1	2	yes	—
161	#13108051	C₂³	1	2	yes	—
162	#13108051	C₂³	1	2	yes	—
163	#13108051	C₂³	1	2	yes	—
164	C₄×Dic₁₀₁	C₂³	1	2	yes	—
165	C₄×Dic₁₀₁	C₂³	1	2	yes	—
166	C₄×Dic₁₀₁	C₂³	1	2	yes	—
167	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
168	C₄×Dic₁₀₁	C₂³	1	2	yes	—
169	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
170	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
171	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
172	C₄×Dic₁₀₁	C₂³	1	2	yes	—
173	C₄×Dic₁₀₁	C₂³	1	2	yes	—
174	C₄×Dic₁₀₁	C₂³	1	2	yes	—
175	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
176	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
177	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
178	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
179	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
180	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
181	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
182	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
183	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
184	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
185	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
186	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
187	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
189	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
195	C₄²×C₁₀₁	C₂³	1	2	yes	—
196	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
197	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
198	C₂²×D₁₀₁	—	2	2	no	—
199	C₂²×D₁₀₁	—	4	1	no	—
200	C₂²×D₁₀₁	—	4	1	no	—
201	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
202	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
203	Q₈×C₁₀₁	—	4	1	no	—
204	D₄×C₁₀₁	—	2	4	no	—
205	D₄×C₁₀₁	—	4	1	no	—
206	C₂×C₄×C₁₀₁	—	2	2	no	—
207	C₂×C₄×C₁₀₁	—	4	1	no	—
208	C₂×C₄×C₁₀₁	—	4	1	no	—
209	C₂×C₄×C₁₀₁	—	4	2	no	—
210	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
211	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
212	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
213	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
214	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
216	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
217	C₂²⋊D₁₀₁	—	2	4	no	—
218	C₂²⋊D₁₀₁	—	2	4	no	—
219	C₂²⋊D₁₀₁	—	4	2	no	—
220	C₂²⋊D₁₀₁	—	4	2	no	—
221	C₂²⋊D₁₀₁	—	4	2	no	—
222	C₂×Dic₁₀₁	—	2	4	no	—
223	C₂×Dic₁₀₁	—	4	1	no	—
224	C₂×Dic₁₀₁	—	4	2	no	—
225	C₂×Dic₁₀₁	—	4	1	no	—
226	C₂×Dic₁₀₁	#41	1	4	yes	—
227	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
228	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
229	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
230	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
231	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
