Subgroups — #27185267

Order 12928.

1058 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265930	C₂	1	1	yes	maximal, characteristic, complemented
2	#20265929	C₂	1	2	yes	maximal, complemented
3	#20265924	C₂	1	2	yes	maximal, complemented
4	#20265922	C₂	1	2	yes	maximal, complemented
5	#20265922	C₂	1	2	yes	maximal, complemented
6	#20265920	C₂	1	1	yes	maximal, characteristic, complemented
7	#20265916	C₂	1	2	yes	maximal, complemented
8	#20265915	C₂	1	2	yes	maximal, complemented
9	#20265914	C₂	1	1	yes	maximal, characteristic, complemented
10	#20265725	C₂	1	1	yes	maximal, characteristic, complemented
11	#20265722	C₂	1	2	yes	maximal, complemented
12	#20265710	C₂	1	2	yes	maximal, complemented
13	#20265708	C₂	1	2	yes	maximal, complemented
14	#20265704	C₂	1	2	yes	maximal, complemented
15	#20265687	C₂	1	2	yes	maximal, complemented
16	#20265685	C₂	1	1	yes	maximal, characteristic, complemented
17	#20265683	C₂	1	1	yes	maximal, characteristic, complemented
18	#20265683	C₂	1	2	yes	maximal, complemented
19	#560×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13108073	C₂²	1	1	yes	characteristic
21	C₂×#13108073	C₂²	1	2	yes	—
22	C₂×#13108073	C₂²	1	1	yes	characteristic, complemented
23	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
25	#15692255	C₂²	1	1	yes	characteristic, complemented
26	#15692254	C₂²	1	2	yes	complemented
27	#15692251	C₂²	1	2	yes	—
28	#15692250	C₂²	1	2	yes	complemented
29	#15692249	C₂²	1	2	yes	complemented
30	#15692248	C₂²	1	2	yes	complemented
31	#15692248	C₂²	1	2	yes	complemented
32	#15692248	C₂²	1	2	yes	complemented
33	#15692246	C₂²	1	2	yes	complemented
34	#15692245	C₂²	1	2	yes	complemented
35	#15692245	C₂²	1	2	yes	complemented
36	#15692242	C₂²	1	2	yes	—
37	#15692242	C₂²	1	1	yes	characteristic
38	#15692242	C₂²	1	1	yes	characteristic, complemented
39	#15692241	C₂²	1	2	yes	—
40	#15692241	C₂²	1	2	yes	—
41	#15692241	C₂²	1	2	yes	—
42	#15692241	C₂²	1	2	yes	complemented
43	#15692240	C₂²	1	2	yes	complemented
44	#15692239	C₂²	1	2	yes	—
45	#15692239	C₂²	1	1	yes	characteristic, complemented
46	#15692238	C₂²	1	2	yes	complemented
47	#15692238	C₂²	1	1	yes	characteristic, complemented
48	#15692237	C₂²	1	2	yes	—
49	#15692237	C₂²	1	2	yes	complemented
50	#15692237	C₂²	1	2	yes	complemented
51	#15692236	C₂²	1	1	yes	characteristic
52	#15692236	C₂²	1	2	yes	complemented
53	#15692236	C₂²	1	2	yes	complemented
54	#15692236	C₂²	1	2	yes	complemented
55	#15692235	C₂²	1	2	yes	complemented
56	#15692234	C₂²	1	2	yes	complemented
57	#15692234	C₂²	1	2	yes	complemented
58	#15692233	C₂²	1	2	yes	complemented
59	#15692233	C₂²	1	2	yes	complemented
60	#15692232	C₂²	1	2	yes	complemented
61	#15692232	C₂²	1	2	yes	complemented
62	#15692232	C₂²	1	2	yes	complemented
63	#15692232	C₂²	1	2	yes	complemented
64	#15692229	C₂²	1	2	yes	complemented
65	#15692228	C₂²	1	2	yes	—
66	#15692228	C₂²	1	2	yes	—
67	#15692227	C₂²	1	2	yes	—
68	#15692227	C₂²	1	2	yes	—
69	#15692227	C₂²	1	2	yes	—
70	#15692227	C₂²	1	2	yes	—
71	#15692227	C₂²	1	2	yes	complemented
72	#15692227	C₂²	1	2	yes	complemented
