Subgroups — #27184556

Order 12928.

1012 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265805	C₂	1	1	yes	maximal, characteristic, complemented
2	#20265800	C₂	1	2	yes	maximal, complemented
3	#20265796	C₂	1	2	yes	maximal, complemented
4	#20265788	C₂	1	2	yes	maximal, complemented
5	#20265787	C₂	1	2	yes	maximal, complemented
6	#20265771	C₂	1	4	yes	maximal, complemented
7	#20265755	C₂	1	1	yes	maximal, characteristic
8	#20265751	C₂	1	1	yes	maximal, characteristic, complemented
9	#20265732	C₂	1	2	yes	maximal, complemented
10	#20265729	C₂	1	2	yes	maximal, complemented
11	#20265713	C₂	1	2	yes	maximal, complemented
12	#20265706	C₂	1	2	yes	maximal, complemented
13	#20265704	C₂	1	4	yes	maximal, complemented
14	#41×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#20265645	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
17	#536×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13108074	C₂²	1	1	yes	characteristic
19	#15692255	C₂²	1	2	yes	—
20	#15692254	C₂²	1	2	yes	—
21	#15692253	C₂²	1	2	yes	—
22	#15692250	C₂²	1	4	yes	—
23	#15692250	C₂²	1	4	yes	—
24	#15692248	C₂²	1	4	yes	—
25	#15692248	C₂²	1	4	yes	—
26	#15692247	C₂²	1	2	yes	—
27	#15692246	C₂²	1	4	yes	—
28	#15692246	C₂²	1	2	yes	—
29	#15692245	C₂²	1	4	yes	—
30	#15692245	C₂²	1	4	yes	—
31	#15692244	C₂²	1	2	yes	—
32	#15692241	C₂²	1	4	yes	—
33	#15692239	C₂²	1	4	yes	—
34	#15692238	C₂²	1	4	yes	—
35	#15692237	C₂²	1	4	yes	—
36	#15692235	C₂²	1	4	yes	—
37	#15692234	C₂²	1	2	yes	—
38	#15692232	C₂²	1	4	yes	—
39	#15692232	C₂²	1	4	yes	—
40	#15692231	C₂²	1	2	yes	—
41	#15692231	C₂²	1	2	yes	—
42	#15692231	C₂²	1	2	yes	—
43	#15692229	C₂²	1	2	yes	—
44	#15692227	C₂²	1	4	yes	—
45	#15692226	C₂²	1	2	yes	—
46	Q₈×Dic₁₀₁	C₂²	1	2	yes	—
47	Q₈×Dic₁₀₁	C₂²	1	1	yes	characteristic
48	Q₈×Dic₁₀₁	C₂²	1	2	yes	—
49	Q₈×Dic₁₀₁	C₂²	1	2	yes	—
50	Q₈×Dic₁₀₁	C₂²	1	1	yes	characteristic
51	Q₈×Dic₁₀₁	C₂²	1	2	yes	—
52	#15692220	C₂²	1	1	yes	characteristic
53	#15692220	C₂²	1	4	yes	—
54	#15692220	C₂²	1	1	yes	characteristic
55	D₄×Dic₁₀₁	C₂²	1	2	yes	—
56	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
57	D₄×Dic₁₀₁	C₂²	1	2	yes	—
58	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
59	#15692217	C₂²	1	1	yes	characteristic
60	#15692217	C₂²	1	1	yes	characteristic
61	#15692215	C₂²	1	2	yes	—
62	#15692215	C₂²	1	2	yes	—
63	#15692215	C₂²	1	4	yes	—
64	#15692214	C₂²	1	1	yes	characteristic
65	#15692214	C₂²	1	2	yes	—
66	#15692213	C₂²	1	4	yes	—
67	#15692212	C₂²	1	2	yes	—
68	#15692211	C₂²	1	4	yes	—
69	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
70	C₂×C₄⋊Dic₁₀₁	C₂²	1	2	yes	—
71	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	—
72	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
73	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	—
74	C₄²×D₁₀₁	C₂²	1	2	yes	—
75	C₂×#41×C₁₀₁	C₂²	1	1	yes	characteristic
76	C₂²×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
77	C₄⋊Q₈×C₁₀₁	C₂²	1	2	yes	—
78	#124×C₁₀₁	C₂²	1	2	yes	—
