Subgroups — #27184545

Order 12928.

1140 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265805	C₂	1	1	yes	maximal, characteristic, complemented
2	#20265796	C₂	1	2	yes	maximal, complemented
3	#20265794	C₂	1	2	yes	maximal, complemented
4	#20265781	C₂	1	2	yes	maximal, complemented
5	#20265780	C₂	1	2	yes	maximal, complemented
6	#20265762	C₂	1	4	yes	maximal, complemented
7	#20265755	C₂	1	1	yes	maximal, characteristic, complemented
8	#20265744	C₂	1	1	yes	maximal, characteristic, complemented
9	#20265725	C₂	1	2	yes	maximal, complemented
10	#20265722	C₂	1	2	yes	maximal, complemented
11	#20265708	C₂	1	2	yes	maximal, complemented
12	#20265706	C₂	1	2	yes	maximal, complemented
13	#20265683	C₂	1	4	yes	maximal, complemented
14	#41×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#20265645	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
17	#535×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13108074	C₂²	1	1	yes	characteristic
19	C₂×#13108073	C₂²	1	4	yes	complemented
20	C₂³×Dic₁₀₁	C₂²	1	2	yes	—
21	#15692255	C₂²	1	2	yes	complemented
22	#15692254	C₂²	1	2	yes	complemented
23	#15692251	C₂²	1	2	yes	—
24	#15692248	C₂²	1	4	yes	complemented
25	#15692248	C₂²	1	4	yes	complemented
26	#15692247	C₂²	1	2	yes	complemented
27	#15692246	C₂²	1	2	yes	complemented
28	#15692242	C₂²	1	2	yes	—
29	#15692242	C₂²	1	4	yes	complemented
30	#15692241	C₂²	1	4	yes	complemented
31	#15692239	C₂²	1	4	yes	complemented
32	#15692237	C₂²	1	4	yes	complemented
33	#15692236	C₂²	1	4	yes	complemented
34	#15692236	C₂²	1	4	yes	complemented
35	#15692234	C₂²	1	2	yes	complemented
36	#15692232	C₂²	1	4	yes	—
37	#15692232	C₂²	1	4	yes	complemented
38	#15692231	C₂²	1	2	yes	complemented
39	#15692229	C₂²	1	2	yes	complemented
40	#15692227	C₂²	1	4	yes	—
41	#15692227	C₂²	1	4	yes	complemented
42	#15692227	C₂²	1	4	yes	complemented
43	#15692226	C₂²	1	2	yes	—
44	#15692226	C₂²	1	2	yes	—
45	#15692226	C₂²	1	2	yes	complemented
46	#15692226	C₂²	1	4	yes	complemented
47	#15692224	C₂²	1	4	yes	—
48	Q₈×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
49	Q₈×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
50	#15692220	C₂²	1	1	yes	characteristic, complemented
51	#15692220	C₂²	1	1	yes	characteristic, complemented
52	D₄×Dic₁₀₁	C₂²	1	2	yes	—
53	D₄×Dic₁₀₁	C₂²	1	2	yes	—
54	D₄×Dic₁₀₁	C₂²	1	2	yes	—
55	D₄×Dic₁₀₁	C₂²	1	2	yes	—
56	D₄×Dic₁₀₁	C₂²	1	2	yes	—
57	D₄×Dic₁₀₁	C₂²	1	2	yes	—
58	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
59	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
60	D₄×Dic₁₀₁	C₂²	1	4	yes	complemented
61	#15692217	C₂²	1	1	yes	characteristic, complemented
62	#15692217	C₂²	1	1	yes	characteristic, complemented
63	#15692215	C₂²	1	2	yes	—
64	#15692215	C₂²	1	2	yes	—
65	#15692215	C₂²	1	4	yes	complemented
66	#15692214	C₂²	1	1	yes	characteristic
