Subgroups — #27184463

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×#13108073	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265756	C₂	1	4	yes	maximal, complemented
4	#20265753	C₂	1	1	yes	maximal, characteristic, complemented
5	#20265748	C₂	1	1	yes	maximal, characteristic, complemented
6	#20265747	C₂	1	2	yes	maximal, complemented
7	#20265744	C₂	1	1	yes	maximal, characteristic, complemented
8	#20265740	C₂	1	2	yes	maximal, complemented
9	#20265737	C₂	1	4	yes	maximal, complemented
10	#20265726	C₂	1	2	yes	maximal, complemented
11	#20265725	C₂	1	2	yes	maximal, complemented
12	#20265687	C₂	1	4	yes	maximal, complemented
13	#20265683	C₂	1	4	yes	maximal, complemented
14	#117×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#535×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13108075	C₂²	1	1	yes	characteristic, complemented
17	C₂×#13108074	C₂²	1	1	yes	characteristic
18	C₂×#13108074	C₂²	1	2	yes	complemented
19	C₂×#13108073	—	2	8	no	—
20	C₂×#13108073	C₂²	1	2	yes	—
21	C₂×#13108073	C₂²	1	2	yes	—
22	C₂×#13108073	C₂²	1	2	yes	—
23	C₂×#13108073	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13108073	C₂²	1	2	yes	complemented
25	C₂×#13108073	C₂²	1	2	yes	complemented
26	#41×D₁₀₁	—	2	8	no	—
27	C₂²×Dic₂₀₂	C₂²	1	1	yes	characteristic, complemented
28	C₂×Q₈×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
30	C₂×D₄×D₁₀₁	C₂²	1	2	yes	—
31	C₂×D₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
32	C₂³×Dic₁₀₁	C₂²	1	2	yes	complemented
33	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
34	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	complemented
35	#15692255	C₂²	1	2	yes	complemented
36	#15692253	C₂²	1	2	yes	complemented
37	#15692251	C₂²	1	2	yes	complemented
38	#15692243	C₂²	1	2	yes	complemented
39	#15692242	C₂²	1	2	yes	complemented
40	#15692242	C₂²	1	2	yes	complemented
41	#15692239	C₂²	1	4	yes	complemented
42	#15692237	C₂²	1	8	yes	complemented
43	#15692236	C₂²	1	4	yes	complemented
44	#15692235	C₂²	1	4	yes	complemented
45	#15692234	C₂²	1	4	yes	complemented
46	#15692232	C₂²	1	8	yes	complemented
47	#15692228	C₂²	1	8	yes	complemented
48	#15692227	C₂²	1	8	yes	complemented
49	#15692226	C₂²	1	8	yes	complemented
50	#15692226	C₂²	1	4	yes	complemented
51	#15692224	C₂²	1	4	yes	complemented
52	#15692223	C₂²	1	8	yes	complemented
53	D₄×Dic₁₀₁	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×D₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
64	#127×C₁₀₁	C₂²	1	2	yes	complemented
65	#124×C₁₀₁	C₂²	1	2	yes	complemented
66	#121×C₁₀₁	C₂²	1	4	yes	complemented
67	#120×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	1	yes	characteristic
71	#13108075	—	2	4	no	—
72	#13108074	—	2	4	no	—
73	#13108074	—	2	8	no	—
74	#13108073	—	2	8	no	—
75	#13108073	—	2	4	no	—
76	#13108073	—	2	8	no	—
77	#13108073	—	2	8	no	—
78	#13108073	—	2	8	no	—
79	#13108073	—	2	8	no	—
80	C₂×Dic₂₀₂	—	2	4	no	—
81	C₂×Dic₂₀₂	C₂³	1	2	yes	—
82	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
83	C₂×Dic₂₀₂	C₂³	1	2	yes	—
84	C₂×Dic₂₀₂	C₂³	1	2	yes	—
85	Q₈×D₁₀₁	—	2	4	no	—
86	C₂×D₄₀₄	C₂³	1	2	yes	—
87	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊D₁₀₁	—	2	8	no	—
89	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
90	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	—
95	D₄×D₁₀₁	—	2	8	no	—
96	D₄×D₁₀₁	—	2	4	no	—
97	C₂²×Dic₁₀₁	—	2	8	no	—