79	#123×C₁₀₁	C₂²	1	4	yes	—
80	C₂²⋊Q₈×C₁₀₁	C₂²	1	2	yes	—
81	C₂²⋊Q₈×C₁₀₁	C₂²	1	2	yes	—
82	#117×C₁₀₁	C₂²	1	1	yes	characteristic
83	#13108074	—	2	4	no	—
84	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
85	C₂×Dic₂₀₂	C₂³	1	4	yes	—
86	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
89	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
90	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
91	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
92	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
93	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
94	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
95	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
96	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
97	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
98	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
99	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
100	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
101	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
102	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
103	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
105	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
106	#13108053	C₂³	1	4	yes	—
107	#13108053	C₂³	1	4	yes	—
108	#13108053	C₂³	1	2	yes	—
109	#13108053	C₂³	1	2	yes	—
110	#13108053	C₂³	1	4	yes	—
111	#13108053	C₂³	1	4	yes	—
112	#13108053	C₂³	1	4	yes	—
113	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
114	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
115	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
116	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
117	#13108051	C₂³	1	2	yes	—
118	#13108051	C₂³	1	2	yes	—
119	#13108051	C₂³	1	4	yes	—
120	#13108051	C₂³	1	4	yes	—
121	#13108051	C₂³	1	4	yes	—
122	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
123	C₄×Dic₁₀₁	C₂³	1	2	yes	—
124	C₄×Dic₁₀₁	C₂³	1	2	yes	—
125	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
126	C₄×Dic₁₀₁	C₂³	1	4	yes	—
127	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
128	C₄×Dic₁₀₁	C₂³	1	2	yes	—
129	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
130	C₄×Dic₁₀₁	C₂³	1	2	yes	—
131	C₄×Dic₁₀₁	C₂³	1	2	yes	—
132	C₄×Dic₁₀₁	C₂³	1	4	yes	—
133	#41×C₁₀₁	—	2	4	no	—
134	C₂×Q₈×C₁₀₁	—	2	4	no	—
135	C₂×Q₈×C₁₀₁	C₂³	1	2	yes	—
136	C₂×Q₈×C₁₀₁	C₂³	1	2	yes	—
137	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
139	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
141	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
146	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
147	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
149	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
150	C₄²×C₁₀₁	C₂³	1	2	yes	—
151	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
152	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
153	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
154	Q₈×C₁₀₁	—	2	4	no	—
155	Q₈×C₁₀₁	—	2	4	no	—
