Subgroups — #27184695

Order 12928.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265901	C₂	1	1	yes	maximal, characteristic, complemented
2	#20265892	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265884	C₂	1	1	yes	maximal, characteristic, complemented
4	#20265879	C₂	1	2	yes	maximal, complemented
5	#20265862	C₂	1	2	yes	maximal, complemented
6	#20265861	C₂	1	2	yes	maximal, complemented
7	#20265850	C₂	1	4	yes	maximal, complemented
8	#20265815	C₂	1	2	yes	maximal, complemented
9	#20265732	C₂	1	1	yes	maximal, characteristic, complemented
10	#20265713	C₂	1	2	yes	maximal, complemented
11	#20265704	C₂	1	4	yes	maximal, complemented
12	#20265687	C₂	1	2	yes	maximal, complemented
13	#41×Dic₁₀₁	C₂	1	2	yes	maximal, complemented
14	C₄×#13108073	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15692213	C₂	1	2	yes	maximal, complemented
17	#547×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13108073	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₁₀₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	—
21	#15692255	C₂²	1	1	yes	characteristic, complemented
22	#15692250	C₂²	1	4	yes	complemented
23	#15692250	C₂²	1	4	yes	complemented
24	#15692248	C₂²	1	4	yes	complemented
25	#15692246	C₂²	1	2	yes	complemented
26	#15692246	C₂²	1	2	yes	complemented
27	#15692245	C₂²	1	4	yes	complemented
28	#15692244	C₂²	1	2	yes	—
29	#15692241	C₂²	1	4	yes	complemented
30	#15692239	C₂²	1	4	yes	complemented
31	#15692238	C₂²	1	4	yes	—
32	#15692237	C₂²	1	4	yes	—
33	#15692235	C₂²	1	2	yes	—
34	#15692235	C₂²	1	2	yes	complemented
35	#15692234	C₂²	1	2	yes	complemented
36	#15692232	C₂²	1	4	yes	complemented
37	#15692231	C₂²	1	2	yes	—
38	#15692229	C₂²	1	2	yes	—
39	#15692227	C₂²	1	4	yes	—
40	#15692226	C₂²	1	2	yes	complemented
41	#15692223	C₂²	1	4	yes	—
42	Q₈×Dic₁₀₁	C₂²	1	2	yes	complemented
43	Q₈×Dic₁₀₁	C₂²	1	2	yes	complemented
44	C₄×Dic₂₀₂	C₂²	1	1	yes	characteristic, complemented
45	#15692220	C₂²	1	2	yes	complemented
46	#15692220	C₂²	1	1	yes	characteristic, complemented
47	C₄×D₄₀₄	C₂²	1	1	yes	characteristic
48	D₄×Dic₁₀₁	C₂²	1	2	yes	—
49	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
50	D₄×Dic₁₀₁	C₂²	1	4	yes	complemented
51	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
52	D₄×Dic₁₀₁	C₂²	1	4	yes	complemented
53	#15692217	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
55	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
56	#15692215	C₂²	1	2	yes	—
57	#15692215	C₂²	1	2	yes	—
58	#15692215	C₂²	1	4	yes	complemented
59	#15692214	C₂²	1	4	yes	complemented
60	#15692214	C₂²	1	2	yes	complemented
61	#15692213	C₂²	1	2	yes	—
62	#15692213	C₂²	1	4	yes	—
63	#15692213	C₂²	1	1	yes	characteristic
64	#15692213	C₂²	1	2	yes	complemented
65	#15692213	C₂²	1	2	yes	complemented
66	#15692213	C₂²	1	4	yes	complemented
