Subgroups — #27185277

Order 12928.

930 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
2	#20265931	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265930	C₂	1	2	yes	maximal, complemented
4	#20265929	C₂	1	2	yes	maximal, complemented
5	#20265929	C₂	1	2	yes	maximal, complemented
6	#20265928	C₂	1	2	yes	maximal, complemented
7	#20265927	C₂	1	1	yes	maximal, characteristic, complemented
8	#20265924	C₂	1	2	yes	maximal, complemented
9	#20265922	C₂	1	2	yes	maximal, complemented
10	#20265921	C₂	1	1	yes	maximal, characteristic, complemented
11	#20265734	C₂	1	1	yes	maximal, characteristic, complemented
12	#20265731	C₂	1	2	yes	maximal, complemented
13	#20265730	C₂	1	2	yes	maximal, complemented
14	#20265711	C₂	1	1	yes	maximal, characteristic, complemented
15	#20265709	C₂	1	2	yes	maximal, complemented
16	#20265707	C₂	1	2	yes	maximal, complemented
17	#20265707	C₂	1	2	yes	maximal, complemented
18	#20265705	C₂	1	2	yes	maximal, complemented
19	#529×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
20	#15692255	C₂²	1	1	yes	characteristic
21	#15692255	C₂²	1	1	yes	characteristic
22	#15692254	C₂²	1	2	yes	—
23	#15692254	C₂²	1	2	yes	—
24	#15692254	C₂²	1	2	yes	—
25	#15692253	C₂²	1	2	yes	—
26	#15692250	C₂²	1	2	yes	—
27	#15692250	C₂²	1	2	yes	—
28	#15692250	C₂²	1	2	yes	—
29	#15692249	C₂²	1	2	yes	—
30	#15692248	C₂²	1	2	yes	—
31	#15692248	C₂²	1	2	yes	—
32	#15692248	C₂²	1	2	yes	—
33	#15692248	C₂²	1	2	yes	—
34	#15692248	C₂²	1	2	yes	—
35	#15692247	C₂²	1	1	yes	characteristic
36	#15692247	C₂²	1	1	yes	characteristic
37	#15692247	C₂²	1	1	yes	characteristic
38	#15692246	C₂²	1	2	yes	—
39	#15692246	C₂²	1	2	yes	—
40	#15692246	C₂²	1	2	yes	—
41	#15692245	C₂²	1	2	yes	—
42	#15692245	C₂²	1	2	yes	—
43	#15692245	C₂²	1	2	yes	—
44	#15692245	C₂²	1	2	yes	—
45	#15692245	C₂²	1	2	yes	—
46	#15692243	C₂²	1	1	yes	characteristic
47	#15692242	C₂²	1	2	yes	—
48	#15692241	C₂²	1	2	yes	—
49	#15692241	C₂²	1	2	yes	—
50	#15692241	C₂²	1	2	yes	—
51	#15692240	C₂²	1	2	yes	—
52	#15692239	C₂²	1	2	yes	—
53	#15692239	C₂²	1	2	yes	—
54	#15692238	C₂²	1	2	yes	—
55	#15692237	C₂²	1	2	yes	—
56	#15692237	C₂²	1	2	yes	—
57	#15692237	C₂²	1	2	yes	—
58	#15692236	C₂²	1	2	yes	—
59	#15692236	C₂²	1	2	yes	—
60	#15692235	C₂²	1	2	yes	—
61	#15692235	C₂²	1	2	yes	—
62	#15692234	C₂²	1	2	yes	—
63	#15692234	C₂²	1	2	yes	—
64	#15692234	C₂²	1	1	yes	characteristic
65	#15692233	C₂²	1	2	yes	—
66	#15692233	C₂²	1	2	yes	—
67	#15692233	C₂²	1	2	yes	—
68	#15692232	C₂²	1	2	yes	—
69	#15692232	C₂²	1	2	yes	—
70	#15692232	C₂²	1	2	yes	—
71	#15692232	C₂²	1	2	yes	—
72	#15692232	C₂²	1	2	yes	—
73	#15692232	C₂²	1	2	yes	—
74	#15692231	C₂²	1	2	yes	—
75	#15692229	C₂²	1	1	yes	characteristic
76	#15692228	C₂²	1	2	yes	—
77	#15692227	C₂²	1	2	yes	—
78	#15692227	C₂²	1	2	yes	—
79	#15692226	C₂²	1	2	yes	—
80	C₄×Dic₂₀₂	C₂²	1	1	yes	characteristic
81	C₄×Dic₂₀₂	C₂²	1	2	yes	—
82	C₄×Dic₂₀₂	C₂²	1	2	yes	—
83	C₄×Dic₂₀₂	C₂²	1	2	yes	—
84	C₄×Dic₂₀₂	C₂²	1	2	yes	—
85	C₄×D₄₀₄	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
87	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
88	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
89	#15692214	C₂²	1	2	yes	—
90	#15692214	C₂²	1	1	yes	characteristic
91	#15692214	C₂²	1	1	yes	characteristic
92	#15692212	C₂²	1	2	yes	—
93	#15692212	C₂²	1	2	yes	—
94	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	—
95	C₄²×D₁₀₁	C₂²	1	2	yes	—
96	#126×C₁₀₁	C₂²	1	2	yes	—
97	#125×C₁₀₁	C₂²	1	1	yes	characteristic
98	#124×C₁₀₁	C₂²	1	1	yes	characteristic
99	#123×C₁₀₁	C₂²	1	2	yes	—
100	C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
