Subgroups — C₅×#60293 #11983013

Order 1280.

1762 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3444	C₂	1	1	yes	maximal, characteristic
2	C₅×#2990	C₂	1	4	yes	maximal, complemented
3	C₅×#2989	C₂	1	4	yes	maximal, complemented
4	C₅×#2987	C₂	1	2	yes	maximal, complemented
5	C₅×#2980	C₂	1	2	yes	maximal, complemented
6	C₅×#2976	C₂	1	4	yes	maximal, complemented
7	C₅×#2968	C₂	1	4	yes	maximal, complemented
8	C₅×#2967	C₂	1	4	yes	maximal, complemented
9	C₅×#2925	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×#533	C₄	1	1	yes	characteristic
13	C₅×#533	C₄	1	1	yes	characteristic
14	C₅×#533	C₂²	1	1	yes	characteristic
15	C₅×#532	C₄	1	1	yes	characteristic
16	C₅×#532	C₄	1	1	yes	characteristic
17	C₅×#532	C₂²	1	1	yes	characteristic
18	C₅×#529	C₄	1	2	yes	—
19	C₅×#529	C₄	1	2	yes	—
20	C₅×#529	C₄	1	2	yes	—
21	C₅×#529	C₄	1	2	yes	—
22	C₅×#529	C₂²	1	2	yes	—
23	C₅×#529	C₂²	1	2	yes	—
24	C₅×#525	C₄	1	2	yes	—
25	C₅×#525	C₄	1	2	yes	—
26	C₅×#525	C₂²	1	2	yes	—
27	C₄×C₅×#41	C₂²	1	2	yes	—
28	C₄×C₅×#41	C₂²	1	2	yes	—
29	C₄×C₅×#41	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	—
34	C₅×#435	C₂²	1	8	yes	—
35	C₅×#435	C₂²	1	8	yes	—
36	C₅×#435	C₂²	1	8	yes	complemented
37	C₅×#435	C₂²	1	8	yes	complemented
38	C₅×C₈×D₄	C₂²	1	8	yes	—
39	C₅×#433	C₂²	1	8	yes	—
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	2	yes	—
44	C₅×#432	C₂²	1	2	yes	—
45	C₅×#432	C₂²	1	2	yes	—
46	C₅×#432	C₂²	1	2	yes	—
47	C₅×#432	C₂²	1	4	yes	complemented
48	C₅×#431	C₂²	1	2	yes	—
49	C₅×#431	C₂²	1	2	yes	—
50	C₅×#431	C₂²	1	4	yes	complemented
51	C₅×#423	C₂²	1	2	yes	—
52	C₅×#423	C₂²	1	4	yes	complemented
53	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
54	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
55	C₅×#408	C₂²	1	8	yes	—
56	C₅×#407	C₂²	1	2	yes	—
57	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
58	C₅×#405	C₂²	1	8	yes	complemented
59	C₄×C₅×M₁₆	C₂²	1	2	yes	—
60	C₂×C₅×#97	C₂²	1	2	yes	—
61	#60293	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂×C₅×#41	C₂×C₄	1	2	yes	—
63	C₂×C₅×#41	C₂×C₄	1	2	yes	—
64	C₂×C₅×#41	C₂³	1	2	yes	—
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	C₂×C₅×M₁₆	C₂³	1	4	yes	—
69	C₂×C₅×M₁₆	C₂³	1	8	yes	—
70	C₂²×C₅×C₈	C₂³	1	4	yes	—
71	C₂²×C₅×C₈	C₂³	1	8	yes	—
72	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
73	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
74	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
75	C₅×#127	C₂×C₄	1	1	yes	characteristic
76	C₅×#126	C₂×C₄	1	4	yes	—
77	C₅×#126	C₂×C₄	1	4	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×#123	C₂×C₄	1	4	yes	—
85	C₅×#123	C₂×C₄	1	4	yes	—
86	C₅×#123	C₂×C₄	1	4	yes	—
87	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
88	C₅×C₂²⋊Q₈	C₂×C₄	1	2	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	C₅×#121	C₂×C₄	1	2	yes	—
98	C₅×#121	C₂×C₄	1	2	yes	—
99	C₅×#120	C₂×C₄	1	4	yes	—
100	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
101	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
102	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
103	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
104	C₄×C₅×Q₈	C₂³	1	2	yes	—
105	C₄×C₅×Q₈	C₂³	1	2	yes	—
106	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
107	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
108	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
109	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
110	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
111	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
