Subgroups — #27184561

Order 12928.

1012 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265806	C₂	1	1	yes	maximal, characteristic, complemented
2	#20265793	C₂	1	2	yes	maximal, complemented
3	#20265791	C₂	1	2	yes	maximal, complemented
4	#20265786	C₂	1	2	yes	maximal, complemented
5	#20265784	C₂	1	2	yes	maximal, complemented
6	#20265776	C₂	1	1	yes	maximal, characteristic, complemented
7	#20265772	C₂	1	1	yes	maximal, characteristic, complemented
8	#20265771	C₂	1	2	yes	maximal, complemented
9	#20265754	C₂	1	1	yes	maximal, characteristic
10	#20265749	C₂	1	2	yes	maximal, complemented
11	#20265731	C₂	1	2	yes	maximal, complemented
12	#20265730	C₂	1	2	yes	maximal, complemented
13	#20265711	C₂	1	1	yes	maximal, characteristic, complemented
14	#20265707	C₂	1	2	yes	maximal, complemented
15	#20265707	C₂	1	2	yes	maximal, complemented
16	#20265705	C₂	1	2	yes	maximal, complemented
17	C₄×#13108073	C₂	1	2	yes	maximal, complemented
18	C₂×C₄×Dic₂₀₂	C₂	1	1	yes	maximal, characteristic, complemented
19	#529×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13108073	C₂²	1	2	yes	—
21	C₂²×Dic₂₀₂	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	#15692247	C₂²	1	1	yes	characteristic
34	#15692246	C₂²	1	2	yes	—
35	#15692246	C₂²	1	2	yes	—
36	#15692245	C₂²	1	2	yes	—
37	#15692245	C₂²	1	2	yes	—
38	#15692245	C₂²	1	2	yes	—
39	#15692245	C₂²	1	2	yes	—
40	#15692245	C₂²	1	2	yes	—
41	#15692243	C₂²	1	1	yes	characteristic
42	#15692241	C₂²	1	2	yes	—
43	#15692241	C₂²	1	2	yes	—
44	#15692241	C₂²	1	2	yes	—
45	#15692240	C₂²	1	2	yes	—
46	#15692239	C₂²	1	2	yes	—
47	#15692239	C₂²	1	2	yes	—
48	#15692238	C₂²	1	2	yes	—
49	#15692237	C₂²	1	2	yes	—
50	#15692236	C₂²	1	2	yes	—
51	#15692236	C₂²	1	2	yes	—
52	#15692235	C₂²	1	2	yes	—
53	#15692234	C₂²	1	1	yes	characteristic
54	#15692233	C₂²	1	2	yes	—
55	#15692233	C₂²	1	2	yes	—
56	#15692233	C₂²	1	2	yes	—
57	#15692232	C₂²	1	2	yes	—
58	#15692232	C₂²	1	2	yes	—
59	#15692232	C₂²	1	2	yes	—
60	#15692232	C₂²	1	2	yes	—
61	#15692232	C₂²	1	2	yes	—
62	#15692232	C₂²	1	2	yes	—
63	#15692231	C₂²	1	2	yes	—
64	#15692229	C₂²	1	1	yes	characteristic
65	#15692228	C₂²	1	2	yes	—
66	#15692227	C₂²	1	2	yes	—
67	#15692227	C₂²	1	2	yes	—
68	C₄×Dic₂₀₂	C₂²	1	1	yes	characteristic
69	C₄×Dic₂₀₂	C₂²	1	2	yes	—
70	C₄×Dic₂₀₂	C₂²	1	2	yes	—
71	C₄×Dic₂₀₂	C₂²	1	2	yes	—
72	C₄×Dic₂₀₂	C₂²	1	2	yes	—
73	C₄×Dic₂₀₂	C₂²	1	2	yes	—
74	C₄×Dic₂₀₂	C₂²	1	2	yes	—
75	#15692220	C₂²	1	2	yes	—
76	C₄×D₄₀₄	C₂²	1	1	yes	characteristic
77	D₄×Dic₁₀₁	C₂²	1	2	yes	—
78	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
79	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
80	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
81	#15692215	C₂²	1	2	yes	—
82	#15692215	C₂²	1	2	yes	—
83	#15692214	C₂²	1	2	yes	—
84	#15692213	C₂²	1	2	yes	—
85	#15692212	C₂²	1	2	yes	—
86	#15692212	C₂²	1	2	yes	—
87	#15692211	C₂²	1	2	yes	—
88	#15692211	C₂²	1	2	yes	—
89	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
90	C₂×#13108053	C₂²	1	1	yes	characteristic
91	C₂×#13108053	C₂²	1	1	yes	characteristic
92	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	—
93	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
94	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
