Subgroups — #27185342

Order 12928.

1038 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265926	C₂	1	2	yes	maximal, complemented
2	#20265925	C₂	1	2	yes	maximal, complemented
3	#20265881	C₂	1	2	yes	maximal, complemented
4	#20265859	C₂	1	2	yes	maximal, complemented
5	#20265851	C₂	1	2	yes	maximal, complemented
6	#20265851	C₂	1	2	yes	maximal, complemented
7	#20265830	C₂	1	2	yes	maximal, complemented
8	#20265818	C₂	1	2	yes	maximal, complemented
9	#20265802	C₂	1	1	yes	maximal, characteristic, complemented
10	#20265801	C₂	1	2	yes	maximal, complemented
11	#20265775	C₂	1	2	yes	maximal, complemented
12	#20265775	C₂	1	2	yes	maximal, complemented
13	#20265774	C₂	1	1	yes	maximal, characteristic, complemented
14	#20265767	C₂	1	1	yes	maximal, characteristic, complemented
15	#20265752	C₂	1	2	yes	maximal, complemented
16	#20265690	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#15692240	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²⋊Q₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
19	#544×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13108075	C₂²	1	2	yes	—
21	C₂×#13108075	C₂²	1	1	yes	characteristic, complemented
22	C₂×Q₈×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
23	C₂²×D₄₀₄	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
25	#15692253	C₂²	1	2	yes	complemented
26	#15692250	C₂²	1	2	yes	complemented
27	#15692250	C₂²	1	2	yes	complemented
28	#15692250	C₂²	1	2	yes	complemented
29	#15692250	C₂²	1	2	yes	complemented
30	#15692249	C₂²	1	2	yes	complemented
31	#15692249	C₂²	1	2	yes	complemented
32	#15692245	C₂²	1	2	yes	complemented
33	#15692245	C₂²	1	2	yes	complemented
34	#15692245	C₂²	1	2	yes	complemented
35	#15692244	C₂²	1	2	yes	—
36	#15692244	C₂²	1	2	yes	complemented
37	#15692243	C₂²	1	2	yes	complemented
38	#15692243	C₂²	1	2	yes	complemented
39	#15692240	C₂²	1	2	yes	—
40	#15692240	C₂²	1	2	yes	—
41	#15692240	C₂²	1	2	yes	—
42	#15692240	C₂²	1	2	yes	—
43	#15692240	C₂²	1	2	yes	—
44	#15692240	C₂²	1	2	yes	—
45	#15692240	C₂²	1	2	yes	complemented
46	#15692240	C₂²	1	2	yes	complemented
47	#15692240	C₂²	1	2	yes	complemented
48	#15692240	C₂²	1	2	yes	complemented
49	#15692240	C₂²	1	2	yes	complemented
50	#15692240	C₂²	1	2	yes	complemented
51	#15692240	C₂²	1	2	yes	complemented
52	#15692238	C₂²	1	2	yes	—
53	#15692235	C₂²	1	1	yes	characteristic, complemented
54	#15692235	C₂²	1	2	yes	complemented
55	#15692234	C₂²	1	1	yes	characteristic
56	#15692233	C₂²	1	2	yes	complemented
57	#15692233	C₂²	1	2	yes	complemented
58	#15692233	C₂²	1	2	yes	complemented
59	#15692233	C₂²	1	2	yes	complemented
60	#15692233	C₂²	1	2	yes	complemented
61	#15692233	C₂²	1	2	yes	complemented
62	#15692233	C₂²	1	2	yes	complemented
63	#15692233	C₂²	1	2	yes	complemented
64	#15692232	C₂²	1	2	yes	—
65	#15692232	C₂²	1	2	yes	—
66	#15692231	C₂²	1	1	yes	characteristic, complemented
67	#15692231	C₂²	1	2	yes	complemented
68	#15692231	C₂²	1	2	yes	complemented
69	#15692231	C₂²	1	1	yes	characteristic, complemented
70	#15692230	C₂²	1	2	yes	—
71	#15692230	C₂²	1	2	yes	—
72	#15692230	C₂²	1	2	yes	—
73	#15692230	C₂²	1	2	yes	complemented
74	#15692230	C₂²	1	1	yes	characteristic, complemented
75	#15692229	C₂²	1	1	yes	characteristic
76	#15692225	C₂²	1	2	yes	—
77	#15692225	C₂²	1	2	yes	—
78	#15692220	C₂²	1	2	yes	complemented
79	C₄×D₄₀₄	C₂²	1	2	yes	complemented
80	C₄×D₄₀₄	C₂²	1	2	yes	complemented
