Subgroups — #27184462

Order 12928.

1556 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13108074	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265757	C₂	1	2	yes	maximal, complemented
4	#20265756	C₂	1	2	yes	maximal, complemented
5	#20265750	C₂	1	2	yes	maximal, complemented
6	#20265749	C₂	1	2	yes	maximal, complemented
7	#20265743	C₂	1	2	yes	maximal, complemented
8	#20265742	C₂	1	2	yes	maximal, complemented
9	#20265738	C₂	1	2	yes	maximal, complemented
10	#20265737	C₂	1	2	yes	maximal, complemented
11	#20265724	C₂	1	4	yes	maximal, complemented
12	#20265689	C₂	1	1	yes	maximal, characteristic, complemented
13	#20265688	C₂	1	1	yes	maximal, characteristic, complemented
14	#20265686	C₂	1	4	yes	maximal, complemented
15	#20265684	C₂	1	1	yes	maximal, characteristic, complemented
16	#117×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
17	#525×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13108075	C₂²	1	1	yes	characteristic, complemented
19	C₂×#13108074	—	2	8	no	—
20	C₂×#13108074	C₂²	1	2	yes	—
21	C₂×#13108074	C₂²	1	1	yes	characteristic
22	C₂×#13108074	C₂²	1	2	yes	—
23	C₂×#13108074	C₂²	1	2	yes	complemented
24	C₂×#13108074	C₂²	1	2	yes	complemented
25	C₂×#13108074	C₂²	1	2	yes	complemented
26	C₂×#13108073	C₂²	1	2	yes	—
27	C₂×#13108073	C₂²	1	1	yes	characteristic, complemented
28	#41×D₁₀₁	—	2	8	no	—
29	C₂²×Dic₂₀₂	C₂²	1	1	yes	characteristic, complemented
30	C₂×Q₈×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₄₀₄	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₄×D₁₀₁	C₂²	1	2	yes	—
35	C₂×D₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	complemented
38	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
39	#15692254	C₂²	1	4	yes	complemented
40	#15692251	C₂²	1	4	yes	complemented
41	#15692241	C₂²	1	4	yes	complemented
42	#15692241	C₂²	1	4	yes	complemented
43	#15692240	C₂²	1	4	yes	complemented
44	#15692239	C₂²	1	2	yes	complemented
45	#15692238	C₂²	1	2	yes	complemented
46	#15692237	C₂²	1	4	yes	complemented
47	#15692236	C₂²	1	2	yes	complemented
48	#15692235	C₂²	1	2	yes	complemented
49	#15692234	C₂²	1	2	yes	complemented
50	#15692233	C₂²	1	4	yes	complemented
51	#15692232	C₂²	1	4	yes	complemented
52	#15692231	C₂²	1	2	yes	complemented
53	#15692230	C₂²	1	4	yes	complemented
54	#15692230	C₂²	1	2	yes	complemented
55	#15692229	C₂²	1	2	yes	complemented
56	#15692228	C₂²	1	4	yes	complemented
57	#15692228	C₂²	1	4	yes	complemented
58	#15692228	C₂²	1	4	yes	complemented
59	#15692227	C₂²	1	4	yes	complemented
60	#15692226	C₂²	1	4	yes	complemented
61	#15692226	C₂²	1	2	yes	complemented
62	#15692225	C₂²	1	2	yes	complemented
63	#15692225	C₂²	1	4	yes	complemented
64	#15692224	C₂²	1	2	yes	complemented
65	#15692223	C₂²	1	4	yes	complemented
66	#15692223	C₂²	1	2	yes	complemented
67	C₄×D₄₀₄	C₂²	1	4	yes	complemented
68	C₄×C₂²⋊D₁₀₁	C₂²	1	4	yes	complemented
69	C₄×C₂²⋊D₁₀₁	C₂²	1	4	yes	complemented
