Subgroups — #27184773

Order 12928.

1560 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15692300	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13108073	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265827	C₂	1	4	yes	maximal, complemented
4	#20265825	C₂	1	4	yes	maximal, complemented
5	#20265816	C₂	1	4	yes	maximal, complemented
6	#20265814	C₂	1	4	yes	maximal, complemented
7	#20265749	C₂	1	2	yes	maximal, complemented
8	#20265737	C₂	1	2	yes	maximal, complemented
9	#20265736	C₂	1	1	yes	maximal, characteristic, complemented
10	#20265683	C₂	1	2	yes	maximal, complemented
11	C₂×#15692239	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15692236	C₂	1	1	yes	maximal, characteristic, complemented
13	#123×D₁₀₁	C₂	1	2	yes	maximal, complemented
14	#20265650	C₂	1	1	yes	maximal, characteristic, complemented
15	#534×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
16	#15692300	—	2	8	no	—
17	C₂×#13108074	C₂²	1	2	yes	complemented
18	C₂×#13108073	—	2	8	no	—
19	C₂×#13108073	C₂²	1	2	yes	—
20	C₂×#13108073	C₂²	1	4	yes	complemented
21	C₂×#13108073	C₂²	1	4	yes	complemented
22	C₂×#13108073	C₂²	1	2	yes	complemented
23	C₂²×Dic₂₀₂	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
28	C₂×D₄×D₁₀₁	C₂²	1	2	yes	—
29	C₂×D₄×D₁₀₁	C₂²	1	2	yes	complemented
30	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
31	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
33	#15692254	C₂²	1	4	yes	complemented
34	#15692241	C₂²	1	4	yes	complemented
35	#15692240	C₂²	1	4	yes	complemented
36	#15692239	C₂²	1	2	yes	complemented
37	#15692239	C₂²	1	4	yes	complemented
38	#15692239	C₂²	1	2	yes	complemented
39	#15692238	C₂²	1	2	yes	complemented
40	#15692237	C₂²	1	4	yes	complemented
41	#15692237	C₂²	1	4	yes	complemented
42	#15692236	C₂²	1	2	yes	complemented
43	#15692236	C₂²	1	2	yes	complemented
44	#15692236	C₂²	1	4	yes	complemented
45	#15692236	C₂²	1	2	yes	complemented
46	#15692233	C₂²	1	4	yes	complemented
47	#15692232	C₂²	1	4	yes	complemented
48	#15692232	C₂²	1	4	yes	complemented
49	#15692228	C₂²	1	4	yes	complemented
50	#15692227	C₂²	1	4	yes	complemented
51	#15692227	C₂²	1	4	yes	complemented
52	#15692226	C₂²	1	4	yes	complemented
53	#15692224	C₂²	1	2	yes	complemented
54	#15692223	C₂²	1	2	yes	complemented
55	#15692223	C₂²	1	4	yes	complemented
56	D₄×Dic₁₀₁	C₂²	1	4	yes	complemented
57	C₄×C₂²⋊D₁₀₁	C₂²	1	4	yes	complemented
58	#15692215	C₂²	1	4	yes	complemented
59	#15692215	C₂²	1	4	yes	complemented
60	#15692211	C₂²	1	2	yes	complemented
61	C₂×C₄⋊Dic₁₀₁	C₂²	1	2	yes	complemented
62	C₂×#13108053	C₂²	1	2	yes	complemented
63	C₄⋊C₄×D₁₀₁	C₂²	1	4	yes	complemented
64	C₂×C₂²⋊Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	complemented
66	C₂×#13108051	C₂²	1	2	yes	complemented
67	C₂²⋊C₄×D₁₀₁	C₂²	1	2	yes	complemented
68	C₂²⋊C₄×D₁₀₁	C₂²	1	4	yes	complemented
69	C₂²×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
70	C₂²×D₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
71	#123×C₁₀₁	C₂²	1	2	yes	complemented
72	#123×C₁₀₁	C₂²	1	2	yes	complemented
73	#121×C₁₀₁	C₂²	1	4	yes	complemented
74	#120×C₁₀₁	C₂²	1	2	yes	complemented
75	#120×C₁₀₁	C₂²	1	2	yes	complemented