81	#15692217	C₂²	1	2	yes	—
82	#15692217	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
84	#15692215	C₂²	1	2	yes	—
85	#15692215	C₂²	1	2	yes	—
86	#15692213	C₂²	1	1	yes	characteristic, complemented
87	#15692212	C₂²	1	2	yes	complemented
88	#15692212	C₂²	1	2	yes	complemented
89	C₂×#13108053	C₂²	1	1	yes	characteristic
90	C₄⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
91	C₄⋊C₄×D₁₀₁	C₂²	1	2	yes	complemented
92	C₄⋊C₄×D₁₀₁	C₂²	1	2	yes	complemented
93	C₂×#13108051	C₂²	1	1	yes	characteristic
94	C₂×#13108051	C₂²	1	1	yes	characteristic
95	C₂×#13108051	C₂²	1	1	yes	characteristic
96	C₂²⋊C₄×D₁₀₁	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₁₀₁	C₂²	1	2	yes	—
98	C₄⋊Q₈×C₁₀₁	C₂²	1	2	yes	complemented
99	C₄⋊Q₈×C₁₀₁	C₂²	1	2	yes	complemented
100	#125×C₁₀₁	C₂²	1	2	yes	complemented
101	#125×C₁₀₁	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
103	C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
104	C₂²⋊Q₈×C₁₀₁	C₂²	1	2	yes	—
105	#117×C₁₀₁	C₂²	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
107	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
108	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
109	#13108075	—	4	4	no	—
110	#13108075	—	4	2	no	—
111	C₂×Dic₂₀₂	C₂³	1	2	yes	—
112	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
113	C₂×Dic₂₀₂	C₂³	1	2	yes	—
114	Q₈×D₁₀₁	—	4	2	no	—
115	C₂×D₄₀₄	—	4	2	no	—
116	C₂×D₄₀₄	C₂³	1	2	yes	—
117	C₂×D₄₀₄	C₂³	1	2	yes	—
118	C₂×D₄₀₄	C₂³	1	2	yes	—
119	C₂×D₄₀₄	C₂³	1	2	yes	—
120	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
121	C₂×D₄₀₄	C₂³	1	2	yes	—
122	C₂×D₄₀₄	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
124	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
125	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₁₀₁	—	4	2	no	—
127	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
128	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
129	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
130	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
131	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
133	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
134	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
135	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
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	1	yes	characteristic
140	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
142	#13108053	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	#13108053	C₂³	1	2	yes	—
154	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
155	#13108051	C₂³	1	2	yes	—
156	#13108051	C₂³	1	2	yes	—
157	#13108051	C₂³	1	2	yes	—
158	#13108051	C₂³	1	2	yes	—
159	#13108051	C₂³	1	2	yes	—
160	#13108051	C₂³	1	2	yes	—
161	#13108051	C₂³	1	2	yes	—
162	#13108051	C₂³	1	2	yes	—
163	#13108051	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	#13108051	C₂³	1	2	yes	—
173	#13108051	C₂³	1	2	yes	—
174	#13108051	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	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
179	C₂×Q₈×C₁₀₁	C₂³	1	2	yes	—
180	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
181	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
182	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
183	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
184	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
185	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