67	#15692211	C₂²	1	2	yes	complemented
68	C₂×C₄⋊Dic₁₀₁	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic
70	C₂×#13108051	C₂²	1	4	yes	—
71	C₂²⋊C₄×D₁₀₁	C₂²	1	2	yes	—
72	C₂×C₄×Dic₁₀₁	C₂²	1	4	yes	complemented
73	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	complemented
74	C₄²×D₁₀₁	C₂²	1	1	yes	characteristic
75	C₂×#41×C₁₀₁	C₂²	1	2	yes	—
76	C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
77	#123×C₁₀₁	C₂²	1	4	yes	complemented
78	C₂²⋊Q₈×C₁₀₁	C₂²	1	2	yes	complemented
79	#121×C₁₀₁	C₂²	1	2	yes	complemented
80	C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
81	C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	complemented
83	C₂³×D₁₀₁	C₂³	1	2	yes	—
84	#13108073	—	2	4	no	—
85	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
86	C₂×Dic₂₀₂	C₂³	1	2	yes	—
87	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
90	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
91	D₄×D₁₀₁	—	2	4	no	—
92	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
93	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
94	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
95	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
96	C₂×C₄×D₁₀₁	—	2	8	no	—
97	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
98	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
99	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
100	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
103	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
105	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
106	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
107	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
108	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
109	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
110	#13108053	C₂³	1	2	yes	—
111	#13108053	C₂³	1	2	yes	—
112	#13108053	C₂³	1	2	yes	—
113	#13108053	C₂³	1	4	yes	—
114	#13108053	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
116	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
117	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
119	#13108051	C₂³	1	2	yes	—
120	#13108051	C₂³	1	2	yes	—
121	#13108051	C₂³	1	2	yes	—
122	#13108051	C₂³	1	4	yes	—
123	#13108051	C₂³	1	4	yes	—
124	#13108051	C₂³	1	4	yes	—
125	#13108051	C₂³	1	4	yes	—
126	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
127	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
128	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
129	C₄×Dic₁₀₁	C₂³	1	2	yes	—
130	C₄×Dic₁₀₁	C₂³	1	4	yes	—
131	C₄×Dic₁₀₁	C₂³	1	4	yes	—
132	C₄×Dic₁₀₁	C₂³	1	4	yes	—
133	C₄×Dic₁₀₁	C₂³	1	2	yes	—
134	C₄×Dic₁₀₁	C₂³	1	2	yes	—
135	#41×C₁₀₁	—	2	8	no	—
136	C₂×Q₈×C₁₀₁	C₂³	1	2	yes	—
137	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₁₀₁	C₂³	1	4	yes	—
