Subgroups — #27184464

Order 12928.

1556 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13108075	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265757	C₂	1	4	yes	maximal, complemented
4	#20265752	C₂	1	2	yes	maximal, complemented
5	#20265751	C₂	1	1	yes	maximal, characteristic, complemented
6	#20265746	C₂	1	1	yes	maximal, characteristic, complemented
7	#20265745	C₂	1	2	yes	maximal, complemented
8	#20265741	C₂	1	1	yes	maximal, characteristic, complemented
9	#20265738	C₂	1	4	yes	maximal, complemented
10	#20265728	C₂	1	2	yes	maximal, complemented
11	#20265726	C₂	1	2	yes	maximal, complemented
12	#20265690	C₂	1	4	yes	maximal, complemented
13	#20265685	C₂	1	4	yes	maximal, complemented
14	#117×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#536×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13108075	—	2	8	no	—
17	C₂×#13108075	C₂²	1	2	yes	—
18	C₂×#13108075	C₂²	1	2	yes	—
19	C₂×#13108075	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13108075	C₂²	1	2	yes	complemented
21	C₂×#13108075	C₂²	1	2	yes	complemented
22	C₂×#13108074	C₂²	1	1	yes	characteristic
23	C₂×#13108074	C₂²	1	2	yes	complemented
24	C₂×#13108073	C₂²	1	2	yes	—
25	C₂×#13108073	C₂²	1	1	yes	characteristic, complemented
26	#41×D₁₀₁	—	2	8	no	—
27	C₂×Q₈×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₄₀₄	C₂²	1	2	yes	—
29	C₂²×D₄₀₄	C₂²	1	1	yes	characteristic, complemented
30	C₂×D₄×D₁₀₁	C₂²	1	2	yes	—
31	C₂×D₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	complemented
34	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	complemented
35	#15692253	C₂²	1	2	yes	complemented
36	#15692252	C₂²	1	2	yes	complemented
37	#15692251	C₂²	1	2	yes	complemented
38	#15692244	C₂²	1	2	yes	complemented
39	#15692244	C₂²	1	2	yes	complemented
40	#15692243	C₂²	1	2	yes	complemented
41	#15692240	C₂²	1	8	yes	complemented
42	#15692238	C₂²	1	4	yes	complemented
43	#15692233	C₂²	1	8	yes	complemented
44	#15692231	C₂²	1	4	yes	complemented
45	#15692230	C₂²	1	8	yes	complemented
46	#15692230	C₂²	1	4	yes	complemented
47	#15692229	C₂²	1	4	yes	complemented
48	#15692228	C₂²	1	8	yes	complemented
49	#15692228	C₂²	1	8	yes	complemented
50	#15692225	C₂²	1	8	yes	complemented
51	#15692225	C₂²	1	4	yes	complemented
52	#15692223	C₂²	1	4	yes	complemented
53	#15692217	C₂²	1	8	yes	complemented
54	#15692215	C₂²	1	8	yes	complemented
55	#15692214	C₂²	1	1	yes	characteristic, complemented
56	#15692213	C₂²	1	2	yes	complemented
57	#15692212	C₂²	1	2	yes	complemented
58	#15692211	C₂²	1	2	yes	complemented
59	C₄⋊C₄×D₁₀₁	C₂²	1	2	yes	complemented
60	C₂²⋊C₄×D₁₀₁	C₂²	1	2	yes	—
61	C₄²×D₁₀₁	C₂²	1	2	yes	complemented
62	C₂×#41×C₁₀₁	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
64	C₄⋊Q₈×C₁₀₁	C₂²	1	2	yes	complemented
