Subgroups — #27185225

Order 12928.

992 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265905	C₂	1	1	yes	maximal, characteristic, complemented
2	#20265904	C₂	1	2	yes	maximal, complemented
3	#20265900	C₂	1	1	yes	maximal, characteristic, complemented
4	#20265899	C₂	1	2	yes	maximal, complemented
5	#20265868	C₂	1	2	yes	maximal, complemented
6	#20265859	C₂	1	4	yes	maximal, complemented
7	#20265842	C₂	1	2	yes	maximal, complemented
8	#20265842	C₂	1	1	yes	maximal, characteristic, complemented
9	#20265788	C₂	1	2	yes	maximal, complemented
10	#20265786	C₂	1	4	yes	maximal, complemented
11	#20265732	C₂	1	1	yes	maximal, characteristic, complemented
12	#20265731	C₂	1	2	yes	maximal, complemented
13	#20265714	C₂	1	1	yes	maximal, characteristic
14	#20265712	C₂	1	2	yes	maximal
15	#20265653	C₂	1	2	yes	maximal, complemented
16	C₄×Q₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
17	#557×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₈×D₁₀₁	C₂²	1	1	yes	characteristic
19	C₂×Q₈×D₁₀₁	C₂²	1	2	yes	—
20	#15692255	C₂²	1	1	yes	characteristic
21	#15692254	C₂²	1	2	yes	—
22	#15692254	C₂²	1	4	yes	—
23	#15692253	C₂²	1	2	yes	—
24	#15692250	C₂²	1	2	yes	—
25	#15692250	C₂²	1	4	yes	—
26	#15692250	C₂²	1	4	yes	—
27	#15692250	C₂²	1	4	yes	—
28	#15692249	C₂²	1	4	yes	—
29	#15692247	C₂²	1	2	yes	—
30	#15692246	C₂²	1	2	yes	—
31	#15692246	C₂²	1	1	yes	characteristic
32	#15692245	C₂²	1	4	yes	—
33	#15692245	C₂²	1	4	yes	—
34	#15692245	C₂²	1	4	yes	—
35	#15692245	C₂²	1	4	yes	—
36	#15692244	C₂²	1	1	yes	characteristic
37	#15692243	C₂²	1	2	yes	—
38	#15692240	C₂²	1	2	yes	—
39	#15692240	C₂²	1	4	yes	—
40	#15692235	C₂²	1	2	yes	—
41	#15692233	C₂²	1	4	yes	—
42	#15692233	C₂²	1	4	yes	—
43	#15692233	C₂²	1	4	yes	—
44	#15692231	C₂²	1	1	yes	characteristic
45	#15692231	C₂²	1	2	yes	—
46	#15692231	C₂²	1	2	yes	—
47	#15692231	C₂²	1	2	yes	—
48	#15692230	C₂²	1	1	yes	characteristic
49	Q₈×Dic₁₀₁	C₂²	1	2	yes	—
50	Q₈×Dic₁₀₁	C₂²	1	1	yes	characteristic
51	C₄×Dic₂₀₂	C₂²	1	4	yes	—
52	C₄×Dic₂₀₂	C₂²	1	2	yes	—
53	C₄×Dic₂₀₂	C₂²	1	1	yes	characteristic
54	C₄×Dic₂₀₂	C₂²	1	2	yes	—
55	C₄×Dic₂₀₂	C₂²	1	2	yes	—
56	#15692220	C₂²	1	2	yes	—
57	#15692220	C₂²	1	2	yes	—
58	#15692220	C₂²	1	4	yes	—
59	#15692220	C₂²	1	1	yes	characteristic
60	#15692220	C₂²	1	2	yes	—
61	C₄×D₄₀₄	C₂²	1	2	yes	—
62	C₄×D₄₀₄	C₂²	1	1	yes	characteristic
63	#15692217	C₂²	1	4	yes	—
64	#15692217	C₂²	1	2	yes	—
65	#15692213	C₂²	1	2	yes	—
66	#15692213	C₂²	1	4	yes	—
67	#15692213	C₂²	1	2	yes	—
68	#15692212	C₂²	1	4	yes	—
69	#15692212	C₂²	1	2	yes	—
70	#15692212	C₂²	1	4	yes	—
71	C₄⋊C₄×D₁₀₁	C₂²	1	2	yes	—
72	C₄⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic
73	C₄²×D₁₀₁	C₂²	1	2	yes	—
74	C₄²×D₁₀₁	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
76	C₄⋊Q₈×C₁₀₁	C₂²	1	2	yes	—
77	#125×C₁₀₁	C₂²	1	4	yes	—
78	#125×C₁₀₁	C₂²	1	2	yes	—
