Subgroups — C₅×#60291 #11983011

Order 1280.

1772 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#529	C₂	1	1	yes	maximal, characteristic
2	C₅×#2995	C₂	1	4	yes	maximal, complemented
3	C₅×#2992	C₂	1	4	yes	maximal, complemented
4	C₅×#2983	C₂	1	2	yes	maximal, complemented
5	C₅×#2974	C₂	1	4	yes	maximal, complemented
6	C₅×#2973	C₂	1	2	yes	maximal, complemented
7	C₅×#2968	C₂	1	4	yes	maximal, complemented
8	C₅×#2967	C₂	1	4	yes	maximal, complemented
9	C₅×#2924	C₂	1	4	yes	maximal, complemented
10	C₅×#2920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#529	C₄	1	2	yes	—
13	C₅×#529	C₄	1	2	yes	—
14	C₅×#529	C₄	1	2	yes	—
15	C₅×#529	C₄	1	2	yes	—
16	C₅×#529	C₂²	1	2	yes	—
17	C₅×#529	C₂²	1	2	yes	—
18	C₅×#529	C₂²	1	2	yes	—
19	C₅×#529	C₂²	1	2	yes	—
20	C₂×C₅×#126	C₄	1	2	yes	—
21	C₂×C₅×#125	C₄	1	1	yes	characteristic
22	C₂×C₅×#124	C₄	1	1	yes	characteristic
23	C₂×C₅×#123	C₄	1	2	yes	—
24	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
25	C₂×C₅×#121	C₄	1	1	yes	characteristic
26	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
29	C₂×C₅×#117	C₂²	1	2	yes	—
30	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
31	C₅×#446	C₂²	1	8	yes	complemented
32	C₅×#446	C₂²	1	8	yes	complemented
33	C₅×#436	C₂²	1	8	yes	complemented
34	C₅×#435	C₂²	1	8	yes	complemented
35	C₅×#435	C₂²	1	8	yes	complemented
36	C₅×#435	C₂²	1	8	yes	complemented
37	C₅×#435	C₂²	1	8	yes	complemented
38	C₅×C₈×D₄	C₂²	1	8	yes	complemented
39	C₅×#433	C₂²	1	8	yes	complemented
40	C₅×#433	C₂²	1	8	yes	complemented
41	C₅×#432	C₂²	1	2	yes	—
42	C₅×#432	C₂²	1	2	yes	—
43	C₅×#432	C₂²	1	4	yes	—
44	C₅×#432	C₂²	1	2	yes	—
45	C₅×#432	C₂²	1	2	yes	complemented
46	C₅×#432	C₂²	1	2	yes	complemented
47	C₅×#432	C₂²	1	2	yes	complemented
48	C₅×#431	C₂²	1	4	yes	—
49	C₅×#431	C₂²	1	2	yes	—
50	C₅×#431	C₂²	1	2	yes	complemented
51	C₅×#424	C₂²	1	8	yes	complemented
52	C₅×#423	C₂²	1	2	yes	complemented
53	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
54	C₅×#407	C₂²	1	2	yes	—
55	C₅×#407	C₂²	1	4	yes	—
56	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
57	C₂×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
58	C₅×#405	C₂²	1	8	yes	complemented
59	C₄×C₅×M₁₆	C₂²	1	2	yes	complemented
60	C₂×C₅×#97	C₂²	1	2	yes	complemented
61	#60291	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
64	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₅	C₂³	1	2	yes	—
69	C₂×C₅×M₁₆	C₂³	1	4	yes	—
70	C₂×C₅×M₁₆	C₂³	1	8	yes	—
71	C₂²×C₅×C₈	C₂³	1	4	yes	—
72	C₂²×C₅×C₈	C₂³	1	8	yes	—
73	C₅×#126	C₂×C₄	1	4	yes	—
74	C₅×#126	C₂×C₄	1	4	yes	—
75	C₅×#126	C₂×C₄	1	4	yes	—
76	C₅×#126	C₂×C₄	1	4	yes	—
77	C₅×#125	C₂×C₄	1	2	yes	—
78	C₅×#125	C₂×C₄	1	2	yes	—
79	C₅×#125	C₂×C₄	1	2	yes	—
80	C₅×#125	C₂×C₄	1	2	yes	—
81	C₅×#124	C₂×C₄	1	2	yes	—
82	C₅×#124	C₂×C₄	1	2	yes	—
83	C₅×#124	C₂×C₄	1	2	yes	—
84	C₅×#124	C₂×C₄	1	2	yes	—
85	C₅×#123	C₂×C₄	1	4	yes	—
86	C₅×#123	C₂×C₄	1	4	yes	—
87	C₅×#123	C₂×C₄	1	4	yes	—
88	C₅×#123	C₂×C₄	1	4	yes	—
89	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
90	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
91	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
92	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
93	C₅×#121	C₂×C₄	1	2	yes	—
94	C₅×#121	C₂×C₄	1	2	yes	—
95	C₅×#121	C₂×C₄	1	2	yes	—
96	C₅×#121	C₂×C₄	1	2	yes	—
97	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
98	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
99	C₄×C₅×Q₈	C₂³	1	2	yes	—
100	C₄×C₅×Q₈	C₂³	1	2	yes	—
101	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
102	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
103	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
104	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
105	C₄×C₅×D₄	C₂³	1	4	yes	—
106	C₄×C₅×D₄	C₂³	1	2	yes	—
107	C₄×C₅×D₄	C₂³	1	2	yes	—
108	C₄×C₅×D₄	C₂³	1	4	yes	—
109	C₅×#117	C₂×C₄	1	4	yes	—
110	C₅×#117	C₂×C₄	1	4	yes	—
111	C₅×#117	C₂³	1	4	yes	—
112	C₅×#117	C₂³	1	4	yes	—
113	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
114	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
115	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
117	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
119	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