76	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
77	C₂³×D₁₀₁	C₂³	1	2	yes	—
78	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
79	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
80	#13108074	—	2	8	no	—
81	#13108073	—	2	16	no	—
82	#13108073	—	2	16	no	—
83	#13108073	—	2	8	no	—
84	#13108073	—	2	8	no	—
85	C₂×Dic₂₀₂	—	2	4	no	—
86	C₂×Dic₂₀₂	C₂³	1	4	yes	—
87	C₂×Dic₂₀₂	C₂³	1	2	yes	—
88	C₂×D₄₀₄	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
90	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
91	C₂×C₂²⋊D₁₀₁	—	2	8	no	—
92	C₂×C₂²⋊D₁₀₁	D₄	1	8	yes	complemented
93	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
100	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
101	D₄×D₁₀₁	—	2	8	no	—
102	D₄×D₁₀₁	—	2	8	no	—
103	C₂²×Dic₁₀₁	—	2	4	no	—
104	C₂²×Dic₁₀₁	—	2	4	no	—
105	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
106	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
107	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
108	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
109	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
110	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
111	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
112	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
113	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
114	C₂×C₄×D₁₀₁	—	2	4	no	—
115	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
116	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
117	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
118	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
119	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
120	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
121	#13108053	C₂³	1	4	yes	—
122	#13108053	C₂³	1	4	yes	—
123	#13108053	C₂³	1	4	yes	—
124	#13108053	C₂³	1	4	yes	—
125	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
126	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
127	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
128	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
129	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
130	#13108051	C₂³	1	4	yes	—
131	#13108051	C₂³	1	4	yes	—
132	#13108051	C₂³	1	4	yes	—
133	#13108051	C₂³	1	4	yes	—
134	C₄×Dic₁₀₁	C₂³	1	4	yes	—
135	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
136	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
137	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₁₀₁	—	2	4	no	—
139	C₂×D₄×C₁₀₁	—	2	4	no	—
140	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
141	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
142	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
143	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
144	C₂×D₄×C₁₀₁	C₂³	1	4	yes	—
145	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
146	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
147	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
148	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
149	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
152	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
153	C₂³×C₁₀₁	—	2	2	no	—
154	C₂³×C₁₀₁	—	2	2	no	—