112	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
113	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
114	C₄×C₅×D₄	C₂³	1	4	yes	—
115	C₄×C₅×D₄	C₂³	1	4	yes	—
116	C₄×C₅×D₄	C₂³	1	2	yes	—
117	C₄×C₅×D₄	C₂³	1	2	yes	—
118	C₅×#117	C₂×C₄	1	2	yes	—
119	C₅×#117	C₂×C₄	1	2	yes	—
120	C₅×#117	C₂×C₄	1	4	yes	—
121	C₅×#117	C₂×C₄	1	4	yes	—
122	C₅×#117	C₂³	1	4	yes	—
123	C₅×#117	C₂³	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	4	yes	—
134	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	8	yes	—
141	C₅×C₄⋊C₈	C₂³	1	4	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	4	yes	—
147	C₅×C₂²⋊C₈	C₂³	1	8	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	#3444	C₂×C₅	1	1	yes	characteristic
156	#2990	C₂×C₅	1	4	yes	complemented
157	#2989	C₂×C₅	1	4	yes	complemented
158	#2987	C₂×C₅	1	2	yes	complemented
159	#2980	C₂×C₅	1	2	yes	complemented
160	#2976	C₂×C₅	1	4	yes	complemented
161	#2968	C₂×C₅	1	4	yes	complemented
162	#2967	C₂×C₅	1	4	yes	complemented
163	#2925	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	C₅×#41	—	4	4	no	—
168	C₅×#41	—	4	2	no	—
169	C₅×#41	—	4	2	no	—
170	C₅×#41	—	4	4	no	—
171	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
172	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
173	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
174	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
175	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
176	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
177	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
178	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
179	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
180	C₂²×C₄×C₅	—	4	2	no	—
181	C₂²×C₄×C₅	—	4	2	no	—
182	C₂²×C₄×C₅	—	4	2	no	—
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	1	yes	characteristic
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	4	yes	—
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	1	yes	characteristic
198	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
211	C₅×C₄⋊C₄	C₂²×C₄	1	2	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	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
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	#533	C₄×C₅	1	1	yes	characteristic
251	#533	C₄×C₅	1	1	yes	characteristic
252	#533	C₂²×C₅	1	1	yes	characteristic
253	#532	C₄×C₅	1	1	yes	characteristic
254	#532	C₄×C₅	1	1	yes	characteristic
255	#532	C₂²×C₅	1	1	yes	characteristic
256	#529	C₄×C₅	1	2	yes	—
257	#529	C₄×C₅	1	2	yes	—
258	#529	C₄×C₅	1	2	yes	—
259	#529	C₄×C₅	1	2	yes	—
260	#529	C₂²×C₅	1	2	yes	—
261	#529	C₂²×C₅	1	2	yes	—
262	#525	C₄×C₅	1	2	yes	—
263	#525	C₄×C₅	1	2	yes	—
264	#525	C₂²×C₅	1	2	yes	—
265	C₄×#41	C₂²×C₅	1	2	yes	—
266	C₄×#41	C₂²×C₅	1	2	yes	—
267	C₄×#41	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	—
272	#435	C₂²×C₅	1	8	yes	—
273	#435	C₂²×C₅	1	8	yes	—
274	#435	C₂²×C₅	1	8	yes	complemented
275	#435	C₂²×C₅	1	8	yes	complemented
276	C₈×D₄	C₂²×C₅	1	8	yes	—
277	#433	C₂²×C₅	1	8	yes	—
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	2	yes	—
283	#432	C₂²×C₅	1	2	yes	—
284	#432	C₂²×C₅	1	2	yes	—
285	#432	C₂²×C₅	1	4	yes	complemented
286	#431	C₂²×C₅	1	2	yes	—
287	#431	C₂²×C₅	1	2	yes	—
288	#431	C₂²×C₅	1	4	yes	complemented
289	#423	C₂²×C₅	1	2	yes	—
290	#423	C₂²×C₅	1	4	yes	complemented
291	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
292	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
293	#408	C₂²×C₅	1	8	yes	—
294	#407	C₂²×C₅	1	2	yes	—