120	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
122	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
124	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
127	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
128	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
129	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₅	C₂³	1	2	yes	—
136	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
137	C₅×C₄⋊C₈	C₂³	1	4	yes	—
138	C₅×C₄⋊C₈	C₂³	1	4	yes	—
139	C₅×C₄⋊C₈	C₂³	1	4	yes	—
140	C₅×C₄⋊C₈	C₂³	1	4	yes	—
141	C₅×C₄⋊C₈	C₂³	1	8	yes	—
142	C₅×C₄⋊C₈	C₂³	1	8	yes	—
143	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
144	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
145	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
146	C₅×C₂²⋊C₈	C₂³	1	8	yes	—
147	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
148	C₅×C₂²⋊C₈	C₂³	1	8	yes	—
149	C₅×#97	C₂³	1	4	yes	—
150	C₅×#97	C₂³	1	4	yes	—
151	C₅×#97	C₂³	1	4	yes	—
152	C₅×#97	C₂³	1	8	yes	—
153	C₄×C₅×C₈	C₂³	1	4	yes	—
154	C₄×C₅×C₈	C₂³	1	8	yes	—
155	C₂×#529	C₂×C₅	1	1	yes	characteristic
156	#2995	C₂×C₅	1	4	yes	complemented
157	#2992	C₂×C₅	1	4	yes	complemented
158	#2983	C₂×C₅	1	2	yes	complemented
159	#2974	C₂×C₅	1	4	yes	complemented
160	#2973	C₂×C₅	1	2	yes	complemented
161	#2968	C₂×C₅	1	4	yes	complemented
162	#2967	C₂×C₅	1	4	yes	complemented
163	#2924	C₂×C₅	1	4	yes	complemented
164	#2920	C₂×C₅	1	1	yes	characteristic, complemented
165	C₂×#432	C₂×C₅	1	1	yes	characteristic, complemented
166	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
167	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
168	C₂×C₅×Q₈	—	4	2	no	—
169	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
170	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
171	C₂×C₅×D₄	—	4	2	no	—
172	C₂×C₅×D₄	—	4	4	no	—
173	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
174	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
175	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
176	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
177	C₂²×C₄×C₅	—	4	2	no	—
178	C₂²×C₄×C₅	—	4	4	no	—
179	C₂²×C₄×C₅	—	4	2	no	—
180	C₂²×C₄×C₅	—	4	2	no	—
181	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
186	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
198	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
199	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
200	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
204	C₅×M₁₆	—	4	8	no	—
205	C₅×M₁₆	—	4	4	no	—
206	C₂×C₅×C₈	—	4	4	no	—
207	C₂×C₅×C₈	—	4	8	no	—
208	C₂×C₅×C₈	C₂⁴	1	8	yes	—
209	C₂×C₅×C₈	C₂⁴	1	8	yes	—
210	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
211	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
212	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
213	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
214	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
215	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
216	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
217	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
218	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
219	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
220	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
221	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
222	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
223	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
224	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
225	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
226	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
227	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
228	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
229	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
230	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
231	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
232	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
233	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
234	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
235	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
236	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