79	C₄×Q₈×C₁₀₁	C₂²	1	2	yes	—
80	C₄×Q₈×C₁₀₁	C₂²	1	2	yes	—
81	C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
82	C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
83	C₂×Dic₂₀₂	C₂³	1	2	yes	—
84	C₂×Dic₂₀₂	C₂³	1	4	yes	—
85	C₂×Dic₂₀₂	C₂³	1	2	yes	—
86	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
87	Q₈×D₁₀₁	—	2	4	no	—
88	Q₈×D₁₀₁	—	2	8	no	—
89	C₂×D₄₀₄	C₂³	1	2	yes	—
90	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
91	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
92	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
93	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
94	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
95	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
97	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
100	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
101	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
102	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
103	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
105	#13108053	C₂³	1	2	yes	—
106	#13108053	C₂³	1	2	yes	—
107	#13108053	C₂³	1	2	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	#13108053	C₂³	1	4	yes	—
114	#13108053	C₂³	1	4	yes	—
115	#13108053	C₂³	1	4	yes	—
116	#13108051	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	#13108051	C₂³	1	4	yes	—
123	#13108051	C₂³	1	2	yes	—
124	#13108051	C₂³	1	2	yes	—
125	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
126	C₄×Dic₁₀₁	C₂³	1	2	yes	—
127	C₄×Dic₁₀₁	C₂³	1	2	yes	—
128	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
129	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
130	C₄×Dic₁₀₁	C₂³	1	2	yes	—
131	C₄×Dic₁₀₁	C₂³	1	4	yes	—
132	C₄×Dic₁₀₁	C₂³	1	4	yes	—
133	C₄×Dic₁₀₁	C₂³	1	4	yes	—
134	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
135	C₂×Q₈×C₁₀₁	C₂³	1	2	yes	—
136	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
139	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
140	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
142	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
143	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
144	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
146	C₄²×C₁₀₁	C₂³	1	2	yes	—
147	C₄²×C₁₀₁	C₂³	1	4	yes	—
148	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
149	C₄²×C₁₀₁	C₂³	1	2	yes	—
150	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
151	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
152	Q₈×C₁₀₁	—	2	2	no	—
153	Q₈×C₁₀₁	—	2	4	no	—
154	Q₈×C₁₀₁	—	2	2	no	—
155	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
156	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
157	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
158	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
160	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