155	C₂³×C₁₀₁	—	4	2	no	—
156	C₂³×C₁₀₁	—	4	2	no	—
157	C₂³×C₁₀₁	—	4	2	no	—
158	C₂³×C₁₀₁	C₂×D₄	1	4	yes	—
159	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
160	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
161	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
162	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
163	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
164	C₂²×D₁₀₁	—	2	2	no	—
165	C₂²×D₁₀₁	—	2	4	no	—
166	C₂²×D₁₀₁	—	4	2	no	—
167	C₂²×D₁₀₁	—	4	4	no	—
168	C₂²×D₁₀₁	—	4	2	no	—
169	C₂²×D₁₀₁	C₂×D₄	1	4	yes	—
170	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
171	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
172	D₄×C₁₀₁	—	2	4	no	—
173	D₄×C₁₀₁	—	2	4	no	—
174	D₄×C₁₀₁	—	2	4	no	—
175	D₄×C₁₀₁	—	2	4	no	—
176	D₄×C₁₀₁	—	4	4	no	—
177	C₂×C₄×C₁₀₁	—	2	2	no	—
178	C₂×C₄×C₁₀₁	—	2	2	no	—
179	C₂×C₄×C₁₀₁	—	4	2	no	—
180	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
181	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
182	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
183	C₂²⋊D₁₀₁	—	2	4	no	—
184	C₂²⋊D₁₀₁	—	2	4	no	—
185	C₂²⋊D₁₀₁	—	2	4	no	—
186	C₂²⋊D₁₀₁	—	2	8	no	—
187	C₂²⋊D₁₀₁	—	2	4	no	—
188	C₂²⋊D₁₀₁	—	4	4	no	—
189	C₂²⋊D₁₀₁	C₂×D₄	1	8	yes	—
190	C₂²⋊D₁₀₁	C₂×D₄	1	8	yes	—
191	C₂×Dic₁₀₁	—	2	2	no	—
192	C₂×Dic₁₀₁	—	2	2	no	—
193	C₂×Dic₁₀₁	—	2	4	no	—
194	C₂×Dic₁₀₁	—	2	4	no	—
195	C₂×Dic₁₀₁	—	2	2	no	—
196	C₂×Dic₁₀₁	—	2	8	no	—
197	C₂×Dic₁₀₁	—	2	4	no	—
198	C₂×Dic₁₀₁	—	4	2	no	—
199	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
200	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
201	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
202	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
203	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
204	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
205	D₄₀₄	—	2	4	no	—
206	C₄×D₁₀₁	—	2	8	no	—
207	C₄×D₁₀₁	—	2	4	no	—
208	C₄×D₁₀₁	—	2	4	no	—
209	C₄×D₁₀₁	—	4	4	no	—
210	Dic₂₀₂	—	2	8	no	—
211	Dic₂₀₂	—	2	4	no	—
212	C₂²×C₁₀₁	—	2	2	no	—
213	C₂²×C₁₀₁	—	2	2	no	—
214	C₂²×C₁₀₁	—	2	2	no	—
215	C₂²×C₁₀₁	—	2	2	no	—
216	C₂²×C₁₀₁	—	2	2	no	—
217	C₂²×C₁₀₁	—	2	4	no	—
218	C₂²×C₁₀₁	—	2	4	no	—
219	C₂²×C₁₀₁	—	4	4	no	—
220	C₂²×C₁₀₁	—	4	4	no	—
221	C₂²×C₁₀₁	—	8	2	no	—
222	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
223	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
224	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
225	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
226	C₂×D₁₀₁	—	2	4	no	—
227	C₂×D₁₀₁	—	2	2	no	—
228	C₂×D₁₀₁	—	2	4	no	—
229	C₂×D₁₀₁	—	4	4	no	—
230	C₂×D₁₀₁	—	8	4	no	—
231	C₂×D₁₀₁	—	8	2	no	—
232	C₂×D₁₀₁	C₂²×D₄	1	4	yes	—
233	C₄×C₁₀₁	—	2	2	no	—
234	C₄×C₁₀₁	—	2	2	no	—
235	C₄×C₁₀₁	—	2	4	no	—
236	Dic₁₀₁	—	2	2	no	—
237	Dic₁₀₁	—	2	2	no	—
238	Dic₁₀₁	—	2	2	no	—
239	Dic₁₀₁	—	2	4	no	—
240	Dic₁₀₁	C₂²×D₄	1	4	yes	—
241	C₂×C₁₀₁	—	2	2	no	—
242	C₂×C₁₀₁	—	2	2	no	—
243	C₂×C₁₀₁	—	2	2	no	—
244	C₂×C₁₀₁	—	4	2	no	—
245	C₂×C₁₀₁	—	4	2	no	—
246	C₂×C₁₀₁	C₂³×D₄	1	1	yes	characteristic
247	C₂×C₁₀₁	#585	1	2	yes	—
248	D₁₀₁	—	2	4	no	—
249	D₁₀₁	—	4	2	no	—
250	#3485	—	101	1	no	maximal, Sylow
251	C₁₀₁	#3485	1	1	yes	characteristic, complemented, Sylow