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	2	yes	—
104	C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
105	#117×C₁₀₁	C₂²	1	2	yes	—
106	C₂×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
107	#13108073	—	2	8	no	—
108	C₂×Dic₂₀₂	—	2	4	no	—
109	C₂×Dic₂₀₂	C₂³	1	2	yes	—
110	C₂×Dic₂₀₂	C₂³	1	2	yes	—
111	C₂×Dic₂₀₂	C₂³	1	2	yes	—
112	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
113	C₂×Dic₂₀₂	C₂³	1	2	yes	—
114	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
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	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
119	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
120	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
121	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
122	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
123	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
124	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
125	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
126	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
127	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
128	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
129	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
130	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
131	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
132	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
133	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₁₀₁	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	#13108053	C₂³	1	2	yes	—
150	#13108053	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	C₄×Dic₁₀₁	C₂³	1	2	yes	—
172	C₄×Dic₁₀₁	C₂³	1	2	yes	—
173	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
174	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
175	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
176	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
177	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
178	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
179	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
180	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
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	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
185	C₄⋊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	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
191	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
192	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
193	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
194	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
195	C₄²×C₁₀₁	C₂³	1	2	yes	—
196	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
197	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
198	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
199	Q₈×C₁₀₁	—	4	1	no	—
200	D₄×C₁₀₁	—	2	4	no	—
201	D₄×C₁₀₁	—	4	1	no	—
202	C₂×C₄×C₁₀₁	—	2	2	no	—
203	C₂×C₄×C₁₀₁	—	2	2	no	—
204	C₂×C₄×C₁₀₁	—	2	4	no	—
205	C₂×C₄×C₁₀₁	—	4	1	no	—
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	1	yes	characteristic
210	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
212	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
