Subgroups — #27184692

Order 12928.

1132 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265898	C₂	1	1	yes	maximal, characteristic, complemented
2	#20265891	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265885	C₂	1	1	yes	maximal, characteristic, complemented
4	#20265879	C₂	1	1	yes	maximal, characteristic, complemented
5	#20265874	C₂	1	1	yes	maximal, characteristic, complemented
6	#20265869	C₂	1	1	yes	maximal, characteristic, complemented
7	#20265864	C₂	1	2	yes	maximal, complemented
8	#20265861	C₂	1	1	yes	maximal, characteristic, complemented
9	#20265858	C₂	1	2	yes	maximal, complemented
10	#20265850	C₂	1	2	yes	maximal, complemented
11	#20265827	C₂	1	1	yes	maximal, characteristic, complemented
12	#20265814	C₂	1	2	yes	maximal, complemented
13	#20265730	C₂	1	1	yes	maximal, characteristic, complemented
14	#20265709	C₂	1	2	yes	maximal, complemented
15	#20265707	C₂	1	2	yes	maximal, complemented
16	#20265707	C₂	1	2	yes	maximal, complemented
17	#20265684	C₂	1	1	yes	maximal, characteristic, complemented
18	#41×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13108073	C₂	1	2	yes	maximal, complemented
20	C₂×C₄×C₂²⋊D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#15692214	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#525×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13108073	C₂²	1	2	yes	—
25	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
27	#15692254	C₂²	1	1	yes	characteristic, complemented
28	#15692254	C₂²	1	1	yes	characteristic, complemented
29	#15692250	C₂²	1	2	yes	complemented
30	#15692250	C₂²	1	2	yes	complemented
31	#15692248	C₂²	1	2	yes	complemented
32	#15692248	C₂²	1	2	yes	complemented
33	#15692248	C₂²	1	2	yes	complemented
34	#15692248	C₂²	1	2	yes	complemented
35	#15692246	C₂²	1	1	yes	characteristic, complemented
36	#15692246	C₂²	1	1	yes	characteristic, complemented
37	#15692246	C₂²	1	2	yes	complemented
38	#15692245	C₂²	1	2	yes	complemented
39	#15692245	C₂²	1	2	yes	complemented
40	#15692242	C₂²	1	2	yes	complemented
41	#15692241	C₂²	1	2	yes	—
42	#15692241	C₂²	1	2	yes	complemented
43	#15692239	C₂²	1	2	yes	—
44	#15692239	C₂²	1	2	yes	complemented
45	#15692237	C₂²	1	2	yes	—
46	#15692237	C₂²	1	2	yes	complemented
47	#15692236	C₂²	1	2	yes	—
48	#15692236	C₂²	1	2	yes	complemented
49	#15692236	C₂²	1	2	yes	complemented
50	#15692235	C₂²	1	2	yes	complemented
51	#15692232	C₂²	1	2	yes	—
52	#15692232	C₂²	1	2	yes	—
53	#15692232	C₂²	1	2	yes	complemented
54	#15692232	C₂²	1	2	yes	complemented
55	#15692231	C₂²	1	1	yes	characteristic, complemented
56	#15692231	C₂²	1	1	yes	characteristic, complemented
57	#15692227	C₂²	1	2	yes	—
58	#15692227	C₂²	1	2	yes	—
59	#15692226	C₂²	1	2	yes	—
60	#15692226	C₂²	1	1	yes	characteristic, complemented