252	C₂×H(5,𝔽₂)	—	101	1	no	—
253	C₂²×#41	—	101	1	no	—
254	#547	—	101	4	no	—
255	#547	—	101	4	no	—
256	#546	—	101	4	no	—
257	#546	—	101	4	no	—
258	#536	—	101	2	no	—
259	#534	—	101	1	no	—
260	#534	—	101	2	no	—
261	#534	D₁₀₁	1	1	yes	characteristic, complemented
262	#525	—	101	2	no	—
263	C₂×#123	—	101	1	no	—
264	C₂×#123	—	101	2	no	—
265	C₂×#123	—	101	1	no	—
266	#518	—	101	1	no	—
267	H(5,𝔽₂)	—	202	8	no	—
268	C₂×#41	—	101	2	no	—
269	C₂×#41	—	101	4	no	—
270	C₂×#41	—	101	4	no	—
271	C₂×#41	—	101	2	no	—
272	C₂×#41	—	101	2	no	—
273	C₂×#41	—	202	8	no	—
274	C₂²×Q₈	—	101	1	no	—
275	C₂²×D₄	—	101	1	no	—
276	C₂²×D₄	—	101	1	no	—
277	C₂²×D₄	—	101	1	no	—
278	C₂²×D₄	—	101	2	no	—
279	C₂²×D₄	—	101	2	no	—
280	C₂²×D₄	—	101	2	no	—
281	C₂²×D₄	C₂×D₁₀₁	1	1	yes	characteristic
282	C₂²×D₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
283	C₂³×C₄	—	101	1	no	—
284	C₂³×C₄	—	101	1	no	—
285	C₂³×C₄	—	101	1	no	—
286	C₄⋊Q₈	—	101	4	no	—
287	#124	—	101	4	no	—
288	#123	—	101	2	no	—
289	#123	—	101	2	no	—
290	#123	—	101	4	no	—
291	#123	—	101	2	no	—
292	#123	—	101	2	no	—
293	#123	—	101	4	no	—
294	#123	—	101	2	no	—
295	#123	—	101	2	no	—
296	#123	—	101	4	no	—
297	#123	—	101	4	no	—
298	#123	—	101	4	no	—
299	#123	C₂×D₁₀₁	1	2	yes	complemented
300	#123	C₂×D₁₀₁	1	2	yes	complemented
301	C₂²⋊Q₈	—	101	4	no	—
302	C₂²⋊Q₈	—	101	4	no	—
303	C₂²⋊Q₈	—	101	4	no	—
304	#121	—	101	4	no	—
305	#121	—	101	4	no	—
306	#121	—	101	4	no	—
307	#121	—	101	4	no	—
308	#121	C₂×D₁₀₁	1	4	yes	complemented
309	#120	—	101	2	no	—
310	#120	—	101	2	no	—
311	#120	—	101	4	no	—
312	#120	C₂×D₁₀₁	1	2	yes	complemented
313	#120	C₂×D₁₀₁	1	2	yes	complemented
314	C₄×D₄	—	101	4	no	—
315	C₄×D₄	—	101	4	no	—
316	C₄×D₄	—	101	4	no	—
317	C₄×D₄	—	101	4	no	—
318	#117	—	101	2	no	—
319	C₂×C₄⋊C₄	—	101	2	no	—
320	C₂×C₄⋊C₄	—	101	2	no	—
321	C₂×C₄⋊C₄	—	101	4	no	—
322	C₂×C₂²⋊C₄	—	101	1	no	—
323	C₂×C₂²⋊C₄	—	101	2	no	—
324	C₂×C₂²⋊C₄	—	101	2	no	—
325	C₂×C₂²⋊C₄	—	101	2	no	—
326	C₂×C₂²⋊C₄	—	101	4	no	—
327	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
328	C₂⁴	—	101	1	no	—
329	C₂⁴	—	101	2	no	—
330	C₂⁴	—	101	1	no	—
331	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
332	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
333	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
334	#41	—	202	8	no	—
335	#41	—	202	8	no	—
336	#41	—	202	16	no	—
337	#41	—	202	16	no	—
338	#41	—	202	8	no	—
339	C₂×Q₈	—	101	4	no	—
340	C₂×Q₈	—	101	2	no	—
341	C₂×Q₈	—	202	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	101	8	no	—
345	C₂×D₄	—	101	2	no	—
346	C₂×D₄	—	101	2	no	—
347	C₂×D₄	—	101	4	no	—
348	C₂×D₄	—	101	4	no	—
349	C₂×D₄	—	101	2	no	—
350	C₂×D₄	—	101	2	no	—
351	C₂×D₄	—	101	2	no	—
352	C₂×D₄	—	101	2	no	—
353	C₂×D₄	—	101	2	no	—
354	C₂×D₄	—	202	8	no	—
355	C₂×D₄	—	202	8	no	—
356	C₂×D₄	—	202	8	no	—
357	C₂×D₄	—	202	4	no	—
358	C₂×D₄	—	202	4	no	—
359	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
360	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
361	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
362	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
363	C₂×D₄	C₂²×D₁₀₁	1	4	yes	—
364	C₂²×C₄	—	101	1	no	—
365	C₂²×C₄	—	101	2	no	—
