Subgroups — C₂×C₅×#3294 #11983832

Order 1280.

2858 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3294	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#480	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#466	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#447	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×#102	C₂	1	2	yes	maximal, complemented
13	C₂²×C₅×#41	—	2	1	no	—
14	C₂³×C₅×D₄	—	2	1	no	—
15	C₂³×C₅×D₄	C₂²	1	2	yes	—
16	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×D₈	C₂²	1	2	yes	complemented
18	C₂³×C₅×C₈	C₂²	1	2	yes	complemented
19	C₅×#547	—	2	4	no	—
20	C₅×#547	C₂²	1	8	yes	complemented
21	C₅×D₄²	—	2	4	no	—
22	C₅×D₄²	C₂²	1	8	yes	complemented
23	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×#127	C₂²	1	1	yes	characteristic
25	C₂×C₅×#123	—	2	2	no	—
26	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₅×#121	—	2	1	no	—
28	C₂×C₅×#121	C₂²	1	2	yes	—
29	C₂×C₅×#121	C₂²	1	2	yes	complemented
30	C₂×C₅×#120	—	2	2	no	—
31	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
35	C₅×#486	C₂²	1	8	yes	complemented
36	C₅×#480	C₂²	1	16	yes	complemented
37	C₅×#474	C₂²	1	8	yes	complemented
38	C₅×#466	C₂²	1	16	yes	complemented
39	C₅×#459	C₂²	1	8	yes	complemented
40	C₅×#447	C₂²	1	16	yes	complemented
41	C₄×C₅×D₈	C₂²	1	8	yes	complemented
42	C₅×C₈×D₄	C₂²	1	8	yes	complemented
43	C₂×C₅×#107	C₂²	1	2	yes	complemented
44	C₂×C₅×#107	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₅×#102	C₂²	1	2	yes	—
47	C₂×C₅×#102	C₂²	1	1	yes	characteristic
48	C₂×C₅×#102	C₂²	1	2	yes	complemented
49	C₂×C₅×#102	C₂²	1	2	yes	complemented
50	C₂×C₅×#102	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₅×#102	C₂²	1	2	yes	complemented
52	C₂×C₅×#102	C₂²	1	16	yes	complemented
53	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
54	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
55	C₂×#3294	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂⁵×C₅	—	2	2	no	—
57	C₂×C₅×#41	—	2	8	no	—
58	C₂×C₅×#41	—	4	8	no	—
59	C₂²×C₅×Q₈	—	2	1	no	—
60	C₂²×C₅×D₄	—	2	8	no	—
61	C₂²×C₅×D₄	—	2	2	no	—
62	C₂²×C₅×D₄	—	2	2	no	—
63	C₂²×C₅×D₄	—	2	8	no	—
64	C₂²×C₅×D₄	—	2	2	no	—
65	C₂²×C₅×D₄	—	2	1	no	—
66	C₂²×C₅×D₄	—	2	4	no	—
67	C₂²×C₅×D₄	—	2	1	no	—
68	C₂²×C₅×D₄	—	4	4	no	—
69	C₂²×C₅×D₄	—	4	8	no	—
70	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
71	C₂²×C₅×D₄	C₂³	1	2	yes	—
72	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
73	C₂²×C₅×D₄	C₂³	1	8	yes	—
74	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₅	—	2	2	no	—
76	C₂³×C₄×C₅	—	2	1	no	—
77	C₂³×C₄×C₅	—	2	1	no	—
78	C₂³×C₄×C₅	C₂³	1	2	yes	—
79	C₂×C₅×D₈	—	2	4	no	—
80	C₂×C₅×D₈	—	4	4	no	—
81	C₂×C₅×D₈	C₂³	1	4	yes	—