67	#15692214	C₂²	1	2	yes	complemented
68	#15692212	C₂²	1	2	yes	complemented
69	#15692211	C₂²	1	4	yes	complemented
70	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
71	C₂×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	—
72	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
73	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	complemented
74	C₄²×D₁₀₁	C₂²	1	2	yes	complemented
75	C₂×#41×C₁₀₁	C₂²	1	1	yes	characteristic
76	C₂²×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
77	#127×C₁₀₁	C₂²	1	2	yes	—
78	#124×C₁₀₁	C₂²	1	2	yes	—
79	#121×C₁₀₁	C₂²	1	2	yes	—
80	#121×C₁₀₁	C₂²	1	2	yes	—
81	#120×C₁₀₁	C₂²	1	4	yes	—
82	#117×C₁₀₁	C₂²	1	1	yes	characteristic
83	#13108074	—	2	4	no	—
84	#13108073	—	4	8	no	—
85	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
86	C₂×Dic₂₀₂	C₂³	1	4	yes	—
87	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
92	C₂²×Dic₁₀₁	—	4	4	no	—
93	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
94	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
95	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
96	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
97	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
98	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
99	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
100	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
101	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
102	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
103	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
104	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
105	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
106	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
108	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
109	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
110	#13108053	C₂³	1	4	yes	—
111	#13108053	C₂³	1	4	yes	—
112	#13108053	C₂³	1	2	yes	—
113	#13108053	C₂³	1	2	yes	—
114	#13108053	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
116	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
119	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
120	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
121	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
122	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
123	#13108051	C₂³	1	2	yes	—
124	#13108051	C₂³	1	2	yes	—
125	#13108051	C₂³	1	4	yes	—
126	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
127	C₄×Dic₁₀₁	C₂³	1	2	yes	—
128	C₄×Dic₁₀₁	C₂³	1	2	yes	—
129	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
130	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
131	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
132	C₄×Dic₁₀₁	C₂³	1	2	yes	—
133	C₄×Dic₁₀₁	C₂³	1	2	yes	—