70	#15692214	C₂²	1	1	yes	characteristic, complemented
71	#15692213	C₂²	1	2	yes	complemented
72	#15692212	C₂²	1	2	yes	complemented
73	#15692211	C₂²	1	2	yes	complemented
74	C₄⋊C₄×D₁₀₁	C₂²	1	2	yes	complemented
75	C₂²⋊C₄×D₁₀₁	C₂²	1	2	yes	—
76	C₄²×D₁₀₁	C₂²	1	2	yes	complemented
77	C₂×#41×C₁₀₁	C₂²	1	1	yes	characteristic
78	C₂³×C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
79	#123×C₁₀₁	C₂²	1	2	yes	complemented
80	C₂²⋊Q₈×C₁₀₁	C₂²	1	2	yes	complemented
81	#121×C₁₀₁	C₂²	1	2	yes	complemented
82	#120×C₁₀₁	C₂²	1	2	yes	complemented
83	C₄×D₄×C₁₀₁	C₂²	1	4	yes	complemented
84	#117×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
85	C₂³×D₁₀₁	C₂³	1	2	yes	—
86	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
87	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
88	#13108075	—	2	4	no	—
89	#13108074	—	2	4	no	—
90	#13108074	—	2	8	no	—
91	#13108074	—	2	8	no	—
92	#13108074	—	2	8	no	—
93	#13108074	—	2	8	no	—
94	#13108074	—	2	8	no	—
95	#13108073	—	2	8	no	—
96	#13108073	—	2	4	no	—
97	C₂×Dic₂₀₂	—	2	4	no	—
98	C₂×Dic₂₀₂	C₂³	1	2	yes	—
99	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
100	C₂×Dic₂₀₂	C₂³	1	2	yes	—
101	C₂×Dic₂₀₂	C₂³	1	2	yes	—
102	Q₈×D₁₀₁	—	2	4	no	—
103	C₂×D₄₀₄	—	2	4	no	—
104	C₂×D₄₀₄	C₂³	1	2	yes	—
105	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
106	C₂×D₄₀₄	C₂³	1	2	yes	—
107	C₂×D₄₀₄	C₂³	1	2	yes	—
108	C₂×D₄₀₄	C₂³	1	4	yes	—
109	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
110	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
111	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
112	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
113	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
114	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
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	4	yes	—
119	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
120	D₄×D₁₀₁	—	2	8	no	—
121	D₄×D₁₀₁	—	2	4	no	—
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	—	2	8	no	—
127	C₂×C₄×D₁₀₁	D₄	1	8	yes	complemented
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	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
132	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
133	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
134	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
139	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
140	#13108053	C₂³	1	4	yes	—
141	#13108053	C₂³	1	4	yes	—
142	#13108053	C₂³	1	4	yes	—
143	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
144	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
145	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
146	#13108051	C₂³	1	4	yes	—
147	#13108051	C₂³	1	4	yes	—
148	#13108051	C₂³	1	4	yes	—
149	#13108051	C₂³	1	4	yes	—
150	#13108051	C₂³	1	4	yes	—
151	C₄×Dic₁₀₁	C₂³	1	4	yes	—
152	C₄×Dic₁₀₁	C₂³	1	2	yes	—