73	#15692226	C₂²	1	2	yes	—
74	#15692226	C₂²	1	2	yes	complemented
75	#15692226	C₂²	1	2	yes	complemented
76	#15692225	C₂²	1	1	yes	characteristic, complemented
77	#15692224	C₂²	1	2	yes	—
78	#15692224	C₂²	1	1	yes	characteristic, complemented
79	#15692223	C₂²	1	1	yes	characteristic
80	#15692223	C₂²	1	2	yes	—
81	#15692223	C₂²	1	2	yes	complemented
82	#15692220	C₂²	1	2	yes	complemented
83	D₄×Dic₁₀₁	C₂²	1	2	yes	—
84	D₄×Dic₁₀₁	C₂²	1	2	yes	complemented
85	D₄×Dic₁₀₁	C₂²	1	2	yes	complemented
86	D₄×Dic₁₀₁	C₂²	1	2	yes	complemented
87	#15692217	C₂²	1	2	yes	complemented
88	#15692215	C₂²	1	2	yes	—
89	#15692215	C₂²	1	2	yes	—
90	#15692215	C₂²	1	2	yes	complemented
91	#15692215	C₂²	1	2	yes	complemented
92	#15692213	C₂²	1	2	yes	complemented
93	#15692211	C₂²	1	1	yes	characteristic, complemented
94	#15692211	C₂²	1	2	yes	complemented
95	#15692211	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	complemented
97	C₄²×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
98	#127×C₁₀₁	C₂²	1	1	yes	characteristic
99	#126×C₁₀₁	C₂²	1	2	yes	complemented
100	#123×C₁₀₁	C₂²	1	1	yes	characteristic
101	#123×C₁₀₁	C₂²	1	2	yes	complemented
102	#121×C₁₀₁	C₂²	1	2	yes	—
103	#121×C₁₀₁	C₂²	1	2	yes	—
104	#121×C₁₀₁	C₂²	1	2	yes	complemented
105	#120×C₁₀₁	C₂²	1	1	yes	characteristic
106	#120×C₁₀₁	C₂²	1	2	yes	complemented
107	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
108	#13108073	—	4	4	no	—
109	#13108073	—	4	2	no	—
110	#13108073	—	4	2	no	—
111	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
112	C₂×Dic₂₀₂	C₂³	1	2	yes	—
113	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
114	C₂×Dic₂₀₂	C₂³	1	2	yes	—
115	C₂×D₄₀₄	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	1	yes	characteristic
119	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
125	C₂²×Dic₁₀₁	—	4	2	no	—
126	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
127	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
128	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
129	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
130	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
131	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
132	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
133	C₂×C₄×D₁₀₁	—	4	2	no	—
134	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
135	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
137	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
138	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
139	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
140	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
141	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
142	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
143	#13108053	C₂³	1	2	yes	—
144	#13108053	C₂³	1	2	yes	—
145	#13108053	C₂³	1	2	yes	—
146	#13108053	C₂³	1	2	yes	—
147	#13108053	C₂³	1	2	yes	—
148	#13108053	C₂³	1	2	yes	—
149	#13108053	C₂³	1	2	yes	—
150	#13108053	C₂³	1	2	yes	—
151	#13108053	C₂³	1	2	yes	—
152	#13108053	C₂³	1	2	yes	—
