Subgroups — C₅×#21994 #11944714

Order 1280.

704 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic
4	C₅×#1950	C₂	1	4	yes	maximal, complemented
5	C₅×#1855	C₂	1	4	yes	maximal
6	C₅×#1849	C₂	1	2	yes	maximal, complemented
7	C₅×#1838	C₂	1	2	yes	maximal, complemented
8	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₅×#432	—	2	1	no	—
11	C₅×#432	—	2	1	no	—
12	C₅×#432	C₄	1	2	yes	—
13	C₅×#432	C₄	1	2	yes	—
14	C₅×#432	C₄	1	2	yes	—
15	C₅×#432	C₄	1	2	yes	—
16	C₅×#431	—	2	1	no	—
17	C₅×#431	—	2	1	no	—
18	C₂×C₅×#108	C₂²	1	8	yes	—
19	C₅×#423	—	2	1	no	—
20	C₅×#423	—	2	1	no	—
21	C₅×#423	C₂²	1	1	yes	characteristic
22	C₅×#423	C₂²	1	2	yes	—
23	C₅×#423	C₂²	1	1	yes	characteristic
24	C₅×#423	C₂²	1	2	yes	—
25	C₂×C₅×C₄⋊C₈	—	2	1	no	—
26	C₂×C₅×C₄⋊C₈	—	2	1	no	—
27	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
28	C₅×#407	C₂²	1	2	yes	—
29	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₄×C₅×M₁₆	C₂²	1	2	yes	—
31	C₂×C₅×#97	C₂²	1	2	yes	—
32	C₅×#341	C₂²	1	8	yes	—
33	#21994	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
35	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
36	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×M₁₆	—	2	2	no	—
38	C₂×C₅×M₁₆	—	4	4	no	—
39	C₂×C₅×M₁₆	C₂³	1	2	yes	—
40	C₂×C₅×M₁₆	C₂³	1	2	yes	—
41	C₂×C₅×M₁₆	C₂³	1	4	yes	—
42	C₂²×C₅×C₈	—	2	2	no	—
43	C₂²×C₅×C₈	C₂³	1	4	yes	—
44	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
53	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
54	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
56	C₅×#108	—	4	8	no	—
57	C₅×C₄⋊C₈	—	2	2	no	—
58	C₅×C₄⋊C₈	—	2	2	no	—
59	C₅×C₄⋊C₈	—	2	2	no	—
60	C₅×C₄⋊C₈	—	2	2	no	—
61	C₅×C₄⋊C₈	—	2	1	no	—
62	C₅×C₄⋊C₈	—	2	1	no	—
63	C₅×C₄⋊C₈	—	2	1	no	—
64	C₅×C₄⋊C₈	—	2	1	no	—
65	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
66	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
67	C₅×C₂²⋊C₈	—	2	2	no	—
68	C₅×C₂²⋊C₈	—	2	2	no	—
69	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
70	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
71	C₅×#97	—	2	2	no	—
72	C₅×#97	C₂×C₄	1	4	yes	—
73	C₅×#97	C₂×C₄	1	4	yes	—
74	C₄×C₅×C₈	—	2	2	no	—
75	#2920	C₂×C₅	1	1	yes	characteristic
76	C₂×#432	C₂×C₅	1	1	yes	characteristic
77	C₂×#423	C₂×C₅	1	1	yes	characteristic
78	#1950	C₂×C₅	1	4	yes	complemented
79	#1855	C₂×C₅	1	4	yes	—
80	#1849	C₂×C₅	1	2	yes	complemented
81	#1838	C₂×C₅	1	2	yes	complemented
82	C₂⁴×C₅	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₅	—	2	2	no	—
84	C₂²×C₄×C₅	—	2	2	no	—
85	C₂²×C₄×C₅	—	4	2	no	—
86	C₂²×C₄×C₅	—	4	2	no	—
87	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
105	C₅×M₁₆	—	2	8	no	—
106	C₅×M₁₆	—	2	4	no	—
107	C₅×M₁₆	—	2	4	no	—
108	C₅×M₁₆	—	4	4	no	—
109	C₂×C₅×C₈	—	2	4	no	—
110	C₂×C₅×C₈	—	2	4	no	—
111	C₂×C₅×C₈	—	2	4	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	4	4	no	—
115	C₂×C₅×C₈	C₂²×C₄	1	8	yes	—
116	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
119	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
120	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
121	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
122	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
123	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
124	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
133	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
134	#432	—	2	1	no	—
135	#432	—	2	1	no	—
136	#432	C₄×C₅	1	2	yes	—
137	#432	C₄×C₅	1	2	yes	—
138	#432	C₄×C₅	1	2	yes	—