139	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
141	C₂²×C₄×C₁₀₁	C₂³	1	4	yes	—
142	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
143	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
146	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
151	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
152	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
153	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
154	C₂²×D₁₀₁	—	2	4	no	—
155	C₂²×D₁₀₁	—	2	4	no	—
156	C₂²×D₁₀₁	—	4	2	no	—
157	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
158	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
159	Q₈×C₁₀₁	—	2	4	no	—
160	D₄×C₁₀₁	—	2	8	no	—
161	D₄×C₁₀₁	—	2	2	no	—
162	D₄×C₁₀₁	#41	1	4	yes	complemented
163	C₂×C₄×C₁₀₁	—	2	8	no	—
164	C₂×C₄×C₁₀₁	—	2	4	no	—
165	C₂×C₄×C₁₀₁	—	2	4	no	—
166	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
170	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
172	C₂²⋊D₁₀₁	—	2	4	no	—
173	C₂²⋊D₁₀₁	—	2	4	no	—
174	C₂²⋊D₁₀₁	—	4	4	no	—
175	C₂×Dic₁₀₁	—	2	4	no	—
176	C₂×Dic₁₀₁	—	2	4	no	—
177	C₂×Dic₁₀₁	—	4	4	no	—
178	C₂×Dic₁₀₁	—	4	2	no	—
179	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
180	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
181	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
182	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
183	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
184	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
186	D₄₀₄	—	2	2	no	—
187	C₄×D₁₀₁	—	2	4	no	—
188	C₄×D₁₀₁	—	2	4	no	—
189	C₄×D₁₀₁	—	2	2	no	—
190	C₄×D₁₀₁	—	2	4	no	—
191	C₄×D₁₀₁	—	4	1	no	—
192	C₄×D₁₀₁	#41	1	4	yes	complemented
193	Dic₂₀₂	—	2	2	no	—
194	Dic₂₀₂	—	4	2	no	—
195	C₂²×C₁₀₁	—	2	2	no	—
196	C₂²×C₁₀₁	—	2	2	no	—
197	C₂²×C₁₀₁	—	2	2	no	—
198	C₂²×C₁₀₁	—	2	2	no	—
199	C₂²×C₁₀₁	—	2	2	no	—
200	C₂²×C₁₀₁	C₂×#41	1	4	yes	—
201	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
202	C₂×D₁₀₁	—	2	1	no	—
203	C₂×D₁₀₁	—	2	1	no	—
204	C₂×D₁₀₁	—	2	2	no	—
205	C₂×D₁₀₁	—	2	2	no	—
206	C₂×D₁₀₁	—	2	2	no	—
207	C₂×D₁₀₁	—	4	8	no	—
208	C₂×D₁₀₁	C₂×#41	1	2	yes	—
209	C₄×C₁₀₁	—	2	2	no	—
210	C₄×C₁₀₁	—	2	2	no	—
211	C₄×C₁₀₁	—	2	4	no	—
212	C₄×C₁₀₁	—	2	1	no	—
213	C₄×C₁₀₁	C₂×#41	1	2	yes	—
214	C₄×C₁₀₁	C₂×#41	1	2	yes	—
215	Dic₁₀₁	—	2	2	no	—
216	Dic₁₀₁	—	2	2	no	—
217	Dic₁₀₁	—	2	1	no	—
218	Dic₁₀₁	—	2	4	no	—
219	Dic₁₀₁	—	2	1	no	—
220	Dic₁₀₁	—	2	2	no	—
221	Dic₁₀₁	C₂×#41	1	2	yes	—
222	C₂×C₁₀₁	—	2	4	no	—
223	C₂×C₁₀₁	—	4	2	no	—
224	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
225	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
226	C₂×C₁₀₁	#585	1	1	yes	characteristic
227	D₁₀₁	—	2	2	no	—
228	D₁₀₁	—	4	2	no	—
229	#3475	—	101	1	no	maximal, Sylow
230	C₁₀₁	#3475	1	1	yes	characteristic, complemented, Sylow
231	#556	—	101	1	no	—