295	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
296	#405	C₂²×C₅	1	8	yes	complemented
297	C₄×M₁₆	C₂²×C₅	1	2	yes	—
298	C₂×#97	C₂²×C₅	1	2	yes	—
299	C₂³×C₅	—	2	2	no	—
300	C₂³×C₅	—	4	1	no	—
301	C₂³×C₅	—	4	1	no	—
302	C₂³×C₅	C₂³×C₄	1	4	yes	—
303	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
304	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
305	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
306	C₅×Q₈	—	4	2	no	—
307	C₅×Q₈	—	4	2	no	—
308	C₅×Q₈	—	4	2	no	—
309	C₅×D₄	—	2	8	no	—
310	C₅×D₄	—	4	2	no	—
311	C₅×D₄	—	4	4	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	2	no	—
320	C₂×C₄×C₅	—	2	8	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	4	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	4	no	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	1	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	4	no	—
337	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
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	4	yes	—
348	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
349	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
350	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
351	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
352	C₅×C₈	—	2	8	no	—
353	C₅×C₈	—	2	8	no	—
354	C₂×#41	C₂×C₄×C₅	1	2	yes	—
355	C₂×#41	C₂×C₄×C₅	1	2	yes	—
356	C₂×#41	C₂³×C₅	1	2	yes	—
357	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
358	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
360	C₂×M₁₆	C₂³×C₅	1	4	yes	—
361	C₂×M₁₆	C₂³×C₅	1	8	yes	—
362	C₂²×C₈	C₂³×C₅	1	4	yes	—
363	C₂²×C₈	C₂³×C₅	1	8	yes	—
364	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
365	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
366	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
367	#127	C₂×C₄×C₅	1	1	yes	characteristic
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	#124	C₂×C₄×C₅	1	2	yes	—
374	#124	C₂×C₄×C₅	1	2	yes	—
375	#124	C₂×C₄×C₅	1	2	yes	—
376	#123	C₂×C₄×C₅	1	4	yes	—
377	#123	C₂×C₄×C₅	1	4	yes	—
378	#123	C₂×C₄×C₅	1	4	yes	—
379	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
380	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
381	C₂²⋊Q₈	C₂×C₄×C₅	1	2	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	#121	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	#121	C₂×C₄×C₅	1	2	yes	—
391	#120	C₂×C₄×C₅	1	4	yes	—
392	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
393	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
394	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
395	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
396	C₄×Q₈	C₂³×C₅	1	2	yes	—
397	C₄×Q₈	C₂³×C₅	1	2	yes	—
398	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
399	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
400	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
401	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
402	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
403	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
404	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
405	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
406	C₄×D₄	C₂³×C₅	1	4	yes	—
407	C₄×D₄	C₂³×C₅	1	4	yes	—
408	C₄×D₄	C₂³×C₅	1	2	yes	—
409	C₄×D₄	C₂³×C₅	1	2	yes	—
410	#117	C₂×C₄×C₅	1	2	yes	—
411	#117	C₂×C₄×C₅	1	2	yes	—
412	#117	C₂×C₄×C₅	1	4	yes	—
413	#117	C₂×C₄×C₅	1	4	yes	—
414	#117	C₂³×C₅	1	2	yes	—
415	#117	C₂³×C₅	1	4	yes	—
416	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
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	C₂³×C₅	1	4	yes	—