82	C₂×C₅×D₈	C₂³	1	8	yes	complemented
83	C₂²×C₅×C₈	—	4	4	no	—
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₅×C₈	C₂³	1	2	yes	—
87	C₂²×C₅×C₈	C₂³	1	8	yes	complemented
88	C₅×C₄⋊Q₈	—	2	2	no	—
89	C₅×C₄⋊Q₈	C₂³	1	4	yes	complemented
90	C₅×#127	—	2	2	no	—
91	C₅×#127	C₂³	1	4	yes	—
92	C₅×#123	—	2	16	no	—
93	C₅×C₂²⋊Q₈	—	2	8	no	—
94	C₅×#121	—	2	4	no	—
95	C₅×#121	—	2	4	no	—
96	C₅×#121	—	2	8	no	—
97	C₅×#121	C₂³	1	8	yes	—
98	C₅×#121	C₂³	1	8	yes	complemented
99	C₅×#120	—	2	16	no	—
100	C₄×C₅×D₄	—	2	2	no	—
101	C₄×C₅×D₄	—	2	2	no	—
102	C₄×C₅×D₄	D₄	1	4	yes	—
103	C₄×C₅×D₄	C₂³	1	4	yes	—
104	C₄×C₅×D₄	C₂³	1	4	yes	—
105	C₄×C₅×D₄	C₂³	1	4	yes	complemented
106	C₂×C₅×C₄⋊C₄	—	2	2	no	—
107	C₂×C₅×C₄⋊C₄	—	2	4	no	—
108	C₂×C₅×C₄⋊C₄	—	2	1	no	—
109	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	complemented
114	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
118	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
119	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
120	C₅×#107	C₂³	1	4	yes	complemented
121	C₅×#107	C₂³	1	8	yes	complemented
122	C₅×C₄⋊C₈	C₂³	1	4	yes	complemented
123	C₅×#102	C₂³	1	4	yes	—
124	C₅×#102	C₂³	1	8	yes	—
125	C₅×#102	C₂³	1	8	yes	complemented
126	C₅×#102	C₂³	1	8	yes	complemented
127	C₅×#102	C₂³	1	4	yes	complemented
128	C₅×#102	C₂³	1	8	yes	complemented
129	C₅×C₂²⋊C₈	C₂³	1	8	yes	complemented
130	C₄×C₅×C₈	C₂³	1	4	yes	complemented
131	C₂×#547	C₂×C₅	1	1	yes	characteristic, complemented
132	C₂×D₄²	C₂×C₅	1	1	yes	characteristic, complemented
133	#3294	C₂×C₅	1	16	yes	direct product factor
134	C₂×#486	C₂×C₅	1	1	yes	characteristic, complemented
135	C₂×#480	C₂×C₅	1	2	yes	complemented
136	C₂×#474	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂×#466	C₂×C₅	1	2	yes	complemented
138	C₂×#459	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂×#447	C₂×C₅	1	2	yes	complemented
140	C₂×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂²×#102	C₂×C₅	1	2	yes	complemented
143	C₂⁴×C₅	—	2	1	no	—
144	C₂⁴×C₅	—	2	1	no	—
145	C₂⁴×C₅	—	2	2	no	—
146	C₂⁴×C₅	—	2	8	no	—
147	C₂⁴×C₅	—	4	8	no	—
148	C₂⁴×C₅	—	4	8	no	—
149	C₂⁴×C₅	—	8	4	no	—
150	C₂⁴×C₅	C₂×D₄	1	2	yes	—
151	C₅×#41	—	4	32	no	—
152	C₂×C₅×Q₈	—	2	4	no	—
153	C₂×C₅×Q₈	—	4	4	no	—
154	C₂×C₅×D₄	—	2	16	no	—
155	C₂×C₅×D₄	—	2	8	no	—
156	C₂×C₅×D₄	—	2	8	no	—
157	C₂×C₅×D₄	—	2	1	no	—
158	C₂×C₅×D₄	—	2	1	no	—
159	C₂×C₅×D₄	—	2	8	no	—
160	C₂×C₅×D₄	—	2	2	no	—
161	C₂×C₅×D₄	—	2	4	no	—
162	C₂×C₅×D₄	—	2	4	no	—
163	C₂×C₅×D₄	—	2	2	no	—
164	C₂×C₅×D₄	—	2	4	no	—
165	C₂×C₅×D₄	—	2	2	no	—
166	C₂×C₅×D₄	—	2	2	no	—
167	C₂×C₅×D₄	—	2	4	no	—
168	C₂×C₅×D₄	—	4	8	no	—
169	C₂×C₅×D₄	—	4	16	no	—
170	C₂×C₅×D₄	—	4	8	no	—
171	C₂×C₅×D₄	—	4	8	no	—