161	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
163	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
164	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
165	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
166	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
167	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
168	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
169	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
170	D₄₀₄	—	2	4	no	—
171	D₄₀₄	—	2	2	no	—
172	C₄×D₁₀₁	—	2	4	no	—
173	C₄×D₁₀₁	—	2	2	no	—
174	C₄×D₁₀₁	—	2	2	no	—
175	C₄×D₁₀₁	—	2	4	no	—
176	C₄×D₁₀₁	—	2	2	no	—
177	C₄×D₁₀₁	—	2	4	no	—
178	C₄×D₁₀₁	—	2	8	no	—
179	Dic₂₀₂	—	2	4	no	—
180	Dic₂₀₂	—	2	4	no	—
181	Dic₂₀₂	—	2	8	no	—
182	Dic₂₀₂	#41	1	4	yes	—
183	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
184	C₂×D₁₀₁	—	2	1	no	—
185	C₂×D₁₀₁	—	2	1	no	—
186	C₂×D₁₀₁	—	2	2	no	—
187	C₂×D₁₀₁	—	2	2	no	—
188	C₂×D₁₀₁	—	2	2	no	—
189	C₂×D₁₀₁	2₋¹⁺⁴	1	2	yes	—
190	C₄×C₁₀₁	—	2	2	no	—
191	C₄×C₁₀₁	—	2	4	no	—
192	C₄×C₁₀₁	—	2	2	no	—
193	C₄×C₁₀₁	—	2	1	no	—
194	C₄×C₁₀₁	—	2	2	no	—
195	C₄×C₁₀₁	—	2	2	no	—
196	C₄×C₁₀₁	C₂×#41	1	2	yes	—
197	C₄×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
198	Dic₁₀₁	—	2	1	no	—
199	Dic₁₀₁	—	2	2	no	—
200	Dic₁₀₁	—	2	4	no	—
201	Dic₁₀₁	—	2	1	no	—
202	Dic₁₀₁	—	2	2	no	—
203	Dic₁₀₁	—	2	1	no	—
204	Dic₁₀₁	C₂×#41	1	4	yes	—
205	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
206	C₂×C₁₀₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
207	C₂×C₁₀₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
208	D₁₀₁	—	2	2	no	—
209	D₁₀₁	—	4	2	no	—
210	#3523	—	101	1	no	maximal, Sylow
211	C₁₀₁	#3523	1	1	yes	characteristic, complemented, Sylow
212	#557	—	101	2	no	—
213	#557	—	101	1	no	—
214	#557	D₁₀₁	1	1	yes	characteristic, complemented
215	#556	—	101	2	no	—
216	#556	—	101	1	no	—
217	#552	—	101	4	no	—
218	#552	—	101	2	no	—
219	D₄×Q₈	—	101	2	no	—
220	D₄×Q₈	—	101	1	no	—
221	#541	—	101	2	no	—
222	#541	—	101	4	no	—
223	#533	—	101	1	no	—
224	#533	—	101	2	no	—
225	#529	—	101	2	no	—
226	#529	—	101	1	no	—
227	#519	—	101	2	no	—
228	C₂×C₄×Q₈	—	101	1	no	—
229	C₂²×Q₈	—	101	1	no	—
230	C₂²×Q₈	—	101	2	no	—
231	C₄⋊Q₈	—	101	2	no	—
232	C₄⋊Q₈	—	101	2	no	—
233	C₄⋊Q₈	—	101	4	no	—
234	C₄⋊Q₈	—	101	1	no	—
235	C₄⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic
236	C₄⋊Q₈	C₂×D₁₀₁	1	2	yes	—
237	#126	—	101	2	no	—
238	#126	—	101	4	no	—
239	#126	—	101	4	no	—
240	#126	—	101	4	no	—
241	#126	—	101	4	no	—
242	#125	—	101	1	no	—
243	#125	—	101	4	no	—
244	#125	—	101	2	no	—
245	#125	—	101	4	no	—
246	#125	—	101	4	no	—
247	#125	—	101	4	no	—
248	#125	—	101	2	no	—
249	#125	C₂×D₁₀₁	1	2	yes	—
250	#125	C₂×D₁₀₁	1	4	yes	—
251	#124	—	101	1	no	—
252	#124	—	101	2	no	—
253	#123	—	101	2	no	—
254	#123	—	101	4	no	—
255	C₂²⋊Q₈	—	101	1	no	—