65	#124×C₁₀₁	C₂²	1	2	yes	complemented
66	#123×C₁₀₁	C₂²	1	4	yes	complemented
67	C₂²⋊Q₈×C₁₀₁	C₂²	1	4	yes	complemented
68	#117×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
69	C₂³×D₁₀₁	C₂³	1	2	yes	—
70	C₂³×D₁₀₁	C₂³	1	2	yes	—
71	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
72	#13108075	—	2	4	no	—
73	#13108075	—	2	8	no	—
74	#13108075	—	2	8	no	—
75	#13108075	—	2	8	no	—
76	#13108075	—	2	8	no	—
77	#13108074	—	2	4	no	—
78	#13108074	—	2	8	no	—
79	#13108073	—	2	8	no	—
80	#13108073	—	2	4	no	—
81	C₂×Dic₂₀₂	C₂³	1	2	yes	—
82	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
83	Q₈×D₁₀₁	—	2	4	no	—
84	C₂×D₄₀₄	—	2	8	no	—
85	C₂×D₄₀₄	—	2	4	no	—
86	C₂×D₄₀₄	C₂³	1	2	yes	—
87	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
88	C₂×D₄₀₄	C₂³	1	4	yes	—
89	C₂×D₄₀₄	C₂³	1	4	yes	—
90	C₂×D₄₀₄	C₂³	1	2	yes	—
91	C₂×D₄₀₄	C₂³	1	2	yes	—
92	C₂×D₄₀₄	C₂³	1	8	yes	—
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	8	yes	—
97	D₄×D₁₀₁	—	2	8	no	—
98	D₄×D₁₀₁	—	2	4	no	—
99	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
100	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₀₁	—	2	8	no	—
102	C₂×C₄×D₁₀₁	—	2	8	no	—
103	C₂×C₄×D₁₀₁	D₄	1	8	yes	complemented
104	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
105	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
106	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
107	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
108	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
109	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
110	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
112	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
114	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
115	#13108053	C₂³	1	4	yes	—
116	#13108053	C₂³	1	8	yes	—
117	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
118	#13108051	C₂³	1	4	yes	—
119	#13108051	C₂³	1	8	yes	—
120	#13108051	C₂³	1	8	yes	—
121	#13108051	C₂³	1	8	yes	—
122	C₄×Dic₁₀₁	C₂³	1	4	yes	—
123	C₄×Dic₁₀₁	C₂³	1	2	yes	—
124	#41×C₁₀₁	—	2	4	no	—
125	C₂×Q₈×C₁₀₁	—	2	4	no	—
126	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₀₁	C₂³	1	2	yes	—
128	C₂×Q₈×C₁₀₁	C₂³	1	2	yes	—
129	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
130	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
134	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
135	C₄⋊C₄×C₁₀₁	C₂³	1	8	yes	—
136	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
137	C₂²⋊C₄×C₁₀₁	C₂³	1	8	yes	—
138	C₄²×C₁₀₁	C₂³	1	2	yes	—
139	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
140	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
141	C₂²×D₁₀₁	—	2	4	no	—
142	C₂²×D₁₀₁	—	2	4	no	—
143	C₂²×D₁₀₁	—	4	2	no	—
144	C₂²×D₁₀₁	—	4	4	no	—
145	C₂²×D₁₀₁	—	4	4	no	—