172	C₂×C₅×D₄	—	4	8	no	—
173	C₂×C₅×D₄	—	4	32	no	—
174	C₂×C₅×D₄	—	4	4	no	—
175	C₂×C₅×D₄	—	8	2	no	—
176	C₂×C₅×D₄	D₈	1	8	yes	complemented
177	C₂×C₅×D₄	C₂×D₄	1	4	yes	—
178	C₂×C₅×D₄	#41	1	4	yes	complemented
179	C₂×C₅×D₄	C₂⁴	1	2	yes	—
180	C₂×C₅×D₄	C₂⁴	1	4	yes	—
181	C₂×C₅×D₄	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₅	—	2	4	no	—
183	C₂²×C₄×C₅	—	2	4	no	—
184	C₂²×C₄×C₅	—	2	8	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	2	2	no	—
188	C₂²×C₄×C₅	—	2	4	no	—
189	C₂²×C₄×C₅	—	2	4	no	—
190	C₂²×C₄×C₅	—	4	8	no	—
191	C₂²×C₄×C₅	—	4	4	no	—
192	C₂²×C₄×C₅	—	4	4	no	—
193	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
194	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
199	C₅×D₈	—	2	8	no	—
200	C₅×D₈	—	4	8	no	—
201	C₂×C₅×C₈	—	2	2	no	—
202	C₂×C₅×C₈	—	2	2	no	—
203	C₂×C₅×C₈	—	2	4	no	—
204	C₂×C₅×C₈	—	4	8	no	—
205	C₂×C₅×C₈	C₂⁴	1	2	yes	—
206	C₂×C₅×C₈	C₂⁴	1	4	yes	—
207	C₂×C₅×C₈	C₂⁴	1	2	yes	—
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	2	no	—
210	C₅×C₄⋊C₄	—	2	8	no	—
211	C₅×C₄⋊C₄	—	2	4	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
214	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
215	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
216	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
217	C₅×C₂²⋊C₄	—	2	4	no	—
218	C₅×C₂²⋊C₄	—	2	4	no	—
219	C₅×C₂²⋊C₄	—	2	8	no	—
220	C₅×C₂²⋊C₄	—	2	8	no	—
221	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
222	C₄²×C₅	C₂×D₄	1	2	yes	—
223	C₄²×C₅	C₂⁴	1	2	yes	—
224	C₂²×#41	—	2	1	no	—
225	C₂³×D₄	—	2	1	no	—
226	C₂³×D₄	C₂²×C₅	1	2	yes	—
227	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
228	C₂²×D₈	C₂²×C₅	1	2	yes	complemented
229	C₂³×C₈	C₂²×C₅	1	2	yes	complemented
230	#547	—	2	4	no	—
231	#547	C₂²×C₅	1	8	yes	complemented
232	D₄²	—	2	4	no	—
233	D₄²	C₂²×C₅	1	8	yes	complemented
234	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
235	C₂×#127	C₂²×C₅	1	1	yes	characteristic
236	C₂×#123	—	2	2	no	—
237	C₂×C₂²⋊Q₈	—	2	1	no	—
238	C₂×#121	—	2	1	no	—
239	C₂×#121	C₂²×C₅	1	2	yes	—
240	C₂×#121	C₂²×C₅	1	2	yes	complemented
241	C₂×#120	—	2	2	no	—
242	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
245	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
246	#486	C₂²×C₅	1	8	yes	complemented
247	#480	C₂²×C₅	1	16	yes	complemented
248	#474	C₂²×C₅	1	8	yes	complemented
249	#466	C₂²×C₅	1	16	yes	complemented
250	#459	C₂²×C₅	1	8	yes	complemented
251	#447	C₂²×C₅	1	16	yes	complemented
252	C₄×D₈	C₂²×C₅	1	8	yes	complemented
253	C₈×D₄	C₂²×C₅	1	8	yes	complemented
254	C₂×#107	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₂×#107	C₂²×C₅	1	2	yes	complemented
256	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₂×#102	C₂²×C₅	1	1	yes	characteristic