139	#432	C₄×C₅	1	2	yes	—
140	#431	—	2	1	no	—
141	#431	—	2	1	no	—
142	C₂×#108	C₂²×C₅	1	8	yes	—
143	#423	—	2	1	no	—
144	#423	—	2	1	no	—
145	#423	C₂²×C₅	1	1	yes	characteristic
146	#423	C₂²×C₅	1	2	yes	—
147	#423	C₂²×C₅	1	1	yes	characteristic
148	#423	C₂²×C₅	1	2	yes	—
149	C₂×C₄⋊C₈	—	2	1	no	—
150	C₂×C₄⋊C₈	—	2	1	no	—
151	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
152	#407	C₂²×C₅	1	2	yes	—
153	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
154	C₄×M₁₆	C₂²×C₅	1	2	yes	—
155	C₂×#97	C₂²×C₅	1	2	yes	—
156	#341	C₂²×C₅	1	8	yes	—
157	C₂³×C₅	—	2	2	no	—
158	C₂³×C₅	—	2	2	no	—
159	C₂³×C₅	—	4	1	no	—
160	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂³×C₅	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₅	—	2	2	no	—
164	C₂×C₄×C₅	—	2	2	no	—
165	C₂×C₄×C₅	—	2	2	no	—
166	C₂×C₄×C₅	—	2	2	no	—
167	C₂×C₄×C₅	—	2	2	no	—
168	C₂×C₄×C₅	—	2	1	no	—
169	C₂×C₄×C₅	—	2	1	no	—
170	C₂×C₄×C₅	—	2	1	no	—
171	C₂×C₄×C₅	—	2	1	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	4	1	no	—
176	C₂×C₄×C₅	—	4	1	no	—
177	C₂×C₄×C₅	—	4	1	no	—
178	C₂×C₄×C₅	—	4	1	no	—
179	C₂×C₄×C₅	—	4	1	no	—
180	C₂×C₄×C₅	—	4	1	no	—
181	C₂×C₄×C₅	—	4	1	no	—
182	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
195	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
196	C₅×C₈	—	2	8	no	—
197	C₅×C₈	—	4	4	no	—
198	C₅×C₈	—	4	2	no	—
199	C₅×C₈	—	4	2	no	—
200	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
201	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
202	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	—	4	4	no	—
205	C₂×M₁₆	C₂³×C₅	1	4	yes	—
206	C₂×M₁₆	C₂³×C₅	1	2	yes	—
207	C₂×M₁₆	C₂³×C₅	1	2	yes	—
208	C₂²×C₈	—	2	2	no	—
209	C₂²×C₈	C₂³×C₅	1	4	yes	—
210	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
211	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
212	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
213	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
214	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
215	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
216	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
217	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
218	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
219	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
220	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
221	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
222	#108	—	4	8	no	—
223	C₄⋊C₈	—	2	2	no	—
224	C₄⋊C₈	—	2	2	no	—
225	C₄⋊C₈	—	2	2	no	—
226	C₄⋊C₈	—	2	2	no	—
227	C₄⋊C₈	—	2	1	no	—
228	C₄⋊C₈	—	2	1	no	—
229	C₄⋊C₈	—	2	1	no	—
230	C₄⋊C₈	—	2	1	no	—
231	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
232	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
233	C₂²⋊C₈	—	2	2	no	—
234	C₂²⋊C₈	—	2	2	no	—
235	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
236	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
237	#97	—	2	2	no	—
238	#97	C₂×C₄×C₅	1	4	yes	—
239	#97	C₂×C₄×C₅	1	4	yes	—
240	C₄×C₈	—	2	2	no	—
241	C₂²×C₅	—	2	1	no	—
242	C₂²×C₅	—	2	1	no	—
243	C₂²×C₅	—	2	1	no	—
244	C₂²×C₅	—	2	1	no	—
245	C₂²×C₅	—	2	1	no	—
246	C₂²×C₅	—	2	1	no	—
247	C₂²×C₅	—	2	1	no	—
248	C₂²×C₅	—	4	4	no	—
249	C₂²×C₅	#430	1	2	yes	—
250	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
251	C₂²×C₅	#544	1	2	yes	—
252	C₄×C₅	—	2	1	no	—
253	C₄×C₅	—	2	1	no	—
254	C₄×C₅	—	2	1	no	—
255	C₄×C₅	—	2	1	no	—
256	C₄×C₅	—	2	1	no	—
257	C₄×C₅	—	2	1	no	—
258	C₄×C₅	—	2	1	no	—
259	C₄×C₅	—	2	1	no	—