256	C₂²⋊Q₈	—	101	2	no	—
257	C₂²⋊Q₈	—	101	2	no	—
258	C₂²⋊Q₈	—	101	2	no	—
259	C₂²⋊Q₈	—	101	2	no	—
260	C₂²⋊Q₈	—	101	4	no	—
261	C₂²⋊Q₈	—	101	4	no	—
262	C₂²⋊Q₈	—	101	4	no	—
263	#121	—	101	1	no	—
264	C₄×Q₈	—	101	1	no	—
265	C₄×Q₈	—	101	2	no	—
266	C₄×Q₈	—	101	1	no	—
267	C₄×Q₈	—	101	2	no	—
268	C₄×Q₈	—	101	4	no	—
269	C₄×Q₈	—	101	2	no	—
270	C₄×Q₈	—	101	2	no	—
271	C₄×Q₈	—	101	1	no	—
272	C₄×Q₈	—	101	2	no	—
273	C₄×Q₈	—	101	4	no	—
274	C₄×Q₈	—	101	2	no	—
275	C₄×Q₈	—	101	2	no	—
276	C₄×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
277	C₄×Q₈	C₂×D₁₀₁	1	2	yes	—
278	C₄×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
279	C₄×Q₈	C₂×D₁₀₁	1	2	yes	—
280	C₄×D₄	—	101	4	no	—
281	C₄×D₄	—	101	2	no	—
282	C₄×D₄	—	101	2	no	—
283	C₄×D₄	—	101	1	no	—
284	#117	—	101	4	no	—
285	#117	—	101	2	no	—
286	#117	—	101	2	no	—
287	#117	—	101	2	no	—
288	#117	—	101	4	no	—
289	#117	—	101	4	no	—
290	C₂×C₄⋊C₄	—	101	2	no	—
291	C₂×C₄⋊C₄	—	101	1	no	—
292	C₂×C₄²	—	101	2	no	—
293	C₂×C₄²	—	101	1	no	—
294	C₂×Q₈	—	101	1	no	—
295	C₂×Q₈	—	101	2	no	—
296	C₂×Q₈	—	101	2	no	—
297	C₂×Q₈	—	101	4	no	—
298	C₂×Q₈	—	202	4	no	—
299	C₂×Q₈	—	202	8	no	—
300	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
301	C₂×Q₈	C₂²×D₁₀₁	1	2	yes	—
302	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
303	C₂×D₄	—	101	2	no	—
304	C₂×D₄	—	101	1	no	—
305	C₂²×C₄	—	101	1	no	—
306	C₂²×C₄	—	101	1	no	—
307	C₂²×C₄	—	101	2	no	—
308	C₂²×C₄	—	101	2	no	—
309	C₂²×C₄	—	101	1	no	—
310	C₂²×C₄	—	101	4	no	—
311	C₂²×C₄	—	101	2	no	—
312	C₄⋊C₄	—	101	2	no	—
313	C₄⋊C₄	—	101	2	no	—
314	C₄⋊C₄	—	101	2	no	—
315	C₄⋊C₄	—	101	4	no	—
316	C₄⋊C₄	—	101	2	no	—
317	C₄⋊C₄	—	101	2	no	—
318	C₄⋊C₄	—	101	4	no	—
319	C₄⋊C₄	—	101	4	no	—
320	C₄⋊C₄	—	101	4	no	—
321	C₄⋊C₄	—	101	4	no	—
322	C₄⋊C₄	—	101	4	no	—
323	C₄⋊C₄	—	101	1	no	—
324	C₄⋊C₄	—	101	2	no	—
325	C₄⋊C₄	—	101	2	no	—
326	C₄⋊C₄	—	101	4	no	—
327	C₄⋊C₄	—	101	2	no	—
328	C₄⋊C₄	—	101	1	no	—
329	C₄⋊C₄	—	101	2	no	—
330	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
331	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
332	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
333	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
334	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
335	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
336	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
337	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
338	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
339	C₂²⋊C₄	—	101	2	no	—
340	C₂²⋊C₄	—	101	2	no	—
341	C₂²⋊C₄	—	101	4	no	—
342	C₂²⋊C₄	—	101	4	no	—
343	C₂²⋊C₄	—	101	2	no	—
344	C₂²⋊C₄	—	101	4	no	—
345	C₂²⋊C₄	—	101	2	no	—
346	C₂²⋊C₄	—	101	4	no	—
347	C₂²⋊C₄	—	101	2	no	—
348	C₄²	—	101	2	no	—
349	C₄²	—	101	1	no	—
350	C₄²	—	101	2	no	—
351	C₄²	—	101	1	no	—
352	C₄²	—	101	2	no	—
353	C₄²	—	101	1	no	—
354	C₄²	—	101	4	no	—