423	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
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	C₄⋊C₈	C₂³×C₅	1	4	yes	—
430	C₄⋊C₈	C₂³×C₅	1	4	yes	—
431	C₄⋊C₈	C₂³×C₅	1	4	yes	—
432	C₄⋊C₈	C₂³×C₅	1	8	yes	—
433	C₄⋊C₈	C₂³×C₅	1	4	yes	—
434	C₄⋊C₈	C₂³×C₅	1	8	yes	—
435	C₂²⋊C₈	C₂³×C₅	1	4	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	8	yes	—
441	#97	C₂³×C₅	1	4	yes	—
442	#97	C₂³×C₅	1	4	yes	—
443	#97	C₂³×C₅	1	4	yes	—
444	#97	C₂³×C₅	1	8	yes	—
445	C₄×C₈	C₂³×C₅	1	4	yes	—
446	C₄×C₈	C₂³×C₅	1	8	yes	—
447	C₂²×C₅	—	2	1	no	—
448	C₂²×C₅	—	2	1	no	—
449	C₂²×C₅	—	2	1	no	—
450	C₂²×C₅	—	2	1	no	—
451	C₂²×C₅	—	2	4	no	—
452	C₂²×C₅	—	2	1	no	—
453	C₂²×C₅	—	2	1	no	—
454	C₂²×C₅	—	2	4	no	—
455	C₂²×C₅	—	2	1	no	—
456	C₂²×C₅	—	2	1	no	—
457	C₂²×C₅	—	2	4	no	—
458	C₂²×C₅	—	4	4	no	—
459	C₂²×C₅	#568	1	2	yes	—
460	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
461	C₄×C₅	—	2	1	no	—
462	C₄×C₅	—	2	1	no	—
463	C₄×C₅	—	2	1	no	—
464	C₄×C₅	—	2	4	no	—
465	C₄×C₅	—	2	1	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	4	no	—
473	C₄×C₅	—	2	4	no	—
474	C₄×C₅	#568	1	2	yes	—
475	C₄×C₅	#585	1	2	yes	—
476	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
477	#41	—	4	4	no	—
478	#41	—	4	2	no	—
479	#41	—	4	2	no	—
480	#41	—	4	4	no	—
481	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
482	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
483	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
484	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
485	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
486	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
487	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
488	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
489	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
490	C₂²×C₄	—	4	2	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	1	yes	characteristic
498	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
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	4	yes	—
510	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
511	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
514	M₁₆	—	4	8	no	—
515	M₁₆	—	4	4	no	—
516	C₂×C₈	—	4	4	no	—
517	C₂×C₈	—	4	8	no	—
518	C₂×C₈	C₂⁴×C₅	1	8	yes	—
519	C₂×C₈	C₂⁴×C₅	1	8	yes	—
520	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
521	C₄⋊C₄	C₂²×C₄×C₅	1	2	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	2	yes	—
525	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
526	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
527	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
528	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
529	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
530	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
531	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
532	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
533	C₂²⋊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	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
542	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
543	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
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	4	yes	—
554	C₄²	C₂²×C₄×C₅	1	4	yes	—
555	C₄²	C₂⁴×C₅	1	1	yes	characteristic
556	C₄²	C₂⁴×C₅	1	4	yes	—
557	C₄²	C₂⁴×C₅	1	1	yes	characteristic
558	C₄²	C₂⁴×C₅	1	1	yes	characteristic
559	C₄²	C₂⁴×C₅	1	1	yes	characteristic
560	C₂×C₅	—	2	2	no	—
561	C₂×C₅	—	4	4	no	—
562	C₂×C₅	—	4	1	no	—
563	C₂×C₅	—	4	1	no	—