101	#121×C₁₀₁	C₂²	1	1	yes	characteristic
102	C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
103	C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
105	#117×C₁₀₁	C₂²	1	2	yes	—
106	C₂×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
107	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
108	C₂×Dic₂₀₂	C₂³	1	2	yes	—
109	C₂×Dic₂₀₂	C₂³	1	2	yes	—
110	C₂×Dic₂₀₂	C₂³	1	2	yes	—
111	C₂×Dic₂₀₂	C₂³	1	2	yes	—
112	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
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	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
117	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
118	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
119	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
120	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
121	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
122	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
123	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
124	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
125	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
126	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
127	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
128	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
129	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
130	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
131	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
132	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
133	#13108053	C₂³	1	2	yes	—
134	#13108053	C₂³	1	2	yes	—
135	#13108053	C₂³	1	2	yes	—
136	#13108053	C₂³	1	2	yes	—
137	#13108053	C₂³	1	2	yes	—
138	#13108053	C₂³	1	2	yes	—
139	#13108053	C₂³	1	2	yes	—
140	#13108053	C₂³	1	2	yes	—
141	#13108053	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	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
150	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
151	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
152	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
153	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
154	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
155	C₂²⋊Dic₁₀₁	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	C₄×Dic₁₀₁	C₂³	1	2	yes	—
165	C₄×Dic₁₀₁	C₂³	1	2	yes	—
166	C₄×Dic₁₀₁	C₂³	1	2	yes	—
167	C₄×Dic₁₀₁	C₂³	1	2	yes	—
168	C₄×Dic₁₀₁	C₂³	1	2	yes	—
169	C₄×Dic₁₀₁	C₂³	1	2	yes	—
170	C₄×Dic₁₀₁	C₂³	1	2	yes	—
171	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
172	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
173	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
174	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
175	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
176	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
177	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
179	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
180	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
182	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
183	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
189	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
190	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
191	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
192	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
193	C₄²×C₁₀₁	C₂³	1	2	yes	—
194	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
195	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
196	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