237	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
238	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
239	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
240	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
241	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
242	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
243	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
244	C₄²×C₅	C₂²×C₄	1	4	yes	—
245	C₄²×C₅	C₂⁴	1	1	yes	characteristic
246	C₄²×C₅	C₂⁴	1	1	yes	characteristic
247	C₄²×C₅	C₂⁴	1	1	yes	characteristic
248	C₄²×C₅	C₂⁴	1	1	yes	characteristic
249	C₄²×C₅	C₂⁴	1	4	yes	—
250	#529	C₄×C₅	1	2	yes	—
251	#529	C₄×C₅	1	2	yes	—
252	#529	C₄×C₅	1	2	yes	—
253	#529	C₄×C₅	1	2	yes	—
254	#529	C₂²×C₅	1	2	yes	—
255	#529	C₂²×C₅	1	2	yes	—
256	#529	C₂²×C₅	1	2	yes	—
257	#529	C₂²×C₅	1	2	yes	—
258	C₂×#126	C₄×C₅	1	2	yes	—
259	C₂×#125	C₄×C₅	1	1	yes	characteristic
260	C₂×#124	C₄×C₅	1	1	yes	characteristic
261	C₂×#123	C₄×C₅	1	2	yes	—
262	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
263	C₂×#121	C₄×C₅	1	1	yes	characteristic
264	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
267	C₂×#117	C₂²×C₅	1	2	yes	—
268	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
269	#446	C₂²×C₅	1	8	yes	complemented
270	#446	C₂²×C₅	1	8	yes	complemented
271	#436	C₂²×C₅	1	8	yes	complemented
272	#435	C₂²×C₅	1	8	yes	complemented
273	#435	C₂²×C₅	1	8	yes	complemented
274	#435	C₂²×C₅	1	8	yes	complemented
275	#435	C₂²×C₅	1	8	yes	complemented
276	C₈×D₄	C₂²×C₅	1	8	yes	complemented
277	#433	C₂²×C₅	1	8	yes	complemented
278	#433	C₂²×C₅	1	8	yes	complemented
279	#432	C₂²×C₅	1	2	yes	—
280	#432	C₂²×C₅	1	2	yes	—
281	#432	C₂²×C₅	1	2	yes	—
282	#432	C₂²×C₅	1	4	yes	—
283	#432	C₂²×C₅	1	2	yes	complemented
284	#432	C₂²×C₅	1	2	yes	complemented
285	#432	C₂²×C₅	1	2	yes	complemented
286	#431	C₂²×C₅	1	2	yes	—
287	#431	C₂²×C₅	1	4	yes	—
288	#431	C₂²×C₅	1	2	yes	complemented
289	#424	C₂²×C₅	1	8	yes	complemented
290	#423	C₂²×C₅	1	2	yes	complemented
291	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
292	#407	C₂²×C₅	1	2	yes	—
293	#407	C₂²×C₅	1	4	yes	—
294	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
295	C₂×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
296	#405	C₂²×C₅	1	8	yes	complemented
297	C₄×M₁₆	C₂²×C₅	1	2	yes	complemented
298	C₂×#97	C₂²×C₅	1	2	yes	complemented
299	C₂³×C₅	—	2	2	no	—
300	C₂³×C₅	—	2	2	no	—
301	C₂³×C₅	—	2	4	no	—
302	C₂³×C₅	—	4	1	no	—
303	C₂³×C₅	—	4	2	no	—
304	C₂³×C₅	—	4	2	no	—
305	C₂³×C₅	C₂³×C₄	1	4	yes	—
306	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
307	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
308	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
309	C₅×Q₈	—	4	2	no	—
310	C₅×Q₈	—	4	2	no	—
311	C₅×D₄	—	2	8	no	—
312	C₅×D₄	—	4	2	no	—
313	C₅×D₄	—	4	2	no	—
314	C₅×D₄	—	4	4	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	4	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	8	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	4	1	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	—	4	4	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	2	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	—	4	1	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	4	1	no	—
334	C₂×C₄×C₅	—	4	1	no	—
335	C₂×C₄×C₅	—	4	1	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	4	2	no	—
338	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
340	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
342	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
343	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
344	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
345	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
346	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
347	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
348	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
350	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
351	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
352	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
353	C₅×C₈	—	2	8	no	—
354	C₅×C₈	—	2	8	no	—
355	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
356	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