156	Q₈×C₁₀₁	—	2	2	no	—
157	D₄×C₁₀₁	—	2	4	no	—
158	D₄×C₁₀₁	—	2	2	no	—
159	C₂×C₄×C₁₀₁	—	2	4	no	—
160	C₂×C₄×C₁₀₁	—	2	4	no	—
161	C₂×C₄×C₁₀₁	#41	1	4	yes	—
162	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
163	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
164	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
165	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
166	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
168	C₂²⋊D₁₀₁	—	2	4	no	—
169	C₂²⋊D₁₀₁	—	4	4	no	—
170	C₂×Dic₁₀₁	—	2	2	no	—
171	C₂×Dic₁₀₁	—	2	4	no	—
172	C₂×Dic₁₀₁	—	4	2	no	—
173	C₂×Dic₁₀₁	—	4	2	no	—
174	C₂×Dic₁₀₁	—	4	1	no	—
175	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
176	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
179	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
180	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
181	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
182	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
183	D₄₀₄	—	2	2	no	—
184	C₄×D₁₀₁	—	2	4	no	—
185	C₄×D₁₀₁	—	2	4	no	—
186	C₄×D₁₀₁	—	4	2	no	—
187	Dic₂₀₂	—	2	2	no	—
188	Dic₂₀₂	—	4	4	no	—
189	C₂²×C₁₀₁	—	2	1	no	—
190	C₂²×C₁₀₁	—	2	1	no	—
191	C₂²×C₁₀₁	—	2	2	no	—
192	C₂²×C₁₀₁	—	2	2	no	—
193	C₂²×C₁₀₁	—	2	2	no	—
194	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
195	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
196	C₂×D₁₀₁	—	2	2	no	—
197	C₂×D₁₀₁	—	2	2	no	—
198	C₂×D₁₀₁	—	2	2	no	—
199	C₄×C₁₀₁	—	2	2	no	—
200	C₄×C₁₀₁	—	2	4	no	—
201	C₄×C₁₀₁	—	2	2	no	—
202	C₄×C₁₀₁	—	2	2	no	—
203	C₄×C₁₀₁	C₂×#41	1	2	yes	—
204	C₄×C₁₀₁	C₂×#41	1	2	yes	—
205	Dic₁₀₁	—	2	2	no	—
206	Dic₁₀₁	—	2	1	no	—
207	Dic₁₀₁	—	2	2	no	—
208	Dic₁₀₁	—	2	2	no	—
209	Dic₁₀₁	—	2	4	no	—
210	Dic₁₀₁	—	2	1	no	—
211	Dic₁₀₁	—	2	1	no	—
212	Dic₁₀₁	2₋¹⁺⁴	1	2	yes	—
213	C₂×C₁₀₁	—	2	2	no	—
214	C₂×C₁₀₁	—	4	2	no	—
215	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
216	C₂×C₁₀₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
217	C₂×C₁₀₁	#585	1	1	yes	characteristic
218	D₁₀₁	—	4	2	no	—
219	#3461	—	101	1	no	maximal, Sylow
220	C₁₀₁	#3461	1	1	yes	characteristic, complemented, Sylow
221	#544	—	101	1	no	—
222	#542	—	101	2	no	—
223	#542	—	101	2	no	—
224	#541	—	101	2	no	—
225	#541	—	101	2	no	—
226	#539	—	101	4	no	—
227	#537	—	101	1	no	—
228	#536	—	101	1	no	—
229	#536	D₁₀₁	1	1	yes	characteristic, complemented
230	#533	—	101	2	no	—
231	#533	—	101	2	no	—
232	#529	—	101	2	no	—
233	#529	—	101	4	no	—
234	#529	—	101	2	no	—
235	C₄×#41	—	101	1	no	—
236	C₄×#41	—	101	1	no	—
237	C₂×C₄×Q₈	—	101	1	no	—
238	C₂×#41	—	101	1	no	—
239	C₂×#41	C₂×D₁₀₁	1	1	yes	characteristic
240	C₂²×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
241	C₄⋊Q₈	—	101	2	no	—
242	C₄⋊Q₈	—	101	2	no	—
243	C₄⋊Q₈	—	101	2	no	—
244	C₄⋊Q₈	C₂×D₁₀₁	1	2	yes	—
245	#126	—	101	4	no	—
246	#126	—	101	4	no	—
247	#126	—	101	4	no	—
248	#126	—	101	4	no	—
249	#125	—	101	4	no	—
250	#125	—	101	2	no	—
251	#125	—	101	4	no	—
252	#125	—	101	4	no	—
253	#125	—	101	2	no	—