153	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
154	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
155	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
156	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
157	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
158	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
159	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
161	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
162	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
163	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
164	#13108051	C₂³	1	2	yes	—
165	#13108051	C₂³	1	2	yes	—
166	#13108051	C₂³	1	2	yes	—
167	#13108051	C₂³	1	2	yes	—
168	#13108051	C₂³	1	2	yes	—
169	#13108051	C₂³	1	2	yes	—
170	#13108051	C₂³	1	2	yes	—
171	#13108051	C₂³	1	2	yes	—
172	C₄×Dic₁₀₁	C₂³	1	2	yes	—
173	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
174	C₄×Dic₁₀₁	C₂³	1	2	yes	—
175	C₄×Dic₁₀₁	C₂³	1	2	yes	—
176	C₄×Dic₁₀₁	C₂³	1	2	yes	—
177	C₄×Dic₁₀₁	C₂³	1	2	yes	—
178	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
180	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
181	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
182	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
183	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
184	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
185	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
186	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
188	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
189	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
190	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
193	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
197	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
198	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
199	C₂³×C₁₀₁	—	4	2	no	—
200	C₂³×C₁₀₁	—	4	1	no	—
201	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
202	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
203	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
204	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
205	C₂²×D₁₀₁	—	4	1	no	—
206	C₂²×D₁₀₁	—	4	2	no	—
207	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
208	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
209	D₄×C₁₀₁	—	4	2	no	—
210	D₄×C₁₀₁	—	4	2	no	—
211	D₄×C₁₀₁	—	4	2	no	—
212	D₄×C₁₀₁	—	4	2	no	—
213	D₄×C₁₀₁	—	4	1	no	—
214	D₄×C₁₀₁	—	4	1	no	—
215	D₄×C₁₀₁	—	4	2	no	—
216	C₂×C₄×C₁₀₁	—	4	2	no	—
217	C₂×C₄×C₁₀₁	—	4	1	no	—
218	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
219	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
220	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
221	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
222	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
223	C₂²⋊D₁₀₁	—	4	2	no	—
224	C₂²⋊D₁₀₁	—	4	2	no	—
225	C₂²⋊D₁₀₁	—	4	2	no	—
226	C₂²⋊D₁₀₁	—	4	2	no	—
227	C₂²⋊D₁₀₁	—	4	2	no	—
228	C₂²⋊D₁₀₁	—	4	2	no	—
229	C₂²⋊D₁₀₁	—	4	1	no	—
230	C₂²⋊D₁₀₁	—	4	2	no	—
231	C₂²⋊D₁₀₁	—	4	1	no	—
232	C₂×Dic₁₀₁	—	2	2	no	—