357	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
358	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
359	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₅	1	2	yes	—
361	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
362	C₂×M₁₆	C₂³×C₅	1	4	yes	—
363	C₂×M₁₆	C₂³×C₅	1	8	yes	—
364	C₂²×C₈	C₂³×C₅	1	4	yes	—
365	C₂²×C₈	C₂³×C₅	1	8	yes	—
366	#126	C₂×C₄×C₅	1	4	yes	—
367	#126	C₂×C₄×C₅	1	4	yes	—
368	#126	C₂×C₄×C₅	1	4	yes	—
369	#126	C₂×C₄×C₅	1	4	yes	—
370	#125	C₂×C₄×C₅	1	2	yes	—
371	#125	C₂×C₄×C₅	1	2	yes	—
372	#125	C₂×C₄×C₅	1	2	yes	—
373	#125	C₂×C₄×C₅	1	2	yes	—
374	#124	C₂×C₄×C₅	1	2	yes	—
375	#124	C₂×C₄×C₅	1	2	yes	—
376	#124	C₂×C₄×C₅	1	2	yes	—
377	#124	C₂×C₄×C₅	1	2	yes	—
378	#123	C₂×C₄×C₅	1	4	yes	—
379	#123	C₂×C₄×C₅	1	4	yes	—
380	#123	C₂×C₄×C₅	1	4	yes	—
381	#123	C₂×C₄×C₅	1	4	yes	—
382	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
383	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
384	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
385	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
386	#121	C₂×C₄×C₅	1	2	yes	—
387	#121	C₂×C₄×C₅	1	2	yes	—
388	#121	C₂×C₄×C₅	1	2	yes	—
389	#121	C₂×C₄×C₅	1	2	yes	—
390	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
391	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
392	C₄×Q₈	C₂³×C₅	1	2	yes	—
393	C₄×Q₈	C₂³×C₅	1	2	yes	—
394	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
395	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
396	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
397	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
398	C₄×D₄	C₂³×C₅	1	4	yes	—
399	C₄×D₄	C₂³×C₅	1	2	yes	—
400	C₄×D₄	C₂³×C₅	1	2	yes	—
401	C₄×D₄	C₂³×C₅	1	4	yes	—
402	#117	C₂×C₄×C₅	1	4	yes	—
403	#117	C₂×C₄×C₅	1	4	yes	—
404	#117	C₂³×C₅	1	4	yes	—
405	#117	C₂³×C₅	1	4	yes	—
406	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
407	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
408	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
410	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
412	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
417	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
418	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
419	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
420	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
421	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
422	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₅	1	2	yes	—
425	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
430	C₄⋊C₈	C₂³×C₅	1	4	yes	—
431	C₄⋊C₈	C₂³×C₅	1	4	yes	—
432	C₄⋊C₈	C₂³×C₅	1	4	yes	—
433	C₄⋊C₈	C₂³×C₅	1	4	yes	—
434	C₄⋊C₈	C₂³×C₅	1	8	yes	—
435	C₄⋊C₈	C₂³×C₅	1	8	yes	—
436	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
437	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
438	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
439	C₂²⋊C₈	C₂³×C₅	1	8	yes	—
440	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
441	C₂²⋊C₈	C₂³×C₅	1	8	yes	—
442	#97	C₂³×C₅	1	4	yes	—
443	#97	C₂³×C₅	1	4	yes	—
444	#97	C₂³×C₅	1	4	yes	—
445	#97	C₂³×C₅	1	8	yes	—
446	C₄×C₈	C₂³×C₅	1	4	yes	—
447	C₄×C₈	C₂³×C₅	1	8	yes	—
448	C₂²×C₅	—	2	1	no	—
449	C₂²×C₅	—	2	1	no	—
450	C₂²×C₅	—	2	1	no	—
451	C₂²×C₅	—	2	1	no	—
452	C₂²×C₅	—	2	1	no	—
453	C₂²×C₅	—	2	4	no	—
454	C₂²×C₅	—	2	1	no	—
455	C₂²×C₅	—	2	1	no	—
456	C₂²×C₅	—	2	4	no	—
457	C₂²×C₅	—	2	4	no	—
458	C₂²×C₅	—	4	4	no	—
459	C₂²×C₅	—	8	4	no	—
460	C₂²×C₅	#568	1	2	yes	—
461	C₂²×C₅	#568	1	2	yes	—
462	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
463	C₄×C₅	—	2	1	no	—
464	C₄×C₅	—	2	1	no	—
465	C₄×C₅	—	2	4	no	—
466	C₄×C₅	—	2	1	no	—
467	C₄×C₅	—	2	1	no	—
468	C₄×C₅	—	2	1	no	—
469	C₄×C₅	—	2	1	no	—
470	C₄×C₅	—	2	1	no	—
471	C₄×C₅	—	2	1	no	—
472	C₄×C₅	—	2	1	no	—
473	C₄×C₅	—	2	1	no	—
474	C₄×C₅	—	2	1	no	—
475	C₄×C₅	—	2	4	no	—
476	C₄×C₅	—	2	4	no	—
477	C₄×C₅	#585	1	2	yes	—
478	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
479	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
480	C₂×Q₈	—	4	2	no	—
481	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
482	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
483	C₂×D₄	—	4	2	no	—
484	C₂×D₄	—	4	4	no	—