98	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
99	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
100	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
101	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
102	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₁₀₁	—	2	8	no	—
104	C₂×C₄×D₁₀₁	D₄	1	8	yes	complemented
105	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
106	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
107	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
108	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
109	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
114	C₄⋊Dic₁₀₁	C₂³	1	8	yes	—
115	#13108053	C₂³	1	4	yes	—
116	#13108053	C₂³	1	8	yes	—
117	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₀₁	C₂³	1	8	yes	—
119	C₂²⋊Dic₁₀₁	C₂³	1	8	yes	—
120	#13108051	C₂³	1	4	yes	—
121	#13108051	C₂³	1	8	yes	—
122	C₄×Dic₁₀₁	C₂³	1	4	yes	—
123	C₄×Dic₁₀₁	C₂³	1	2	yes	—
124	C₂⁴×C₁₀₁	C₂³	1	2	yes	—
125	#41×C₁₀₁	—	2	4	no	—
126	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₀₁	—	2	4	no	—
128	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
129	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
131	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
132	C₂×D₄×C₁₀₁	C₂³	1	8	yes	—
133	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
135	C₄⋊C₄×C₁₀₁	C₂³	1	2	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	—	2	4	no	—
140	C₂³×C₁₀₁	—	4	4	no	—
141	C₂³×C₁₀₁	C₂⁴	1	4	yes	—
142	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
143	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
144	C₂²×D₁₀₁	—	2	4	no	—
145	C₂²×D₁₀₁	—	4	2	no	—
146	C₂²×D₁₀₁	—	4	4	no	—
147	C₂²×D₁₀₁	C₂×D₄	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	2	no	—
152	D₄×C₁₀₁	—	2	4	no	—
153	D₄×C₁₀₁	—	2	4	no	—
154	D₄×C₁₀₁	—	2	4	no	—
155	D₄×C₁₀₁	—	2	2	no	—
156	D₄×C₁₀₁	—	4	8	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	2	yes	—
161	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
163	C₂²⋊D₁₀₁	—	2	4	no	—
164	C₂²⋊D₁₀₁	—	2	4	no	—
165	C₂²⋊D₁₀₁	—	2	8	no	—
166	C₂²⋊D₁₀₁	—	2	8	no	—
167	C₂²⋊D₁₀₁	—	2	4	no	—
168	C₂²⋊D₁₀₁	—	4	8	no	—
169	C₂×Dic₁₀₁	—	2	4	no	—
170	C₂×Dic₁₀₁	—	2	4	no	—
171	C₂×Dic₁₀₁	—	2	8	no	—
172	C₂×Dic₁₀₁	—	2	8	no	—
173	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
174	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
175	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
176	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
177	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
179	D₄₀₄	—	2	4	no	—
180	D₄₀₄	—	2	2	no	—
181	C₄×D₁₀₁	—	2	4	no	—
182	C₄×D₁₀₁	—	2	4	no	—
183	C₄×D₁₀₁	—	2	4	no	—
184	C₄×D₁₀₁	—	4	4	no	—
185	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
186	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
187	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
188	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
189	Dic₂₀₂	—	2	2	no	—
190	Dic₂₀₂	—	2	4	no	—
191	Dic₂₀₂	—	2	4	no	—
192	Dic₂₀₂	—	2	4	no	—
193	C₂²×C₁₀₁	—	2	2	no	—
194	C₂²×C₁₀₁	—	2	4	no	—
195	C₂²×C₁₀₁	—	2	2	no	—
196	C₂²×C₁₀₁	—	2	8	no	—
197	C₂²×C₁₀₁	—	2	4	no	—
198	C₂²×C₁₀₁	—	4	8	no	—
199	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
200	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
201	C₂×D₁₀₁	—	2	2	no	—
202	C₂×D₁₀₁	—	2	2	no	—
203	C₂×D₁₀₁	—	2	2	no	—
204	C₂×D₁₀₁	—	2	4	no	—