366	C₂²×C₄	—	101	2	no	—
367	C₂²×C₄	—	101	2	no	—
368	C₂²×C₄	—	101	1	no	—
369	C₂²×C₄	—	101	4	no	—
370	C₂²×C₄	—	101	2	no	—
371	C₂²×C₄	—	101	1	no	—
372	C₂²×C₄	—	101	1	no	—
373	C₂²×C₄	—	101	4	no	—
374	C₂²×C₄	—	101	4	no	—
375	C₂²×C₄	—	101	2	no	—
376	C₂²×C₄	—	101	2	no	—
377	C₂²×C₄	—	202	4	no	—
378	C₂²×C₄	—	202	4	no	—
379	C₂²×C₄	—	202	4	no	—
380	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
381	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
382	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
383	C₄⋊C₄	—	101	4	no	—
384	C₄⋊C₄	—	101	4	no	—
385	C₄⋊C₄	—	101	4	no	—
386	C₄⋊C₄	—	101	4	no	—
387	C₄⋊C₄	—	101	4	no	—
388	C₄⋊C₄	—	101	4	no	—
389	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
390	C₂²⋊C₄	—	101	2	no	—
391	C₂²⋊C₄	—	101	4	no	—
392	C₂²⋊C₄	—	101	2	no	—
393	C₂²⋊C₄	—	101	4	no	—
394	C₂²⋊C₄	—	101	4	no	—
395	C₂²⋊C₄	—	101	4	no	—
396	C₂²⋊C₄	—	101	4	no	—
397	C₂²⋊C₄	—	101	4	no	—
398	C₂²⋊C₄	—	101	4	no	—
399	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
400	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
401	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
402	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
403	C₄²	—	101	4	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	101	4	no	—
410	C₂³	—	101	2	no	—
411	C₂³	—	101	2	no	—
412	C₂³	—	404	2	no	—
413	C₂³	—	404	4	no	—
414	C₂³	—	404	2	no	—
415	C₂³	—	202	4	no	—
416	C₂³	—	202	2	no	—
417	C₂³	D₄×D₁₀₁	1	4	yes	—
418	C₂³	C₂³×D₁₀₁	1	2	yes	—
419	C₂³	C₂³×D₁₀₁	1	2	yes	—
420	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
421	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
422	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
423	Q₈	—	202	8	no	—
424	Q₈	—	202	4	no	—
425	D₄	—	2	4	no	—
426	D₄	—	2	4	no	—
427	D₄	—	2	4	no	—
428	D₄	—	2	4	no	—
429	D₄	—	4	4	no	—
430	D₄	—	101	8	no	—
431	D₄	—	101	8	no	—
432	D₄	—	404	4	no	—
433	D₄	—	202	4	no	—
434	D₄	—	202	4	no	—
435	D₄	—	202	4	no	—
436	D₄	—	202	8	no	—
437	D₄	—	202	4	no	—
438	D₄	—	202	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	101	4	no	—
443	C₂×C₄	—	101	2	no	—
444	C₂×C₄	—	101	4	no	—
445	C₂×C₄	—	101	2	no	—
446	C₂×C₄	—	101	2	no	—
447	C₂×C₄	—	101	2	no	—
448	C₂×C₄	—	404	4	no	—
449	C₂×C₄	—	404	2	no	—
450	C₂×C₄	—	202	4	no	—
451	C₂×C₄	—	202	8	no	—
452	C₂×C₄	—	202	4	no	—
453	C₂×C₄	—	202	8	no	—
454	C₂×C₄	—	202	4	no	—
455	C₂×C₄	—	202	2	no	—
456	C₂×C₄	—	202	2	no	—
457	C₂×C₄	—	202	4	no	—
458	C₂×C₄	—	202	4	no	—
459	C₂×C₄	—	202	2	no	—
460	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
461	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
462	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	808	2	no	—
474	C₂²	—	808	4	no	—
475	C₂²	—	101	4	no	—
476	C₂²	—	404	4	no	—
477	C₂²	—	202	2	no	—
478	C₂²	—	202	4	no	—
479	C₂²	—	202	4	no	—
480	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
481	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
482	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
483	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	4	no	—
487	C₄	—	101	4	no	—
488	C₄	—	202	2	no	—
489	C₄	—	202	2	no	—
490	C₄	—	202	2	no	—
491	C₄	—	202	4	no	—
492	C₂	—	2	2	no	—
493	C₂	—	2	2	no	—
494	C₂	—	2	2	no	—
