Subgroups — C₂×C₅×#1764 #11943138

Order 1280.

1558 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#131	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#416	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1764	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₅×#131	—	2	4	no	—
11	C₂×C₅×#131	—	2	2	no	—
12	C₂×C₅×#131	C₄	1	8	yes	complemented
13	C₂×C₅×#131	C₂²	1	4	yes	—
14	C₂²×C₅×M₁₆	—	2	1	no	—
15	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	—	2	1	no	—
18	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₂×C₅×#104	C₄	1	8	yes	complemented
23	C₂×C₅×#104	C₂²	1	4	yes	—
24	C₅×#416	C₄	1	4	yes	complemented
25	C₅×#416	C₂²	1	4	yes	—
26	C₂×C₅×#103	C₄	1	2	yes	complemented
27	C₂×C₅×#102	C₄	1	2	yes	complemented
28	C₅×#405	—	2	2	no	—
29	C₅×#405	C₂²	1	4	yes	complemented
30	C₂×C₅×#97	—	2	1	no	—
31	C₂×C₄×C₅×C₈	—	2	4	no	—
32	C₂×C₄×C₅×C₈	—	2	1	no	—
33	C₂×C₄×C₅×C₈	C₂²	1	4	yes	complemented
34	C₅×#341	C₂²	1	4	yes	complemented
35	C₅×#339	C₂²	1	4	yes	complemented
36	C₂×#1764	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₅×#41	—	2	2	no	—
38	C₂×C₅×#41	—	2	1	no	—
39	C₂×C₅×#41	—	2	1	no	—
40	C₂×C₅×#41	—	2	2	no	—
41	C₂×C₅×#41	C₂×C₄	1	4	yes	—
42	C₂×C₅×#41	C₂×C₄	1	4	yes	—
43	C₂×C₅×#41	C₂×C₄	1	2	yes	—
44	C₂×C₅×#41	C₂³	1	2	yes	—
45	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₅×D₄	—	2	1	no	—
47	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	—	2	1	no	—
49	C₂³×C₄×C₅	—	2	1	no	—
50	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₅×#131	—	2	16	no	—
52	C₅×#131	—	2	8	no	—
53	C₅×#131	C₂×C₄	1	16	yes	complemented
54	C₂×C₅×M₁₆	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂×C₅×M₁₆	—	2	8	no	—
59	C₂×C₅×M₁₆	—	2	4	no	—
60	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
61	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
62	C₂×C₅×M₁₆	C₂³	1	2	yes	—
63	C₂×C₅×M₁₆	C₂³	1	2	yes	—
64	C₂²×C₅×C₈	—	2	2	no	—
65	C₂²×C₅×C₈	—	2	1	no	—
66	C₂²×C₅×C₈	—	2	1	no	—
67	C₂²×C₅×C₈	—	2	2	no	—
68	C₂²×C₅×C₈	—	2	8	no	—
69	C₂²×C₅×C₈	—	2	4	no	—
70	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
71	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
72	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
73	C₂²×C₅×C₈	D₄	1	4	yes	—
74	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
75	C₂²×C₅×C₈	D₄	1	2	yes	—
76	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂³	1	2	yes	—
78	C₂²×C₅×C₈	C₂³	1	2	yes	—
79	C₅×#117	—	2	1	no	—
80	C₅×#117	—	2	1	no	—
81	C₅×#117	C₂×C₄	1	2	yes	—
82	C₅×#117	C₂³	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
84	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₄²×C₅	—	2	2	no	—
86	C₂×C₄²×C₅	—	2	1	no	—
87	C₂×C₄²×C₅	—	2	1	no	—
88	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
89	C₂×C₄²×C₅	C₂³	1	2	yes	—
90	C₅×#104	C₂×C₄	1	16	yes	complemented
91	C₅×#103	C₂×C₄	1	8	yes	complemented
92	C₅×#102	C₂×C₄	1	8	yes	complemented
93	C₅×#97	—	2	4	no	—
94	C₄×C₅×C₈	—	2	8	no	—
95	C₄×C₅×C₈	—	2	4	no	—
96	C₂²×#131	C₂×C₅	1	1	yes	characteristic
97	C₂²×#104	C₂×C₅	1	1	yes	characteristic
98	C₂×#416	C₂×C₅	1	1	yes	characteristic
99	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂²×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
101	#1764	C₂×C₅	1	8	yes	direct product factor