232	#555	—	101	1	no	—
233	#554	—	101	1	no	—
234	#553	—	101	2	no	—
235	#552	—	101	2	no	—
236	#552	—	101	2	no	—
237	#551	—	101	4	no	—
238	#547	D₁₀₁	1	1	yes	characteristic, complemented
239	#546	—	101	2	no	—
240	#533	—	101	1	no	—
241	#529	—	101	4	no	—
242	#529	—	101	2	no	—
243	#525	—	101	2	no	—
244	C₄×#41	—	101	2	no	—
245	C₄×#41	—	101	1	no	—
246	C₂×C₄×D₄	—	101	1	no	—
247	C₂×#117	—	101	2	no	—
248	C₂×#41	—	101	1	no	—
249	C₂×#41	C₂×D₁₀₁	1	2	yes	—
250	C₂²×D₄	—	101	1	no	—
251	C₂³×C₄	—	101	2	no	—
252	C₄⋊Q₈	—	101	1	no	—
253	C₄⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic, complemented
254	#126	—	101	4	no	—
255	#126	—	101	4	no	—
256	#126	—	101	4	no	—
257	#125	—	101	4	no	—
258	#125	—	101	2	no	—
259	#125	—	101	2	no	—
260	#124	—	101	2	no	—
261	#124	—	101	4	no	—
262	#123	—	101	4	no	—
263	#123	—	101	4	no	—
264	#123	—	101	4	no	—
265	#123	C₂×D₁₀₁	1	4	yes	complemented
266	C₂²⋊Q₈	—	101	2	no	—
267	C₂²⋊Q₈	—	101	2	no	—
268	C₂²⋊Q₈	—	101	2	no	—
269	C₂²⋊Q₈	—	101	2	no	—
270	C₂²⋊Q₈	—	101	4	no	—
271	C₂²⋊Q₈	C₂×D₁₀₁	1	2	yes	complemented
272	#121	—	101	2	no	—
273	#121	—	101	4	no	—
274	#121	—	101	2	no	—
275	#121	C₂×D₁₀₁	1	2	yes	complemented
276	#120	—	101	4	no	—
277	C₄×Q₈	—	101	2	no	—
278	C₄×Q₈	—	101	2	no	—
279	C₄×Q₈	—	101	1	no	—
280	C₄×Q₈	—	101	2	no	—
281	C₄×Q₈	—	101	1	no	—
282	C₄×D₄	—	101	1	no	—
283	C₄×D₄	—	101	4	no	—
284	C₄×D₄	—	101	2	no	—
285	C₄×D₄	—	101	4	no	—
286	C₄×D₄	—	101	1	no	—
287	C₄×D₄	—	101	2	no	—
288	C₄×D₄	—	101	2	no	—
289	C₄×D₄	—	101	1	no	—
290	C₄×D₄	—	101	2	no	—
291	C₄×D₄	—	101	2	no	—
292	C₄×D₄	—	101	4	no	—
293	C₄×D₄	—	101	1	no	—
294	C₄×D₄	C₂×D₁₀₁	1	1	yes	characteristic
295	C₄×D₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
296	#117	—	101	4	no	—
297	#117	—	101	2	no	—
298	#117	—	101	1	no	—
299	#117	—	101	2	no	—
300	#117	—	101	4	no	—
301	#117	—	101	4	no	—
302	#117	—	101	2	no	—
303	#117	—	101	2	no	—
304	#117	—	101	2	no	—
305	C₂×C₄⋊C₄	—	101	2	no	—
306	C₂×C₄⋊C₄	—	101	1	no	—
307	C₂×C₄⋊C₄	C₂×D₁₀₁	1	2	yes	complemented
308	C₂×C₂²⋊C₄	—	101	4	no	—
309	C₂×C₂²⋊C₄	—	101	2	no	—
310	C₂×C₄²	—	101	4	no	—
311	C₂×C₄²	—	101	2	no	—
312	C₂×C₄²	—	101	1	no	—
313	C₂⁴	—	101	2	no	—
314	#41	—	2	8	no	—
315	#41	—	202	4	no	—
316	C₂×Q₈	—	101	2	no	—
317	C₂×Q₈	—	101	1	no	—
318	C₂×Q₈	C₂²×D₁₀₁	1	2	yes	—
319	C₂×D₄	—	101	4	no	—
320	C₂×D₄	—	101	2	no	—
321	C₂×D₄	—	101	2	no	—
322	C₂×D₄	—	101	1	no	—
323	C₂×D₄	—	202	4	no	—
324	C₂×D₄	C₂²×D₁₀₁	1	4	yes	—
325	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
326	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
327	C₂²×C₄	—	101	1	no	—
328	C₂²×C₄	—	101	4	no	—
329	C₂²×C₄	—	101	2	no	—
330	C₂²×C₄	—	101	2	no	—
331	C₂²×C₄	—	101	2	no	—
332	C₂²×C₄	—	101	1	no	—
333	C₂²×C₄	—	101	1	no	—
334	C₂²×C₄	—	101	2	no	—
335	C₂²×C₄	—	101	2	no	—
336	C₂²×C₄	—	101	2	no	—
337	C₂²×C₄	—	202	8	no	—