205	C₂×D₁₀₁	—	4	4	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	C₂²×D₄	1	2	yes	—
212	C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
213	Dic₁₀₁	—	2	2	no	—
214	Dic₁₀₁	—	2	4	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	—	4	4	no	—
221	C₂×C₁₀₁	C₂³×D₄	1	1	yes	characteristic
222	C₂×C₁₀₁	#585	1	2	yes	—
223	D₁₀₁	—	2	2	no	—
224	D₁₀₁	—	2	2	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	—	101	1	no	—
234	#535	—	101	1	no	—
235	#535	—	101	2	no	—
236	#535	D₁₀₁	1	1	yes	characteristic, complemented
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	1	no	—
244	C₂×#41	—	101	2	no	—
245	C₂×#41	—	101	2	no	—
246	C₂×#41	—	101	2	no	—
247	C₂×#41	—	101	1	no	—
248	C₂×#41	—	101	2	no	—
249	C₂×#41	—	101	2	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	—	101	1	no	—
257	C₂²×D₄	—	101	2	no	—
258	C₂²×D₄	—	101	2	no	—
259	C₂²×D₄	—	101	1	no	—
260	C₂²×D₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
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	—	101	2	no	—
266	#127	—	101	2	no	—
267	#127	C₂×D₁₀₁	1	2	yes	complemented
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	—	101	4	no	—
275	C₂²⋊Q₈	—	101	4	no	—
276	C₂²⋊Q₈	—	101	4	no	—
277	C₂²⋊Q₈	—	101	8	no	—
278	#121	—	101	4	no	—
279	#121	—	101	8	no	—
280	#121	—	101	8	no	—
281	#121	—	101	8	no	—
282	#121	C₂×D₁₀₁	1	4	yes	complemented
283	#120	—	101	4	no	—
284	#120	—	101	8	no	—
285	#120	C₂×D₁₀₁	1	4	yes	complemented
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	C₂²×D₁₀₁	1	2	yes	—
299	#41	—	2	4	no	—
300	#41	—	202	8	no	—
301	#41	—	202	8	no	—
302	#41	—	202	8	no	—
303	#41	—	202	8	no	—
304	#41	—	202	8	no	—
305	#41	—	202	8	no	—
306	#41	—	202	4	no	—
307	#41	—	202	4	no	—
308	#41	—	202	4	no	—
309	C₂×Q₈	—	101	2	no	—
310	C₂×Q₈	—	101	2	no	—
311	C₂×Q₈	—	101	1	no	—
312	C₂×Q₈	—	101	2	no	—
313	C₂×Q₈	—	202	4	no	—
314	C₂×Q₈	—	202	4	no	—
315	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	101	8	no	—
318	C₂×D₄	—	101	4	no	—
319	C₂×D₄	—	101	2	no	—
320	C₂×D₄	—	101	2	no	—
321	C₂×D₄	—	101	2	no	—
322	C₂×D₄	—	101	4	no	—
323	C₂×D₄	—	101	2	no	—
324	C₂×D₄	—	101	1	no	—
325	C₂×D₄	—	202	4	no	—
326	C₂×D₄	—	202	8	no	—
327	C₂×D₄	—	202	8	no	—
328	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
329	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
330	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
331	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
332	C₂×D₄	C₂²×D₁₀₁	1	8	yes	—
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	4	no	—
342	C₂²×C₄	—	101	2	no	—
343	C₂²×C₄	—	101	4	no	—
344	C₂²×C₄	—	101	2	no	—
345	C₂²×C₄	—	101	2	no	—
346	C₂²×C₄	—	101	2	no	—
347	C₂²×C₄	—	202	8	no	—
348	C₂²×C₄	—	202	8	no	—
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	—	101	8	no	—
355	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
356	C₂²⋊C₄	—	101	2	no	—
357	C₂²⋊C₄	—	101	8	no	—
358	C₂²⋊C₄	—	101	8	no	—
359	C₂²⋊C₄	—	101	4	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	—	2	4	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	101	4	no	—
369	C₂³	—	101	1	no	—
370	C₂³	—	101	1	no	—
371	C₂³	—	101	2	no	—
372	C₂³	—	404	2	no	—
373	C₂³	—	404	4	no	—
374	C₂³	—	202	4	no	—
375	C₂³	C₂³×D₁₀₁	1	2	yes	—
376	C₂³	C₂³×D₁₀₁	1	4	yes	—
377	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
378	Q₈	—	2	2	no	—
379	Q₈	—	202	4	no	—
380	Q₈	—	202	4	no	—
381	Q₈	—	202	2	no	—
382	Q₈	—	202	4	no	—
383	D₄	—	2	4	no	—
384	D₄	—	2	4	no	—