102	C₂×#341	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×#339	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂⁴×C₅	—	2	1	no	—
105	C₂⁴×C₅	#41	1	1	yes	characteristic
106	C₅×#41	—	2	4	no	—
107	C₅×#41	—	2	4	no	—
108	C₅×#41	—	2	4	no	—
109	C₅×#41	—	2	4	no	—
110	C₅×#41	—	2	4	no	—
111	C₅×#41	—	2	2	no	—
112	C₅×#41	—	2	2	no	—
113	C₅×#41	C₄²	1	8	yes	—
114	C₅×#41	C₂²×C₄	1	4	yes	—
115	C₅×#41	C₂²×C₄	1	4	yes	—
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×Q₈	—	2	2	no	—
118	C₂×C₅×Q₈	C₄²	1	4	yes	—
119	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
120	C₂×C₅×D₄	—	2	4	no	—
121	C₂×C₅×D₄	—	2	2	no	—
122	C₂×C₅×D₄	—	2	4	no	—
123	C₂×C₅×D₄	—	2	2	no	—
124	C₂×C₅×D₄	—	2	2	no	—
125	C₂×C₅×D₄	—	2	1	no	—
126	C₂×C₅×D₄	C₄²	1	4	yes	—
127	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₅	—	2	8	no	—
129	C₂²×C₄×C₅	—	2	4	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	2	4	no	—
133	C₂²×C₄×C₅	—	2	2	no	—
134	C₂²×C₄×C₅	—	2	4	no	—
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	—	2	2	no	—
137	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	#41	1	1	yes	characteristic
145	C₂²×C₄×C₅	#41	1	2	yes	—
146	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₅×M₁₆	—	2	4	no	—
148	C₅×M₁₆	—	2	4	no	—
149	C₅×M₁₆	—	2	2	no	—
150	C₅×M₁₆	—	2	2	no	—
151	C₅×M₁₆	—	2	16	no	—
152	C₅×M₁₆	C₂²×C₄	1	4	yes	—
153	C₅×M₁₆	C₂²×C₄	1	4	yes	—
154	C₂×C₅×C₈	—	2	4	no	—
155	C₂×C₅×C₈	—	2	4	no	—
156	C₂×C₅×C₈	—	2	4	no	—
157	C₂×C₅×C₈	—	2	4	no	—
158	C₂×C₅×C₈	—	2	2	no	—
159	C₂×C₅×C₈	—	2	2	no	—
160	C₂×C₅×C₈	—	2	2	no	—
161	C₂×C₅×C₈	—	2	2	no	—
162	C₂×C₅×C₈	—	2	16	no	—
163	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
164	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
165	C₂×C₅×C₈	C₂²⋊C₄	1	8	yes	—
166	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
167	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
168	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
169	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
170	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
173	C₅×C₂²⋊C₄	—	2	2	no	—
174	C₅×C₂²⋊C₄	—	2	2	no	—
175	C₄²×C₅	—	2	4	no	—
176	C₄²×C₅	—	2	2	no	—
177	C₄²×C₅	—	2	2	no	—
178	C₄²×C₅	—	2	2	no	—
179	C₄²×C₅	C₂²×C₄	1	4	yes	—
180	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
181	C₂×#131	—	2	4	no	—
182	C₂×#131	—	2	2	no	—
183	C₂×#131	C₄×C₅	1	8	yes	complemented
184	C₂×#131	C₂²×C₅	1	4	yes	—
185	C₂²×M₁₆	—	2	1	no	—
186	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
187	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
188	C₂³×C₈	—	2	1	no	—
189	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
190	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
191	C₂×#117	C₂²×C₅	1	1	yes	characteristic
192	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
193	C₂×#104	C₄×C₅	1	8	yes	complemented
194	C₂×#104	C₂²×C₅	1	4	yes	—
195	#416	C₄×C₅	1	4	yes	complemented
196	#416	C₂²×C₅	1	4	yes	—
197	C₂×#103	C₄×C₅	1	2	yes	complemented
198	C₂×#102	C₄×C₅	1	2	yes	complemented
199	#405	—	2	2	no	—
200	#405	C₂²×C₅	1	4	yes	complemented
201	C₂×#97	—	2	1	no	—
202	C₂×C₄×C₈	—	2	4	no	—
203	C₂×C₄×C₈	—	2	1	no	—
204	C₂×C₄×C₈	C₂²×C₅	1	4	yes	complemented
205	#341	C₂²×C₅	1	4	yes	complemented
206	#339	C₂²×C₅	1	4	yes	complemented
207	C₂³×C₅	—	2	4	no	—
208	C₂³×C₅	—	2	2	no	—
209	C₂³×C₅	—	2	4	no	—
210	C₂³×C₅	—	4	4	no	—