186	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
187	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
188	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
189	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
190	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
191	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
192	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
193	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
194	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
197	C₄²×C₁₀₁	C₂³	1	2	yes	—
198	C₄²×C₁₀₁	C₂³	1	2	yes	—
199	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
200	C₂²×D₁₀₁	—	2	2	no	—
201	C₂²×D₁₀₁	—	2	2	no	—
202	C₂²×D₁₀₁	—	2	2	no	—
203	C₂²×D₁₀₁	—	4	1	no	—
204	C₂²×D₁₀₁	—	4	1	no	—
205	C₂²×D₁₀₁	—	4	1	no	—
206	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
207	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
208	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
209	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
210	Q₈×C₁₀₁	—	4	1	no	—
211	Q₈×C₁₀₁	—	4	2	no	—
212	Q₈×C₁₀₁	—	4	1	no	—
213	C₂×C₄×C₁₀₁	—	2	2	no	—
214	C₂×C₄×C₁₀₁	—	4	1	no	—
215	C₂×C₄×C₁₀₁	—	4	1	no	—
216	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
217	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
218	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
219	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
220	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
221	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
222	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
223	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
224	C₂²⋊D₁₀₁	—	2	4	no	—
225	C₂×Dic₁₀₁	—	4	1	no	—
226	C₂×Dic₁₀₁	—	4	1	no	—
227	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
228	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
229	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
230	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
231	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
232	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
233	D₄₀₄	—	2	4	no	—
234	D₄₀₄	—	2	4	no	—
235	D₄₀₄	—	4	2	no	—
236	D₄₀₄	—	4	2	no	—
237	D₄₀₄	—	4	2	no	—
238	D₄₀₄	—	4	2	no	—
239	D₄₀₄	—	4	1	no	—
240	C₄×D₁₀₁	—	2	2	no	—
241	C₄×D₁₀₁	—	2	2	no	—
242	C₄×D₁₀₁	—	2	4	no	—
243	C₄×D₁₀₁	—	4	1	no	—
244	C₄×D₁₀₁	—	4	1	no	—
245	C₄×D₁₀₁	—	4	2	no	—
246	C₄×D₁₀₁	—	4	2	no	—
247	C₄×D₁₀₁	—	4	2	no	—
248	C₄×D₁₀₁	—	4	2	no	—
249	C₄×D₁₀₁	—	4	2	no	—
250	C₄×D₁₀₁	—	4	2	no	—
251	Dic₂₀₂	—	4	1	no	—
252	Dic₂₀₂	—	4	2	no	—
253	Dic₂₀₂	—	4	2	no	—
254	C₂²×C₁₀₁	—	2	1	no	—
255	C₂²×C₁₀₁	—	2	1	no	—
256	C₂²×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
257	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
258	C₂×D₁₀₁	—	2	1	no	—
259	C₂×D₁₀₁	—	2	1	no	—
260	C₂×D₁₀₁	—	2	2	no	—
261	C₂×D₁₀₁	—	2	1	no	—
262	C₂×D₁₀₁	—	2	2	no	—
263	C₂×D₁₀₁	—	2	2	no	—
264	C₂×D₁₀₁	—	2	1	no	—
265	C₂×D₁₀₁	—	2	2	no	—
266	C₂×D₁₀₁	—	2	2	no	—
267	C₂×D₁₀₁	—	2	2	no	—
268	C₂×D₁₀₁	—	2	1	no	—
269	C₂×D₁₀₁	—	4	4	no	—
270	C₂×D₁₀₁	—	8	2	no	—
271	C₂×D₁₀₁	H(5,𝔽₂)	1	2	yes	—
272	C₄×C₁₀₁	—	2	1	no	—
273	C₄×C₁₀₁	—	2	2	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	C₄×C₁₀₁	—	2	2	no	—
280	Dic₁₀₁	—	2	2	no	—
281	Dic₁₀₁	—	2	1	no	—
282	Dic₁₀₁	—	2	1	no	—
283	Dic₁₀₁	—	2	2	no	—
284	Dic₁₀₁	—	2	2	no	—
285	Dic₁₀₁	—	2	2	no	—
286	C₂×C₁₀₁	—	2	2	no	—