485	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
486	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
487	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
488	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	4	4	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
494	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
495	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
496	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
497	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
498	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
499	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
500	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
501	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
502	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
503	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
504	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
505	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
506	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
507	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
508	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
509	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
510	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
511	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
512	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
514	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
515	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
516	M₁₆	—	4	8	no	—
517	M₁₆	—	4	4	no	—
518	C₂×C₈	—	4	4	no	—
519	C₂×C₈	—	4	8	no	—
520	C₂×C₈	C₂⁴×C₅	1	8	yes	—
521	C₂×C₈	C₂⁴×C₅	1	8	yes	—
522	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
523	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
524	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
525	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
526	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
527	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
528	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
529	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
530	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
531	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
532	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
533	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
534	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
535	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
536	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
537	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
538	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
539	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
540	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
541	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
542	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
543	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
544	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
545	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
546	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
547	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
548	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
549	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
550	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
551	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
552	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
553	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
554	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
555	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
556	C₄²	C₂²×C₄×C₅	1	4	yes	—
557	C₄²	C₂⁴×C₅	1	1	yes	characteristic
558	C₄²	C₂⁴×C₅	1	4	yes	—
559	C₄²	C₂⁴×C₅	1	1	yes	characteristic
560	C₄²	C₂⁴×C₅	1	1	yes	characteristic
561	C₄²	C₂⁴×C₅	1	1	yes	characteristic
562	C₂×C₅	—	2	2	no	—
563	C₂×C₅	—	2	2	no	—
564	C₂×C₅	—	4	1	no	—
565	C₂×C₅	—	4	4	no	—
566	C₂×C₅	#3428	1	1	yes	characteristic
567	C₂×C₅	C₂×#568	1	1	yes	characteristic
568	C₂×C₅	C₂×#568	1	1	yes	characteristic
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	4	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	2	no	—