153	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
154	#41×C₁₀₁	—	2	4	no	—
155	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
156	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
157	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
158	C₂×D₄×C₁₀₁	C₂³	1	4	yes	—
159	C₂²×C₄×C₁₀₁	—	2	4	no	—
160	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
161	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
162	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
163	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
164	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
166	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
167	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
169	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
170	C₄²×C₁₀₁	C₂³	1	2	yes	—
171	C₂³×C₁₀₁	—	2	2	no	—
172	C₂³×C₁₀₁	—	4	2	no	—
173	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
174	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
175	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
176	C₂²×D₁₀₁	—	2	2	no	—
177	C₂²×D₁₀₁	—	2	4	no	—
178	C₂²×D₁₀₁	—	4	2	no	—
179	C₂²×D₁₀₁	—	4	4	no	—
180	C₂²×D₁₀₁	—	4	2	no	—
181	C₂²×D₁₀₁	C₂×D₄	1	4	yes	—
182	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
183	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
184	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
185	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
186	Q₈×C₁₀₁	—	2	2	no	—
187	D₄×C₁₀₁	—	2	4	no	—
188	D₄×C₁₀₁	—	2	2	no	—
189	D₄×C₁₀₁	—	4	4	no	—
190	C₂×C₄×C₁₀₁	—	2	2	no	—
191	C₂×C₄×C₁₀₁	—	2	4	no	—
192	C₂×C₄×C₁₀₁	—	2	4	no	—
193	C₂×C₄×C₁₀₁	—	2	4	no	—
194	C₂×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
195	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
196	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
197	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
198	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
199	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
200	C₂²⋊D₁₀₁	—	2	4	no	—
201	C₂²⋊D₁₀₁	—	2	4	no	—
202	C₂²⋊D₁₀₁	—	2	4	no	—
203	C₂²⋊D₁₀₁	—	2	4	no	—
204	C₂²⋊D₁₀₁	—	2	4	no	—
205	C₂²⋊D₁₀₁	—	2	4	no	—
206	C₂²⋊D₁₀₁	—	2	4	no	—
207	C₂²⋊D₁₀₁	—	4	4	no	—
208	C₂²⋊D₁₀₁	—	4	4	no	—
209	C₂×Dic₁₀₁	—	2	2	no	—
210	C₂×Dic₁₀₁	—	2	4	no	—
211	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
212	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
213	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
214	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
215	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
216	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
217	D₄₀₄	—	2	4	no	—
218	D₄₀₄	—	2	4	no	—
219	D₄₀₄	—	2	4	no	—
220	D₄₀₄	—	2	2	no	—
221	D₄₀₄	—	4	4	no	—
222	C₄×D₁₀₁	—	2	4	no	—
223	C₄×D₁₀₁	—	2	4	no	—
224	C₄×D₁₀₁	—	2	4	no	—
225	C₄×D₁₀₁	—	2	4	no	—
226	C₄×D₁₀₁	—	2	4	no	—
227	C₄×D₁₀₁	—	4	4	no	—
228	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