61	#15692226	C₂²	1	1	yes	characteristic, complemented
62	#15692223	C₂²	1	2	yes	—
63	Q₈×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
64	Q₈×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
65	C₄×Dic₂₀₂	C₂²	1	2	yes	complemented
66	C₄×Dic₂₀₂	C₂²	1	2	yes	complemented
67	#15692220	C₂²	1	2	yes	complemented
68	D₄×Dic₁₀₁	C₂²	1	2	yes	—
69	D₄×Dic₁₀₁	C₂²	1	2	yes	—
70	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
71	D₄×Dic₁₀₁	C₂²	1	2	yes	complemented
72	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
73	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
77	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
78	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
79	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
80	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
83	#15692215	C₂²	1	2	yes	—
84	#15692215	C₂²	1	2	yes	complemented
85	#15692214	C₂²	1	1	yes	characteristic
86	#15692214	C₂²	1	2	yes	—
87	#15692214	C₂²	1	1	yes	characteristic
88	#15692214	C₂²	1	1	yes	characteristic, complemented
89	#15692214	C₂²	1	1	yes	characteristic, complemented
90	#15692214	C₂²	1	2	yes	complemented
91	#15692214	C₂²	1	2	yes	complemented
92	#15692213	C₂²	1	2	yes	complemented
93	#15692213	C₂²	1	1	yes	characteristic, complemented
94	#15692213	C₂²	1	1	yes	characteristic, complemented
95	#15692212	C₂²	1	2	yes	complemented
96	#15692211	C₂²	1	2	yes	—
97	#15692211	C₂²	1	2	yes	complemented
98	#15692211	C₂²	1	2	yes	complemented
99	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
101	C₂×#13108053	C₂²	1	1	yes	characteristic
102	C₄⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	—
105	C₂×C₂²⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
106	C₂×#13108051	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₁₀₁	C₂²	1	2	yes	—
108	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
109	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	complemented
110	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	complemented
111	C₄²×D₁₀₁	C₂²	1	2	yes	complemented
112	C₂×#41×C₁₀₁	C₂²	1	1	yes	characteristic
113	C₂³×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
114	#123×C₁₀₁	C₂²	1	2	yes	—
115	C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
116	C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
118	#121×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
119	#120×C₁₀₁	C₂²	1	2	yes	—
120	C₄×D₄×C₁₀₁	C₂²	1	2	yes	complemented
121	C₄×D₄×C₁₀₁	C₂²	1	2	yes	complemented
122	#117×C₁₀₁	C₂²	1	1	yes	characteristic
123	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
124	#13108073	—	2	8	no	—
125	C₂×Dic₂₀₂	C₂³	1	2	yes	—
126	C₂×Dic₂₀₂	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
128	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