355	C₄²	—	101	4	no	—
356	C₄²	—	101	4	no	—
357	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
358	C₄²	C₂²×D₁₀₁	1	2	yes	—
359	C₄²	C₂²×D₁₀₁	1	4	yes	—
360	C₄²	C₂²×D₁₀₁	1	2	yes	—
361	C₂³	—	101	1	no	—
362	C₂³	—	101	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	2	4	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	101	4	no	—
367	Q₈	—	202	4	no	—
368	Q₈	—	202	8	no	—
369	Q₈	—	202	4	no	—
370	D₄	—	202	4	no	—
371	D₄	—	202	2	no	—
372	C₂×C₄	—	101	2	no	—
373	C₂×C₄	—	101	1	no	—
374	C₂×C₄	—	101	1	no	—
375	C₂×C₄	—	101	4	no	—
376	C₂×C₄	—	101	2	no	—
377	C₂×C₄	—	101	1	no	—
378	C₂×C₄	—	101	2	no	—
379	C₂×C₄	—	202	8	no	—
380	C₂×C₄	—	202	4	no	—
381	C₂×C₄	—	202	4	no	—
382	C₂×C₄	—	202	2	no	—
383	C₂×C₄	—	202	4	no	—
384	C₂×C₄	—	202	2	no	—
385	C₂×C₄	—	202	2	no	—
386	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
387	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
388	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
389	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
390	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
391	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
392	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
394	C₂²	—	101	2	no	—
395	C₂²	—	202	2	no	—
396	C₂²	—	202	2	no	—
397	C₂²	—	202	2	no	—
398	C₂²	—	202	1	no	—
399	C₂²	—	202	1	no	—
400	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
401	C₄	—	2	4	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	101	4	no	—
408	C₄	—	202	1	no	—
409	C₄	—	202	2	no	—
410	C₄	—	202	1	no	—
411	C₄	—	202	2	no	—
412	C₄	—	202	1	no	—
413	C₄	—	202	4	no	—
414	C₄	#41×D₁₀₁	1	2	yes	—
415	C₄	#15692303	1	2	yes	—
416	C₂	—	404	2	no	—
417	C₂	—	202	2	no	—
418	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
419	C₂	2₋¹⁺⁴×D₁₀₁	1	1	yes	characteristic
420	C₂	C₂×#15692303	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#557×C₁₀₁	C₂
prime radical	#15692230	C₂²
hypercenter	#557	D₁₀₁
hypocenter	C₁₀₁	#3523
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #557

Complements

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

N	H ≅ G/N	type
1. #20265905	C₂	semidirect
2. #20265904	C₂	semidirect
3. #20265900	C₂	semidirect
4. #20265899	C₂	semidirect
5. #20265868	C₂	semidirect
6. #20265859	C₂	semidirect
7. #20265842	C₂	semidirect
8. #20265842	C₂	semidirect
9. #20265788	C₂	semidirect
10. #20265786	C₂	semidirect
11. #20265732	C₂	semidirect
12. #20265731	C₂	semidirect
15. #20265653	C₂	semidirect
16. C₄×Q₈×D₁₀₁	C₂	semidirect
17. #557×C₁₀₁	C₂	semidirect
211. C₁₀₁	#3523	semidirect
214. #557	D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265905	2
#20265904	2
#20265900	2
#20265899	2
#20265868	2
#20265859	2
#20265842	2
#20265788	2
#20265786	2
#20265732	2
#20265731	2
#20265714	2
#20265712	2
#20265653	2
C₄×Q₈×D₁₀₁	2
#557×C₁₀₁	2
#3523	101