232	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
233	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
234	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
235	D₄₀₄	—	4	2	no	—
236	D₄₀₄	—	4	1	no	—
237	D₄₀₄	—	4	2	no	—
238	C₄×D₁₀₁	—	2	4	no	—
239	C₄×D₁₀₁	—	2	4	no	—
240	C₄×D₁₀₁	—	2	4	no	—
241	C₄×D₁₀₁	—	4	2	no	—
242	C₄×D₁₀₁	—	4	2	no	—
243	Dic₂₀₂	—	2	4	no	—
244	Dic₂₀₂	—	4	2	no	—
245	Dic₂₀₂	—	4	1	no	—
246	C₂²×C₁₀₁	—	2	1	no	—
247	C₂²×C₁₀₁	—	2	1	no	—
248	C₂²×C₁₀₁	—	2	2	no	—
249	C₂²×C₁₀₁	—	2	2	no	—
250	C₂²×C₁₀₁	—	2	2	no	—
251	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
252	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
253	C₂×D₁₀₁	—	2	2	no	—
254	C₂×D₁₀₁	—	2	2	no	—
255	C₂×D₁₀₁	—	2	2	no	—
256	C₂×D₁₀₁	—	2	2	no	—
257	C₂×D₁₀₁	—	2	2	no	—
258	C₂×D₁₀₁	—	2	2	no	—
259	C₂×D₁₀₁	—	4	4	no	—
260	C₄×C₁₀₁	—	2	2	no	—
261	C₄×C₁₀₁	—	2	2	no	—
262	C₄×C₁₀₁	—	2	2	no	—
263	C₄×C₁₀₁	—	2	1	no	—
264	C₄×C₁₀₁	—	2	2	no	—
265	C₄×C₁₀₁	—	2	1	no	—
266	C₄×C₁₀₁	—	2	2	no	—
267	Dic₁₀₁	—	2	2	no	—
268	Dic₁₀₁	—	2	1	no	—
269	Dic₁₀₁	—	2	2	no	—
270	Dic₁₀₁	—	2	2	no	—
271	Dic₁₀₁	—	2	2	no	—
272	Dic₁₀₁	—	2	1	no	—
273	Dic₁₀₁	C₂×#41	1	2	yes	—
274	Dic₁₀₁	C₂×#41	1	2	yes	—
275	C₂×C₁₀₁	—	2	2	no	—
276	C₂×C₁₀₁	—	4	2	no	—
277	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
278	C₂×C₁₀₁	#585	1	1	yes	characteristic
279	C₂×C₁₀₁	#585	1	1	yes	characteristic
280	D₁₀₁	—	4	2	no	—
281	D₁₀₁	—	4	2	no	—
282	#3455	—	101	1	no	maximal, Sylow
283	C₁₀₁	#3455	1	1	yes	characteristic, complemented, Sylow
284	#542	—	101	2	no	—
285	#542	—	101	2	no	—
286	#541	—	101	2	no	—
287	#540	—	101	2	no	—
288	#539	—	101	2	no	—
289	#539	—	101	1	no	—
290	#539	D₁₀₁	1	1	yes	characteristic, complemented
291	#538	—	101	1	no	—
292	#538	—	101	1	no	—
293	#538	—	101	2	no	—
294	#533	—	101	1	no	—
295	#532	—	101	1	no	—
296	#529	—	101	2	no	—
297	#529	—	101	2	no	—
298	#529	—	101	2	no	—
299	#529	—	101	2	no	—
300	#525	—	101	2	no	—
301	C₄×#41	—	101	2	no	—
302	C₂×#117	—	101	1	no	—
303	C₂×#41	—	101	2	no	—
304	C₂³×C₄	—	101	1	no	—
305	C₄⋊Q₈	—	101	1	no	—
306	C₄⋊Q₈	—	101	1	no	—
307	C₄⋊Q₈	—	101	1	no	—
308	#127	—	101	1	no	—
309	#126	—	101	2	no	—
310	#126	—	101	2	no	—
311	#126	—	101	2	no	—
312	#126	—	101	2	no	—
313	#126	—	101	2	no	—
314	#126	—	101	2	no	—
315	#126	—	101	2	no	—
316	#126	C₂×D₁₀₁	1	2	yes	complemented
317	#125	—	101	2	no	—
318	#125	—	101	2	no	—
319	#125	—	101	2	no	—
320	#125	—	101	2	no	—
321	#125	C₂×D₁₀₁	1	2	yes	complemented
322	#124	—	101	2	no	—
323	#124	—	101	2	no	—
324	#124	—	101	2	no	—
325	#124	—	101	2	no	—
326	#124	—	101	2	no	—
327	#123	—	101	2	no	—
328	#123	—	101	2	no	—
329	#123	—	101	2	no	—
330	#123	—	101	2	no	—
331	#123	—	101	2	no	—
332	#123	—	101	2	no	—
333	#123	—	101	2	no	—
334	#123	—	101	2	no	—
335	#123	C₂×D₁₀₁	1	2	yes	—
336	#123	C₂×D₁₀₁	1	2	yes	complemented