287	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₁₀₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
289	C₂×C₁₀₁	#585	1	1	yes	characteristic
290	D₁₀₁	—	2	2	no	—
291	D₁₀₁	—	4	2	no	—
292	D₁₀₁	—	4	1	no	—
293	D₁₀₁	—	4	2	no	—
294	#3535	—	101	1	no	maximal, Sylow
295	C₁₀₁	#3535	1	1	yes	characteristic, complemented, Sylow
296	#563	—	101	2	no	—
297	#562	—	101	2	no	—
298	#554	—	101	2	no	—
299	#552	—	101	2	no	—
300	#551	—	101	2	no	—
301	#551	—	101	2	no	—
302	#547	—	101	2	no	—
303	#546	—	101	2	no	—
304	#544	D₁₀₁	1	1	yes	characteristic, complemented
305	#543	—	101	1	no	—
306	#542	—	101	2	no	—
307	#539	—	101	2	no	—
308	#539	—	101	2	no	—
309	#539	—	101	1	no	—
310	#538	—	101	1	no	—
311	#536	—	101	2	no	—
312	#525	—	101	1	no	—
313	C₂×#123	—	101	1	no	—
314	C₂×C₂²⋊Q₈	—	101	1	no	—
315	C₂×#41	—	101	2	no	—
316	C₂×#41	—	101	1	no	—
317	C₂²×Q₈	—	101	1	no	—
318	C₂²×D₄	—	101	1	no	—
319	C₂³×C₄	—	101	1	no	—
320	C₄⋊Q₈	—	101	2	no	—
321	C₄⋊Q₈	C₂×D₁₀₁	1	2	yes	complemented
322	C₄⋊Q₈	C₂×D₁₀₁	1	2	yes	complemented
323	#126	—	101	2	no	—
324	#126	—	101	2	no	—
325	#126	—	101	2	no	—
326	#126	—	101	2	no	—
327	#126	—	101	2	no	—
328	#126	—	101	2	no	—
329	#125	—	101	2	no	—
330	#125	—	101	2	no	—
331	#125	—	101	2	no	—
332	#125	C₂×D₁₀₁	1	2	yes	complemented
333	#125	C₂×D₁₀₁	1	2	yes	complemented
334	#124	—	101	2	no	—
335	#124	—	101	2	no	—
336	#124	—	101	2	no	—
337	#124	—	101	2	no	—
338	#123	—	101	2	no	—
339	#123	—	101	2	no	—
340	#123	—	101	2	no	—
341	#123	—	101	2	no	—
342	#123	—	101	2	no	—
343	#123	—	101	2	no	—
344	#123	—	101	2	no	—
345	#123	—	101	2	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	2	no	—
352	C₂²⋊Q₈	—	101	1	no	—
353	C₂²⋊Q₈	—	101	1	no	—
354	C₂²⋊Q₈	—	101	2	no	—
355	C₂²⋊Q₈	—	101	2	no	—
356	C₂²⋊Q₈	—	101	1	no	—
357	C₂²⋊Q₈	—	101	1	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	C₂²⋊Q₈	—	101	2	no	—
365	C₂²⋊Q₈	—	101	2	no	—
366	C₂²⋊Q₈	—	101	2	no	—
367	C₂²⋊Q₈	—	101	2	no	—
368	C₂²⋊Q₈	—	101	2	no	—
369	C₂²⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic
370	C₂²⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic
371	C₂²⋊Q₈	C₂×D₁₀₁	1	2	yes	—
372	#121	—	101	1	no	—
373	#121	—	101	1	no	—
374	#121	—	101	2	no	—
375	#121	—	101	2	no	—
376	#121	—	101	2	no	—
377	#121	—	101	2	no	—
378	#120	—	101	2	no	—
379	#120	—	101	2	no	—
380	C₄×Q₈	—	101	2	no	—
381	C₄×D₄	—	101	2	no	—
382	C₄×D₄	—	101	2	no	—
383	C₄×D₄	—	101	2	no	—
384	C₄×D₄	—	101	2	no	—
385	C₄×D₄	—	101	2	no	—
386	C₄×D₄	—	101	2	no	—
387	C₄×D₄	—	101	2	no	—
388	#117	—	101	1	no	—
389	#117	—	101	2	no	—
390	#117	—	101	2	no	—
391	#117	C₂×D₁₀₁	1	2	yes	—
392	C₂×C₄⋊C₄	—	101	1	no	—
393	C₂×C₄⋊C₄	—	101	1	no	—
394	C₂×C₄⋊C₄	—	101	2	no	—
395	C₂×C₄⋊C₄	—	101	2	no	—
396	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	—	101	1	no	—
398	C₂×C₂²⋊C₄	—	101	1	no	—
399	C₂×C₂²⋊C₄	—	101	1	no	—
400	C₂×C₂²⋊C₄	—	101	2	no	—
401	C₂×C₂²⋊C₄	—	101	2	no	—
402	C₂⁴	—	101	1	no	—
403	C₂⁴	—	101	1	no	—
404	#41	—	404	2	no	—
405	#41	—	404	4	no	—
406	C₂×Q₈	—	101	2	no	—
407	C₂×Q₈	—	101	1	no	—
408	C₂×Q₈	—	101	2	no	—
409	C₂×Q₈	—	404	2	no	—
410	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
411	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
412	C₂×Q₈	C₂²×D₁₀₁	1	2	yes	—
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	1	no	—
418	C₂×D₄	—	101	2	no	—
419	C₂×D₄	—	101	2	no	—
420	C₂×D₄	—	101	2	no	—
421	C₂×D₄	—	404	2	no	—
422	C₂²×C₄	—	101	1	no	—