211	C₂³×C₅	#117	1	2	yes	—
212	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
213	C₂³×C₅	C₄×D₄	1	2	yes	—
214	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₅	C₂×#41	1	1	yes	characteristic
216	C₅×Q₈	—	2	2	no	—
217	C₅×Q₈	—	2	4	no	—
218	C₅×Q₈	C₂×C₄²	1	4	yes	—
219	C₅×D₄	—	2	4	no	—
220	C₅×D₄	—	2	4	no	—
221	C₅×D₄	—	2	8	no	—
222	C₅×D₄	—	2	2	no	—
223	C₅×D₄	—	2	4	no	—
224	C₅×D₄	C₂×C₄²	1	4	yes	—
225	C₂×C₄×C₅	—	2	8	no	—
226	C₂×C₄×C₅	—	2	16	no	—
227	C₂×C₄×C₅	—	2	4	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	4	no	—
230	C₂×C₄×C₅	—	2	4	no	—
231	C₂×C₄×C₅	—	2	4	no	—
232	C₂×C₄×C₅	—	2	8	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	4	4	no	—
235	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
236	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
237	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
238	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
239	C₂×C₄×C₅	#117	1	2	yes	—
240	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
241	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
242	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
243	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
244	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
246	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
253	C₅×C₈	—	2	4	no	—
254	C₅×C₈	—	2	4	no	—
255	C₅×C₈	—	2	4	no	—
256	C₅×C₈	C₂×C₂²⋊C₄	1	4	yes	—
257	C₅×C₈	C₂×C₂²⋊C₄	1	4	yes	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	2	1	no	—
260	C₂×#41	—	2	1	no	—
261	C₂×#41	—	2	2	no	—
262	C₂×#41	C₂×C₄×C₅	1	4	yes	—
263	C₂×#41	C₂×C₄×C₅	1	4	yes	—
264	C₂×#41	C₂×C₄×C₅	1	2	yes	—
265	C₂×#41	C₂³×C₅	1	2	yes	—
266	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
272	#131	—	2	16	no	—
273	#131	—	2	8	no	—
274	#131	C₂×C₄×C₅	1	16	yes	complemented
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	8	no	—
280	C₂×M₁₆	—	2	4	no	—
281	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
282	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
283	C₂×M₁₆	C₂³×C₅	1	2	yes	—
284	C₂×M₁₆	C₂³×C₅	1	2	yes	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	—	2	2	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	8	no	—
290	C₂²×C₈	—	2	4	no	—
291	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
292	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
293	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
294	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
295	C₂²×C₈	C₅×D₄	1	4	yes	—
296	C₂²×C₈	C₅×D₄	1	2	yes	—
297	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₅	1	2	yes	—
299	C₂²×C₈	C₂³×C₅	1	2	yes	—
300	#117	—	2	1	no	—
301	#117	—	2	1	no	—
302	#117	C₂×C₄×C₅	1	2	yes	—
303	#117	C₂³×C₅	1	2	yes	—
304	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
310	C₂×C₄²	C₂³×C₅	1	2	yes	—
311	#104	C₂×C₄×C₅	1	16	yes	complemented
312	#103	C₂×C₄×C₅	1	8	yes	complemented
313	#102	C₂×C₄×C₅	1	8	yes	complemented
314	#97	—	2	4	no	—
315	C₄×C₈	—	2	8	no	—
316	C₄×C₈	—	2	4	no	—
317	C₂²×C₅	—	2	2	no	—
318	C₂²×C₅	—	2	2	no	—
319	C₂²×C₅	—	2	4	no	—
320	C₂²×C₅	—	2	4	no	—
321	C₂²×C₅	—	2	4	no	—
322	C₂²×C₅	—	4	4	no	—
323	C₂²×C₅	—	4	8	no	—
324	C₂²×C₅	C₄×C₂²⋊C₄	1	2	yes	—
325	C₂²×C₅	C₄×C₂²⋊C₄	1	2	yes	—
326	C₂²×C₅	#443	1	4	yes	—
327	C₂²×C₅	C₂×#117	1	1	yes	characteristic
328	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