337	C₂²⋊Q₈	—	101	1	no	—
338	C₂²⋊Q₈	—	101	2	no	—
339	C₂²⋊Q₈	—	101	2	no	—
340	C₂²⋊Q₈	—	101	2	no	—
341	C₂²⋊Q₈	—	101	2	no	—
342	C₂²⋊Q₈	—	101	2	no	—
343	C₂²⋊Q₈	—	101	2	no	—
344	C₂²⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic
345	C₂²⋊Q₈	C₂×D₁₀₁	1	2	yes	complemented
346	#121	—	101	2	no	—
347	#121	—	101	2	no	—
348	#121	—	101	2	no	—
349	#121	—	101	1	no	—
350	#121	—	101	2	no	—
351	#121	—	101	2	no	—
352	#121	—	101	2	no	—
353	#121	—	101	2	no	—
354	#121	C₂×D₁₀₁	1	1	yes	characteristic
355	#120	—	101	2	no	—
356	#120	—	101	2	no	—
357	C₄×Q₈	—	101	1	no	—
358	C₄×Q₈	—	101	2	no	—
359	C₄×Q₈	—	101	1	no	—
360	C₄×Q₈	—	101	2	no	—
361	C₄×Q₈	—	101	2	no	—
362	C₄×D₄	—	101	2	no	—
363	C₄×D₄	—	101	1	no	—
364	C₄×D₄	—	101	2	no	—
365	C₄×D₄	—	101	2	no	—
366	C₄×D₄	—	101	2	no	—
367	C₄×D₄	—	101	2	no	—
368	C₄×D₄	—	101	1	no	—
369	C₄×D₄	—	101	2	no	—
370	C₄×D₄	—	101	2	no	—
371	C₄×D₄	—	101	2	no	—
372	C₄×D₄	—	101	2	no	—
373	C₄×D₄	—	101	2	no	—
374	C₄×D₄	C₂×D₁₀₁	1	2	yes	—
375	#117	—	101	2	no	—
376	#117	—	101	2	no	—
377	#117	—	101	2	no	—
378	#117	—	101	2	no	—
379	#117	—	101	2	no	—
380	#117	—	101	2	no	—
381	#117	—	101	2	no	—
382	C₂×C₄⋊C₄	—	101	1	no	—
383	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	—	101	1	no	—
385	C₂×C₂²⋊C₄	—	101	1	no	—
386	C₂×C₄²	—	101	1	no	—
387	C₂×C₄²	—	101	1	no	—
388	C₂×C₄²	—	101	2	no	—
389	C₂×C₄²	—	101	2	no	—
390	C₂⁴	—	101	1	no	—
391	#41	—	202	8	no	—
392	C₂×Q₈	—	101	2	no	—
393	C₂×Q₈	—	101	1	no	—
394	C₂×Q₈	—	101	2	no	—
395	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
396	C₂×D₄	—	101	2	no	—
397	C₂×D₄	—	101	2	no	—
398	C₂×D₄	—	101	2	no	—
399	C₂×D₄	—	101	2	no	—
400	C₂×D₄	—	101	2	no	—
401	C₂×D₄	—	101	2	no	—
402	C₂×D₄	—	101	2	no	—
403	C₂×D₄	—	101	1	no	—
404	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
405	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
406	C₂²×C₄	—	101	1	no	—
407	C₂²×C₄	—	101	1	no	—
408	C₂²×C₄	—	101	1	no	—
409	C₂²×C₄	—	101	2	no	—
410	C₂²×C₄	—	101	2	no	—
411	C₂²×C₄	—	101	2	no	—
412	C₂²×C₄	—	101	2	no	—
413	C₂²×C₄	—	101	2	no	—
414	C₂²×C₄	—	101	2	no	—
415	C₂²×C₄	—	101	2	no	—
416	C₂²×C₄	—	202	4	no	—
417	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
418	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
419	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
420	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
421	C₄⋊C₄	—	101	2	no	—
422	C₄⋊C₄	—	101	2	no	—
423	C₄⋊C₄	—	101	2	no	—
424	C₄⋊C₄	—	101	2	no	—
425	C₄⋊C₄	—	101	2	no	—
426	C₄⋊C₄	—	101	2	no	—
427	C₄⋊C₄	—	101	2	no	—
428	C₄⋊C₄	—	101	2	no	—
429	C₄⋊C₄	—	101	2	no	—
430	C₄⋊C₄	—	101	2	no	—
431	C₄⋊C₄	—	101	2	no	—
432	C₄⋊C₄	—	101	2	no	—
433	C₄⋊C₄	—	101	2	no	—
434	C₄⋊C₄	—	101	1	no	—
435	C₄⋊C₄	—	101	2	no	—
436	C₄⋊C₄	—	101	1	no	—
437	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
438	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