229	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
230	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
231	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
232	Dic₂₀₂	—	2	2	no	—
233	Dic₂₀₂	—	2	4	no	—
234	Dic₂₀₂	—	2	4	no	—
235	Dic₂₀₂	—	2	4	no	—
236	C₂²×C₁₀₁	—	2	2	no	—
237	C₂²×C₁₀₁	—	2	2	no	—
238	C₂²×C₁₀₁	—	2	2	no	—
239	C₂²×C₁₀₁	—	2	2	no	—
240	C₂²×C₁₀₁	—	2	4	no	—
241	C₂²×C₁₀₁	—	2	2	no	—
242	C₂²×C₁₀₁	—	4	4	no	—
243	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
244	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
245	C₂×D₁₀₁	—	2	2	no	—
246	C₂×D₁₀₁	—	2	2	no	—
247	C₂×D₁₀₁	—	2	2	no	—
248	C₂×D₁₀₁	—	2	2	no	—
249	C₂×D₁₀₁	—	2	2	no	—
250	C₂×D₁₀₁	—	2	4	no	—
251	C₂×D₁₀₁	—	2	2	no	—
252	C₂×D₁₀₁	—	4	4	no	—
253	C₂×D₁₀₁	—	4	8	no	—
254	C₂×D₁₀₁	—	4	4	no	—
255	C₂×D₁₀₁	C₂²×D₄	1	2	yes	—
256	C₂×D₁₀₁	C₂²×D₄	1	2	yes	—
257	C₄×C₁₀₁	—	2	2	no	—
258	C₄×C₁₀₁	—	2	2	no	—
259	C₄×C₁₀₁	—	2	4	no	—
260	C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
261	C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
262	Dic₁₀₁	—	2	2	no	—
263	Dic₁₀₁	—	2	2	no	—
264	Dic₁₀₁	—	2	4	no	—
265	Dic₁₀₁	C₂²×D₄	1	2	yes	—
266	Dic₁₀₁	C₂²×D₄	1	2	yes	—
267	C₂×C₁₀₁	—	2	2	no	—
268	C₂×C₁₀₁	—	4	2	no	—
269	C₂×C₁₀₁	—	4	2	no	—
270	C₂×C₁₀₁	C₂³×D₄	1	1	yes	characteristic
271	C₂×C₁₀₁	#585	1	2	yes	—
272	D₁₀₁	—	2	2	no	—
273	D₁₀₁	—	2	2	no	—
274	D₁₀₁	—	4	2	no	—
275	D₁₀₁	—	4	2	no	—
276	#3449	—	101	1	no	maximal, Sylow
277	C₁₀₁	#3449	1	1	yes	characteristic, complemented, Sylow
278	C₂²×#41	—	101	1	no	—
279	C₂²×#41	—	101	1	no	—
280	#537	—	101	2	no	—
281	#537	—	101	2	no	—
282	#536	—	101	2	no	—
283	#536	—	101	2	no	—
284	#535	—	101	2	no	—
285	#535	—	101	2	no	—
286	#534	—	101	2	no	—
287	#534	—	101	2	no	—
288	#532	—	101	4	no	—
289	#525	—	101	1	no	—
290	#525	—	101	1	no	—
291	#525	—	101	4	no	—
292	#525	—	101	1	no	—
293	#525	D₁₀₁	1	1	yes	characteristic, complemented
294	C₂×#117	—	101	1	no	—
295	C₂×#41	—	101	1	no	—
296	C₂×#41	—	101	2	no	—
297	C₂×#41	—	101	1	no	—
298	C₂×#41	—	101	2	no	—
299	C₂×#41	—	101	1	no	—
300	C₂×#41	—	101	2	no	—
301	C₂×#41	—	101	2	no	—
302	C₂×#41	—	101	2	no	—
303	C₂×#41	—	101	2	no	—
304	C₂×#41	—	202	8	no	—
305	C₂×#41	—	202	8	no	—
306	C₂×#41	C₂×D₁₀₁	1	1	yes	characteristic
307	C₂²×Q₈	—	101	1	no	—
308	C₂²×Q₈	—	101	1	no	—
309	C₂²×D₄	—	101	1	no	—
310	C₂²×D₄	—	101	1	no	—
311	C₂²×D₄	—	101	2	no	—
312	C₂²×D₄	—	101	1	no	—
313	C₂²×D₄	—	101	1	no	—
314	C₂³×C₄	—	101	1	no	—
315	C₂³×C₄	—	101	2	no	—
316	C₂³×C₄	—	101	1	no	—
317	C₂³×C₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
318	C₄⋊Q₈	—	101	4	no	—
319	#127	—	101	4	no	—
320	#124	—	101	4	no	—
321	#124	—	101	4	no	—
322	#123	—	101	2	no	—
323	#123	—	101	2	no	—
324	#123	—	101	4	no	—
325	#123	—	101	4	no	—
326	#123	—	101	2	no	—
327	#123	C₂×D₁₀₁	1	2	yes	complemented
328	C₂²⋊Q₈	—	101	2	no	—
329	C₂²⋊Q₈	—	101	2	no	—
330	C₂²⋊Q₈	—	101	4	no	—