329	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
330	C₄×C₅	—	2	8	no	—
331	C₄×C₅	—	2	4	no	—
332	C₄×C₅	—	4	4	no	—
333	C₄×C₅	C₄×C₂²⋊C₄	1	2	yes	—
334	C₄×C₅	C₄×C₂²⋊C₄	1	2	yes	—
335	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
336	C₄×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
337	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
338	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
339	C₂⁴	—	2	1	no	—
340	C₂⁴	C₅×#41	1	1	yes	characteristic
341	#41	—	2	4	no	—
342	#41	—	2	4	no	—
343	#41	—	2	4	no	—
344	#41	—	2	4	no	—
345	#41	—	2	4	no	—
346	#41	—	2	2	no	—
347	#41	—	2	2	no	—
348	#41	C₄²×C₅	1	8	yes	—
349	#41	C₂²×C₄×C₅	1	4	yes	—
350	#41	C₂²×C₄×C₅	1	4	yes	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	C₄²×C₅	1	4	yes	—
354	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	C₄²×C₅	1	4	yes	—
362	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
373	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
374	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
375	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
378	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
379	C₂²×C₄	C₅×#41	1	1	yes	characteristic
380	C₂²×C₄	C₅×#41	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
382	M₁₆	—	2	4	no	—
383	M₁₆	—	2	4	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	2	16	no	—
387	M₁₆	C₂²×C₄×C₅	1	4	yes	—
388	M₁₆	C₂²×C₄×C₅	1	4	yes	—
389	C₂×C₈	—	2	4	no	—
390	C₂×C₈	—	2	4	no	—
391	C₂×C₈	—	2	4	no	—
392	C₂×C₈	—	2	4	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	16	no	—
398	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
399	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
400	C₂×C₈	C₅×C₂²⋊C₄	1	8	yes	—
401	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
402	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
403	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
404	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
405	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₄²	—	2	4	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	C₂²×C₄×C₅	1	4	yes	—
415	C₂×C₅	—	2	1	no	—
416	C₂×C₅	—	2	1	no	—
417	C₂×C₅	—	2	2	no	—
418	C₂×C₅	—	4	4	no	—
419	C₂×C₅	#1764	1	4	yes	direct product factor
420	C₂×C₅	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
421	C₂×C₅	C₂×#443	1	2	yes	—
422	C₂³	—	2	4	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	4	4	no	—
426	C₂³	C₅×#117	1	2	yes	—
427	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
428	C₂³	C₄×C₅×D₄	1	2	yes	—
429	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
430	C₂³	C₂×C₅×#41	1	1	yes	characteristic
431	Q₈	—	2	4	no	—
432	Q₈	—	2	2	no	—
433	Q₈	C₂×C₄²×C₅	1	4	yes	—
434	D₄	—	2	8	no	—
435	D₄	—	2	4	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	2	no	—
439	D₄	C₂×C₄²×C₅	1	4	yes	—
440	C₂×C₄	—	2	16	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
451	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
452	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
453	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
454	C₂×C₄	C₅×#117	1	2	yes	—
455	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
456	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
457	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