134	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
137	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
138	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
139	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
140	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
141	C₂×C₄×D₁₀₁	—	2	4	no	—
142	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
147	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
148	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
153	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
154	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
155	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
156	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
157	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
158	#13108053	C₂³	1	2	yes	—
159	#13108053	C₂³	1	2	yes	—
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	1	yes	characteristic
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	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
182	#13108051	C₂³	1	2	yes	—
183	#13108051	C₂³	1	2	yes	—
184	#13108051	C₂³	1	1	yes	characteristic
185	#13108051	C₂³	1	1	yes	characteristic
186	#13108051	C₂³	1	1	yes	characteristic
187	#13108051	C₂³	1	1	yes	characteristic
188	#13108051	C₂³	1	2	yes	—
189	#13108051	C₂³	1	2	yes	—
190	C₄×Dic₁₀₁	C₂³	1	2	yes	—
191	C₄×Dic₁₀₁	C₂³	1	2	yes	—
192	C₄×Dic₁₀₁	C₂³	1	2	yes	—
193	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
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	2	yes	—
199	C₄×Dic₁₀₁	C₂³	1	2	yes	—
200	C₄×Dic₁₀₁	C₂³	1	2	yes	—
201	C₄×Dic₁₀₁	C₂³	1	2	yes	—
202	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
203	#41×C₁₀₁	—	2	4	no	—
204	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
206	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
207	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₀₁	—	2	4	no	—
210	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
213	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
220	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
226	C₄²×C₁₀₁	C₂³	1	2	yes	—
227	C₂³×C₁₀₁	—	2	2	no	—
228	C₂³×C₁₀₁	—	2	2	no	—
229	C₂³×C₁₀₁	—	4	1	no	—
230	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
232	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₀₁	—	2	2	no	—
235	C₂²×D₁₀₁	—	2	2	no	—
236	C₂²×D₁₀₁	—	4	1	no	—
237	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
239	Q₈×C₁₀₁	—	2	2	no	—
240	D₄×C₁₀₁	—	2	4	no	—
241	D₄×C₁₀₁	—	2	4	no	—
242	D₄×C₁₀₁	—	2	2	no	—
243	D₄×C₁₀₁	—	4	2	no	—
244	C₂×C₄×C₁₀₁	—	2	2	no	—
245	C₂×C₄×C₁₀₁	—	2	2	no	—
246	C₂×C₄×C₁₀₁	—	2	2	no	—
247	C₂×C₄×C₁₀₁	—	2	2	no	—
248	C₂×C₄×C₁₀₁	—	2	2	no	—
249	C₂×C₄×C₁₀₁	—	2	4	no	—
250	C₂×C₄×C₁₀₁	#41	1	4	yes	complemented
251	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₁₀₁	—	2	2	no	—