146	C₂²×D₁₀₁	C₂×D₄	1	4	yes	—
147	C₂²×D₁₀₁	C₂⁴	1	4	yes	—
148	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
149	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
150	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
151	Q₈×C₁₀₁	—	2	4	no	—
152	Q₈×C₁₀₁	—	2	4	no	—
153	Q₈×C₁₀₁	—	2	2	no	—
154	D₄×C₁₀₁	—	2	4	no	—
155	D₄×C₁₀₁	—	2	2	no	—
156	C₂×C₄×C₁₀₁	—	2	4	no	—
157	C₂×C₄×C₁₀₁	—	2	4	no	—
158	C₂×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
159	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
160	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
161	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
162	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
164	C₂²⋊D₁₀₁	—	2	4	no	—
165	C₂²⋊D₁₀₁	—	2	4	no	—
166	C₂²⋊D₁₀₁	—	2	4	no	—
167	C₂²⋊D₁₀₁	—	4	8	no	—
168	C₂×Dic₁₀₁	—	2	4	no	—
169	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
170	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
171	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
172	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
173	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
174	D₄₀₄	—	2	4	no	—
175	D₄₀₄	—	2	8	no	—
176	D₄₀₄	—	2	8	no	—
177	D₄₀₄	—	2	2	no	—
178	D₄₀₄	—	2	4	no	—
179	D₄₀₄	—	2	4	no	—
180	D₄₀₄	—	4	8	no	—
181	C₄×D₁₀₁	—	2	4	no	—
182	C₄×D₁₀₁	—	2	4	no	—
183	C₄×D₁₀₁	—	2	4	no	—
184	C₄×D₁₀₁	—	2	8	no	—
185	C₄×D₁₀₁	—	2	8	no	—
186	C₄×D₁₀₁	—	4	4	no	—
187	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
188	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
189	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
190	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
191	Dic₂₀₂	—	2	2	no	—
192	Dic₂₀₂	—	2	4	no	—
193	C₂²×C₁₀₁	—	2	2	no	—
194	C₂²×C₁₀₁	—	2	2	no	—
195	C₂²×C₁₀₁	—	2	4	no	—
196	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
197	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
198	C₂×D₁₀₁	—	2	2	no	—
199	C₂×D₁₀₁	—	2	2	no	—
200	C₂×D₁₀₁	—	2	4	no	—
201	C₂×D₁₀₁	—	2	2	no	—
202	C₂×D₁₀₁	—	2	4	no	—
203	C₂×D₁₀₁	—	2	8	no	—
204	C₂×D₁₀₁	—	4	4	no	—
205	C₂×D₁₀₁	—	4	8	no	—
206	C₂×D₁₀₁	—	4	8	no	—
207	C₂×D₁₀₁	C₂²×D₄	1	2	yes	—
208	C₂×D₁₀₁	C₂²×D₄	1	2	yes	—
209	C₄×C₁₀₁	—	2	2	no	—
210	C₄×C₁₀₁	—	2	4	no	—
211	C₄×C₁₀₁	—	2	4	no	—
212	C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
213	C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
214	Dic₁₀₁	—	2	2	no	—
215	Dic₁₀₁	—	2	4	no	—
216	Dic₁₀₁	C₂²×D₄	1	2	yes	—
217	Dic₁₀₁	C₂²×D₄	1	2	yes	—
218	C₂×C₁₀₁	—	2	2	no	—
219	C₂×C₁₀₁	—	4	2	no	—
220	C₂×C₁₀₁	C₂³×D₄	1	1	yes	characteristic
221	C₂×C₁₀₁	#585	1	2	yes	—
222	D₁₀₁	—	2	2	no	—
223	D₁₀₁	—	2	2	no	—
224	D₁₀₁	—	4	4	no	—
225	D₁₀₁	—	4	2	no	—
226	#3449	—	101	1	no	maximal, Sylow
227	C₁₀₁	#3449	1	1	yes	characteristic, complemented, Sylow