254	#124	—	101	2	no	—
255	#124	—	101	4	no	—
256	#124	C₂×D₁₀₁	1	2	yes	—
257	#123	—	101	4	no	—
258	#123	—	101	4	no	—
259	#123	—	101	4	no	—
260	#123	C₂×D₁₀₁	1	4	yes	—
261	C₂²⋊Q₈	—	101	2	no	—
262	C₂²⋊Q₈	—	101	2	no	—
263	C₂²⋊Q₈	—	101	2	no	—
264	C₂²⋊Q₈	—	101	2	no	—
265	C₂²⋊Q₈	—	101	4	no	—
266	C₂²⋊Q₈	—	101	4	no	—
267	C₂²⋊Q₈	—	101	4	no	—
268	C₂²⋊Q₈	C₂×D₁₀₁	1	2	yes	—
269	C₂²⋊Q₈	C₂×D₁₀₁	1	2	yes	—
270	#121	—	101	4	no	—
271	#121	—	101	2	no	—
272	#121	—	101	2	no	—
273	C₄×Q₈	—	101	2	no	—
274	C₄×Q₈	—	101	2	no	—
275	C₄×Q₈	—	101	2	no	—
276	C₄×Q₈	—	101	2	no	—
277	C₄×Q₈	—	101	1	no	—
278	C₄×Q₈	—	101	1	no	—
279	C₄×Q₈	—	101	1	no	—
280	C₄×Q₈	—	101	1	no	—
281	C₄×Q₈	—	101	4	no	—
282	C₄×D₄	—	101	1	no	—
283	C₄×D₄	—	101	2	no	—
284	C₄×D₄	—	101	2	no	—
285	C₄×D₄	—	101	1	no	—
286	C₄×D₄	—	101	1	no	—
287	C₄×D₄	—	101	1	no	—
288	C₄×D₄	—	101	2	no	—
289	C₄×D₄	—	101	2	no	—
290	C₄×D₄	—	101	4	no	—
291	#117	—	101	1	no	—
292	#117	—	101	2	no	—
293	#117	—	101	4	no	—
294	#117	—	101	4	no	—
295	#117	—	101	2	no	—
296	#117	C₂×D₁₀₁	1	1	yes	characteristic
297	C₂×C₄⋊C₄	—	101	1	no	—
298	C₂×C₄⋊C₄	—	101	2	no	—
299	C₂×C₄²	—	101	1	no	—
300	C₂×C₄²	—	101	2	no	—
301	C₂×C₄²	—	101	2	no	—
302	C₂×C₄²	—	101	2	no	—
303	#41	—	2	4	no	—
304	#41	—	202	4	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	101	4	no	—
307	C₂×Q₈	—	101	1	no	—
308	C₂×Q₈	C₂²×D₁₀₁	1	2	yes	—
309	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
310	C₂×Q₈	C₂²×D₁₀₁	1	2	yes	—
311	C₂×D₄	—	101	4	no	—
312	C₂×D₄	—	101	2	no	—
313	C₂×D₄	—	101	1	no	—
314	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
315	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
316	C₂²×C₄	—	101	1	no	—
317	C₂²×C₄	—	101	2	no	—
318	C₂²×C₄	—	101	2	no	—
319	C₂²×C₄	—	101	1	no	—
320	C₂²×C₄	—	101	2	no	—
321	C₂²×C₄	—	101	2	no	—
322	C₂²×C₄	—	101	2	no	—
323	C₂²×C₄	—	101	2	no	—
324	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
325	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
326	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
327	C₄⋊C₄	—	101	2	no	—
328	C₄⋊C₄	—	101	2	no	—
329	C₄⋊C₄	—	101	4	no	—
330	C₄⋊C₄	—	101	4	no	—
331	C₄⋊C₄	—	101	4	no	—
332	C₄⋊C₄	—	101	4	no	—
333	C₄⋊C₄	—	101	4	no	—
334	C₄⋊C₄	—	101	2	no	—
335	C₄⋊C₄	—	101	2	no	—
336	C₄⋊C₄	—	101	4	no	—
337	C₄⋊C₄	—	101	4	no	—
338	C₄⋊C₄	—	101	2	no	—
339	C₄⋊C₄	—	101	1	no	—
340	C₄⋊C₄	—	101	1	no	—
341	C₄⋊C₄	—	101	2	no	—
342	C₄⋊C₄	—	101	4	no	—
343	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
344	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
345	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
346	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
347	C₂²⋊C₄	—	101	2	no	—
348	C₂²⋊C₄	—	101	2	no	—
349	C₂²⋊C₄	—	101	2	no	—
350	C₂²⋊C₄	—	101	4	no	—
351	C₂²⋊C₄	—	101	2	no	—
352	C₂²⋊C₄	—	101	2	no	—
353	C₂²⋊C₄	—	101	4	no	—
354	C₂²⋊C₄	—	101	4	no	—
355	C₂²⋊C₄	—	101	4	no	—
356	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
357	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