259	C₂²⋊D₁₀₁	—	2	2	no	—
260	C₂²⋊D₁₀₁	—	2	4	no	—
261	C₂²⋊D₁₀₁	—	2	2	no	—
262	C₂²⋊D₁₀₁	—	4	2	no	—
263	C₂²⋊D₁₀₁	#41	1	4	yes	complemented
264	C₂×Dic₁₀₁	—	2	2	no	—
265	C₂×Dic₁₀₁	—	2	4	no	—
266	C₂×Dic₁₀₁	—	2	2	no	—
267	C₂×Dic₁₀₁	—	2	4	no	—
268	C₂×Dic₁₀₁	—	4	1	no	—
269	C₂×Dic₁₀₁	—	4	2	no	—
270	C₂×Dic₁₀₁	—	4	2	no	—
271	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
273	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
274	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
277	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
278	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
281	C₄×D₁₀₁	—	2	4	no	—
282	C₄×D₁₀₁	—	2	2	no	—
283	C₄×D₁₀₁	—	2	2	no	—
284	C₄×D₁₀₁	—	2	2	no	—
285	C₄×D₁₀₁	—	2	2	no	—
286	C₄×D₁₀₁	—	4	2	no	—
287	Dic₂₀₂	—	2	4	no	—
288	Dic₂₀₂	—	4	2	no	—
289	C₂²×C₁₀₁	—	2	1	no	—
290	C₂²×C₁₀₁	—	2	1	no	—
291	C₂²×C₁₀₁	—	2	1	no	—
292	C₂²×C₁₀₁	—	2	1	no	—
293	C₂²×C₁₀₁	—	2	2	no	—
294	C₂²×C₁₀₁	—	2	1	no	—
295	C₂²×C₁₀₁	—	2	1	no	—
296	C₂²×C₁₀₁	—	2	2	no	—
297	C₂²×C₁₀₁	—	2	2	no	—
298	C₂²×C₁₀₁	—	2	1	no	—
299	C₂²×C₁₀₁	—	4	4	no	—
300	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
301	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
302	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
303	C₂×D₁₀₁	—	2	1	no	—
304	C₂×D₁₀₁	—	2	1	no	—
305	C₂×D₁₀₁	—	2	1	no	—
306	C₂×D₁₀₁	—	2	1	no	—
307	C₂×D₁₀₁	—	2	1	no	—
308	C₂×D₁₀₁	—	4	4	no	—
309	C₂×D₁₀₁	C₂×#41	1	2	yes	—
310	C₄×C₁₀₁	—	2	2	no	—
311	C₄×C₁₀₁	—	2	1	no	—
312	C₄×C₁₀₁	—	2	1	no	—
313	C₄×C₁₀₁	—	2	2	no	—
314	C₄×C₁₀₁	—	2	2	no	—
315	C₄×C₁₀₁	C₂×#41	1	2	yes	—
316	C₄×C₁₀₁	C₂×#41	1	2	yes	—
317	Dic₁₀₁	—	2	2	no	—
318	Dic₁₀₁	—	2	1	no	—
319	Dic₁₀₁	—	2	1	no	—
320	Dic₁₀₁	—	2	2	no	—
321	Dic₁₀₁	—	2	1	no	—
322	Dic₁₀₁	—	2	1	no	—
323	Dic₁₀₁	—	2	2	no	—
324	Dic₁₀₁	—	2	2	no	—
325	Dic₁₀₁	—	2	1	no	—
326	Dic₁₀₁	C₂×#41	1	2	yes	—
327	C₂×C₁₀₁	—	2	2	no	—
328	C₂×C₁₀₁	—	2	2	no	—
329	C₂×C₁₀₁	—	4	2	no	—
330	C₂×C₁₀₁	—	4	1	no	—
331	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
332	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
333	C₂×C₁₀₁	#585	1	1	yes	characteristic
334	D₁₀₁	—	2	2	no	—
335	D₁₀₁	—	4	1	no	—
336	#3475	—	101	1	no	maximal, Sylow
337	C₁₀₁	#3475	1	1	yes	characteristic, complemented, Sylow
338	#556	—	101	1	no	—
339	#555	—	101	1	no	—
340	#554	—	101	1	no	—
341	#553	—	101	1	no	—
342	#553	—	101	1	no	—
343	#552	—	101	2	no	—
344	#552	—	101	1	no	—
345	#552	—	101	1	no	—
346	#551	—	101	2	no	—
347	#551	—	101	2	no	—
348	#547	—	101	1	no	—
349	#546	—	101	2	no	—
350	#533	—	101	1	no	—
351	#529	—	101	2	no	—
352	#529	—	101	2	no	—
353	#529	—	101	2	no	—
354	#525	—	101	1	no	—
355	#525	D₁₀₁	1	1	yes	characteristic, complemented
356	C₄×#41	—	101	1	no	—
357	C₄×#41	—	101	2	no	—
358	C₂×C₄×D₄	—	101	1	no	—
359	C₂×#117	—	101	1	no	—