385	D₄	—	2	4	no	—
386	D₄	—	2	2	no	—
387	D₄	—	4	8	no	—
388	D₄	—	404	8	no	—
389	D₄	—	202	4	no	—
390	D₄	—	202	4	no	—
391	D₄	—	202	4	no	—
392	D₄	—	202	8	no	—
393	D₄	—	202	8	no	—
394	D₄	—	202	4	no	—
395	D₄	—	202	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	101	4	no	—
398	C₂×C₄	—	101	1	no	—
399	C₂×C₄	—	101	1	no	—
400	C₂×C₄	—	101	4	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	2	no	—
406	C₂×C₄	—	101	4	no	—
407	C₂×C₄	—	404	4	no	—
408	C₂×C₄	—	202	4	no	—
409	C₂×C₄	—	202	4	no	—
410	C₂×C₄	—	202	4	no	—
411	C₂×C₄	—	202	8	no	—
412	C₂×C₄	—	202	8	no	—
413	C₂×C₄	—	202	4	no	—
414	C₂×C₄	—	202	4	no	—
415	C₂×C₄	D₄×D₁₀₁	1	4	yes	—
416	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
417	C₂×C₄	C₂³×D₁₀₁	1	2	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	—	2	4	no	—
424	C₂²	—	2	8	no	—
425	C₂²	—	4	8	no	—
426	C₂²	—	101	2	no	—
427	C₂²	—	101	2	no	—
428	C₂²	—	404	4	no	—
429	C₂²	—	404	8	no	—
430	C₂²	—	202	2	no	—
431	C₂²	—	202	4	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	—	101	2	no	—
439	C₄	—	101	2	no	—
440	C₄	—	202	2	no	—
441	C₄	—	202	4	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	4	no	—
447	C₂	—	4	2	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	#20266012	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#535×C₁₀₁	C₂
hypercenter	#535	D₁₀₁
hypocenter	C₁₀₁	#3449
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. C₂²×#13108073	C₂	semidirect
2. C₂×#41×D₁₀₁	C₂	semidirect
3. #20265756	C₂	semidirect
4. #20265753	C₂	semidirect
5. #20265748	C₂	semidirect
6. #20265747	C₂	semidirect
7. #20265744	C₂	semidirect
8. #20265740	C₂	semidirect
9. #20265737	C₂	semidirect
10. #20265726	C₂	semidirect
11. #20265725	C₂	semidirect
12. #20265687	C₂	semidirect
13. #20265683	C₂	semidirect
14. #117×D₁₀₁	C₂	semidirect
15. #535×C₁₀₁	C₂	semidirect
16. C₂×#13108075	C₂²	semidirect
18. C₂×#13108074	C₂²	semidirect
23. C₂×#13108073	C₂²	semidirect
24. C₂×#13108073	C₂²	semidirect
25. C₂×#13108073	C₂²	semidirect
27. C₂²×Dic₂₀₂	C₂²	semidirect
28. C₂×Q₈×D₁₀₁	C₂²	semidirect
31. C₂×D₄×D₁₀₁	C₂²	semidirect
32. C₂³×Dic₁₀₁	C₂²	semidirect
34. C₂²×C₄×D₁₀₁	C₂²	semidirect
35. #15692255	C₂²	semidirect
36. #15692253	C₂²	semidirect
37. #15692251	C₂²	semidirect
38. #15692243	C₂²	semidirect
39. #15692242	C₂²	semidirect
40. #15692242	C₂²	semidirect
41. #15692239	C₂²	semidirect
42. #15692237	C₂²	semidirect
43. #15692236	C₂²	semidirect
44. #15692235	C₂²	semidirect
45. #15692234	C₂²	semidirect
46. #15692232	C₂²	semidirect
47. #15692228	C₂²	semidirect
48. #15692227	C₂²	semidirect
49. #15692226	C₂²	semidirect
50. #15692226	C₂²	semidirect
51. #15692224	C₂²	semidirect
52. #15692223	C₂²	semidirect
53. D₄×Dic₁₀₁	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×D₄×C₁₀₁	C₂²	semidirect
64. #127×C₁₀₁	C₂²	semidirect
65. #124×C₁₀₁	C₂²	semidirect
66. #121×C₁₀₁	C₂²	semidirect
67. #120×C₁₀₁	C₂²	semidirect
68. #117×C₁₀₁	C₂²	semidirect
104. C₂×C₄×D₁₀₁	D₄	semidirect
227. C₁₀₁	#3449	semidirect
236. #535	D₁₀₁	semidirect
260. C₂²×D₄	C₂×D₁₀₁	semidirect
267. #127	C₂×D₁₀₁	semidirect
271. #124	C₂×D₁₀₁	semidirect
282. #121	C₂×D₁₀₁	semidirect
285. #120	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×#13108073	2
C₂×#41×D₁₀₁	2
#20265756	2
#20265753	2
#20265748	2
#20265747	2
#20265744	2
#20265740	2
#20265737	2
#20265726	2
#20265725	2
#20265687	2
#20265683	2
#117×D₁₀₁	2
#535×C₁₀₁	2
#3449	101