260	C₄×C₅	—	2	1	no	—
261	C₄×C₅	#430	1	2	yes	—
262	C₄×C₅	#520	1	2	yes	—
263	C₄×C₅	#535	1	1	yes	characteristic
264	C₄×C₅	#536	1	1	yes	characteristic
265	C₂⁴	C₂×C₅×Q₈	1	1	yes	characteristic
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
274	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
288	M₁₆	—	2	4	no	—
289	M₁₆	—	2	8	no	—
290	M₁₆	—	2	4	no	—
291	M₁₆	—	4	4	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	4	4	no	—
298	C₂×C₈	C₂²×C₄×C₅	1	8	yes	—
299	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
300	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
301	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
302	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
303	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
304	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
305	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
306	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
307	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
308	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
309	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
310	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
311	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
312	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
313	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
314	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂×C₅	—	2	2	no	—
316	C₂×C₅	—	2	2	no	—
317	C₂×C₅	—	4	1	no	—
318	C₂×C₅	#2317	1	1	yes	characteristic
319	C₂×C₅	C₂×#430	1	1	yes	characteristic
320	C₂×C₅	C₂×#430	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	4	1	no	—
324	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
325	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
326	C₂³	C₂²×C₅×Q₈	1	1	yes	characteristic
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
347	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
348	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
351	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
352	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
353	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
358	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
359	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
360	C₈	—	2	8	no	—
361	C₈	—	4	4	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₅	#21994	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	4	4	no	—
373	C₂²	C₅×#430	1	2	yes	—
374	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
375	C₂²	C₅×#544	1	2	yes	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	C₅×#430	1	2	yes	—
386	C₄	C₅×#520	1	2	yes	—
387	C₄	C₅×#535	1	1	yes	characteristic
388	C₄	C₅×#536	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	2	2	no	—
391	C₂	—	4	1	no	—
392	C₂	C₅×#2317	1	1	yes	characteristic
393	C₂	C₂×C₅×#430	1	1	yes	characteristic
394	C₂	C₂×C₅×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₅	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1950	C₂	semidirect
6. C₅×#1849	C₂	semidirect
7. C₅×#1838	C₂	semidirect
33. #21994	C₅	direct (N × H)
78. #1950	C₂×C₅	semidirect
80. #1849	C₂×C₅	semidirect
81. #1838	C₂×C₅	semidirect
364. C₅	#21994	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×#2920	2
C₂×C₅×#432	2
C₂×C₅×#423	2
C₅×#1950	2
C₅×#1855	2
C₅×#1849	2
C₅×#1838	2
#21994	5

Subgroups — C5×#21994 #11944714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21994 #11944714