360	C₂×#117	—	101	1	no	—
361	C₂×#41	—	101	2	no	—
362	C₂×#41	C₂×D₁₀₁	1	1	yes	characteristic
363	C₂²×D₄	—	101	1	no	—
364	C₂³×C₄	—	101	1	no	—
365	C₂³×C₄	C₂×D₁₀₁	1	1	yes	characteristic
366	C₄⋊Q₈	—	101	1	no	—
367	C₄⋊Q₈	—	101	1	no	—
368	#126	—	101	2	no	—
369	#126	—	101	2	no	—
370	#126	—	101	2	no	—
371	#126	—	101	2	no	—
372	#126	—	101	2	no	—
373	#126	—	101	2	no	—
374	#125	—	101	2	no	—
375	#125	—	101	2	no	—
376	#125	—	101	2	no	—
377	#125	—	101	1	no	—
378	#125	—	101	1	no	—
379	#124	—	101	2	no	—
380	#124	—	101	2	no	—
381	#124	—	101	2	no	—
382	#123	—	101	2	no	—
383	#123	—	101	2	no	—
384	#123	—	101	2	no	—
385	#123	—	101	2	no	—
386	#123	—	101	2	no	—
387	#123	—	101	2	no	—
388	#123	—	101	2	no	—
389	#123	C₂×D₁₀₁	1	2	yes	—
390	C₂²⋊Q₈	—	101	1	no	—
391	C₂²⋊Q₈	—	101	1	no	—
392	C₂²⋊Q₈	—	101	2	no	—
393	C₂²⋊Q₈	—	101	2	no	—
394	C₂²⋊Q₈	—	101	2	no	—
395	C₂²⋊Q₈	—	101	2	no	—
396	C₂²⋊Q₈	—	101	2	no	—
397	C₂²⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic, complemented
398	C₂²⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic, complemented
399	#121	—	101	1	no	—
400	#121	—	101	1	no	—
401	#121	—	101	2	no	—
402	#121	—	101	2	no	—
403	#121	—	101	2	no	—
404	#121	C₂×D₁₀₁	1	1	yes	characteristic, complemented
405	#121	C₂×D₁₀₁	1	1	yes	characteristic, complemented
406	#120	—	101	2	no	—
407	#120	C₂×D₁₀₁	1	2	yes	—
408	C₄×Q₈	—	101	1	no	—
409	C₄×Q₈	—	101	1	no	—
410	C₄×Q₈	—	101	2	no	—
411	C₄×Q₈	—	101	2	no	—
412	C₄×Q₈	—	101	2	no	—
413	C₄×D₄	—	101	2	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	1	no	—
420	C₄×D₄	—	101	1	no	—
421	C₄×D₄	—	101	1	no	—
422	C₄×D₄	—	101	1	no	—
423	C₄×D₄	—	101	1	no	—
424	C₄×D₄	—	101	1	no	—
425	C₄×D₄	—	101	1	no	—
426	C₄×D₄	—	101	2	no	—
427	C₄×D₄	—	101	2	no	—
428	C₄×D₄	—	101	2	no	—
429	C₄×D₄	—	101	2	no	—
430	C₄×D₄	C₂×D₁₀₁	1	2	yes	complemented
431	C₄×D₄	C₂×D₁₀₁	1	2	yes	complemented
432	#117	—	101	1	no	—
433	#117	—	101	1	no	—
434	#117	—	101	2	no	—
435	#117	—	101	2	no	—
436	#117	—	101	1	no	—
437	#117	—	101	1	no	—
438	#117	—	101	2	no	—
439	#117	—	101	1	no	—
440	#117	—	101	1	no	—
441	#117	—	101	2	no	—
442	#117	—	101	2	no	—
443	#117	—	101	2	no	—
444	#117	—	101	2	no	—
445	#117	—	101	2	no	—
446	#117	C₂×D₁₀₁	1	1	yes	characteristic
447	C₂×C₄⋊C₄	—	101	1	no	—
448	C₂×C₄⋊C₄	—	101	1	no	—
449	C₂×C₄⋊C₄	—	101	1	no	—
450	C₂×C₄⋊C₄	—	101	1	no	—
451	C₂×C₄⋊C₄	—	101	1	no	—
452	C₂×C₂²⋊C₄	—	101	2	no	—
453	C₂×C₂²⋊C₄	—	101	1	no	—
454	C₂×C₂²⋊C₄	—	101	1	no	—
455	C₂×C₂²⋊C₄	—	101	2	no	—
456	C₂×C₄²	—	101	2	no	—
457	C₂×C₄²	—	101	1	no	—
458	C₂×C₄²	—	101	2	no	—
459	C₂×C₄²	—	101	2	no	—
460	C₂⁴	—	101	1	no	—
461	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
462	#41	—	2	4	no	—
463	#41	—	202	8	no	—
464	C₂×Q₈	—	101	2	no	—
465	C₂×Q₈	—	101	2	no	—
466	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