258	C₂×#102	C₂²×C₅	1	2	yes	—
259	C₂×#102	C₂²×C₅	1	16	yes	complemented
260	C₂×#102	C₂²×C₅	1	2	yes	complemented
261	C₂×#102	C₂²×C₅	1	2	yes	complemented
262	C₂×#102	C₂²×C₅	1	2	yes	complemented
263	C₂×#102	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
265	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
266	C₂³×C₅	—	2	4	no	—
267	C₂³×C₅	—	2	4	no	—
268	C₂³×C₅	—	2	4	no	—
269	C₂³×C₅	—	2	2	no	—
270	C₂³×C₅	—	2	2	no	—
271	C₂³×C₅	—	2	4	no	—
272	C₂³×C₅	—	4	16	no	—
273	C₂³×C₅	—	4	2	no	—
274	C₂³×C₅	—	4	2	no	—
275	C₂³×C₅	—	4	4	no	—
276	C₂³×C₅	—	4	2	no	—
277	C₂³×C₅	—	4	2	no	—
278	C₂³×C₅	—	4	16	no	—
279	C₂³×C₅	—	4	4	no	—
280	C₂³×C₅	—	4	4	no	—
281	C₂³×C₅	—	4	2	no	—
282	C₂³×C₅	—	8	8	no	—
283	C₂³×C₅	—	8	32	no	—
284	C₂³×C₅	C₂×D₈	1	8	yes	—
285	C₂³×C₅	C₂²×D₄	1	4	yes	—
286	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
287	C₅×Q₈	—	4	8	no	—
288	C₅×D₄	—	2	4	no	—
289	C₅×D₄	—	2	2	no	—
290	C₅×D₄	—	2	4	no	—
291	C₅×D₄	—	2	2	no	—
292	C₅×D₄	—	2	2	no	—
293	C₅×D₄	—	2	4	no	—
294	C₅×D₄	—	4	16	no	—
295	C₅×D₄	—	4	16	no	—
296	C₅×D₄	—	4	16	no	—
297	C₅×D₄	—	4	2	no	—
298	C₅×D₄	—	4	4	no	—
299	C₅×D₄	—	4	8	no	—
300	C₅×D₄	—	8	4	no	—
301	C₅×D₄	C₂×D₈	1	16	yes	complemented
302	C₅×D₄	C₂×#41	1	4	yes	complemented
303	C₂×C₄×C₅	—	2	4	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	8	no	—
306	C₂×C₄×C₅	—	2	4	no	—
307	C₂×C₄×C₅	—	2	4	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	4	no	—
311	C₂×C₄×C₅	—	4	2	no	—
312	C₂×C₄×C₅	—	4	2	no	—
313	C₂×C₄×C₅	—	4	4	no	—
314	C₂×C₄×C₅	—	4	16	no	—
315	C₂×C₄×C₅	—	4	8	no	—
316	C₂×C₄×C₅	—	4	8	no	—
317	C₂×C₄×C₅	C₂×D₈	1	4	yes	—
318	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
320	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₅	C₂×#41	1	2	yes	—
323	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
324	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
325	C₅×C₈	—	2	2	no	—
326	C₅×C₈	—	2	2	no	—
327	C₅×C₈	—	2	4	no	—
328	C₂⁵	—	2	2	no	—
329	C₂×#41	—	2	8	no	—
330	C₂×#41	—	4	8	no	—
331	C₂²×Q₈	—	2	1	no	—
332	C₂²×D₄	—	2	8	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	2	2	no	—
335	C₂²×D₄	—	2	8	no	—
336	C₂²×D₄	—	2	2	no	—
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	—	2	4	no	—
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	4	4	no	—
341	C₂²×D₄	—	4	8	no	—
342	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
343	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
344	C₂²×D₄	C₂³×C₅	1	2	yes	—
345	C₂²×D₄	C₂³×C₅	1	8	yes	—
346	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
347	C₂³×C₄	—	2	2	no	—
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	C₂³×C₅	1	2	yes	—