197	Q₈×C₁₀₁	—	4	1	no	—
198	D₄×C₁₀₁	—	4	2	no	—
199	D₄×C₁₀₁	—	4	1	no	—
200	C₂×C₄×C₁₀₁	—	2	2	no	—
201	C₂×C₄×C₁₀₁	—	2	4	no	—
202	C₂×C₄×C₁₀₁	—	4	1	no	—
203	C₂×C₄×C₁₀₁	—	4	1	no	—
204	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
205	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
206	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
207	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
208	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
209	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
210	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
211	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
212	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
213	C₂²⋊D₁₀₁	—	4	2	no	—
214	C₂²⋊D₁₀₁	—	4	2	no	—
215	C₂²⋊D₁₀₁	—	4	2	no	—
216	C₂×Dic₁₀₁	—	4	2	no	—
217	C₂×Dic₁₀₁	—	4	2	no	—
218	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
219	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
220	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
221	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
222	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
223	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
224	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
225	D₄₀₄	—	4	1	no	—
226	C₄×D₁₀₁	—	2	4	no	—
227	C₄×D₁₀₁	—	4	2	no	—
228	C₄×D₁₀₁	—	4	2	no	—
229	Dic₂₀₂	—	4	2	no	—
230	Dic₂₀₂	—	4	2	no	—
231	Dic₂₀₂	—	4	1	no	—
232	Dic₂₀₂	—	4	2	no	—
233	Dic₂₀₂	—	4	2	no	—
234	C₂²×C₁₀₁	—	2	2	no	—
235	C₂²×C₁₀₁	—	2	1	no	—
236	C₂²×C₁₀₁	—	2	2	no	—
237	C₂²×C₁₀₁	—	2	2	no	—
238	C₂²×C₁₀₁	—	2	1	no	—
239	C₂²×C₁₀₁	—	2	1	no	—
240	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
241	C₂×D₁₀₁	—	2	2	no	—
242	C₂×D₁₀₁	—	2	2	no	—
243	C₂×D₁₀₁	—	2	2	no	—
244	C₄×C₁₀₁	—	2	1	no	—
245	C₄×C₁₀₁	—	2	2	no	—
246	C₄×C₁₀₁	—	2	1	no	—
247	C₄×C₁₀₁	—	2	1	no	—
248	C₄×C₁₀₁	—	2	2	no	—
249	C₄×C₁₀₁	—	2	2	no	—
250	C₄×C₁₀₁	—	2	1	no	—
251	C₄×C₁₀₁	—	2	1	no	—
252	C₄×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
253	Dic₁₀₁	—	2	2	no	—
254	Dic₁₀₁	—	2	2	no	—
255	Dic₁₀₁	—	2	2	no	—
256	Dic₁₀₁	—	2	2	no	—
257	Dic₁₀₁	—	2	2	no	—
258	Dic₁₀₁	—	2	2	no	—
259	Dic₁₀₁	—	2	2	no	—
260	C₂×C₁₀₁	—	4	2	no	—
261	C₂×C₁₀₁	—	4	1	no	—
262	C₂×C₁₀₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
263	C₂×C₁₀₁	#585	1	1	yes	characteristic
264	C₂×C₁₀₁	#585	1	1	yes	characteristic
265	D₁₀₁	—	4	2	no	—
266	#3531	—	101	1	no	maximal, Sylow
267	C₁₀₁	#3531	1	1	yes	characteristic, complemented, Sylow
268	#564	—	101	1	no	—
269	#563	—	101	2	no	—
270	#563	—	101	2	no	—
271	#563	—	101	1	no	—
272	#563	—	101	1	no	—
273	#563	—	101	2	no	—
274	#563	—	101	2	no	—
275	#562	—	101	1	no	—
276	#562	—	101	2	no	—
277	#562	—	101	2	no	—
278	#533	—	101	2	no	—
279	#533	—	101	2	no	—
280	#533	—	101	1	no	—
281	#529	—	101	2	no	—
282	#529	—	101	2	no	—
283	#529	—	101	2	no	—
284	#529	—	101	2	no	—
285	#529	—	101	1	no	—
286	#529	D₁₀₁	1	1	yes	characteristic, complemented
287	C₄⋊Q₈	—	101	2	no	—
288	C₄⋊Q₈	—	101	2	no	—
289	C₄⋊Q₈	—	101	2	no	—
290	C₄⋊Q₈	—	101	2	no	—
291	C₄⋊Q₈	—	101	1	no	—
292	C₄⋊Q₈	—	101	1	no	—
293	#126	—	101	2	no	—
294	#126	—	101	2	no	—
295	#126	—	101	2	no	—
296	#126	—	101	2	no	—
297	#126	—	101	2	no	—
298	#126	—	101	2	no	—
299	#126	—	101	2	no	—
300	#126	—	101	2	no	—
301	#126	—	101	2	no	—
302	#126	C₂×D₁₀₁	1	2	yes	—
303	#125	—	101	2	no	—
304	#125	—	101	2	no	—
305	#125	—	101	2	no	—
306	#125	—	101	2	no	—
307	#125	—	101	2	no	—
308	#125	—	101	2	no	—
309	#125	—	101	2	no	—
310	#125	—	101	2	no	—
311	#125	—	101	1	no	—
312	#125	—	101	1	no	—
313	#125	—	101	1	no	—
314	#125	C₂×D₁₀₁	1	1	yes	characteristic
315	#124	—	101	2	no	—