467	C₂×D₄	—	101	1	no	—
468	C₂×D₄	—	101	2	no	—
469	C₂×D₄	—	101	2	no	—
470	C₂×D₄	—	101	1	no	—
471	C₂×D₄	—	101	1	no	—
472	C₂×D₄	—	101	1	no	—
473	C₂×D₄	—	202	4	no	—
474	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
475	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
476	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
477	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	101	1	no	—
480	C₂²×C₄	—	101	2	no	—
481	C₂²×C₄	—	101	2	no	—
482	C₂²×C₄	—	101	2	no	—
483	C₂²×C₄	—	101	1	no	—
484	C₂²×C₄	—	101	2	no	—
485	C₂²×C₄	—	101	1	no	—
486	C₂²×C₄	—	101	2	no	—
487	C₂²×C₄	—	101	2	no	—
488	C₂²×C₄	—	101	1	no	—
489	C₂²×C₄	—	101	1	no	—
490	C₂²×C₄	—	101	1	no	—
491	C₂²×C₄	—	101	1	no	—
492	C₂²×C₄	—	202	4	no	—
493	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
494	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
495	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
496	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
498	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
500	C₄⋊C₄	—	101	1	no	—
501	C₄⋊C₄	—	101	2	no	—
502	C₄⋊C₄	—	101	2	no	—
503	C₄⋊C₄	—	101	1	no	—
504	C₄⋊C₄	—	101	1	no	—
505	C₄⋊C₄	—	101	1	no	—
506	C₄⋊C₄	—	101	2	no	—
507	C₄⋊C₄	—	101	2	no	—
508	C₄⋊C₄	—	101	2	no	—
509	C₄⋊C₄	—	101	2	no	—
510	C₄⋊C₄	—	101	2	no	—
511	C₄⋊C₄	—	101	2	no	—
512	C₄⋊C₄	—	101	1	no	—
513	C₄⋊C₄	—	101	1	no	—
514	C₄⋊C₄	—	101	1	no	—
515	C₄⋊C₄	—	101	1	no	—
516	C₄⋊C₄	—	101	2	no	—
517	C₄⋊C₄	—	101	2	no	—
518	C₄⋊C₄	—	101	2	no	—
519	C₄⋊C₄	—	101	2	no	—
520	C₄⋊C₄	—	101	2	no	—
521	C₄⋊C₄	—	101	2	no	—
522	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
525	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
526	C₂²⋊C₄	—	101	2	no	—
527	C₂²⋊C₄	—	101	1	no	—
528	C₂²⋊C₄	—	101	2	no	—
529	C₂²⋊C₄	—	101	2	no	—
530	C₂²⋊C₄	—	101	2	no	—
531	C₂²⋊C₄	—	101	1	no	—
532	C₂²⋊C₄	—	101	1	no	—
533	C₂²⋊C₄	—	101	1	no	—
534	C₂²⋊C₄	—	101	2	no	—
535	C₂²⋊C₄	—	101	2	no	—
536	C₂²⋊C₄	—	101	2	no	—
537	C₂²⋊C₄	—	101	2	no	—
538	C₂²⋊C₄	—	101	1	no	—
539	C₂²⋊C₄	—	101	2	no	—
540	C₂²⋊C₄	—	101	2	no	—
541	C₂²⋊C₄	—	101	1	no	—
542	C₂²⋊C₄	—	101	1	no	—
543	C₂²⋊C₄	—	101	1	no	—
544	C₂²⋊C₄	—	101	2	no	—
545	C₂²⋊C₄	—	101	2	no	—
546	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
551	C₄²	—	101	2	no	—
552	C₄²	—	101	2	no	—
553	C₄²	—	101	2	no	—
554	C₄²	—	101	2	no	—
555	C₄²	—	101	2	no	—
556	C₄²	—	101	1	no	—
557	C₄²	—	101	1	no	—
558	C₄²	—	101	2	no	—
559	C₄²	—	101	2	no	—
560	C₄²	—	101	1	no	—
561	C₄²	—	101	1	no	—
562	C₄²	—	101	2	no	—
563	C₄²	C₂²×D₁₀₁	1	2	yes	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	101	1	no	—
568	C₂³	—	101	1	no	—
569	C₂³	—	404	1	no	—
570	C₂³	—	202	2	no	—
571	C₂³	—	202	2	no	—
572	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
573	C₂³	C₂³×D₁₀₁	1	2	yes	—