351	C₂×D₈	—	2	4	no	—
352	C₂×D₈	—	4	4	no	—
353	C₂×D₈	C₂³×C₅	1	4	yes	—
354	C₂×D₈	C₂³×C₅	1	8	yes	complemented
355	C₂²×C₈	—	4	4	no	—
356	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₅	1	2	yes	—
358	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₅	1	8	yes	complemented
360	C₄⋊Q₈	—	2	2	no	—
361	C₄⋊Q₈	C₂³×C₅	1	4	yes	complemented
362	#127	—	2	2	no	—
363	#127	C₂³×C₅	1	4	yes	—
364	#123	—	2	16	no	—
365	C₂²⋊Q₈	—	2	8	no	—
366	#121	—	2	4	no	—
367	#121	—	2	4	no	—
368	#121	—	2	8	no	—
369	#121	C₂³×C₅	1	8	yes	—
370	#121	C₂³×C₅	1	8	yes	complemented
371	#120	—	2	16	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	C₅×D₄	1	4	yes	—
375	C₄×D₄	C₂³×C₅	1	4	yes	—
376	C₄×D₄	C₂³×C₅	1	4	yes	—
377	C₄×D₄	C₂³×C₅	1	4	yes	complemented
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	—	2	4	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	complemented
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
391	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
392	#107	C₂³×C₅	1	4	yes	complemented
393	#107	C₂³×C₅	1	8	yes	complemented
394	C₄⋊C₈	C₂³×C₅	1	4	yes	complemented
395	#102	C₂³×C₅	1	4	yes	—
396	#102	C₂³×C₅	1	8	yes	—
397	#102	C₂³×C₅	1	8	yes	complemented
398	#102	C₂³×C₅	1	8	yes	complemented
399	#102	C₂³×C₅	1	4	yes	complemented
400	#102	C₂³×C₅	1	8	yes	complemented
401	C₂²⋊C₈	C₂³×C₅	1	8	yes	complemented
402	C₄×C₈	C₂³×C₅	1	4	yes	complemented
403	C₂²×C₅	—	2	4	no	—
404	C₂²×C₅	—	2	16	no	—
405	C₂²×C₅	—	2	4	no	—
406	C₂²×C₅	—	2	4	no	—
407	C₂²×C₅	—	4	8	no	—
408	C₂²×C₅	—	4	2	no	—
409	C₂²×C₅	—	4	2	no	—
410	C₂²×C₅	—	4	4	no	—
411	C₂²×C₅	—	4	2	no	—
412	C₂²×C₅	—	4	2	no	—
413	C₂²×C₅	—	4	4	no	—
414	C₂²×C₅	—	4	4	no	—
415	C₂²×C₅	—	4	2	no	—
416	C₂²×C₅	—	8	32	no	—
417	C₂²×C₅	—	8	4	no	—
418	C₂²×C₅	—	8	8	no	—
419	C₂²×C₅	#546	1	2	yes	—
420	C₂²×C₅	C₂²×D₈	1	8	yes	—
421	C₂²×C₅	C₂²×D₈	1	2	yes	—
422	C₂²×C₅	#577	1	2	yes	—
423	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
424	C₄×C₅	—	2	4	no	—
425	C₄×C₅	—	2	2	no	—
426	C₄×C₅	—	4	2	no	—
427	C₄×C₅	—	4	2	no	—
428	C₄×C₅	—	4	4	no	—
429	C₄×C₅	#546	1	2	yes	—
430	C₄×C₅	C₂²×D₈	1	4	yes	—
431	C₄×C₅	C₂²×#41	1	1	yes	characteristic
432	C₄×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
433	C₂⁴	—	2	1	no	—
434	C₂⁴	—	2	1	no	—
435	C₂⁴	—	2	2	no	—
436	C₂⁴	—	2	8	no	—
437	C₂⁴	—	4	8	no	—
438	C₂⁴	—	4	8	no	—
439	C₂⁴	—	8	4	no	—
440	C₂⁴	C₂×C₅×D₄	1	2	yes	—
441	#41	—	4	32	no	—
442	C₂×Q₈	—	2	4	no	—
443	C₂×Q₈	—	4	4	no	—
444	C₂×D₄	—	2	16	no	—
445	C₂×D₄	—	2	8	no	—
446	C₂×D₄	—	2	8	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	8	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	4	8	no	—
459	C₂×D₄	—	4	16	no	—
460	C₂×D₄	—	4	8	no	—