316	#124	—	101	2	no	—
317	#124	—	101	2	no	—
318	#124	—	101	2	no	—
319	#124	—	101	1	no	—
320	#124	C₂×D₁₀₁	1	1	yes	characteristic
321	#123	—	101	2	no	—
322	#123	—	101	2	no	—
323	#123	—	101	2	no	—
324	#123	—	101	2	no	—
325	#123	—	101	2	no	—
326	#123	—	101	2	no	—
327	#123	—	101	2	no	—
328	#123	—	101	2	no	—
329	#123	—	101	2	no	—
330	#123	C₂×D₁₀₁	1	2	yes	—
331	C₂²⋊Q₈	—	101	2	no	—
332	C₂²⋊Q₈	—	101	1	no	—
333	C₂²⋊Q₈	—	101	2	no	—
334	C₂²⋊Q₈	—	101	2	no	—
335	C₂²⋊Q₈	—	101	2	no	—
336	C₂²⋊Q₈	—	101	2	no	—
337	C₂²⋊Q₈	—	101	2	no	—
338	C₂²⋊Q₈	—	101	2	no	—
339	C₂²⋊Q₈	—	101	2	no	—
340	C₂²⋊Q₈	—	101	2	no	—
341	C₂²⋊Q₈	—	101	2	no	—
342	C₂²⋊Q₈	—	101	2	no	—
343	C₂²⋊Q₈	—	101	2	no	—
344	C₂²⋊Q₈	—	101	2	no	—
345	C₂²⋊Q₈	—	101	2	no	—
346	C₂²⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic
347	#121	—	101	2	no	—
348	#121	—	101	2	no	—
349	#121	—	101	2	no	—
350	#121	—	101	1	no	—
351	#121	—	101	2	no	—
352	#121	C₂×D₁₀₁	1	1	yes	characteristic
353	C₄×Q₈	—	101	2	no	—
354	C₄×Q₈	—	101	2	no	—
355	C₄×Q₈	—	101	2	no	—
356	C₄×Q₈	—	101	2	no	—
357	C₄×Q₈	—	101	1	no	—
358	C₄×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
359	C₄×D₄	—	101	2	no	—
360	C₄×D₄	—	101	2	no	—
361	C₄×D₄	—	101	2	no	—
362	C₄×D₄	—	101	1	no	—
363	C₄×D₄	C₂×D₁₀₁	1	2	yes	—
364	C₄×D₄	C₂×D₁₀₁	1	1	yes	characteristic
365	#117	—	101	2	no	—
366	#117	—	101	1	no	—
367	#117	—	101	1	no	—
368	#117	—	101	2	no	—
369	#117	—	101	2	no	—
370	#117	C₂×D₁₀₁	1	2	yes	—
371	C₂×C₄²	—	101	2	no	—
372	C₂×C₄²	—	101	2	no	—
373	C₂×C₄²	C₂×D₁₀₁	1	1	yes	characteristic
374	C₂×Q₈	—	101	2	no	—
375	C₂×Q₈	—	101	1	no	—
376	C₂×Q₈	—	101	2	no	—
377	C₂×Q₈	—	101	2	no	—
378	C₂×Q₈	—	101	2	no	—
379	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
380	C₂×D₄	—	101	2	no	—
381	C₂×D₄	—	101	2	no	—
382	C₂×D₄	—	101	2	no	—
383	C₂×D₄	—	101	1	no	—
384	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
385	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
386	C₂²×C₄	—	101	2	no	—
387	C₂²×C₄	—	101	2	no	—
388	C₂²×C₄	—	101	2	no	—
389	C₂²×C₄	—	101	2	no	—
390	C₂²×C₄	—	101	2	no	—
391	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
392	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
393	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
394	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
395	C₄⋊C₄	—	101	2	no	—
396	C₄⋊C₄	—	101	2	no	—
397	C₄⋊C₄	—	101	2	no	—
398	C₄⋊C₄	—	101	2	no	—
399	C₄⋊C₄	—	101	2	no	—
400	C₄⋊C₄	—	101	2	no	—
401	C₄⋊C₄	—	101	2	no	—
402	C₄⋊C₄	—	101	2	no	—
403	C₄⋊C₄	—	101	2	no	—
404	C₄⋊C₄	—	101	2	no	—
405	C₄⋊C₄	—	101	2	no	—
406	C₄⋊C₄	—	101	2	no	—
407	C₄⋊C₄	—	101	2	no	—
408	C₄⋊C₄	—	101	2	no	—
409	C₄⋊C₄	—	101	2	no	—
410	C₄⋊C₄	—	101	2	no	—
411	C₄⋊C₄	—	101	2	no	—
412	C₄⋊C₄	—	101	1	no	—
413	C₄⋊C₄	—	101	1	no	—
414	C₄⋊C₄	—	101	2	no	—
415	C₄⋊C₄	—	101	1	no	—
416	C₄⋊C₄	—	101	1	no	—
417	C₄⋊C₄	—	101	1	no	—
418	C₄⋊C₄	—	101	2	no	—
419	C₄⋊C₄	—	101	1	no	—
420	C₄⋊C₄	—	101	2	no	—
421	C₄⋊C₄	—	101	2	no	—
422	C₄⋊C₄	—	101	2	no	—
423	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
424	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
425	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
426	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
427	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
428	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
429	C₂²⋊C₄	—	101	2	no	—
430	C₂²⋊C₄	—	101	2	no	—
431	C₂²⋊C₄	—	101	2	no	—
432	C₂²⋊C₄	—	101	2	no	—
433	C₂²⋊C₄	—	101	2	no	—
434	C₂²⋊C₄	—	101	2	no	—
435	C₂²⋊C₄	—	101	2	no	—
436	C₂²⋊C₄	—	101	2	no	—
437	C₂²⋊C₄	—	101	2	no	—
438	C₂²⋊C₄	—	101	2	no	—
439	C₂²⋊C₄	—	101	2	no	—