134	C₄×Dic₁₀₁	C₂³	1	2	yes	—
135	C₂⁴×C₁₀₁	C₂³	1	2	yes	—
136	#41×C₁₀₁	—	2	4	no	—
137	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₁₀₁	—	2	4	no	—
139	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
140	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
141	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
142	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
143	C₂×D₄×C₁₀₁	C₂³	1	4	yes	—
144	C₂×D₄×C₁₀₁	C₂³	1	4	yes	—
145	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
146	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
149	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
151	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
152	C₄²×C₁₀₁	C₂³	1	2	yes	—
153	C₂³×C₁₀₁	—	2	4	no	—
154	C₂³×C₁₀₁	—	4	2	no	—
155	C₂³×C₁₀₁	—	4	2	no	—
156	C₂³×C₁₀₁	C₂⁴	1	4	yes	—
157	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
158	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
159	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
160	Q₈×C₁₀₁	—	2	2	no	—
161	D₄×C₁₀₁	—	2	4	no	—
162	D₄×C₁₀₁	—	2	4	no	—
163	D₄×C₁₀₁	—	2	4	no	—
164	D₄×C₁₀₁	—	2	2	no	—
165	D₄×C₁₀₁	—	4	4	no	—
166	D₄×C₁₀₁	—	4	4	no	—
167	C₂×C₄×C₁₀₁	—	2	4	no	—
168	C₂×C₄×C₁₀₁	#41	1	4	yes	complemented
169	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
174	C₂²⋊D₁₀₁	—	2	4	no	—
175	C₂²⋊D₁₀₁	—	4	4	no	—
176	C₂²⋊D₁₀₁	—	4	4	no	—
177	C₂²⋊D₁₀₁	—	4	4	no	—
178	C₂×Dic₁₀₁	—	2	2	no	—
179	C₂×Dic₁₀₁	—	2	8	no	—
180	C₂×Dic₁₀₁	—	2	4	no	—
181	C₂×Dic₁₀₁	—	4	2	no	—
182	C₂×Dic₁₀₁	—	4	4	no	—
183	C₂×Dic₁₀₁	—	4	1	no	—
184	C₂×Dic₁₀₁	—	4	2	no	—
185	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
186	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
188	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
189	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
190	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
191	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
192	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
193	D₄₀₄	—	2	2	no	—
194	C₄×D₁₀₁	—	2	4	no	—
195	C₄×D₁₀₁	—	2	4	no	—
196	C₄×D₁₀₁	—	4	2	no	—
197	Dic₂₀₂	—	2	2	no	—
198	Dic₂₀₂	—	4	4	no	—
199	C₂²×C₁₀₁	—	2	1	no	—
200	C₂²×C₁₀₁	—	2	1	no	—
201	C₂²×C₁₀₁	—	2	2	no	—
202	C₂²×C₁₀₁	—	2	4	no	—
203	C₂²×C₁₀₁	—	2	4	no	—
204	C₂²×C₁₀₁	—	2	2	no	—
205	C₂²×C₁₀₁	—	2	2	no	—
206	C₂²×C₁₀₁	—	2	4	no	—
207	C₂²×C₁₀₁	—	4	8	no	—
208	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
209	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
210	C₂×D₁₀₁	—	2	2	no	—
211	C₂×D₁₀₁	—	2	2	no	—
212	C₂×D₁₀₁	—	2	2	no	—
213	C₄×C₁₀₁	—	2	2	no	—
214	C₄×C₁₀₁	—	2	2	no	—
215	C₄×C₁₀₁	—	2	2	no	—
216	C₄×C₁₀₁	C₂×#41	1	2	yes	—
217	C₄×C₁₀₁	C₂×#41	1	2	yes	—
218	Dic₁₀₁	—	2	2	no	—
219	Dic₁₀₁	—	2	2	no	—
220	Dic₁₀₁	—	2	4	no	—
221	Dic₁₀₁	—	2	1	no	—
222	Dic₁₀₁	—	2	1	no	—
223	Dic₁₀₁	—	2	1	no	—