228	C₂²×#41	—	101	1	no	—
229	C₂²×#41	—	101	1	no	—
230	#537	—	101	4	no	—
231	#536	—	101	1	no	—
232	#536	—	101	2	no	—
233	#536	D₁₀₁	1	1	yes	characteristic, complemented
234	#535	—	101	1	no	—
235	#535	—	101	2	no	—
236	#535	—	101	1	no	—
237	#534	—	101	4	no	—
238	#532	—	101	2	no	—
239	#532	—	101	2	no	—
240	#525	—	101	4	no	—
241	#525	—	101	4	no	—
242	C₂×#117	—	101	1	no	—
243	C₂×#41	—	101	2	no	—
244	C₂×#41	—	101	2	no	—
245	C₂×#41	—	101	1	no	—
246	C₂×#41	—	101	2	no	—
247	C₂×#41	—	101	2	no	—
248	C₂×#41	—	101	2	no	—
249	C₂×#41	—	101	1	no	—
250	C₂×#41	—	101	1	no	—
251	C₂×#41	—	101	2	no	—
252	C₂×#41	—	202	8	no	—
253	C₂×#41	—	202	8	no	—
254	C₂×#41	C₂×D₁₀₁	1	1	yes	characteristic
255	C₂²×Q₈	—	101	1	no	—
256	C₂²×Q₈	C₂×D₁₀₁	1	1	yes	characteristic, complemented
257	C₂²×D₄	—	101	2	no	—
258	C₂²×D₄	—	101	1	no	—
259	C₂²×D₄	—	101	2	no	—
260	C₂²×D₄	—	101	1	no	—
261	C₂³×C₄	—	101	1	no	—
262	C₂³×C₄	—	101	2	no	—
263	C₂³×C₄	—	101	2	no	—
264	C₄⋊Q₈	—	101	2	no	—
265	C₄⋊Q₈	C₂×D₁₀₁	1	2	yes	complemented
266	#127	—	101	2	no	—
267	#127	—	101	2	no	—
268	#124	—	101	2	no	—
269	#124	—	101	2	no	—
270	#124	—	101	2	no	—
271	#124	C₂×D₁₀₁	1	2	yes	complemented
272	#123	—	101	4	no	—
273	#123	—	101	8	no	—
274	#123	C₂×D₁₀₁	1	4	yes	complemented
275	C₂²⋊Q₈	—	101	4	no	—
276	C₂²⋊Q₈	—	101	8	no	—
277	C₂²⋊Q₈	C₂×D₁₀₁	1	4	yes	complemented
278	#121	—	101	4	no	—
279	#121	—	101	4	no	—
280	#121	—	101	8	no	—
281	#121	—	101	8	no	—
282	#121	—	101	8	no	—
283	#120	—	101	4	no	—
284	#120	—	101	8	no	—
285	#120	—	101	4	no	—
286	C₄×D₄	—	101	8	no	—
287	C₄×D₄	—	101	8	no	—
288	#117	—	101	1	no	—
289	#117	—	101	2	no	—
290	#117	—	101	2	no	—
291	#117	—	101	2	no	—
292	#117	C₂×D₁₀₁	1	1	yes	characteristic, complemented
293	C₂×C₄⋊C₄	—	101	2	no	—
294	C₂×C₂²⋊C₄	—	101	2	no	—
295	C₂×C₄²	—	101	2	no	—
296	C₂⁴	—	101	1	no	—
297	C₂⁴	—	101	2	no	—
298	C₂⁴	—	101	2	no	—
299	#41	—	2	4	no	—
300	#41	—	202	8	no	—
301	#41	—	202	8	no	—
302	#41	—	202	4	no	—
303	#41	—	202	8	no	—
304	#41	—	202	8	no	—
305	#41	—	202	8	no	—
306	#41	—	202	8	no	—
307	#41	—	202	4	no	—
308	#41	—	202	4	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	101	2	no	—
311	C₂×Q₈	—	101	1	no	—
312	C₂×Q₈	—	202	4	no	—
313	C₂×Q₈	C₂²×D₁₀₁	1	2	yes	—
314	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
315	C₂×Q₈	C₂²×D₁₀₁	1	2	yes	—
316	C₂×D₄	—	101	8	no	—
317	C₂×D₄	—	101	2	no	—
318	C₂×D₄	—	101	2	no	—
319	C₂×D₄	—	101	2	no	—
320	C₂×D₄	—	101	8	no	—
321	C₂×D₄	—	101	4	no	—
322	C₂×D₄	—	101	2	no	—
323	C₂×D₄	—	101	4	no	—
324	C₂×D₄	—	101	2	no	—
325	C₂×D₄	—	101	1	no	—
326	C₂×D₄	—	101	2	no	—
327	C₂×D₄	—	202	8	no	—
328	C₂×D₄	—	202	4	no	—
329	C₂×D₄	—	202	8	no	—
330	C₂×D₄	—	202	4	no	—
331	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