331	C₂²⋊Q₈	—	101	2	no	—
332	C₂²⋊Q₈	—	101	4	no	—
333	C₂²⋊Q₈	C₂×D₁₀₁	1	2	yes	complemented
334	#121	—	101	2	no	—
335	#121	—	101	4	no	—
336	#121	—	101	4	no	—
337	#121	—	101	2	no	—
338	#121	—	101	2	no	—
339	#121	—	101	4	no	—
340	#121	—	101	4	no	—
341	#121	—	101	4	no	—
342	#121	—	101	4	no	—
343	#121	C₂×D₁₀₁	1	2	yes	complemented
344	#120	—	101	2	no	—
345	#120	—	101	2	no	—
346	#120	—	101	4	no	—
347	#120	—	101	4	no	—
348	#120	—	101	2	no	—
349	#120	C₂×D₁₀₁	1	2	yes	complemented
350	C₄×D₄	—	101	4	no	—
351	C₄×D₄	—	101	4	no	—
352	C₄×D₄	—	101	4	no	—
353	C₄×D₄	C₂×D₁₀₁	1	4	yes	complemented
354	#117	—	101	1	no	—
355	#117	—	101	2	no	—
356	#117	—	101	2	no	—
357	#117	—	101	2	no	—
358	#117	C₂×D₁₀₁	1	1	yes	characteristic, complemented
359	C₂×C₄⋊C₄	—	101	2	no	—
360	C₂×C₂²⋊C₄	—	101	2	no	—
361	C₂×C₄²	—	101	2	no	—
362	C₂⁴	—	101	1	no	—
363	C₂⁴	—	101	2	no	—
364	C₂⁴	—	101	1	no	—
365	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
366	#41	—	2	4	no	—
367	#41	—	202	8	no	—
368	#41	—	202	8	no	—
369	#41	—	202	8	no	—
370	#41	—	202	8	no	—
371	#41	—	202	8	no	—
372	#41	—	202	8	no	—
373	#41	—	202	4	no	—
374	#41	—	202	4	no	—
375	#41	—	202	4	no	—
376	C₂×Q₈	—	101	2	no	—
377	C₂×Q₈	—	101	1	no	—
378	C₂×Q₈	—	101	2	no	—
379	C₂×Q₈	—	101	2	no	—
380	C₂×Q₈	—	202	4	no	—
381	C₂×Q₈	—	202	4	no	—
382	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
383	C₂×D₄	—	101	4	no	—
384	C₂×D₄	—	101	4	no	—
385	C₂×D₄	—	101	2	no	—
386	C₂×D₄	—	101	2	no	—
387	C₂×D₄	—	101	2	no	—
388	C₂×D₄	—	101	2	no	—
389	C₂×D₄	—	101	2	no	—
390	C₂×D₄	—	101	2	no	—
391	C₂×D₄	—	101	2	no	—
392	C₂×D₄	—	101	4	no	—
393	C₂×D₄	—	101	2	no	—
394	C₂×D₄	—	101	2	no	—
395	C₂×D₄	—	101	2	no	—
396	C₂×D₄	—	101	1	no	—
397	C₂×D₄	—	202	4	no	—
398	C₂×D₄	—	202	4	no	—
399	C₂×D₄	—	202	4	no	—
400	C₂×D₄	—	202	8	no	—
401	C₂×D₄	—	202	4	no	—
402	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
403	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
404	C₂×D₄	C₂²×D₁₀₁	1	4	yes	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	101	1	no	—
407	C₂²×C₄	—	101	8	no	—
408	C₂²×C₄	—	101	1	no	—
409	C₂²×C₄	—	101	1	no	—
410	C₂²×C₄	—	101	1	no	—
411	C₂²×C₄	—	101	1	no	—
412	C₂²×C₄	—	101	2	no	—
413	C₂²×C₄	—	101	1	no	—
414	C₂²×C₄	—	101	4	no	—
415	C₂²×C₄	—	101	2	no	—
416	C₂²×C₄	—	101	2	no	—
417	C₂²×C₄	—	101	2	no	—
418	C₂²×C₄	—	101	2	no	—
419	C₂²×C₄	—	101	2	no	—
420	C₂²×C₄	—	202	8	no	—
421	C₂²×C₄	—	202	4	no	—
422	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
423	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
424	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
425	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
426	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
427	C₄⋊C₄	—	101	4	no	—
428	C₄⋊C₄	—	101	4	no	—
429	C₄⋊C₄	—	101	4	no	—
430	C₄⋊C₄	—	101	2	no	—
431	C₄⋊C₄	—	101	4	no	—
432	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