213	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
214	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
215	C₂²⋊D₁₀₁	—	2	4	no	—
216	C₂²⋊D₁₀₁	—	2	4	no	—
217	C₂²⋊D₁₀₁	—	4	2	no	—
218	C₂×Dic₁₀₁	—	2	2	no	—
219	C₂×Dic₁₀₁	—	2	4	no	—
220	C₂×Dic₁₀₁	—	4	2	no	—
221	C₂×Dic₁₀₁	—	4	1	no	—
222	C₂×Dic₁₀₁	—	4	1	no	—
223	C₂×Dic₁₀₁	#41	1	4	yes	—
224	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
225	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
226	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
227	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
228	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
229	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
230	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
231	D₄₀₄	—	4	1	no	—
232	C₄×D₁₀₁	—	2	4	no	—
233	C₄×D₁₀₁	—	2	4	no	—
234	C₄×D₁₀₁	—	4	2	no	—
235	Dic₂₀₂	—	2	4	no	—
236	Dic₂₀₂	—	2	4	no	—
237	Dic₂₀₂	—	2	4	no	—
238	Dic₂₀₂	—	4	1	no	—
239	Dic₂₀₂	—	4	2	no	—
240	C₂²×C₁₀₁	—	2	1	no	—
241	C₂²×C₁₀₁	—	2	1	no	—
242	C₂²×C₁₀₁	—	2	2	no	—
243	C₂²×C₁₀₁	—	2	2	no	—
244	C₂²×C₁₀₁	—	2	2	no	—
245	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
246	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
247	C₂×D₁₀₁	—	2	2	no	—
248	C₂×D₁₀₁	—	2	2	no	—
249	C₂×D₁₀₁	—	2	2	no	—
250	C₄×C₁₀₁	—	2	1	no	—
251	C₄×C₁₀₁	—	2	1	no	—
252	C₄×C₁₀₁	—	2	2	no	—
253	C₄×C₁₀₁	—	2	1	no	—
254	C₄×C₁₀₁	—	2	2	no	—
255	C₄×C₁₀₁	—	2	2	no	—
256	C₄×C₁₀₁	—	2	1	no	—
257	C₄×C₁₀₁	—	2	1	no	—
258	C₄×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
259	Dic₁₀₁	—	2	2	no	—
260	Dic₁₀₁	—	2	2	no	—
261	Dic₁₀₁	—	2	2	no	—
262	Dic₁₀₁	—	2	2	no	—
263	Dic₁₀₁	—	2	2	no	—
264	Dic₁₀₁	—	2	2	no	—
265	Dic₁₀₁	C₂×#41	1	4	yes	—
266	C₂×C₁₀₁	—	2	2	no	—
267	C₂×C₁₀₁	—	4	2	no	—
268	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
269	C₂×C₁₀₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
270	C₂×C₁₀₁	#585	1	1	yes	characteristic
271	D₁₀₁	—	4	2	no	—
272	#3461	—	101	1	no	maximal, Sylow
273	C₁₀₁	#3461	1	1	yes	characteristic, complemented, Sylow
274	#544	—	101	1	no	—
275	#542	—	101	2	no	—
276	#542	—	101	2	no	—
277	#541	—	101	2	no	—
278	#541	—	101	2	no	—
279	#539	—	101	2	no	—
280	#539	—	101	1	no	—
281	#539	—	101	1	no	—
282	#537	—	101	1	no	—
283	#536	—	101	2	no	—
284	#533	—	101	2	no	—
285	#533	—	101	2	no	—
286	#529	—	101	2	no	—
287	#529	—	101	2	no	—
288	#529	—	101	2	no	—
289	#529	—	101	1	no	—
290	#529	D₁₀₁	1	1	yes	characteristic, complemented
291	C₄×#41	—	101	2	no	—
292	C₂×C₄×Q₈	—	101	1	no	—
293	C₂×#41	—	101	2	no	—
294	C₂²×Q₈	—	101	1	no	—
295	C₄⋊Q₈	—	101	2	no	—
296	C₄⋊Q₈	—	101	2	no	—
297	C₄⋊Q₈	—	101	2	no	—
298	C₄⋊Q₈	—	101	2	no	—
299	#126	—	101	2	no	—
300	#126	—	101	2	no	—
301	#126	—	101	2	no	—
302	#126	—	101	2	no	—
303	#126	—	101	2	no	—
304	#126	—	101	2	no	—
305	#126	—	101	2	no	—
306	#126	C₂×D₁₀₁	1	2	yes	—
307	#125	—	101	2	no	—
308	#125	—	101	2	no	—
309	#125	—	101	2	no	—
310	#125	—	101	2	no	—
311	#125	—	101	2	no	—
312	#125	—	101	2	no	—
313	#125	—	101	2	no	—
314	#125	—	101	1	no	—
315	#125	C₂×D₁₀₁	1	1	yes	characteristic
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	C₂×D₁₀₁	1	2	yes	—
329	C₂²⋊Q₈	—	101	2	no	—
330	C₂²⋊Q₈	—	101	1	no	—
331	C₂²⋊Q₈	—	101	2	no	—