495	C₂	—	4	2	no	—
496	C₂	—	4	2	no	—
497	C₂	—	404	2	no	—
498	C₂	—	202	4	no	—
499	C₂	C₂²×D₄×D₁₀₁	1	1	yes	characteristic
500	C₂	#20266012	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#534×C₁₀₁	C₂
hypercenter	#534	D₁₀₁
hypocenter	C₁₀₁	#3485
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #534

Complements

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

N	H ≅ G/N	type
1. C₂×#15692300	C₂	semidirect
2. C₂²×#13108073	C₂	semidirect
3. #20265827	C₂	semidirect
4. #20265825	C₂	semidirect
5. #20265816	C₂	semidirect
6. #20265814	C₂	semidirect
7. #20265749	C₂	semidirect
8. #20265737	C₂	semidirect
9. #20265736	C₂	semidirect
10. #20265683	C₂	semidirect
11. C₂×#15692239	C₂	semidirect
12. C₂×#15692236	C₂	semidirect
13. #123×D₁₀₁	C₂	semidirect
14. #20265650	C₂	semidirect
15. #534×C₁₀₁	C₂	semidirect
17. C₂×#13108074	C₂²	semidirect
20. C₂×#13108073	C₂²	semidirect
21. C₂×#13108073	C₂²	semidirect
22. C₂×#13108073	C₂²	semidirect
23. C₂²×Dic₂₀₂	C₂²	semidirect
26. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
27. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
29. C₂×D₄×D₁₀₁	C₂²	semidirect
30. C₂³×Dic₁₀₁	C₂²	semidirect
31. C₂³×Dic₁₀₁	C₂²	semidirect
32. C₂²×C₄×D₁₀₁	C₂²	semidirect
33. #15692254	C₂²	semidirect
34. #15692241	C₂²	semidirect
35. #15692240	C₂²	semidirect
36. #15692239	C₂²	semidirect
37. #15692239	C₂²	semidirect
38. #15692239	C₂²	semidirect
39. #15692238	C₂²	semidirect
40. #15692237	C₂²	semidirect
41. #15692237	C₂²	semidirect
42. #15692236	C₂²	semidirect
43. #15692236	C₂²	semidirect
44. #15692236	C₂²	semidirect
45. #15692236	C₂²	semidirect
46. #15692233	C₂²	semidirect
47. #15692232	C₂²	semidirect
48. #15692232	C₂²	semidirect
49. #15692228	C₂²	semidirect
50. #15692227	C₂²	semidirect
51. #15692227	C₂²	semidirect
52. #15692226	C₂²	semidirect
53. #15692224	C₂²	semidirect
54. #15692223	C₂²	semidirect
55. #15692223	C₂²	semidirect
56. D₄×Dic₁₀₁	C₂²	semidirect
57. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
58. #15692215	C₂²	semidirect
59. #15692215	C₂²	semidirect
60. #15692211	C₂²	semidirect
61. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
62. C₂×#13108053	C₂²	semidirect
63. C₄⋊C₄×D₁₀₁	C₂²	semidirect
64. C₂×C₂²⋊Dic₁₀₁	C₂²	semidirect
65. C₂×C₂²⋊Dic₁₀₁	C₂²	semidirect
66. C₂×#13108051	C₂²	semidirect
67. C₂²⋊C₄×D₁₀₁	C₂²	semidirect
68. C₂²⋊C₄×D₁₀₁	C₂²	semidirect
70. C₂²×D₄×C₁₀₁	C₂²	semidirect
71. #123×C₁₀₁	C₂²	semidirect
72. #123×C₁₀₁	C₂²	semidirect
73. #121×C₁₀₁	C₂²	semidirect
74. #120×C₁₀₁	C₂²	semidirect
75. #120×C₁₀₁	C₂²	semidirect
76. C₂×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
92. C₂×C₂²⋊D₁₀₁	D₄	semidirect
251. C₁₀₁	#3485	semidirect
261. #534	D₁₀₁	semidirect
282. C₂²×D₄	C₂×D₁₀₁	semidirect
299. #123	C₂×D₁₀₁	semidirect
300. #123	C₂×D₁₀₁	semidirect
308. #121	C₂×D₁₀₁	semidirect
312. #120	C₂×D₁₀₁	semidirect
313. #120	C₂×D₁₀₁	semidirect
327. C₂×C₂²⋊C₄	C₂×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15692300	2
C₂²×#13108073	2
#20265827	2
#20265825	2
#20265816	2
#20265814	2
#20265749	2
#20265737	2
#20265736	2
#20265683	2
C₂×#15692239	2
C₂×#15692236	2
#123×D₁₀₁	2
#20265650	2
#534×C₁₀₁	2
#3485	101