233	C₂×Dic₁₀₁	—	2	2	no	—
234	C₂×Dic₁₀₁	—	2	4	no	—
235	C₂×Dic₁₀₁	—	2	4	no	—
236	C₂×Dic₁₀₁	—	4	1	no	—
237	C₂×Dic₁₀₁	—	4	2	no	—
238	C₂×Dic₁₀₁	—	4	2	no	—
239	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
240	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
241	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
242	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
243	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
244	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
247	D₄₀₄	—	4	2	no	—
248	C₄×D₁₀₁	—	2	4	no	—
249	C₄×D₁₀₁	—	2	2	no	—
250	C₄×D₁₀₁	—	4	2	no	—
251	C₄×D₁₀₁	—	4	2	no	—
252	Dic₂₀₂	—	4	2	no	—
253	Dic₂₀₂	—	4	1	no	—
254	Dic₂₀₂	—	4	2	no	—
255	Dic₂₀₂	—	4	1	no	—
256	C₂²×C₁₀₁	—	2	1	no	—
257	C₂²×C₁₀₁	—	2	2	no	—
258	C₂²×C₁₀₁	—	2	2	no	—
259	C₂²×C₁₀₁	—	2	1	no	—
260	C₂²×C₁₀₁	—	2	2	no	—
261	C₂²×C₁₀₁	—	2	2	no	—
262	C₂²×C₁₀₁	—	2	2	no	—
263	C₂²×C₁₀₁	—	2	2	no	—
264	C₂²×C₁₀₁	—	2	2	no	—
265	C₂²×C₁₀₁	—	2	2	no	—
266	C₂²×C₁₀₁	—	4	4	no	—
267	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
268	C₂×D₁₀₁	—	2	2	no	—
269	C₂×D₁₀₁	—	2	1	no	—
270	C₂×D₁₀₁	—	2	2	no	—
271	C₂×D₁₀₁	—	2	2	no	—
272	C₂×D₁₀₁	—	2	2	no	—
273	C₂×D₁₀₁	—	4	4	no	—
274	C₄×C₁₀₁	—	2	1	no	—
275	C₄×C₁₀₁	—	2	2	no	—
276	C₄×C₁₀₁	—	2	2	no	—
277	C₄×C₁₀₁	—	2	2	no	—
278	C₄×C₁₀₁	—	2	2	no	—
279	Dic₁₀₁	—	2	2	no	—
280	Dic₁₀₁	—	2	1	no	—
281	Dic₁₀₁	—	2	2	no	—
282	Dic₁₀₁	—	2	1	no	—
283	Dic₁₀₁	—	2	2	no	—
284	Dic₁₀₁	—	2	2	no	—
285	Dic₁₀₁	—	2	2	no	—
286	Dic₁₀₁	H(5,𝔽₂)	1	2	yes	—
287	C₂×C₁₀₁	—	4	1	no	—
288	C₂×C₁₀₁	—	4	2	no	—
289	C₂×C₁₀₁	—	4	1	no	—
290	C₂×C₁₀₁	—	4	2	no	—
291	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₁₀₁	#585	1	2	yes	—
293	D₁₀₁	—	4	1	no	—
294	D₁₀₁	—	4	2	no	—
295	#3529	—	101	1	no	maximal, Sylow
296	C₁₀₁	#3529	1	1	yes	characteristic, complemented, Sylow
297	#563	—	101	2	no	—
298	#563	—	101	1	no	—
299	#562	—	101	2	no	—
300	#562	—	101	2	no	—
301	#562	—	101	2	no	—
302	H(3,𝔽₄)	—	101	1	no	—
303	#560	—	101	1	no	—
304	#560	—	101	2	no	—
305	#560	—	101	2	no	—
306	#560	D₁₀₁	1	1	yes	characteristic, complemented
307	#532	—	101	1	no	—
308	#532	—	101	2	no	—
309	#529	—	101	2	no	—
310	#529	—	101	2	no	—
311	#529	—	101	2	no	—
312	#525	—	101	1	no	—
313	#525	—	101	2	no	—
314	#525	—	101	1	no	—
315	#525	—	101	2	no	—
316	C₂×#41	—	101	2	no	—
317	C₂×#41	—	101	1	no	—
318	C₂×#41	—	101	1	no	—
319	C₂³×C₄	—	101	1	no	—
320	C₂³×C₄	—	101	1	no	—
321	C₄⋊Q₈	—	101	2	no	—
322	C₄⋊Q₈	—	101	1	no	—
323	#127	—	101	2	no	—
324	#127	C₂×D₁₀₁	1	1	yes	characteristic
325	#126	—	101	2	no	—
326	#126	—	101	2	no	—
327	#126	—	101	2	no	—
328	#126	—	101	2	no	—
329	#126	—	101	2	no	—
330	#126	C₂×D₁₀₁	1	2	yes	complemented
331	#125	—	101	2	no	—
332	#125	—	101	2	no	—
333	#125	—	101	2	no	—
334	#124	—	101	2	no	—
335	#124	—	101	1	no	—
336	#124	—	101	1	no	—
337	#124	—	101	2	no	—
338	#124	—	101	2	no	—
339	#124	—	101	2	no	—
340	#124	—	101	2	no	—
341	#123	—	101	1	no	—
342	#123	—	101	2	no	—
343	#123	—	101	2	no	—
344	#123	—	101	2	no	—
345	#123	—	101	1	no	—
346	#123	—	101	2	no	—
347	#123	—	101	2	no	—
348	#123	—	101	2	no	—