433	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
434	C₂²⋊C₄	—	101	2	no	—
435	C₂²⋊C₄	—	101	4	no	—
436	C₂²⋊C₄	—	101	4	no	—
437	C₂²⋊C₄	—	101	4	no	—
438	C₂²⋊C₄	—	101	4	no	—
439	C₂²⋊C₄	—	101	4	no	—
440	C₂²⋊C₄	—	101	4	no	—
441	C₂²⋊C₄	—	101	4	no	—
442	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
443	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
444	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
445	C₄²	—	101	4	no	—
446	C₄²	—	101	2	no	—
447	C₄²	C₂²×D₁₀₁	1	2	yes	—
448	C₂³	—	2	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	101	4	no	—
451	C₂³	—	101	1	no	—
452	C₂³	—	101	1	no	—
453	C₂³	—	101	2	no	—
454	C₂³	—	101	2	no	—
455	C₂³	—	404	2	no	—
456	C₂³	—	404	2	no	—
457	C₂³	—	404	4	no	—
458	C₂³	—	202	4	no	—
459	C₂³	—	202	2	no	—
460	C₂³	C₂³×D₁₀₁	1	2	yes	—
461	C₂³	C₂³×D₁₀₁	1	2	yes	—
462	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	202	4	no	—
465	Q₈	—	202	4	no	—
466	Q₈	—	202	4	no	—
467	Q₈	—	202	2	no	—
468	D₄	—	2	4	no	—
469	D₄	—	2	2	no	—
470	D₄	—	4	4	no	—
471	D₄	—	404	4	no	—
472	D₄	—	404	4	no	—
473	D₄	—	404	4	no	—
474	D₄	—	202	4	no	—
475	D₄	—	202	4	no	—
476	D₄	—	202	4	no	—
477	D₄	—	202	4	no	—
478	D₄	—	202	4	no	—
479	D₄	—	202	4	no	—
480	D₄	—	202	4	no	—
481	D₄	—	202	4	no	—
482	D₄	—	202	4	no	—
483	D₄	—	202	4	no	—
484	D₄	—	202	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	101	4	no	—
490	C₂×C₄	—	101	1	no	—
491	C₂×C₄	—	101	1	no	—
492	C₂×C₄	—	101	4	no	—
493	C₂×C₄	—	101	4	no	—
494	C₂×C₄	—	101	4	no	—
495	C₂×C₄	—	101	4	no	—
496	C₂×C₄	—	101	4	no	—
497	C₂×C₄	—	101	2	no	—
498	C₂×C₄	—	101	2	no	—
499	C₂×C₄	—	404	4	no	—
500	C₂×C₄	—	202	4	no	—
501	C₂×C₄	—	202	4	no	—
502	C₂×C₄	—	202	4	no	—
503	C₂×C₄	—	202	2	no	—
504	C₂×C₄	—	202	4	no	—
505	C₂×C₄	—	202	4	no	—
506	C₂×C₄	—	202	4	no	—
507	C₂×C₄	D₄×D₁₀₁	1	4	yes	—
508	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
509	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
510	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
511	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
512	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	101	2	no	—
521	C₂²	—	101	2	no	—
522	C₂²	—	404	4	no	—
523	C₂²	—	404	4	no	—
524	C₂²	—	404	8	no	—
525	C₂²	—	202	2	no	—
526	C₂²	—	202	2	no	—
527	C₂²	—	202	2	no	—
528	C₂²	—	202	4	no	—
529	C₂²	—	202	2	no	—
530	C₂²	—	202	2	no	—
531	C₂²	—	202	2	no	—
532	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
533	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	4	no	—
537	C₄	—	101	2	no	—
538	C₄	—	101	2	no	—
539	C₄	—	202	2	no	—
540	C₄	—	202	2	no	—
541	C₄	—	202	4	no	—
542	C₄	C₂×D₄×D₁₀₁	1	2	yes	—
543	C₄	C₂×D₄×D₁₀₁	1	2	yes	—
544	C₂	—	2	2	no	—
545	C₂	—	4	2	no	—
546	C₂	—	4	2	no	—
547	C₂	—	404	2	no	—
548	C₂	—	404	2	no	—
549	C₂	—	202	2	no	—
550	C₂	—	202	2	no	—
551	C₂	C₂²×D₄×D₁₀₁	1	1	yes	characteristic
552	C₂	#20266013	1	2	yes	—

	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	#3449