224	Dic₁₀₁	—	2	2	no	—
225	Dic₁₀₁	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₁₀₁	—	2	2	no	—
227	C₂×C₁₀₁	—	4	2	no	—
228	C₂×C₁₀₁	—	4	4	no	—
229	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
230	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₁₀₁	#585	1	1	yes	characteristic
232	D₁₀₁	—	4	2	no	—
233	#3460	—	101	1	no	maximal, Sylow
234	C₁₀₁	#3460	1	1	yes	characteristic, complemented, Sylow
235	#544	—	101	1	no	—
236	#542	—	101	2	no	—
237	#542	—	101	2	no	—
238	#540	—	101	2	no	—
239	#540	—	101	2	no	—
240	#538	—	101	4	no	—
241	#537	—	101	1	no	—
242	#535	—	101	1	no	—
243	#535	D₁₀₁	1	1	yes	characteristic, complemented
244	#532	—	101	2	no	—
245	#532	—	101	2	no	—
246	#529	—	101	2	no	—
247	#529	—	101	2	no	—
248	#525	—	101	4	no	—
249	C₄×#41	—	101	1	no	—
250	C₄×#41	—	101	1	no	—
251	C₂×C₄×D₄	—	101	1	no	—
252	C₂×#41	—	101	4	no	—
253	C₂×#41	—	101	1	no	—
254	C₂×#41	C₂×D₁₀₁	1	1	yes	characteristic
255	C₂²×D₄	C₂×D₁₀₁	1	1	yes	characteristic
256	C₂³×C₄	—	101	2	no	—
257	C₄⋊Q₈	—	101	2	no	—
258	C₄⋊Q₈	—	101	2	no	—
259	#127	—	101	2	no	—
260	#127	C₂×D₁₀₁	1	2	yes	—
261	#126	—	101	4	no	—
262	#126	—	101	4	no	—
263	#125	—	101	2	no	—
264	#125	—	101	2	no	—
265	#124	—	101	2	no	—
266	#124	—	101	4	no	—
267	#124	—	101	4	no	—
268	#124	C₂×D₁₀₁	1	2	yes	—
269	#123	—	101	4	no	—
270	#123	—	101	4	no	—
271	#123	—	101	4	no	—
272	#123	—	101	4	no	—
273	C₂²⋊Q₈	—	101	2	no	—
274	C₂²⋊Q₈	—	101	2	no	—
275	C₂²⋊Q₈	—	101	4	no	—
276	C₂²⋊Q₈	—	101	4	no	—
277	#121	—	101	4	no	—
278	#121	—	101	4	no	—
279	#121	—	101	2	no	—
280	#121	—	101	2	no	—
281	#121	—	101	2	no	—
282	#121	—	101	4	no	—
283	#121	—	101	4	no	—
284	#121	—	101	2	no	—
285	#121	C₂×D₁₀₁	1	2	yes	—
286	#121	C₂×D₁₀₁	1	2	yes	—
287	#120	—	101	4	no	—
288	#120	C₂×D₁₀₁	1	4	yes	—
289	C₄×Q₈	—	101	1	no	—
290	C₄×Q₈	—	101	1	no	—
291	C₄×Q₈	—	101	1	no	—
292	C₄×Q₈	—	101	1	no	—
293	C₄×D₄	—	101	2	no	—
294	C₄×D₄	—	101	2	no	—
295	C₄×D₄	—	101	2	no	—
296	C₄×D₄	—	101	2	no	—
297	C₄×D₄	—	101	2	no	—
298	C₄×D₄	—	101	1	no	—
299	C₄×D₄	—	101	2	no	—
300	C₄×D₄	—	101	1	no	—
301	C₄×D₄	—	101	4	no	—
302	C₄×D₄	—	101	1	no	—
303	C₄×D₄	—	101	1	no	—
304	C₄×D₄	—	101	2	no	—
305	C₄×D₄	—	101	2	no	—
306	C₄×D₄	—	101	4	no	—
307	#117	—	101	1	no	—
308	#117	—	101	2	no	—
309	#117	—	101	4	no	—
310	#117	—	101	2	no	—
311	#117	C₂×D₁₀₁	1	1	yes	characteristic
312	C₂×C₄⋊C₄	—	101	1	no	—
313	C₂×C₂²⋊C₄	—	101	2	no	—
314	C₂×C₄²	—	101	1	no	—
315	C₂×C₄²	—	101	2	no	—
316	C₂×C₄²	—	101	2	no	—
317	C₂⁴	C₂²×D₁₀₁	1	2	yes	—
318	#41	—	2	4	no	—
319	#41	—	404	8	no	—
320	#41	—	202	4	no	—
321	C₂×Q₈	—	101	4	no	—
322	C₂×Q₈	—	101	1	no	—
323	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	101	4	no	—
326	C₂×D₄	—	101	4	no	—
327	C₂×D₄	—	101	4	no	—
328	C₂×D₄	—	101	2	no	—
329	C₂×D₄	—	101	1	no	—
330	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