349	#123	—	101	2	no	—
350	#123	—	101	2	no	—
351	#123	—	101	1	no	—
352	#123	—	101	2	no	—
353	#123	C₂×D₁₀₁	1	1	yes	characteristic
354	#123	C₂×D₁₀₁	1	2	yes	complemented
355	C₂²⋊Q₈	—	101	2	no	—
356	C₂²⋊Q₈	—	101	2	no	—
357	C₂²⋊Q₈	—	101	2	no	—
358	C₂²⋊Q₈	—	101	2	no	—
359	C₂²⋊Q₈	—	101	2	no	—
360	C₂²⋊Q₈	—	101	2	no	—
361	C₂²⋊Q₈	—	101	2	no	—
362	C₂²⋊Q₈	—	101	2	no	—
363	C₂²⋊Q₈	—	101	2	no	—
364	#121	—	101	2	no	—
365	#121	—	101	2	no	—
366	#121	—	101	2	no	—
367	#121	—	101	2	no	—
368	#121	—	101	2	no	—
369	#121	—	101	2	no	—
370	#121	—	101	2	no	—
371	#121	—	101	2	no	—
372	#121	—	101	2	no	—
373	#121	—	101	2	no	—
374	#121	—	101	2	no	—
375	#121	—	101	2	no	—
376	#121	C₂×D₁₀₁	1	2	yes	—
377	#121	C₂×D₁₀₁	1	2	yes	—
378	#121	C₂×D₁₀₁	1	2	yes	complemented
379	#120	—	101	1	no	—
380	#120	—	101	2	no	—
381	#120	—	101	2	no	—
382	#120	—	101	1	no	—
383	#120	—	101	2	no	—
384	#120	—	101	1	no	—
385	#120	C₂×D₁₀₁	1	1	yes	characteristic
386	#120	C₂×D₁₀₁	1	2	yes	complemented
387	C₄×Q₈	—	101	2	no	—
388	C₄×D₄	—	101	2	no	—
389	C₄×D₄	—	101	2	no	—
390	C₄×D₄	—	101	2	no	—
391	C₄×D₄	—	101	2	no	—
392	C₄×D₄	—	101	2	no	—
393	C₄×D₄	—	101	2	no	—
394	C₄×D₄	—	101	2	no	—
395	C₄×D₄	—	101	2	no	—
396	C₄×D₄	—	101	2	no	—
397	#117	—	101	2	no	—
398	#117	—	101	1	no	—
399	#117	—	101	1	no	—
400	#117	—	101	2	no	—
401	C₂×C₄²	—	101	2	no	—
402	C₂×C₄²	—	101	1	no	—
403	C₂⁴	—	101	1	no	—
404	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
405	#41	—	404	4	no	—
406	#41	—	404	2	no	—
407	#41	—	404	2	no	—
408	C₂×Q₈	—	101	2	no	—
409	C₂×Q₈	—	101	2	no	—
410	C₂×Q₈	—	101	1	no	—
411	C₂×Q₈	—	101	1	no	—
412	C₂×D₄	—	101	2	no	—
413	C₂×D₄	—	101	2	no	—
414	C₂×D₄	—	101	2	no	—
415	C₂×D₄	—	101	2	no	—
416	C₂×D₄	—	101	2	no	—
417	C₂×D₄	—	101	2	no	—
418	C₂×D₄	—	101	1	no	—
419	C₂×D₄	—	101	1	no	—
420	C₂×D₄	—	101	2	no	—
421	C₂×D₄	—	101	2	no	—
422	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
423	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
424	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
425	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
426	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
427	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
428	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
429	C₂²×C₄	—	101	2	no	—
430	C₂²×C₄	—	101	1	no	—
431	C₂²×C₄	—	101	2	no	—
432	C₂²×C₄	—	101	2	no	—
433	C₂²×C₄	—	101	1	no	—
434	C₂²×C₄	—	101	1	no	—
435	C₂²×C₄	—	101	2	no	—
436	C₂²×C₄	—	101	2	no	—
437	C₂²×C₄	—	101	2	no	—
438	C₂²×C₄	—	101	1	no	—
439	C₂²×C₄	—	101	2	no	—
440	C₂²×C₄	—	404	2	no	—
441	C₂²×C₄	—	404	2	no	—
442	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
443	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
444	C₄⋊C₄	—	101	2	no	—
445	C₄⋊C₄	—	101	2	no	—
446	C₄⋊C₄	—	101	2	no	—
447	C₄⋊C₄	—	101	2	no	—
448	C₄⋊C₄	—	101	2	no	—
449	C₄⋊C₄	—	101	2	no	—
450	C₄⋊C₄	—	101	2	no	—
451	C₄⋊C₄	—	101	2	no	—
452	C₄⋊C₄	—	101	2	no	—
453	C₄⋊C₄	—	101	2	no	—
454	C₄⋊C₄	—	101	2	no	—
455	C₄⋊C₄	—	101	2	no	—
456	C₄⋊C₄	—	101	2	no	—
457	C₄⋊C₄	—	101	2	no	—
458	C₄⋊C₄	—	101	2	no	—
459	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