461	C₂×D₄	—	4	8	no	—
462	C₂×D₄	—	4	8	no	—
463	C₂×D₄	—	4	32	no	—
464	C₂×D₄	—	4	4	no	—
465	C₂×D₄	—	8	2	no	—
466	C₂×D₄	C₅×D₈	1	8	yes	complemented
467	C₂×D₄	C₂×C₅×D₄	1	4	yes	—
468	C₂×D₄	C₅×#41	1	4	yes	complemented
469	C₂×D₄	C₂⁴×C₅	1	4	yes	—
470	C₂×D₄	C₂⁴×C₅	1	2	yes	—
471	C₂×D₄	C₂⁴×C₅	1	2	yes	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	8	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	4	8	no	—
481	C₂²×C₄	—	4	4	no	—
482	C₂²×C₄	—	4	4	no	—
483	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
484	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
485	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
486	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
489	D₈	—	2	8	no	—
490	D₈	—	4	8	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	4	no	—
494	C₂×C₈	—	4	8	no	—
495	C₂×C₈	C₂⁴×C₅	1	2	yes	—
496	C₂×C₈	C₂⁴×C₅	1	2	yes	—
497	C₂×C₈	C₂⁴×C₅	1	4	yes	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	8	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
504	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
505	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
506	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	8	no	—
510	C₂²⋊C₄	—	2	8	no	—
511	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
512	C₄²	C₂×C₅×D₄	1	2	yes	—
513	C₄²	C₂⁴×C₅	1	2	yes	—
514	C₂×C₅	—	2	8	no	—
515	C₂×C₅	—	4	4	no	—
516	C₂×C₅	—	8	2	no	—
517	C₂×C₅	—	8	4	no	—
518	C₂×C₅	#3294	1	4	yes	direct product factor
519	C₂×C₅	C₂×#546	1	1	yes	characteristic
520	C₂×C₅	C₂³×D₈	1	1	yes	characteristic
521	C₂×C₅	C₂×#577	1	1	yes	characteristic
522	C₂³	—	2	4	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	4	16	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	4	no	—
532	C₂³	—	4	2	no	—
533	C₂³	—	4	2	no	—
534	C₂³	—	4	16	no	—
535	C₂³	—	4	4	no	—
536	C₂³	—	4	4	no	—
537	C₂³	—	4	2	no	—
538	C₂³	—	8	8	no	—
539	C₂³	—	8	32	no	—
540	C₂³	C₂×C₅×D₈	1	8	yes	—
541	C₂³	C₂²×C₅×D₄	1	4	yes	—
542	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
543	Q₈	—	4	8	no	—
544	D₄	—	2	4	no	—
545	D₄	—	2	2	no	—
546	D₄	—	2	4	no	—
547	D₄	—	2	2	no	—
548	D₄	—	2	2	no	—
549	D₄	—	2	4	no	—
550	D₄	—	4	16	no	—
551	D₄	—	4	16	no	—
552	D₄	—	4	16	no	—
553	D₄	—	4	4	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	8	no	—
556	D₄	—	8	4	no	—
557	D₄	C₂×C₅×D₈	1	16	yes	complemented
558	D₄	C₂×C₅×#41	1	4	yes	complemented
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	8	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	4	no	—
570	C₂×C₄	—	4	16	no	—
571	C₂×C₄	—	4	8	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	C₂×C₅×D₈	1	4	yes	—
574	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