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. C₂²×#13108074	C₂	semidirect
2. C₂×#41×D₁₀₁	C₂	semidirect
3. #20265757	C₂	semidirect
4. #20265756	C₂	semidirect
5. #20265750	C₂	semidirect
6. #20265749	C₂	semidirect
7. #20265743	C₂	semidirect
8. #20265742	C₂	semidirect
9. #20265738	C₂	semidirect
10. #20265737	C₂	semidirect
11. #20265724	C₂	semidirect
12. #20265689	C₂	semidirect
13. #20265688	C₂	semidirect
14. #20265686	C₂	semidirect
15. #20265684	C₂	semidirect
16. #117×D₁₀₁	C₂	semidirect
17. #525×C₁₀₁	C₂	semidirect
18. C₂×#13108075	C₂²	semidirect
23. C₂×#13108074	C₂²	semidirect
24. C₂×#13108074	C₂²	semidirect
25. C₂×#13108074	C₂²	semidirect
27. C₂×#13108073	C₂²	semidirect
29. C₂²×Dic₂₀₂	C₂²	semidirect
30. C₂×Q₈×D₁₀₁	C₂²	semidirect
33. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
35. C₂×D₄×D₁₀₁	C₂²	semidirect
37. C₂²×C₄×D₁₀₁	C₂²	semidirect
38. C₂²×C₄×D₁₀₁	C₂²	semidirect
39. #15692254	C₂²	semidirect
40. #15692251	C₂²	semidirect
41. #15692241	C₂²	semidirect
42. #15692241	C₂²	semidirect
43. #15692240	C₂²	semidirect
44. #15692239	C₂²	semidirect
45. #15692238	C₂²	semidirect
46. #15692237	C₂²	semidirect
47. #15692236	C₂²	semidirect
48. #15692235	C₂²	semidirect
49. #15692234	C₂²	semidirect
50. #15692233	C₂²	semidirect
51. #15692232	C₂²	semidirect
52. #15692231	C₂²	semidirect
53. #15692230	C₂²	semidirect
54. #15692230	C₂²	semidirect
55. #15692229	C₂²	semidirect
56. #15692228	C₂²	semidirect
57. #15692228	C₂²	semidirect
58. #15692228	C₂²	semidirect
59. #15692227	C₂²	semidirect
60. #15692226	C₂²	semidirect
61. #15692226	C₂²	semidirect
62. #15692225	C₂²	semidirect
63. #15692225	C₂²	semidirect
64. #15692224	C₂²	semidirect
65. #15692223	C₂²	semidirect
66. #15692223	C₂²	semidirect
67. C₄×D₄₀₄	C₂²	semidirect
68. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
69. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
70. #15692214	C₂²	semidirect
71. #15692213	C₂²	semidirect
72. #15692212	C₂²	semidirect
73. #15692211	C₂²	semidirect
74. C₄⋊C₄×D₁₀₁	C₂²	semidirect
76. C₄²×D₁₀₁	C₂²	semidirect
78. C₂³×C₄×C₁₀₁	C₂²	semidirect
79. #123×C₁₀₁	C₂²	semidirect
80. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
81. #121×C₁₀₁	C₂²	semidirect
82. #120×C₁₀₁	C₂²	semidirect
83. C₄×D₄×C₁₀₁	C₂²	semidirect
84. #117×C₁₀₁	C₂²	semidirect
127. C₂×C₄×D₁₀₁	D₄	semidirect
277. C₁₀₁	#3449	semidirect
293. #525	D₁₀₁	semidirect
317. C₂³×C₄	C₂×D₁₀₁	semidirect
327. #123	C₂×D₁₀₁	semidirect
333. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
343. #121	C₂×D₁₀₁	semidirect
349. #120	C₂×D₁₀₁	semidirect
353. C₄×D₄	C₂×D₁₀₁	semidirect
358. #117	C₂×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13108074	2
C₂×#41×D₁₀₁	2
#20265757	2
#20265756	2
#20265750	2
#20265749	2
#20265743	2
#20265742	2
#20265738	2
#20265737	2
#20265724	2
#20265689	2
#20265688	2
#20265686	2
#20265684	2
#117×D₁₀₁	2
#525×C₁₀₁	2
#3449	101