460	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
461	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
462	C₂²⋊C₄	—	101	1	no	—
463	C₂²⋊C₄	—	101	1	no	—
464	C₂²⋊C₄	—	101	2	no	—
465	C₂²⋊C₄	—	101	2	no	—
466	C₂²⋊C₄	—	101	2	no	—
467	C₂²⋊C₄	—	101	2	no	—
468	C₂²⋊C₄	—	101	2	no	—
469	C₂²⋊C₄	—	101	2	no	—
470	C₂²⋊C₄	—	101	2	no	—
471	C₂²⋊C₄	—	101	2	no	—
472	C₂²⋊C₄	—	101	2	no	—
473	C₂²⋊C₄	—	101	2	no	—
474	C₂²⋊C₄	—	101	2	no	—
475	C₂²⋊C₄	—	101	2	no	—
476	C₂²⋊C₄	—	101	2	no	—
477	C₂²⋊C₄	—	101	2	no	—
478	C₂²⋊C₄	—	101	2	no	—
479	C₂²⋊C₄	—	101	2	no	—
480	C₂²⋊C₄	—	101	2	no	—
481	C₂²⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
482	C₂²⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
483	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
484	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
485	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
486	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
487	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
488	C₄²	—	101	2	no	—
489	C₄²	—	101	2	no	—
490	C₄²	—	101	2	no	—
491	C₄²	—	101	1	no	—
492	C₄²	—	101	2	no	—
493	C₄²	—	101	2	no	—
494	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
495	C₂³	—	4	1	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	101	2	no	—
498	C₂³	—	101	1	no	—
499	C₂³	—	404	1	no	—
500	C₂³	—	404	2	no	—
501	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
502	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
503	C₂³	C₂³×D₁₀₁	1	2	yes	—
504	C₂³	C₂³×D₁₀₁	1	2	yes	—
505	Q₈	—	404	2	no	—
506	Q₈	—	404	1	no	—
507	Q₈	—	404	1	no	—
508	Q₈	—	404	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	404	2	no	—
517	D₄	—	404	1	no	—
518	D₄	—	404	1	no	—
519	D₄	—	404	2	no	—
520	D₄	—	404	2	no	—
521	D₄	—	404	2	no	—
522	D₄	—	404	2	no	—
523	D₄	—	404	2	no	—
524	D₄	—	404	2	no	—
525	D₄	—	404	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	101	1	no	—
529	C₂×C₄	—	101	2	no	—
530	C₂×C₄	—	101	2	no	—
531	C₂×C₄	—	101	2	no	—
532	C₂×C₄	—	101	2	no	—
533	C₂×C₄	—	101	1	no	—
534	C₂×C₄	—	101	2	no	—
535	C₂×C₄	—	101	1	no	—
536	C₂×C₄	—	404	2	no	—
537	C₂×C₄	—	404	2	no	—
538	C₂×C₄	—	404	1	no	—
539	C₂×C₄	—	404	2	no	—
540	C₂×C₄	—	404	2	no	—
541	C₂×C₄	—	202	4	no	—
542	C₂×C₄	—	202	2	no	—
543	C₂×C₄	—	202	2	no	—
544	C₂×C₄	—	202	2	no	—
545	C₂×C₄	—	202	4	no	—
546	C₂×C₄	—	202	4	no	—
547	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
548	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
549	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
550	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
551	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	404	4	no	—
564	C₂²	—	202	2	no	—
565	C₂²	—	202	1	no	—
566	C₂²	—	202	2	no	—
567	C₂²	—	202	2	no	—
568	C₂²	—	202	2	no	—
569	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	101	2	no	—
576	C₄	—	202	1	no	—
577	C₄	—	202	2	no	—
578	C₄	—	202	1	no	—
579	C₄	—	202	2	no	—
580	C₄	—	202	2	no	—
581	C₄	—	202	2	no	—
582	C₄	—	202	2	no	—
583	C₂	—	4	2	no	—
584	C₂	—	4	1	no	—
585	C₂	—	4	1	no	—
586	C₂	—	4	2	no	—