575	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
576	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
577	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
578	C₂×C₄	C₂×C₅×#41	1	2	yes	—
579	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
580	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
581	C₈	—	2	2	no	—
582	C₈	—	2	2	no	—
583	C₈	—	2	4	no	—
584	C₅	C₂×#3294	1	1	yes	characteristic, direct product factor, Sylow
585	C₂²	—	2	16	no	—
586	C₂²	—	2	4	no	—
587	C₂²	—	2	4	no	—
588	C₂²	—	2	4	no	—
589	C₂²	—	4	8	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	8	32	no	—
599	C₂²	—	8	8	no	—
600	C₂²	—	8	4	no	—
601	C₂²	C₅×#546	1	2	yes	—
602	C₂²	C₂²×C₅×D₈	1	8	yes	—
603	C₂²	C₂²×C₅×D₈	1	2	yes	—
604	C₂²	C₅×#577	1	2	yes	—
605	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
606	C₄	—	2	4	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	4	no	—
611	C₄	C₅×#546	1	2	yes	—
612	C₄	C₂²×C₅×D₈	1	4	yes	—
613	C₄	C₂²×C₅×#41	1	1	yes	characteristic
614	C₄	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂	—	2	8	no	—
616	C₂	—	4	4	no	—
617	C₂	—	8	4	no	—
618	C₂	—	8	2	no	—
619	C₂	C₅×#3294	1	4	yes	direct product factor
620	C₂	C₂×C₅×#546	1	1	yes	characteristic
621	C₂	C₂³×C₅×D₈	1	1	yes	characteristic
622	C₂	C₂×C₅×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#547	C₂	semidirect
2. C₂×C₅×D₄²	C₂	semidirect
3. C₅×#3294	C₂	direct (N × H)
4. C₂×C₅×#486	C₂	semidirect
5. C₂×C₅×#480	C₂	semidirect
6. C₂×C₅×#474	C₂	semidirect
7. C₂×C₅×#466	C₂	semidirect
8. C₂×C₅×#459	C₂	semidirect
9. C₂×C₅×#447	C₂	semidirect
10. C₂×C₄×C₅×D₈	C₂	semidirect
11. C₂×C₅×C₈×D₄	C₂	semidirect
12. C₂²×C₅×#102	C₂	semidirect
17. C₂²×C₅×D₈	C₂²	semidirect
18. C₂³×C₅×C₈	C₂²	semidirect
20. C₅×#547	C₂²	semidirect
22. C₅×D₄²	C₂²	semidirect
23. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
29. C₂×C₅×#121	C₂²	semidirect
33. C₂×C₄×C₅×D₄	C₂²	semidirect
34. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
35. C₅×#486	C₂²	semidirect
36. C₅×#480	C₂²	semidirect
37. C₅×#474	C₂²	semidirect
38. C₅×#466	C₂²	semidirect
39. C₅×#459	C₂²	semidirect
40. C₅×#447	C₂²	semidirect
41. C₄×C₅×D₈	C₂²	semidirect
42. C₅×C₈×D₄	C₂²	semidirect
43. C₂×C₅×#107	C₂²	semidirect
44. C₂×C₅×#107	C₂²	semidirect
45. C₂×C₅×C₄⋊C₈	C₂²	semidirect
48. C₂×C₅×#102	C₂²	semidirect
49. C₂×C₅×#102	C₂²	semidirect
50. C₂×C₅×#102	C₂²	semidirect
51. C₂×C₅×#102	C₂²	semidirect
52. C₂×C₅×#102	C₂²	semidirect
53. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
54. C₂×C₄×C₅×C₈	C₂²	semidirect
55. C₂×#3294	C₅	direct (N × H)
82. C₂×C₅×D₈	C₂³	semidirect
87. C₂²×C₅×C₈	C₂³	semidirect
89. C₅×C₄⋊Q₈	C₂³	semidirect
98. C₅×#121	C₂³	semidirect