331	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
332	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
333	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
334	C₂×D₄	C₂²×D₁₀₁	1	4	yes	—
335	C₂×D₄	C₂²×D₁₀₁	1	4	yes	—
336	C₂²×C₄	—	101	1	no	—
337	C₂²×C₄	—	101	2	no	—
338	C₂²×C₄	—	101	2	no	—
339	C₂²×C₄	—	101	4	no	—
340	C₂²×C₄	—	101	1	no	—
341	C₂²×C₄	—	101	2	no	—
342	C₂²×C₄	—	101	4	no	—
343	C₂²×C₄	—	101	2	no	—
344	C₂²×C₄	—	101	2	no	—
345	C₂²×C₄	—	101	2	no	—
346	C₂²×C₄	—	404	4	no	—
347	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
348	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
349	C₄⋊C₄	—	101	2	no	—
350	C₄⋊C₄	—	101	2	no	—
351	C₄⋊C₄	—	101	4	no	—
352	C₄⋊C₄	—	101	4	no	—
353	C₄⋊C₄	—	101	4	no	—
354	C₄⋊C₄	—	101	2	no	—
355	C₄⋊C₄	—	101	2	no	—
356	C₄⋊C₄	—	101	1	no	—
357	C₄⋊C₄	—	101	1	no	—
358	C₄⋊C₄	—	101	2	no	—
359	C₄⋊C₄	—	101	2	no	—
360	C₄⋊C₄	—	101	4	no	—
361	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
362	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
363	C₂²⋊C₄	—	101	4	no	—
364	C₂²⋊C₄	—	101	4	no	—
365	C₂²⋊C₄	—	101	2	no	—
366	C₂²⋊C₄	—	101	2	no	—
367	C₂²⋊C₄	—	101	2	no	—
368	C₂²⋊C₄	—	101	4	no	—
369	C₂²⋊C₄	—	101	4	no	—
370	C₂²⋊C₄	—	101	4	no	—
371	C₂²⋊C₄	—	101	2	no	—
372	C₂²⋊C₄	—	101	2	no	—
373	C₂²⋊C₄	—	101	4	no	—
374	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
375	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
376	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
377	C₄²	—	101	1	no	—
378	C₄²	—	101	1	no	—
379	C₄²	—	101	2	no	—
380	C₄²	—	101	2	no	—
381	C₄²	—	101	1	no	—
382	C₄²	—	101	1	no	—
383	C₄²	—	101	2	no	—
384	C₄²	—	101	2	no	—
385	C₄²	—	101	2	no	—
386	C₄²	C₂²×D₁₀₁	1	2	yes	—
387	C₂³	—	2	4	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	101	2	no	—
391	C₂³	C₂³×D₁₀₁	1	4	yes	—
392	C₂³	C₂³×D₁₀₁	1	2	yes	—
393	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
394	Q₈	—	2	2	no	—
395	Q₈	—	404	4	no	—
396	Q₈	—	202	2	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	4	no	—
402	D₄	—	4	4	no	—
403	D₄	—	404	4	no	—
404	D₄	—	404	4	no	—
405	D₄	—	404	4	no	—
406	D₄	—	202	4	no	—
407	D₄	—	202	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	101	1	no	—
410	C₂×C₄	—	101	1	no	—
411	C₂×C₄	—	101	1	no	—
412	C₂×C₄	—	101	2	no	—
413	C₂×C₄	—	101	2	no	—
414	C₂×C₄	—	101	1	no	—
415	C₂×C₄	—	101	2	no	—
416	C₂×C₄	—	101	4	no	—
417	C₂×C₄	—	404	2	no	—
418	C₂×C₄	—	404	4	no	—
419	C₂×C₄	—	404	2	no	—
420	C₂×C₄	—	404	1	no	—
421	C₂×C₄	—	404	2	no	—
422	C₂×C₄	—	202	4	no	—
423	C₂×C₄	—	202	2	no	—
424	C₂×C₄	—	202	8	no	—
425	C₂×C₄	—	202	4	no	—
426	C₂×C₄	—	202	4	no	—
427	C₂×C₄	#13108073	1	4	yes	complemented
428	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
429	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
430	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