574	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
575	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
576	Q₈	—	2	2	no	—
577	Q₈	—	404	2	no	—
578	Q₈	—	202	4	no	—
579	D₄	—	2	4	no	—
580	D₄	—	2	4	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	101	4	no	—
584	D₄	—	404	2	no	—
585	D₄	—	202	2	no	—
586	D₄	—	202	2	no	—
587	D₄	—	202	4	no	—
588	D₄	—	202	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	101	1	no	—
596	C₂×C₄	—	101	2	no	—
597	C₂×C₄	—	101	1	no	—
598	C₂×C₄	—	101	1	no	—
599	C₂×C₄	—	101	2	no	—
600	C₂×C₄	—	101	1	no	—
601	C₂×C₄	—	101	2	no	—
602	C₂×C₄	—	101	2	no	—
603	C₂×C₄	—	101	1	no	—
604	C₂×C₄	—	101	1	no	—
605	C₂×C₄	—	404	2	no	—
606	C₂×C₄	—	404	2	no	—
607	C₂×C₄	—	404	2	no	—
608	C₂×C₄	—	404	1	no	—
609	C₂×C₄	—	202	4	no	—
610	C₂×C₄	—	202	2	no	—
611	C₂×C₄	—	202	4	no	—
612	C₂×C₄	—	202	4	no	—
613	C₂×C₄	—	202	2	no	—
614	C₂×C₄	—	202	2	no	—
615	C₂×C₄	—	202	2	no	—
616	C₂×C₄	—	202	2	no	—
617	C₂×C₄	—	202	2	no	—
618	C₂×C₄	#13108073	1	4	yes	complemented
619	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
621	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
622	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
623	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	101	2	no	—
638	C₂²	—	404	4	no	—
639	C₂²	—	202	1	no	—
640	C₂²	—	202	1	no	—
641	C₂²	—	202	1	no	—
642	C₂²	—	202	1	no	—
643	C₂²	—	202	1	no	—
644	C₂²	#41×D₁₀₁	1	2	yes	—
645	C₂²	C₂×#13108073	1	2	yes	—
646	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	101	2	no	—
653	C₄	—	202	2	no	—
654	C₄	—	202	1	no	—
655	C₄	—	202	2	no	—
656	C₄	—	202	1	no	—
657	C₄	—	202	1	no	—
658	C₄	—	202	2	no	—
659	C₄	—	202	1	no	—
660	C₄	—	202	2	no	—
661	C₄	—	202	1	no	—
662	C₄	C₂×#13108073	1	2	yes	—
663	C₄	C₂×#13108073	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	2	2	no	—
666	C₂	—	4	1	no	—
667	C₂	—	4	2	no	—
668	C₂	—	404	1	no	—
669	C₂	—	202	2	no	—
670	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
671	C₂	C₂²×#13108073	1	1	yes	characteristic
672	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	#525×C₁₀₁	C₂
hypercenter	#525	D₁₀₁
hypocenter	C₁₀₁	#3475
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #20265898	C₂	semidirect
2. #20265891	C₂	semidirect
3. #20265885	C₂	semidirect
4. #20265879	C₂	semidirect
5. #20265874	C₂	semidirect
6. #20265869	C₂	semidirect
7. #20265864	C₂	semidirect
8. #20265861	C₂	semidirect
9. #20265858	C₂	semidirect
10. #20265850	C₂	semidirect
11. #20265827	C₂	semidirect
12. #20265814	C₂	semidirect
13. #20265730	C₂	semidirect
14. #20265709	C₂	semidirect
15. #20265707	C₂	semidirect
16. #20265707	C₂	semidirect
17. #20265684	C₂	semidirect
18. #41×Dic₁₀₁	C₂	semidirect
19. C₄×#13108073	C₂	semidirect
20. C₂×C₄×C₂²⋊D₁₀₁	C₂	semidirect
21. C₂×#15692214	C₂	semidirect
22. #117×D₁₀₁	C₂	semidirect