564	C₂×C₅	#3428	1	1	yes	characteristic
565	C₂×C₅	C₂×#568	1	1	yes	characteristic
566	C₂×C₅	C₂×#568	1	1	yes	characteristic
567	C₂³	—	2	2	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	C₂³×C₄×C₅	1	4	yes	—
571	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
572	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
573	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
574	Q₈	—	4	2	no	—
575	Q₈	—	4	2	no	—
576	Q₈	—	4	2	no	—
577	D₄	—	2	8	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	4	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	8	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	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	4	no	—
605	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
606	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
607	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
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	4	yes	—
616	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
617	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
618	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
619	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
620	C₈	—	2	8	no	—
621	C₈	—	2	8	no	—
622	C₅	#60293	1	1	yes	characteristic, direct product factor, Sylow
623	C₂²	—	2	1	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	4	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	4	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	4	4	no	—
635	C₂²	C₅×#568	1	2	yes	—
636	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	4	no	—
641	C₄	—	2	1	no	—
642	C₄	—	2	1	no	—
643	C₄	—	2	1	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	4	no	—
649	C₄	—	2	4	no	—
650	C₄	C₅×#568	1	2	yes	—
651	C₄	C₅×#585	1	2	yes	—
652	C₂	—	2	2	no	—
653	C₂	—	4	1	no	—
654	C₂	—	4	1	no	—
655	C₂	—	4	4	no	—
656	C₂	C₅×#3428	1	1	yes	characteristic
657	C₂	C₂×C₅×#568	1	1	yes	characteristic
658	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	C₅×#3444	C₂
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×#2990	C₂	semidirect
3. C₅×#2989	C₂	semidirect
4. C₅×#2987	C₂	semidirect
5. C₅×#2980	C₂	semidirect
6. C₅×#2976	C₂	semidirect
7. C₅×#2968	C₂	semidirect
8. C₅×#2967	C₂	semidirect
9. C₅×#2925	C₂	semidirect
10. C₅×#2920	C₂	semidirect
11. C₂×C₅×#432	C₂	semidirect
31. C₅×#446	C₂²	semidirect
32. C₅×#446	C₂²	semidirect
36. C₅×#435	C₂²	semidirect
37. C₅×#435	C₂²	semidirect
40. C₅×#433	C₂²	semidirect
47. C₅×#432	C₂²	semidirect
50. C₅×#431	C₂²	semidirect
52. C₅×#423	C₂²	semidirect
54. C₂×C₅×C₄⋊C₈	C₂²	semidirect
58. C₅×#405	C₂²	semidirect
61. #60293	C₅	direct (N × H)
156. #2990	C₂×C₅	semidirect
157. #2989	C₂×C₅	semidirect
158. #2987	C₂×C₅	semidirect
159. #2980	C₂×C₅	semidirect
160. #2976	C₂×C₅	semidirect
161. #2968	C₂×C₅	semidirect
162. #2967	C₂×C₅	semidirect
163. #2925	C₂×C₅	semidirect
164. #2920	C₂×C₅	semidirect
165. C₂×#432	C₂×C₅	semidirect
269. #446	C₂²×C₅	semidirect
270. #446	C₂²×C₅	semidirect
274. #435	C₂²×C₅	semidirect
275. #435	C₂²×C₅	semidirect
278. #433	C₂²×C₅	semidirect
285. #432	C₂²×C₅	semidirect
288. #431	C₂²×C₅	semidirect
290. #423	C₂²×C₅	semidirect
292. C₂×C₄⋊C₈	C₂²×C₅	semidirect
296. #405	C₂²×C₅	semidirect
622. C₅	#60293	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3444	2
C₅×#2990	2
C₅×#2989	2
C₅×#2987	2
C₅×#2980	2
C₅×#2976	2
C₅×#2968	2
C₅×#2967	2
C₅×#2925	2
C₅×#2920	2
C₂×C₅×#432	2
#60293	5

Subgroups — C5×#60293 #11983013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60293 #11983013