458	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
459	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
460	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
461	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
462	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
463	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
464	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
467	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
468	C₈	—	2	4	no	—
469	C₈	—	2	4	no	—
470	C₈	—	2	4	no	—
471	C₈	C₂×C₅×C₂²⋊C₄	1	4	yes	—
472	C₈	C₂×C₅×C₂²⋊C₄	1	4	yes	—
473	C₅	C₂×#1764	1	1	yes	characteristic, direct product factor, Sylow
474	C₂²	—	2	4	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	4	8	no	—
480	C₂²	—	4	4	no	—
481	C₂²	C₄×C₅×C₂²⋊C₄	1	2	yes	—
482	C₂²	C₄×C₅×C₂²⋊C₄	1	2	yes	—
483	C₂²	C₅×#443	1	4	yes	—
484	C₂²	C₂×C₅×#117	1	1	yes	characteristic
485	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
486	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
487	C₄	—	2	8	no	—
488	C₄	—	2	4	no	—
489	C₄	—	4	4	no	—
490	C₄	C₄×C₅×C₂²⋊C₄	1	2	yes	—
491	C₄	C₄×C₅×C₂²⋊C₄	1	2	yes	—
492	C₄	C₂²×C₄²×C₅	1	1	yes	characteristic
493	C₄	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
494	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
495	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
496	C₂	—	2	1	no	—
497	C₂	—	2	2	no	—
498	C₂	—	2	1	no	—
499	C₂	—	4	4	no	—
500	C₂	C₅×#1764	1	4	yes	direct product factor
501	C₂	C₂×C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
502	C₂	C₂×C₅×#443	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅×C₈	D₄
commutator	C₄	C₂²×C₄²×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₄×D₄
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅×C₈ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₅×#405	C₂	semidirect
5. C₂²×C₄×C₅×C₈	C₂	semidirect
6. C₅×#1764	C₂	direct (N × H)
7. C₂×C₅×#341	C₂	semidirect
8. C₂×C₅×#339	C₂	semidirect
12. C₂×C₅×#131	C₄	semidirect
22. C₂×C₅×#104	C₄	semidirect
24. C₅×#416	C₄	semidirect
26. C₂×C₅×#103	C₄	semidirect
27. C₂×C₅×#102	C₄	semidirect
29. C₅×#405	C₂²	semidirect
33. C₂×C₄×C₅×C₈	C₂²	semidirect
34. C₅×#341	C₂²	semidirect
35. C₅×#339	C₂²	semidirect
36. C₂×#1764	C₅	direct (N × H)
53. C₅×#131	C₂×C₄	semidirect
90. C₅×#104	C₂×C₄	semidirect
91. C₅×#103	C₂×C₄	semidirect
92. C₅×#102	C₂×C₄	semidirect
99. C₂×#405	C₂×C₅	semidirect
100. C₂²×C₄×C₈	C₂×C₅	semidirect
101. #1764	C₂×C₅	direct (N × H)
102. C₂×#341	C₂×C₅	semidirect
103. C₂×#339	C₂×C₅	semidirect
183. C₂×#131	C₄×C₅	semidirect
193. C₂×#104	C₄×C₅	semidirect
195. #416	C₄×C₅	semidirect
197. C₂×#103	C₄×C₅	semidirect
198. C₂×#102	C₄×C₅	semidirect
200. #405	C₂²×C₅	semidirect
204. C₂×C₄×C₈	C₂²×C₅	semidirect
205. #341	C₂²×C₅	semidirect
206. #339	C₂²×C₅	semidirect
274. #131	C₂×C₄×C₅	semidirect
311. #104	C₂×C₄×C₅	semidirect
312. #103	C₂×C₄×C₅	semidirect
313. #102	C₂×C₄×C₅	semidirect
419. C₂×C₅	#1764	direct (N × H)
473. C₅	C₂×#1764	direct (N × H)
500. C₂	C₅×#1764	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#131	2
C₂²×C₅×#104	2
C₂×C₅×#416	2
C₂×C₅×#405	2
C₂²×C₄×C₅×C₈	2
C₅×#1764	2
C₂×C₅×#341	2
C₂×C₅×#339	2
C₂×#1764	5

Subgroups — C2×C5×#1764 #11943138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1764 #11943138