439	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
440	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
441	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
442	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
443	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
444	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
445	C₂²⋊C₄	—	101	2	no	—
446	C₂²⋊C₄	—	101	2	no	—
447	C₂²⋊C₄	—	101	2	no	—
448	C₂²⋊C₄	—	101	2	no	—
449	C₂²⋊C₄	—	101	2	no	—
450	C₂²⋊C₄	—	101	2	no	—
451	C₂²⋊C₄	—	101	2	no	—
452	C₂²⋊C₄	—	101	2	no	—
453	C₂²⋊C₄	—	101	2	no	—
454	C₂²⋊C₄	—	101	2	no	—
455	C₂²⋊C₄	—	101	2	no	—
456	C₂²⋊C₄	—	101	2	no	—
457	C₂²⋊C₄	—	101	2	no	—
458	C₂²⋊C₄	—	101	2	no	—
459	C₂²⋊C₄	—	101	2	no	—
460	C₂²⋊C₄	—	101	2	no	—
461	C₂²⋊C₄	—	101	2	no	—
462	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
463	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
464	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
465	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
466	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
467	C₄²	—	101	2	no	—
468	C₄²	—	101	1	no	—
469	C₄²	—	101	2	no	—
470	C₄²	—	101	2	no	—
471	C₄²	—	101	1	no	—
472	C₄²	—	101	2	no	—
473	C₄²	—	101	1	no	—
474	C₄²	—	101	1	no	—
475	C₄²	—	101	2	no	—
476	C₄²	—	101	2	no	—
477	C₄²	—	101	2	no	—
478	C₄²	C₂²×D₁₀₁	1	2	yes	—
479	C₂³	—	101	2	no	—
480	C₂³	—	101	2	no	—
481	C₂³	—	404	1	no	—
482	C₂³	—	404	1	no	—
483	C₂³	—	202	2	no	—
484	C₂³	C₂³×D₁₀₁	1	2	yes	—
485	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
486	Q₈	—	4	1	no	—
487	Q₈	—	404	1	no	—
488	Q₈	—	404	2	no	—
489	Q₈	—	202	4	no	—
490	D₄	—	2	4	no	—
491	D₄	—	4	1	no	—
492	D₄	—	404	1	no	—
493	D₄	—	404	2	no	—
494	D₄	—	404	2	no	—
495	D₄	—	404	2	no	—
496	D₄	—	404	2	no	—
497	D₄	—	404	2	no	—
498	D₄	—	202	4	no	—
499	D₄	—	202	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	101	4	no	—
505	C₂×C₄	—	101	1	no	—
506	C₂×C₄	—	101	1	no	—
507	C₂×C₄	—	101	2	no	—
508	C₂×C₄	—	101	1	no	—
509	C₂×C₄	—	101	2	no	—
510	C₂×C₄	—	101	2	no	—
511	C₂×C₄	—	101	2	no	—
512	C₂×C₄	—	101	1	no	—
513	C₂×C₄	—	404	2	no	—
514	C₂×C₄	—	404	2	no	—
515	C₂×C₄	—	404	1	no	—
516	C₂×C₄	—	404	2	no	—
517	C₂×C₄	—	404	1	no	—
518	C₂×C₄	—	202	4	no	—
519	C₂×C₄	—	202	4	no	—
520	C₂×C₄	—	202	4	no	—
521	C₂×C₄	—	202	4	no	—
522	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
523	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
524	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
525	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
526	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
527	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
528	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	404	4	no	—
535	C₂²	—	202	2	no	—
536	C₂²	—	202	2	no	—
537	C₂²	—	202	2	no	—
538	C₂²	—	202	2	no	—