332	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
333	C₂²×C₄	—	101	1	no	—
334	C₂²×C₄	—	101	8	no	—
335	C₂²×C₄	—	101	1	no	—
336	C₂²×C₄	—	101	1	no	—
337	C₂²×C₄	—	101	1	no	—
338	C₂²×C₄	—	101	1	no	—
339	C₂²×C₄	—	101	2	no	—
340	C₂²×C₄	—	101	4	no	—
341	C₂²×C₄	—	101	2	no	—
342	C₂²×C₄	—	101	4	no	—
343	C₂²×C₄	—	101	4	no	—
344	C₂²×C₄	—	101	2	no	—
345	C₂²×C₄	—	101	2	no	—
346	C₂²×C₄	—	202	8	no	—
347	C₂²×C₄	—	202	8	no	—
348	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
349	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
350	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
351	C₄⋊C₄	—	101	4	no	—
352	C₄⋊C₄	—	101	8	no	—
353	C₄⋊C₄	—	101	2	no	—
354	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
355	C₄⋊C₄	C₂²×D₁₀₁	1	8	yes	—
356	C₂²⋊C₄	—	101	2	no	—
357	C₂²⋊C₄	—	101	4	no	—
358	C₂²⋊C₄	—	101	8	no	—
359	C₂²⋊C₄	—	101	8	no	—
360	C₂²⋊C₄	—	101	8	no	—
361	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
362	C₂²⋊C₄	C₂²×D₁₀₁	1	8	yes	—
363	C₄²	—	101	4	no	—
364	C₄²	—	101	2	no	—
365	C₄²	C₂²×D₁₀₁	1	2	yes	—
366	C₂³	—	101	4	no	—
367	C₂³	—	101	1	no	—
368	C₂³	—	101	1	no	—
369	C₂³	—	101	4	no	—
370	C₂³	—	101	2	no	—
371	C₂³	—	404	4	no	—
372	C₂³	—	404	2	no	—
373	C₂³	—	404	4	no	—
374	C₂³	—	202	4	no	—
375	C₂³	—	202	4	no	—
376	C₂³	C₂³×D₁₀₁	1	2	yes	—
377	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
378	Q₈	—	2	4	no	—
379	Q₈	—	2	4	no	—
380	Q₈	—	2	2	no	—
381	Q₈	—	202	4	no	—
382	Q₈	—	202	2	no	—
383	D₄	—	2	4	no	—
384	D₄	—	2	2	no	—
385	D₄	—	404	8	no	—
386	D₄	—	404	8	no	—
387	D₄	—	202	4	no	—
388	D₄	—	202	8	no	—
389	D₄	—	202	8	no	—
390	D₄	—	202	4	no	—
391	D₄	—	202	4	no	—
392	D₄	—	202	4	no	—
393	D₄	—	202	4	no	—
394	D₄	—	202	2	no	—
395	D₄	—	202	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	101	4	no	—
399	C₂×C₄	—	101	1	no	—
400	C₂×C₄	—	101	1	no	—
401	C₂×C₄	—	101	4	no	—
402	C₂×C₄	—	101	4	no	—
403	C₂×C₄	—	101	4	no	—
404	C₂×C₄	—	101	4	no	—
405	C₂×C₄	—	101	4	no	—
406	C₂×C₄	—	101	2	no	—
407	C₂×C₄	—	404	4	no	—
408	C₂×C₄	—	202	4	no	—
409	C₂×C₄	—	202	8	no	—
410	C₂×C₄	—	202	8	no	—
411	C₂×C₄	—	202	4	no	—
412	C₂×C₄	—	202	4	no	—
413	C₂×C₄	—	202	4	no	—
414	C₂×C₄	D₄×D₁₀₁	1	4	yes	—
415	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
416	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
417	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
418	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	101	2	no	—
424	C₂²	—	101	2	no	—
425	C₂²	—	404	8	no	—
426	C₂²	—	404	4	no	—
427	C₂²	—	404	8	no	—
428	C₂²	—	202	4	no	—
429	C₂²	—	202	2	no	—
430	C₂²	—	202	4	no	—
431	C₂²	—	202	8	no	—
432	C₂²	—	202	2	no	—
433	C₂²	—	202	2	no	—
434	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
435	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	4	no	—
438	C₄	—	2	4	no	—