105. C₄×C₅×D₄	C₂³	semidirect
113. C₂×C₅×C₄⋊C₄	C₂³	semidirect
120. C₅×#107	C₂³	semidirect
121. C₅×#107	C₂³	semidirect
122. C₅×C₄⋊C₈	C₂³	semidirect
125. C₅×#102	C₂³	semidirect
126. C₅×#102	C₂³	semidirect
127. C₅×#102	C₂³	semidirect
128. C₅×#102	C₂³	semidirect
129. C₅×C₂²⋊C₈	C₂³	semidirect
130. C₄×C₅×C₈	C₂³	semidirect
131. C₂×#547	C₂×C₅	semidirect
132. C₂×D₄²	C₂×C₅	semidirect
133. #3294	C₂×C₅	direct (N × H)
134. C₂×#486	C₂×C₅	semidirect
135. C₂×#480	C₂×C₅	semidirect
136. C₂×#474	C₂×C₅	semidirect
137. C₂×#466	C₂×C₅	semidirect
138. C₂×#459	C₂×C₅	semidirect
139. C₂×#447	C₂×C₅	semidirect
140. C₂×C₄×D₈	C₂×C₅	semidirect
141. C₂×C₈×D₄	C₂×C₅	semidirect
142. C₂²×#102	C₂×C₅	semidirect
176. C₂×C₅×D₄	D₈	semidirect
178. C₂×C₅×D₄	#41	semidirect
228. C₂²×D₈	C₂²×C₅	semidirect
229. C₂³×C₈	C₂²×C₅	semidirect
231. #547	C₂²×C₅	semidirect
233. D₄²	C₂²×C₅	semidirect
234. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
240. C₂×#121	C₂²×C₅	semidirect
244. C₂×C₄×D₄	C₂²×C₅	semidirect
245. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
246. #486	C₂²×C₅	semidirect
247. #480	C₂²×C₅	semidirect
248. #474	C₂²×C₅	semidirect
249. #466	C₂²×C₅	semidirect
250. #459	C₂²×C₅	semidirect
251. #447	C₂²×C₅	semidirect
252. C₄×D₈	C₂²×C₅	semidirect
253. C₈×D₄	C₂²×C₅	semidirect
254. C₂×#107	C₂²×C₅	semidirect
255. C₂×#107	C₂²×C₅	semidirect
256. C₂×C₄⋊C₈	C₂²×C₅	semidirect
259. C₂×#102	C₂²×C₅	semidirect
260. C₂×#102	C₂²×C₅	semidirect
261. C₂×#102	C₂²×C₅	semidirect
262. C₂×#102	C₂²×C₅	semidirect
263. C₂×#102	C₂²×C₅	semidirect
264. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
265. C₂×C₄×C₈	C₂²×C₅	semidirect
301. C₅×D₄	C₂×D₈	semidirect
302. C₅×D₄	C₂×#41	semidirect
354. C₂×D₈	C₂³×C₅	semidirect
359. C₂²×C₈	C₂³×C₅	semidirect
361. C₄⋊Q₈	C₂³×C₅	semidirect
370. #121	C₂³×C₅	semidirect
377. C₄×D₄	C₂³×C₅	semidirect
385. C₂×C₄⋊C₄	C₂³×C₅	semidirect
392. #107	C₂³×C₅	semidirect
393. #107	C₂³×C₅	semidirect
394. C₄⋊C₈	C₂³×C₅	semidirect
397. #102	C₂³×C₅	semidirect
398. #102	C₂³×C₅	semidirect
399. #102	C₂³×C₅	semidirect
400. #102	C₂³×C₅	semidirect
401. C₂²⋊C₈	C₂³×C₅	semidirect
402. C₄×C₈	C₂³×C₅	semidirect
466. C₂×D₄	C₅×D₈	semidirect
468. C₂×D₄	C₅×#41	semidirect
518. C₂×C₅	#3294	direct (N × H)
557. D₄	C₂×C₅×D₈	semidirect
558. D₄	C₂×C₅×#41	semidirect
584. C₅	C₂×#3294	direct (N × H)
619. C₂	C₅×#3294	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#547	2
C₂×C₅×D₄²	2
C₅×#3294	2
C₂×C₅×#486	2
C₂×C₅×#480	2
C₂×C₅×#474	2
C₂×C₅×#466	2
C₂×C₅×#459	2
C₂×C₅×#447	2
C₂×C₄×C₅×D₈	2
C₂×C₅×C₈×D₄	2
C₂²×C₅×#102	2
C₂×#3294	5

Subgroups — C2×C5×#3294 #11983832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3294 #11983832