440	C₂²⋊C₄	—	101	2	no	—
441	C₂²⋊C₄	—	101	2	no	—
442	C₂²⋊C₄	—	101	2	no	—
443	C₂²⋊C₄	—	101	2	no	—
444	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
445	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
446	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
447	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
448	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
449	C₄²	—	101	2	no	—
450	C₄²	—	101	2	no	—
451	C₄²	—	101	2	no	—
452	C₄²	—	101	2	no	—
453	C₄²	—	101	2	no	—
454	C₄²	—	101	2	no	—
455	C₄²	—	101	2	no	—
456	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
457	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
458	C₄²	C₂²×D₁₀₁	1	2	yes	—
459	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
460	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
461	C₂³	—	101	2	no	—
462	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
463	C₂³	C₂³×D₁₀₁	1	2	yes	—
464	Q₈	—	4	1	no	—
465	Q₈	—	404	1	no	—
466	Q₈	—	404	2	no	—
467	Q₈	—	404	2	no	—
468	Q₈	—	404	2	no	—
469	Q₈	—	404	2	no	—
470	D₄	—	4	1	no	—
471	D₄	—	4	2	no	—
472	D₄	—	404	1	no	—
473	D₄	—	404	2	no	—
474	D₄	—	404	2	no	—
475	D₄	—	404	2	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	101	2	no	—
481	C₂×C₄	—	101	2	no	—
482	C₂×C₄	—	101	2	no	—
483	C₂×C₄	—	101	2	no	—
484	C₂×C₄	—	101	2	no	—
485	C₂×C₄	—	101	2	no	—
486	C₂×C₄	—	101	2	no	—
487	C₂×C₄	—	404	2	no	—
488	C₂×C₄	—	404	2	no	—
489	C₂×C₄	—	404	2	no	—
490	C₂×C₄	—	404	2	no	—
491	C₂×C₄	—	202	4	no	—
492	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
493	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
494	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
495	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
496	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
497	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
498	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
499	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
500	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
501	C₂²	—	2	1	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	202	2	no	—
508	C₂²	—	202	2	no	—
509	C₂²	—	202	2	no	—
510	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
511	C₄	—	2	2	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	202	2	no	—
520	C₄	—	202	2	no	—
521	C₄	—	202	2	no	—
522	C₄	—	202	2	no	—
523	C₄	—	202	2	no	—
524	C₄	—	202	2	no	—
525	C₄	—	202	2	no	—
526	C₄	#15692302	1	2	yes	—
527	C₂	—	4	1	no	—
528	C₂	—	4	2	no	—
529	C₂	—	404	2	no	—
530	C₂	C₂×#15692302	1	1	yes	characteristic
531	C₂	#20266013	1	1	yes	characteristic
532	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	#529×C₁₀₁	C₂
hypercenter	#529	D₁₀₁
hypocenter	C₁₀₁	#3531
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₁₀₁⋊#564	C₂	semidirect
2. #20265931	C₂	semidirect
3. #20265930	C₂	semidirect
4. #20265929	C₂	semidirect
5. #20265929	C₂	semidirect
6. #20265928	C₂	semidirect
7. #20265927	C₂	semidirect
8. #20265924	C₂	semidirect
9. #20265922	C₂	semidirect
10. #20265921	C₂	semidirect
11. #20265734	C₂	semidirect
12. #20265731	C₂	semidirect
13. #20265730	C₂	semidirect
14. #20265711	C₂	semidirect
15. #20265709	C₂	semidirect
16. #20265707	C₂	semidirect
17. #20265707	C₂	semidirect
18. #20265705	C₂	semidirect
19. #529×C₁₀₁	C₂	semidirect
267. C₁₀₁	#3531	semidirect
286. #529	D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁⋊#564	2
#20265931	2
#20265930	2
#20265929	2
#20265928	2
#20265927	2
#20265924	2
#20265922	2
#20265921	2
#20265734	2
#20265731	2
#20265730	2
#20265711	2
#20265709	2
#20265707	2
#20265705	2
#529×C₁₀₁	2
#3531	101