431	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	4	8	no	—
442	C₂²	—	202	2	no	—
443	C₂²	—	202	2	no	—
444	C₂²	—	202	2	no	—
445	C₂²	C₂×#13108073	1	2	yes	—
446	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	101	2	no	—
451	C₄	—	202	2	no	—
452	C₄	—	202	1	no	—
453	C₄	—	202	4	no	—
454	C₄	—	202	2	no	—
455	C₄	—	202	1	no	—
456	C₄	—	202	1	no	—
457	C₄	—	202	2	no	—
458	C₄	C₂×#13108073	1	2	yes	—
459	C₄	C₂×#13108073	1	2	yes	—
460	C₂	—	2	2	no	—
461	C₂	—	4	4	no	—
462	C₂	—	4	2	no	—
463	C₂	—	404	2	no	—
464	C₂	C₂²×#13108073	1	1	yes	characteristic
465	C₂	H(5,𝔽₂)×D₁₀₁	1	1	yes	characteristic
466	C₂	#20266012	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#535×C₁₀₁	C₂
hypercenter	#535	D₁₀₁
hypocenter	C₁₀₁	#3460
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. #20265805	C₂	semidirect
2. #20265796	C₂	semidirect
3. #20265794	C₂	semidirect
4. #20265781	C₂	semidirect
5. #20265780	C₂	semidirect
6. #20265762	C₂	semidirect
7. #20265755	C₂	semidirect
8. #20265744	C₂	semidirect
9. #20265725	C₂	semidirect
10. #20265722	C₂	semidirect
11. #20265708	C₂	semidirect
12. #20265706	C₂	semidirect
13. #20265683	C₂	semidirect
14. #41×Dic₁₀₁	C₂	semidirect
15. #20265645	C₂	semidirect
16. C₂×D₄×Dic₁₀₁	C₂	semidirect
17. #535×C₁₀₁	C₂	semidirect
19. C₂×#13108073	C₂²	semidirect
21. #15692255	C₂²	semidirect
22. #15692254	C₂²	semidirect
24. #15692248	C₂²	semidirect
25. #15692248	C₂²	semidirect
26. #15692247	C₂²	semidirect
27. #15692246	C₂²	semidirect
29. #15692242	C₂²	semidirect
30. #15692241	C₂²	semidirect
31. #15692239	C₂²	semidirect
32. #15692237	C₂²	semidirect
33. #15692236	C₂²	semidirect
34. #15692236	C₂²	semidirect
35. #15692234	C₂²	semidirect
37. #15692232	C₂²	semidirect
38. #15692231	C₂²	semidirect
39. #15692229	C₂²	semidirect
41. #15692227	C₂²	semidirect
42. #15692227	C₂²	semidirect
45. #15692226	C₂²	semidirect
46. #15692226	C₂²	semidirect
48. Q₈×Dic₁₀₁	C₂²	semidirect
49. Q₈×Dic₁₀₁	C₂²	semidirect
50. #15692220	C₂²	semidirect
51. #15692220	C₂²	semidirect
58. D₄×Dic₁₀₁	C₂²	semidirect
59. D₄×Dic₁₀₁	C₂²	semidirect
60. D₄×Dic₁₀₁	C₂²	semidirect
61. #15692217	C₂²	semidirect
62. #15692217	C₂²	semidirect
65. #15692215	C₂²	semidirect
67. #15692214	C₂²	semidirect
68. #15692212	C₂²	semidirect
69. #15692211	C₂²	semidirect
73. C₂×C₄×Dic₁₀₁	C₂²	semidirect
74. C₄²×D₁₀₁	C₂²	semidirect
168. C₂×C₄×C₁₀₁	#41	semidirect
234. C₁₀₁	#3460	semidirect
243. #535	D₁₀₁	semidirect
427. C₂×C₄	#13108073	semidirect

Maximal subgroups

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

subgroup	index
#20265805	2
#20265796	2
#20265794	2
#20265781	2
#20265780	2
#20265762	2
#20265755	2
#20265744	2
#20265725	2
#20265722	2
#20265708	2
#20265706	2
#20265683	2
#41×Dic₁₀₁	2
#20265645	2
C₂×D₄×Dic₁₀₁	2
#535×C₁₀₁	2
#3460	101