23. #525×C₁₀₁	C₂	semidirect
27. #15692254	C₂²	semidirect
28. #15692254	C₂²	semidirect
29. #15692250	C₂²	semidirect
30. #15692250	C₂²	semidirect
31. #15692248	C₂²	semidirect
32. #15692248	C₂²	semidirect
33. #15692248	C₂²	semidirect
34. #15692248	C₂²	semidirect
35. #15692246	C₂²	semidirect
36. #15692246	C₂²	semidirect
37. #15692246	C₂²	semidirect
38. #15692245	C₂²	semidirect
39. #15692245	C₂²	semidirect
40. #15692242	C₂²	semidirect
42. #15692241	C₂²	semidirect
44. #15692239	C₂²	semidirect
46. #15692237	C₂²	semidirect
48. #15692236	C₂²	semidirect
49. #15692236	C₂²	semidirect
50. #15692235	C₂²	semidirect
53. #15692232	C₂²	semidirect
54. #15692232	C₂²	semidirect
55. #15692231	C₂²	semidirect
56. #15692231	C₂²	semidirect
60. #15692226	C₂²	semidirect
61. #15692226	C₂²	semidirect
63. Q₈×Dic₁₀₁	C₂²	semidirect
64. Q₈×Dic₁₀₁	C₂²	semidirect
65. C₄×Dic₂₀₂	C₂²	semidirect
66. C₄×Dic₂₀₂	C₂²	semidirect
67. #15692220	C₂²	semidirect
70. D₄×Dic₁₀₁	C₂²	semidirect
71. D₄×Dic₁₀₁	C₂²	semidirect
72. D₄×Dic₁₀₁	C₂²	semidirect
81. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
82. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
84. #15692215	C₂²	semidirect
88. #15692214	C₂²	semidirect
89. #15692214	C₂²	semidirect
90. #15692214	C₂²	semidirect
91. #15692214	C₂²	semidirect
92. #15692213	C₂²	semidirect
93. #15692213	C₂²	semidirect
94. #15692213	C₂²	semidirect
95. #15692212	C₂²	semidirect
97. #15692211	C₂²	semidirect
98. #15692211	C₂²	semidirect
99. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
100. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
102. C₄⋊C₄×D₁₀₁	C₂²	semidirect
103. C₄⋊C₄×D₁₀₁	C₂²	semidirect
109. C₂×C₄×Dic₁₀₁	C₂²	semidirect
110. C₂×C₄×Dic₁₀₁	C₂²	semidirect
111. C₄²×D₁₀₁	C₂²	semidirect
115. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
116. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
117. #121×C₁₀₁	C₂²	semidirect
118. #121×C₁₀₁	C₂²	semidirect
120. C₄×D₄×C₁₀₁	C₂²	semidirect
121. C₄×D₄×C₁₀₁	C₂²	semidirect
250. C₂×C₄×C₁₀₁	#41	semidirect
263. C₂²⋊D₁₀₁	#41	semidirect
337. C₁₀₁	#3475	semidirect
355. #525	D₁₀₁	semidirect
397. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
398. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
404. #121	C₂×D₁₀₁	semidirect
405. #121	C₂×D₁₀₁	semidirect
430. C₄×D₄	C₂×D₁₀₁	semidirect
431. C₄×D₄	C₂×D₁₀₁	semidirect
618. C₂×C₄	#13108073	semidirect

Maximal subgroups

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

subgroup	index
#20265898	2
#20265891	2
#20265885	2
#20265879	2
#20265874	2
#20265869	2
#20265864	2
#20265861	2
#20265858	2
#20265850	2
#20265827	2
#20265814	2
#20265730	2
#20265709	2
#20265707	2
#20265684	2
#41×Dic₁₀₁	2
C₄×#13108073	2
C₂×C₄×C₂²⋊D₁₀₁	2
C₂×#15692214	2
#117×D₁₀₁	2
#525×C₁₀₁	2
#3475	101