423	C₂²×C₄	—	101	1	no	—
424	C₂²×C₄	—	101	2	no	—
425	C₂²×C₄	—	101	2	no	—
426	C₂²×C₄	—	101	2	no	—
427	C₂²×C₄	—	101	2	no	—
428	C₂²×C₄	—	101	2	no	—
429	C₂²×C₄	—	101	2	no	—
430	C₂²×C₄	—	101	1	no	—
431	C₂²×C₄	—	101	1	no	—
432	C₂²×C₄	—	101	2	no	—
433	C₂²×C₄	—	101	1	no	—
434	C₂²×C₄	—	101	1	no	—
435	C₂²×C₄	—	404	2	no	—
436	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
437	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
438	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
439	C₄⋊C₄	—	101	2	no	—
440	C₄⋊C₄	—	101	2	no	—
441	C₄⋊C₄	—	101	2	no	—
442	C₄⋊C₄	—	101	2	no	—
443	C₄⋊C₄	—	101	2	no	—
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	1	no	—
453	C₄⋊C₄	—	101	1	no	—
454	C₄⋊C₄	—	101	2	no	—
455	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
456	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
457	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
458	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
459	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
460	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
461	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
462	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
463	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
464	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
465	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
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	—	101	2	no	—
482	C₂²⋊C₄	—	101	2	no	—
483	C₂²⋊C₄	—	101	2	no	—
484	C₂²⋊C₄	—	101	2	no	—
485	C₂²⋊C₄	—	101	2	no	—
486	C₂²⋊C₄	—	101	2	no	—
487	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
488	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
489	C₄²	—	101	2	no	—
490	C₄²	—	101	2	no	—
491	C₄²	—	101	2	no	—
492	C₄²	C₂²×D₁₀₁	1	2	yes	—
493	C₄²	C₂²×D₁₀₁	1	2	yes	—
494	C₂³	—	101	1	no	—
495	C₂³	—	101	1	no	—
496	C₂³	—	101	2	no	—
497	C₂³	—	101	2	no	—
498	C₂³	—	404	1	no	—
499	C₂³	—	404	1	no	—
500	C₂³	—	404	1	no	—
501	C₂³	—	202	2	no	—
502	C₂³	—	202	2	no	—
503	C₂³	—	202	2	no	—
504	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	404	1	no	—
509	Q₈	—	404	2	no	—
510	Q₈	—	404	2	no	—
511	D₄	—	404	2	no	—
512	D₄	—	404	1	no	—
513	D₄	—	404	2	no	—
514	D₄	—	404	2	no	—
515	D₄	—	404	2	no	—
516	D₄	—	202	4	no	—
517	D₄	—	202	4	no	—
518	D₄	—	202	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	101	2	no	—
523	C₂×C₄	—	101	1	no	—
524	C₂×C₄	—	101	2	no	—
525	C₂×C₄	—	101	2	no	—
526	C₂×C₄	—	101	2	no	—
527	C₂×C₄	—	101	1	no	—
528	C₂×C₄	—	404	1	no	—
529	C₂×C₄	—	404	1	no	—
530	C₂×C₄	—	404	2	no	—
531	C₂×C₄	—	404	2	no	—
532	C₂×C₄	—	404	2	no	—
533	C₂×C₄	—	404	2	no	—
534	C₂×C₄	—	404	2	no	—
535	C₂×C₄	—	404	2	no	—
536	C₂×C₄	—	404	1	no	—
537	C₂×C₄	—	404	1	no	—
538	C₂×C₄	—	202	2	no	—
539	C₂×C₄	—	202	2	no	—
540	C₂×C₄	—	202	4	no	—
541	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
542	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
543	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
544	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
545	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
546	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
547	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
548	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	808	2	no	—
552	C₂²	—	101	2	no	—
553	C₂²	—	404	4	no	—
554	C₂²	—	202	2	no	—
555	C₂²	—	202	1	no	—
556	C₂²	—	202	2	no	—