358	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
359	C₄²	—	101	1	no	—
360	C₄²	—	101	1	no	—
361	C₄²	—	101	2	no	—
362	C₄²	—	101	4	no	—
363	C₄²	—	101	2	no	—
364	C₄²	—	101	1	no	—
365	C₄²	—	101	1	no	—
366	C₄²	—	101	2	no	—
367	C₄²	—	101	2	no	—
368	C₄²	—	101	2	no	—
369	C₄²	—	101	4	no	—
370	C₄²	C₂²×D₁₀₁	1	2	yes	—
371	C₂³	—	101	2	no	—
372	C₂³	C₂³×D₁₀₁	1	2	yes	—
373	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
374	Q₈	—	2	4	no	—
375	Q₈	—	2	4	no	—
376	Q₈	—	2	2	no	—
377	Q₈	—	404	4	no	—
378	Q₈	—	202	2	no	—
379	D₄	—	2	4	no	—
380	D₄	—	2	2	no	—
381	D₄	—	404	4	no	—
382	D₄	—	202	4	no	—
383	D₄	—	202	2	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	101	1	no	—
387	C₂×C₄	—	101	1	no	—
388	C₂×C₄	—	101	1	no	—
389	C₂×C₄	—	101	1	no	—
390	C₂×C₄	—	101	2	no	—
391	C₂×C₄	—	101	2	no	—
392	C₂×C₄	—	101	2	no	—
393	C₂×C₄	—	101	4	no	—
394	C₂×C₄	—	404	2	no	—
395	C₂×C₄	—	404	1	no	—
396	C₂×C₄	—	404	2	no	—
397	C₂×C₄	—	404	2	no	—
398	C₂×C₄	—	202	4	no	—
399	C₂×C₄	—	202	2	no	—
400	C₂×C₄	—	202	4	no	—
401	C₂×C₄	—	202	4	no	—
402	C₂×C₄	#13108073	1	4	yes	—
403	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
404	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
405	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
406	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
407	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
408	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	202	2	no	—
415	C₂²	—	202	2	no	—
416	C₂²	—	202	2	no	—
417	C₂²	C₂×#13108073	1	2	yes	—
418	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	2	4	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	101	2	no	—
424	C₄	—	202	2	no	—
425	C₄	—	202	1	no	—
426	C₄	—	202	2	no	—
427	C₄	—	202	1	no	—
428	C₄	—	202	1	no	—
429	C₄	—	202	4	no	—
430	C₄	—	202	2	no	—
431	C₄	C₂×#13108073	1	2	yes	—
432	C₄	C₂×#13108073	1	2	yes	—
433	C₂	—	2	2	no	—
434	C₂	—	4	2	no	—
435	C₂	—	404	2	no	—
436	C₂	C₂²×#13108073	1	1	yes	characteristic
437	C₂	2₋¹⁺⁴×D₁₀₁	1	1	yes	characteristic
438	C₂	#20266014	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#536×C₁₀₁	C₂
prime radical	#20265755	C₂
hypercenter	#536	D₁₀₁
hypocenter	C₁₀₁	#3461
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. #20265805	C₂	semidirect
2. #20265800	C₂	semidirect
3. #20265796	C₂	semidirect
4. #20265788	C₂	semidirect
5. #20265787	C₂	semidirect
6. #20265771	C₂	semidirect
8. #20265751	C₂	semidirect
9. #20265732	C₂	semidirect
10. #20265729	C₂	semidirect
11. #20265713	C₂	semidirect
12. #20265706	C₂	semidirect
13. #20265704	C₂	semidirect
14. #41×Dic₁₀₁	C₂	semidirect
15. #20265645	C₂	semidirect
16. C₂×Q₈×Dic₁₀₁	C₂	semidirect
17. #536×C₁₀₁	C₂	semidirect
220. C₁₀₁	#3461	semidirect
229. #536	D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265805	2
#20265800	2
#20265796	2
#20265788	2
#20265787	2
#20265771	2
#20265755	2
#20265751	2
#20265732	2
#20265729	2
#20265713	2
#20265706	2
#20265704	2
#41×Dic₁₀₁	2
#20265645	2
C₂×Q₈×Dic₁₀₁	2
#536×C₁₀₁	2
#3461	101