439	C₄	—	101	2	no	—
440	C₄	—	101	2	no	—
441	C₄	—	202	2	no	—
442	C₄	—	202	4	no	—
443	C₄	C₂×D₄×D₁₀₁	1	2	yes	—
444	C₄	C₂×D₄×D₁₀₁	1	2	yes	—
445	C₂	—	2	2	no	—
446	C₂	—	4	2	no	—
447	C₂	—	404	4	no	—
448	C₂	—	404	2	no	—
449	C₂	—	202	2	no	—
450	C₂	—	202	2	no	—
451	C₂	C₂²×D₄×D₁₀₁	1	1	yes	characteristic
452	C₂	#20266014	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#536×C₁₀₁	C₂
hypercenter	#536	D₁₀₁
hypocenter	C₁₀₁	#3449
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. C₂²×#13108075	C₂	semidirect
2. C₂×#41×D₁₀₁	C₂	semidirect
3. #20265757	C₂	semidirect
4. #20265752	C₂	semidirect
5. #20265751	C₂	semidirect
6. #20265746	C₂	semidirect
7. #20265745	C₂	semidirect
8. #20265741	C₂	semidirect
9. #20265738	C₂	semidirect
10. #20265728	C₂	semidirect
11. #20265726	C₂	semidirect
12. #20265690	C₂	semidirect
13. #20265685	C₂	semidirect
14. #117×D₁₀₁	C₂	semidirect
15. #536×C₁₀₁	C₂	semidirect
19. C₂×#13108075	C₂²	semidirect
20. C₂×#13108075	C₂²	semidirect
21. C₂×#13108075	C₂²	semidirect
23. C₂×#13108074	C₂²	semidirect
25. C₂×#13108073	C₂²	semidirect
27. C₂×Q₈×D₁₀₁	C₂²	semidirect
29. C₂²×D₄₀₄	C₂²	semidirect
31. C₂×D₄×D₁₀₁	C₂²	semidirect
33. C₂²×C₄×D₁₀₁	C₂²	semidirect
34. C₂²×C₄×D₁₀₁	C₂²	semidirect
35. #15692253	C₂²	semidirect
36. #15692252	C₂²	semidirect
37. #15692251	C₂²	semidirect
38. #15692244	C₂²	semidirect
39. #15692244	C₂²	semidirect
40. #15692243	C₂²	semidirect
41. #15692240	C₂²	semidirect
42. #15692238	C₂²	semidirect
43. #15692233	C₂²	semidirect
44. #15692231	C₂²	semidirect
45. #15692230	C₂²	semidirect
46. #15692230	C₂²	semidirect
47. #15692229	C₂²	semidirect
48. #15692228	C₂²	semidirect
49. #15692228	C₂²	semidirect
50. #15692225	C₂²	semidirect
51. #15692225	C₂²	semidirect
52. #15692223	C₂²	semidirect
53. #15692217	C₂²	semidirect
54. #15692215	C₂²	semidirect
55. #15692214	C₂²	semidirect
56. #15692213	C₂²	semidirect
57. #15692212	C₂²	semidirect
58. #15692211	C₂²	semidirect
59. C₄⋊C₄×D₁₀₁	C₂²	semidirect
61. C₄²×D₁₀₁	C₂²	semidirect
63. C₂²×Q₈×C₁₀₁	C₂²	semidirect
64. C₄⋊Q₈×C₁₀₁	C₂²	semidirect
65. #124×C₁₀₁	C₂²	semidirect
66. #123×C₁₀₁	C₂²	semidirect
67. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
68. #117×C₁₀₁	C₂²	semidirect
103. C₂×C₄×D₁₀₁	D₄	semidirect
227. C₁₀₁	#3449	semidirect
233. #536	D₁₀₁	semidirect
256. C₂²×Q₈	C₂×D₁₀₁	semidirect
265. C₄⋊Q₈	C₂×D₁₀₁	semidirect
271. #124	C₂×D₁₀₁	semidirect
274. #123	C₂×D₁₀₁	semidirect
277. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
292. #117	C₂×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13108075	2
C₂×#41×D₁₀₁	2
#20265757	2
#20265752	2
#20265751	2
#20265746	2
#20265745	2
#20265741	2
#20265738	2
#20265728	2
#20265726	2
#20265690	2
#20265685	2
#117×D₁₀₁	2
#536×C₁₀₁	2
#3449	101