332	C₂²⋊Q₈	—	101	2	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	C₂×D₁₀₁	1	1	yes	characteristic
342	#121	—	101	2	no	—
343	#121	—	101	2	no	—
344	#121	—	101	1	no	—
345	#121	—	101	2	no	—
346	#121	C₂×D₁₀₁	1	1	yes	characteristic
347	C₄×Q₈	—	101	2	no	—
348	C₄×Q₈	—	101	2	no	—
349	C₄×Q₈	—	101	2	no	—
350	C₄×Q₈	—	101	2	no	—
351	C₄×Q₈	—	101	2	no	—
352	C₄×Q₈	—	101	2	no	—
353	C₄×Q₈	—	101	2	no	—
354	C₄×Q₈	—	101	1	no	—
355	C₄×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
356	C₄×D₄	—	101	2	no	—
357	C₄×D₄	—	101	2	no	—
358	C₄×D₄	—	101	2	no	—
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	2	no	—
367	#117	—	101	2	no	—
368	#117	—	101	2	no	—
369	#117	—	101	2	no	—
370	#117	—	101	2	no	—
371	#117	C₂×D₁₀₁	1	2	yes	—
372	C₂×C₄⋊C₄	—	101	1	no	—
373	C₂×C₄⋊C₄	—	101	1	no	—
374	C₂×C₄⋊C₄	—	101	1	no	—
375	C₂×C₄²	—	101	1	no	—
376	C₂×C₄²	—	101	1	no	—
377	C₂×C₄²	—	101	2	no	—
378	C₂×C₄²	—	101	2	no	—
379	C₂×C₄²	C₂×D₁₀₁	1	1	yes	characteristic
380	#41	—	202	8	no	—
381	C₂×Q₈	—	101	1	no	—
382	C₂×Q₈	—	101	2	no	—
383	C₂×Q₈	—	101	2	no	—
384	C₂×Q₈	—	101	2	no	—
385	C₂×Q₈	—	101	2	no	—
386	C₂×Q₈	—	202	4	no	—
387	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
388	C₂×D₄	—	101	2	no	—
389	C₂×D₄	—	101	2	no	—
390	C₂×D₄	—	101	2	no	—
391	C₂×D₄	—	101	1	no	—
392	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
393	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
394	C₂²×C₄	—	101	1	no	—
395	C₂²×C₄	—	101	1	no	—
396	C₂²×C₄	—	101	1	no	—
397	C₂²×C₄	—	101	2	no	—
398	C₂²×C₄	—	101	1	no	—
399	C₂²×C₄	—	101	2	no	—
400	C₂²×C₄	—	101	2	no	—
401	C₂²×C₄	—	101	2	no	—
402	C₂²×C₄	—	101	2	no	—
403	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
404	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
405	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
406	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
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	2	no	—
413	C₄⋊C₄	—	101	2	no	—
414	C₄⋊C₄	—	101	2	no	—
415	C₄⋊C₄	—	101	2	no	—
416	C₄⋊C₄	—	101	2	no	—
417	C₄⋊C₄	—	101	2	no	—
418	C₄⋊C₄	—	101	2	no	—
419	C₄⋊C₄	—	101	2	no	—
420	C₄⋊C₄	—	101	2	no	—
421	C₄⋊C₄	—	101	2	no	—
422	C₄⋊C₄	—	101	2	no	—
423	C₄⋊C₄	—	101	2	no	—
424	C₄⋊C₄	—	101	2	no	—
425	C₄⋊C₄	—	101	2	no	—
426	C₄⋊C₄	—	101	2	no	—
427	C₄⋊C₄	—	101	2	no	—
428	C₄⋊C₄	—	101	1	no	—
429	C₄⋊C₄	—	101	1	no	—
430	C₄⋊C₄	—	101	2	no	—
431	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
432	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
433	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
434	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
435	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
436	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
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	—	101	2	no	—
445	C₂²⋊C₄	—	101	2	no	—
446	C₂²⋊C₄	—	101	2	no	—
447	C₂²⋊C₄	—	101	2	no	—
448	C₂²⋊C₄	—	101	2	no	—
449	C₂²⋊C₄	—	101	2	no	—
450	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
451	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
452	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
453	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
454	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
455	C₄²	—	101	2	no	—
456	C₄²	—	101	2	no	—
457	C₄²	—	101	2	no	—