587	C₂	—	404	2	no	—
588	C₂	—	404	1	no	—
589	C₂	H(5,𝔽₂)×D₁₀₁	1	1	yes	characteristic
590	C₂	#20266012	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#560×C₁₀₁	C₂
hypercenter	#560	D₁₀₁
hypocenter	C₁₀₁	#3529
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #560

Complements

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

N	H ≅ G/N	type
1. #20265930	C₂	semidirect
2. #20265929	C₂	semidirect
3. #20265924	C₂	semidirect
4. #20265922	C₂	semidirect
5. #20265922	C₂	semidirect
6. #20265920	C₂	semidirect
7. #20265916	C₂	semidirect
8. #20265915	C₂	semidirect
9. #20265914	C₂	semidirect
10. #20265725	C₂	semidirect
11. #20265722	C₂	semidirect
12. #20265710	C₂	semidirect
13. #20265708	C₂	semidirect
14. #20265704	C₂	semidirect
15. #20265687	C₂	semidirect
16. #20265685	C₂	semidirect
17. #20265683	C₂	semidirect
18. #20265683	C₂	semidirect
19. #560×C₁₀₁	C₂	semidirect
22. C₂×#13108073	C₂²	semidirect
23. C₂³×Dic₁₀₁	C₂²	semidirect
24. C₂²×C₄×D₁₀₁	C₂²	semidirect
25. #15692255	C₂²	semidirect
26. #15692254	C₂²	semidirect
28. #15692250	C₂²	semidirect
29. #15692249	C₂²	semidirect
30. #15692248	C₂²	semidirect
31. #15692248	C₂²	semidirect
32. #15692248	C₂²	semidirect
33. #15692246	C₂²	semidirect
34. #15692245	C₂²	semidirect
35. #15692245	C₂²	semidirect
38. #15692242	C₂²	semidirect
42. #15692241	C₂²	semidirect
43. #15692240	C₂²	semidirect
45. #15692239	C₂²	semidirect
46. #15692238	C₂²	semidirect
47. #15692238	C₂²	semidirect
49. #15692237	C₂²	semidirect
50. #15692237	C₂²	semidirect
52. #15692236	C₂²	semidirect
53. #15692236	C₂²	semidirect
54. #15692236	C₂²	semidirect
55. #15692235	C₂²	semidirect
56. #15692234	C₂²	semidirect
57. #15692234	C₂²	semidirect
58. #15692233	C₂²	semidirect
59. #15692233	C₂²	semidirect
60. #15692232	C₂²	semidirect
61. #15692232	C₂²	semidirect
62. #15692232	C₂²	semidirect
63. #15692232	C₂²	semidirect
64. #15692229	C₂²	semidirect
71. #15692227	C₂²	semidirect
72. #15692227	C₂²	semidirect
74. #15692226	C₂²	semidirect
75. #15692226	C₂²	semidirect
76. #15692225	C₂²	semidirect
78. #15692224	C₂²	semidirect
81. #15692223	C₂²	semidirect
82. #15692220	C₂²	semidirect
84. D₄×Dic₁₀₁	C₂²	semidirect
85. D₄×Dic₁₀₁	C₂²	semidirect
86. D₄×Dic₁₀₁	C₂²	semidirect
87. #15692217	C₂²	semidirect
90. #15692215	C₂²	semidirect
91. #15692215	C₂²	semidirect
92. #15692213	C₂²	semidirect
93. #15692211	C₂²	semidirect
94. #15692211	C₂²	semidirect
95. #15692211	C₂²	semidirect
96. C₂×C₄×Dic₁₀₁	C₂²	semidirect
97. C₄²×D₁₀₁	C₂²	semidirect
99. #126×C₁₀₁	C₂²	semidirect
101. #123×C₁₀₁	C₂²	semidirect
104. #121×C₁₀₁	C₂²	semidirect
106. #120×C₁₀₁	C₂²	semidirect
296. C₁₀₁	#3529	semidirect
306. #560	D₁₀₁	semidirect
330. #126	C₂×D₁₀₁	semidirect
354. #123	C₂×D₁₀₁	semidirect
378. #121	C₂×D₁₀₁	semidirect
386. #120	C₂×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265930	2
#20265929	2
#20265924	2
#20265922	2
#20265920	2
#20265916	2
#20265915	2
#20265914	2
#20265725	2
#20265722	2
#20265710	2
#20265708	2
#20265704	2
#20265687	2
#20265685	2
#20265683	2
#560×C₁₀₁	2
#3529	101