574	C₂³	—	4	2	no	—
575	C₂³	C₂³×C₄×C₅	1	4	yes	—
576	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
577	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
578	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
579	Q₈	—	4	2	no	—
580	Q₈	—	4	2	no	—
581	D₄	—	2	8	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	4	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	8	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
609	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
610	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
611	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
612	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
613	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
614	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
615	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
616	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
617	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
618	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
619	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
620	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
621	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
622	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
623	C₈	—	2	8	no	—
624	C₈	—	2	8	no	—
625	C₅	#60291	1	1	yes	characteristic, direct product factor, Sylow
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	4	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	4	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	8	4	no	—
638	C₂²	C₅×#568	1	2	yes	—
639	C₂²	C₅×#568	1	2	yes	—
640	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
641	C₄	—	2	1	no	—
642	C₄	—	2	1	no	—
643	C₄	—	2	4	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	4	no	—
654	C₄	—	2	4	no	—
655	C₄	C₅×#585	1	2	yes	—
656	C₂	—	2	2	no	—
657	C₂	—	2	2	no	—
658	C₂	—	4	1	no	—
659	C₂	—	4	4	no	—
660	C₂	C₅×#3428	1	1	yes	characteristic
661	C₂	C₂×C₅×#568	1	1	yes	characteristic
662	C₂	C₂×C₅×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂²×C₅	C₂⁴×C₄
prime radical	C₂×C₅×#121	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2995	C₂	semidirect
3. C₅×#2992	C₂	semidirect
4. C₅×#2983	C₂	semidirect
5. C₅×#2974	C₂	semidirect
6. C₅×#2973	C₂	semidirect
7. C₅×#2968	C₂	semidirect
8. C₅×#2967	C₂	semidirect
9. C₅×#2924	C₂	semidirect
10. C₅×#2920	C₂	semidirect
11. C₂×C₅×#432	C₂	semidirect
31. C₅×#446	C₂²	semidirect
32. C₅×#446	C₂²	semidirect
33. C₅×#436	C₂²	semidirect
34. C₅×#435	C₂²	semidirect
35. C₅×#435	C₂²	semidirect
36. C₅×#435	C₂²	semidirect
37. C₅×#435	C₂²	semidirect
38. C₅×C₈×D₄	C₂²	semidirect
39. C₅×#433	C₂²	semidirect
40. C₅×#433	C₂²	semidirect
45. C₅×#432	C₂²	semidirect
46. C₅×#432	C₂²	semidirect
47. C₅×#432	C₂²	semidirect
50. C₅×#431	C₂²	semidirect
51. C₅×#424	C₂²	semidirect
52. C₅×#423	C₂²	semidirect
53. C₂×C₅×C₄⋊C₈	C₂²	semidirect
58. C₅×#405	C₂²	semidirect
59. C₄×C₅×M₁₆	C₂²	semidirect
60. C₂×C₅×#97	C₂²	semidirect
61. #60291	C₅	direct (N × H)
156. #2995	C₂×C₅	semidirect
157. #2992	C₂×C₅	semidirect
158. #2983	C₂×C₅	semidirect
159. #2974	C₂×C₅	semidirect
160. #2973	C₂×C₅	semidirect
161. #2968	C₂×C₅	semidirect
162. #2967	C₂×C₅	semidirect
163. #2924	C₂×C₅	semidirect
164. #2920	C₂×C₅	semidirect
165. C₂×#432	C₂×C₅	semidirect
269. #446	C₂²×C₅	semidirect
270. #446	C₂²×C₅	semidirect
271. #436	C₂²×C₅	semidirect
272. #435	C₂²×C₅	semidirect
273. #435	C₂²×C₅	semidirect
274. #435	C₂²×C₅	semidirect
275. #435	C₂²×C₅	semidirect
276. C₈×D₄	C₂²×C₅	semidirect
277. #433	C₂²×C₅	semidirect
278. #433	C₂²×C₅	semidirect
283. #432	C₂²×C₅	semidirect
284. #432	C₂²×C₅	semidirect
285. #432	C₂²×C₅	semidirect
288. #431	C₂²×C₅	semidirect
289. #424	C₂²×C₅	semidirect
290. #423	C₂²×C₅	semidirect
291. C₂×C₄⋊C₈	C₂²×C₅	semidirect
296. #405	C₂²×C₅	semidirect
297. C₄×M₁₆	C₂²×C₅	semidirect
298. C₂×#97	C₂²×C₅	semidirect
625. C₅	#60291	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×#529	2
C₅×#2995	2
C₅×#2992	2
C₅×#2983	2
C₅×#2974	2
C₅×#2973	2
C₅×#2968	2
C₅×#2967	2
C₅×#2924	2
C₅×#2920	2
C₂×C₅×#432	2
#60291	5

Subgroups — C5×#60291 #11983011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60291 #11983011