458	C₄²	—	101	2	no	—
459	C₄²	—	101	2	no	—
460	C₄²	—	101	2	no	—
461	C₄²	—	101	2	no	—
462	C₄²	—	101	2	no	—
463	C₄²	—	101	2	no	—
464	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
465	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
466	C₄²	C₂²×D₁₀₁	1	2	yes	—
467	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
468	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
469	C₂³	—	101	2	no	—
470	C₂³	C₂³×D₁₀₁	1	2	yes	—
471	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
472	Q₈	—	4	1	no	—
473	Q₈	—	404	1	no	—
474	Q₈	—	404	2	no	—
475	Q₈	—	202	4	no	—
476	Q₈	—	202	4	no	—
477	Q₈	—	202	4	no	—
478	D₄	—	2	4	no	—
479	D₄	—	4	1	no	—
480	D₄	—	404	1	no	—
481	D₄	—	404	2	no	—
482	D₄	—	202	4	no	—
483	D₄	—	202	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	101	4	no	—
489	C₂×C₄	—	101	2	no	—
490	C₂×C₄	—	101	2	no	—
491	C₂×C₄	—	101	2	no	—
492	C₂×C₄	—	101	2	no	—
493	C₂×C₄	—	101	2	no	—
494	C₂×C₄	—	101	2	no	—
495	C₂×C₄	—	101	2	no	—
496	C₂×C₄	—	404	2	no	—
497	C₂×C₄	—	404	1	no	—
498	C₂×C₄	—	404	2	no	—
499	C₂×C₄	—	404	1	no	—
500	C₂×C₄	—	202	4	no	—
501	C₂×C₄	—	202	4	no	—
502	C₂×C₄	—	202	2	no	—
503	C₂×C₄	—	202	4	no	—
504	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
505	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
506	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
507	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
508	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
509	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
510	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
511	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
512	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	202	2	no	—
519	C₂²	—	202	2	no	—
520	C₂²	—	202	2	no	—
521	C₂²	#41×D₁₀₁	1	2	yes	—
522	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	1	no	—
530	C₄	—	2	2	no	—
531	C₄	—	101	4	no	—
532	C₄	—	202	2	no	—
533	C₄	—	202	2	no	—
534	C₄	—	202	2	no	—
535	C₄	—	202	2	no	—
536	C₄	—	202	2	no	—
537	C₄	—	202	2	no	—
538	C₄	#15692302	1	2	yes	—
539	C₂	—	2	2	no	—
540	C₂	—	4	2	no	—
541	C₂	—	404	2	no	—
542	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
543	C₂	C₂×#15692302	1	1	yes	characteristic
544	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
prime radical	#20265754	C₂
hypercenter	#529	D₁₀₁
hypocenter	C₁₀₁	#3461
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. #20265806	C₂	semidirect
2. #20265793	C₂	semidirect
3. #20265791	C₂	semidirect
4. #20265786	C₂	semidirect
5. #20265784	C₂	semidirect
6. #20265776	C₂	semidirect
7. #20265772	C₂	semidirect
8. #20265771	C₂	semidirect
10. #20265749	C₂	semidirect
11. #20265731	C₂	semidirect
12. #20265730	C₂	semidirect
13. #20265711	C₂	semidirect
14. #20265707	C₂	semidirect
15. #20265707	C₂	semidirect
16. #20265705	C₂	semidirect
17. C₄×#13108073	C₂	semidirect
18. C₂×C₄×Dic₂₀₂	C₂	semidirect
19. #529×C₁₀₁	C₂	semidirect
273. C₁₀₁	#3461	semidirect
290. #529	D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265806	2
#20265793	2
#20265791	2
#20265786	2
#20265784	2
#20265776	2
#20265772	2
#20265771	2
#20265754	2
#20265749	2
#20265731	2
#20265730	2
#20265711	2
#20265707	2
#20265705	2
C₄×#13108073	2
C₂×C₄×Dic₂₀₂	2
#529×C₁₀₁	2
#3461	101