338	C₂²×C₄	C₂²×D₁₀₁	1	4	yes	—
339	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
340	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
341	C₄⋊C₄	—	101	2	no	—
342	C₄⋊C₄	—	101	2	no	—
343	C₄⋊C₄	—	101	2	no	—
344	C₄⋊C₄	—	101	4	no	—
345	C₄⋊C₄	—	101	4	no	—
346	C₄⋊C₄	—	101	1	no	—
347	C₄⋊C₄	—	101	1	no	—
348	C₄⋊C₄	—	101	2	no	—
349	C₄⋊C₄	—	101	4	no	—
350	C₄⋊C₄	—	101	2	no	—
351	C₄⋊C₄	—	101	4	no	—
352	C₄⋊C₄	—	101	4	no	—
353	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
354	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
355	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
356	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
357	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
358	C₂²⋊C₄	—	101	2	no	—
359	C₂²⋊C₄	—	101	4	no	—
360	C₂²⋊C₄	—	101	2	no	—
361	C₂²⋊C₄	—	101	4	no	—
362	C₂²⋊C₄	—	101	2	no	—
363	C₂²⋊C₄	—	101	4	no	—
364	C₂²⋊C₄	—	101	4	no	—
365	C₂²⋊C₄	—	101	4	no	—
366	C₂²⋊C₄	—	101	2	no	—
367	C₂²⋊C₄	—	101	2	no	—
368	C₂²⋊C₄	—	101	4	no	—
369	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
371	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
372	C₄²	—	101	2	no	—
373	C₄²	—	101	1	no	—
374	C₄²	—	101	4	no	—
375	C₄²	—	101	4	no	—
376	C₄²	—	101	1	no	—
377	C₄²	—	101	4	no	—
378	C₄²	—	101	2	no	—
379	C₄²	—	101	1	no	—
380	C₄²	—	101	2	no	—
381	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
382	C₂³	—	101	1	no	—
383	C₂³	—	101	2	no	—
384	C₂³	—	404	2	no	—
385	C₂³	—	202	4	no	—
386	C₂³	—	202	4	no	—
387	C₂³	C₂³×D₁₀₁	1	2	yes	—
388	C₂³	C₂³×D₁₀₁	1	2	yes	—
389	Q₈	—	2	4	no	—
390	Q₈	—	404	2	no	—
391	Q₈	—	202	2	no	—
392	D₄	—	2	8	no	—
393	D₄	—	2	2	no	—
394	D₄	—	404	4	no	—
395	D₄	—	202	4	no	—
396	D₄	—	202	4	no	—
397	D₄	—	202	2	no	—
398	D₄	#13108073	1	4	yes	complemented
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	101	1	no	—
403	C₂×C₄	—	101	4	no	—
404	C₂×C₄	—	101	2	no	—
405	C₂×C₄	—	101	2	no	—
406	C₂×C₄	—	101	1	no	—
407	C₂×C₄	—	101	2	no	—
408	C₂×C₄	—	101	4	no	—
409	C₂×C₄	—	101	1	no	—
410	C₂×C₄	—	404	1	no	—
411	C₂×C₄	—	404	2	no	—
412	C₂×C₄	—	404	4	no	—
413	C₂×C₄	—	202	4	no	—
414	C₂×C₄	—	202	4	no	—
415	C₂×C₄	—	202	4	no	—
416	C₂×C₄	—	202	4	no	—
417	C₂×C₄	—	202	4	no	—
418	C₂×C₄	—	202	2	no	—
419	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
420	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
421	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
423	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	101	2	no	—
431	C₂²	—	404	8	no	—
432	C₂²	—	202	2	no	—
433	C₂²	—	202	2	no	—
434	C₂²	—	202	2	no	—
435	C₂²	—	202	1	no	—
436	C₂²	—	202	1	no	—
437	C₂²	C₂×#13108073	1	4	yes	—
438	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	1	no	—
443	C₄	—	101	2	no	—
444	C₄	—	202	2	no	—
445	C₄	—	202	2	no	—
446	C₄	—	202	1	no	—
447	C₄	—	202	1	no	—