539	C₂²	—	202	2	no	—
540	C₂²	—	202	2	no	—
541	C₂²	#41×D₁₀₁	1	2	yes	—
542	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	2	no	—
550	C₄	—	101	2	no	—
551	C₄	—	101	2	no	—
552	C₄	—	202	2	no	—
553	C₄	—	202	2	no	—
554	C₄	—	202	2	no	—
555	C₄	—	202	1	no	—
556	C₄	—	202	2	no	—
557	C₄	—	202	1	no	—
558	C₂	—	2	2	no	—
559	C₂	—	4	2	no	—
560	C₂	—	404	2	no	—
561	C₂	—	404	2	no	—
562	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
563	C₂	#20266012	1	1	yes	characteristic
564	C₂	#20266014	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#539×C₁₀₁	C₂
hypercenter	#539	D₁₀₁
hypocenter	C₁₀₁	#3455
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #20265797	C₂	semidirect
2. #20265793	C₂	semidirect
3. #20265786	C₂	semidirect
4. #20265779	C₂	semidirect
5. #20265774	C₂	semidirect
6. #20265771	C₂	semidirect
7. #20265767	C₂	semidirect
8. #20265764	C₂	semidirect
9. #20265760	C₂	semidirect
10. #20265729	C₂	semidirect
11. #20265722	C₂	semidirect
12. #20265713	C₂	semidirect
13. #20265712	C₂	semidirect
14. #20265710	C₂	semidirect
15. #20265704	C₂	semidirect
16. #20265685	C₂	semidirect
17. C₄×#13108073	C₂	semidirect
18. C₂×#15692213	C₂	semidirect
19. #539×C₁₀₁	C₂	semidirect
22. #15692254	C₂²	semidirect
23. #15692254	C₂²	semidirect
24. #15692253	C₂²	semidirect
25. #15692251	C₂²	semidirect
29. #15692250	C₂²	semidirect
30. #15692250	C₂²	semidirect
32. #15692248	C₂²	semidirect
33. #15692246	C₂²	semidirect
34. #15692245	C₂²	semidirect
35. #15692245	C₂²	semidirect
36. #15692245	C₂²	semidirect
41. #15692241	C₂²	semidirect
44. #15692240	C₂²	semidirect
46. #15692239	C₂²	semidirect
49. #15692237	C₂²	semidirect
50. #15692235	C₂²	semidirect
54. #15692233	C₂²	semidirect
56. #15692232	C₂²	semidirect
67. Q₈×Dic₁₀₁	C₂²	semidirect
68. C₄×Dic₂₀₂	C₂²	semidirect
69. #15692220	C₂²	semidirect
70. #15692220	C₂²	semidirect
71. #15692220	C₂²	semidirect
73. D₄×Dic₁₀₁	C₂²	semidirect
76. #15692217	C₂²	semidirect
78. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
82. #15692215	C₂²	semidirect
83. #15692215	C₂²	semidirect
88. #15692213	C₂²	semidirect
90. #15692211	C₂²	semidirect
96. C₂×C₄×Dic₁₀₁	C₂²	semidirect
97. C₄²×D₁₀₁	C₂²	semidirect
98. #126×C₁₀₁	C₂²	semidirect
99. #125×C₁₀₁	C₂²	semidirect
101. #123×C₁₀₁	C₂²	semidirect
103. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
283. C₁₀₁	#3455	semidirect
290. #539	D₁₀₁	semidirect
316. #126	C₂×D₁₀₁	semidirect
321. #125	C₂×D₁₀₁	semidirect
336. #123	C₂×D₁₀₁	semidirect
345. C₂²⋊Q₈	C₂×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265797	2
#20265793	2
#20265786	2
#20265779	2
#20265774	2
#20265771	2
#20265767	2
#20265764	2
#20265760	2
#20265729	2
#20265722	2
#20265713	2
#20265712	2
#20265710	2
#20265704	2
#20265685	2
C₄×#13108073	2
C₂×#15692213	2
#539×C₁₀₁	2
#3455	101