557	C₂²	—	202	2	no	—
558	C₂²	—	202	2	no	—
559	C₂²	—	202	1	no	—
560	C₂²	—	202	2	no	—
561	C₂²	—	202	2	no	—
562	C₂²	—	202	1	no	—
563	C₂²	—	202	1	no	—
564	C₂²	—	202	1	no	—
565	C₂²	#15692303	1	2	yes	—
566	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	202	1	no	—
576	C₄	—	202	1	no	—
577	C₄	—	202	2	no	—
578	C₄	—	202	2	no	—
579	C₄	—	202	2	no	—
580	C₄	—	202	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	404	2	no	—
583	C₂	—	404	1	no	—
584	C₂	—	404	2	no	—
585	C₂	—	202	2	no	—
586	C₂	H(5,𝔽₂)×D₁₀₁	1	1	yes	characteristic
587	C₂	C₂×#15692303	1	1	yes	characteristic
588	C₂	#20266014	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#544×C₁₀₁	C₂
hypercenter	#544	D₁₀₁
hypocenter	C₁₀₁	#3535
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #544

Complements

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

N	H ≅ G/N	type
1. #20265926	C₂	semidirect
2. #20265925	C₂	semidirect
3. #20265881	C₂	semidirect
4. #20265859	C₂	semidirect
5. #20265851	C₂	semidirect
6. #20265851	C₂	semidirect
7. #20265830	C₂	semidirect
8. #20265818	C₂	semidirect
9. #20265802	C₂	semidirect
10. #20265801	C₂	semidirect
11. #20265775	C₂	semidirect
12. #20265775	C₂	semidirect
13. #20265774	C₂	semidirect
14. #20265767	C₂	semidirect
15. #20265752	C₂	semidirect
16. #20265690	C₂	semidirect
17. C₂×#15692240	C₂	semidirect
18. C₂²⋊Q₈×D₁₀₁	C₂	semidirect
19. #544×C₁₀₁	C₂	semidirect
21. C₂×#13108075	C₂²	semidirect
22. C₂×Q₈×D₁₀₁	C₂²	semidirect
25. #15692253	C₂²	semidirect
26. #15692250	C₂²	semidirect
27. #15692250	C₂²	semidirect
28. #15692250	C₂²	semidirect
29. #15692250	C₂²	semidirect
30. #15692249	C₂²	semidirect
31. #15692249	C₂²	semidirect
32. #15692245	C₂²	semidirect
33. #15692245	C₂²	semidirect
34. #15692245	C₂²	semidirect
36. #15692244	C₂²	semidirect
37. #15692243	C₂²	semidirect
38. #15692243	C₂²	semidirect
45. #15692240	C₂²	semidirect
46. #15692240	C₂²	semidirect
47. #15692240	C₂²	semidirect
48. #15692240	C₂²	semidirect
49. #15692240	C₂²	semidirect
50. #15692240	C₂²	semidirect
51. #15692240	C₂²	semidirect
53. #15692235	C₂²	semidirect
54. #15692235	C₂²	semidirect
56. #15692233	C₂²	semidirect
57. #15692233	C₂²	semidirect
58. #15692233	C₂²	semidirect
59. #15692233	C₂²	semidirect
60. #15692233	C₂²	semidirect
61. #15692233	C₂²	semidirect
62. #15692233	C₂²	semidirect
63. #15692233	C₂²	semidirect
66. #15692231	C₂²	semidirect
67. #15692231	C₂²	semidirect
68. #15692231	C₂²	semidirect
69. #15692231	C₂²	semidirect
73. #15692230	C₂²	semidirect
74. #15692230	C₂²	semidirect
78. #15692220	C₂²	semidirect
79. C₄×D₄₀₄	C₂²	semidirect
80. C₄×D₄₀₄	C₂²	semidirect
82. #15692217	C₂²	semidirect
86. #15692213	C₂²	semidirect
87. #15692212	C₂²	semidirect
88. #15692212	C₂²	semidirect
90. C₄⋊C₄×D₁₀₁	C₂²	semidirect
91. C₄⋊C₄×D₁₀₁	C₂²	semidirect
92. C₄⋊C₄×D₁₀₁	C₂²	semidirect
98. C₄⋊Q₈×C₁₀₁	C₂²	semidirect
99. C₄⋊Q₈×C₁₀₁	C₂²	semidirect
100. #125×C₁₀₁	C₂²	semidirect
101. #125×C₁₀₁	C₂²	semidirect
295. C₁₀₁	#3535	semidirect
304. #544	D₁₀₁	semidirect
321. C₄⋊Q₈	C₂×D₁₀₁	semidirect
322. C₄⋊Q₈	C₂×D₁₀₁	semidirect
332. #125	C₂×D₁₀₁	semidirect
333. #125	C₂×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265926	2
#20265925	2
#20265881	2
#20265859	2
#20265851	2
#20265830	2
#20265818	2
#20265802	2
#20265801	2
#20265775	2
#20265774	2
#20265767	2
#20265752	2
#20265690	2
C₂×#15692240	2
C₂²⋊Q₈×D₁₀₁	2
#544×C₁₀₁	2
#3535	101