448	C₄	—	202	2	no	—
449	C₄	—	202	4	no	—
450	C₄	#41×D₁₀₁	1	2	yes	—
451	C₄	C₂×#13108073	1	2	yes	—
452	C₂	—	2	4	no	—
453	C₂	—	4	2	no	—
454	C₂	—	404	2	no	—
455	C₂	—	202	2	no	—
456	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
457	C₂	C₂²×#13108073	1	1	yes	characteristic
458	C₂	#20266014	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#547×C₁₀₁	C₂
hypercenter	#547	D₁₀₁
hypocenter	C₁₀₁	#3475
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. #20265901	C₂	semidirect
2. #20265892	C₂	semidirect
3. #20265884	C₂	semidirect
4. #20265879	C₂	semidirect
5. #20265862	C₂	semidirect
6. #20265861	C₂	semidirect
7. #20265850	C₂	semidirect
8. #20265815	C₂	semidirect
9. #20265732	C₂	semidirect
10. #20265713	C₂	semidirect
11. #20265704	C₂	semidirect
12. #20265687	C₂	semidirect
13. #41×Dic₁₀₁	C₂	semidirect
14. C₄×#13108073	C₂	semidirect
15. C₄×D₄×D₁₀₁	C₂	semidirect
16. C₂×#15692213	C₂	semidirect
17. #547×C₁₀₁	C₂	semidirect
21. #15692255	C₂²	semidirect
22. #15692250	C₂²	semidirect
23. #15692250	C₂²	semidirect
24. #15692248	C₂²	semidirect
25. #15692246	C₂²	semidirect
26. #15692246	C₂²	semidirect
27. #15692245	C₂²	semidirect
29. #15692241	C₂²	semidirect
30. #15692239	C₂²	semidirect
34. #15692235	C₂²	semidirect
35. #15692234	C₂²	semidirect
36. #15692232	C₂²	semidirect
40. #15692226	C₂²	semidirect
42. Q₈×Dic₁₀₁	C₂²	semidirect
43. Q₈×Dic₁₀₁	C₂²	semidirect
44. C₄×Dic₂₀₂	C₂²	semidirect
45. #15692220	C₂²	semidirect
46. #15692220	C₂²	semidirect
50. D₄×Dic₁₀₁	C₂²	semidirect
51. D₄×Dic₁₀₁	C₂²	semidirect
52. D₄×Dic₁₀₁	C₂²	semidirect
58. #15692215	C₂²	semidirect
59. #15692214	C₂²	semidirect
60. #15692214	C₂²	semidirect
64. #15692213	C₂²	semidirect
65. #15692213	C₂²	semidirect
66. #15692213	C₂²	semidirect
67. #15692211	C₂²	semidirect
68. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
72. C₂×C₄×Dic₁₀₁	C₂²	semidirect
73. C₂×C₄×Dic₁₀₁	C₂²	semidirect
76. C₄⋊Q₈×C₁₀₁	C₂²	semidirect
77. #123×C₁₀₁	C₂²	semidirect
78. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
79. #121×C₁₀₁	C₂²	semidirect
81. C₄×D₄×C₁₀₁	C₂²	semidirect
82. C₂×C₄⋊C₄×C₁₀₁	C₂²	semidirect
162. D₄×C₁₀₁	#41	semidirect
192. C₄×D₁₀₁	#41	semidirect
230. C₁₀₁	#3475	semidirect
238. #547	D₁₀₁	semidirect
253. C₄⋊Q₈	C₂×D₁₀₁	semidirect
265. #123	C₂×D₁₀₁	semidirect
271. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
275. #121	C₂×D₁₀₁	semidirect
295. C₄×D₄	C₂×D₁₀₁	semidirect
307. C₂×C₄⋊C₄	C₂×D₁₀₁	semidirect
398. D₄	#13108073	semidirect

Maximal subgroups

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

subgroup	index
#20265901	2
#20265892	2
#20265884	2
#20265879	2
#20265862	2
#20265861	2
#20265850	2
#20265815	2
#20265732	2
#20265713	2
#20265704	2
#20265687	2
#41×Dic₁₀₁	2
C₄×#13108073	2
C₄×D₄×D₁₀₁	2
C₂×#15692213	2
#547×C₁₀₁	2
#3475	101