Subgroups — C₅×#10869 #11933589

Order 1280.

774 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#108	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#106	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#343	C₂	1	2	yes	maximal
5	C₅×#1736	C₂	1	2	yes	maximal
6	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
7	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
8	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₅×#117	C₂²	1	1	yes	characteristic
10	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₅×#108	—	2	2	no	—
12	C₂×C₅×#108	—	2	2	no	—
13	C₂×C₅×#108	C₄	1	4	yes	complemented
14	C₂×C₅×#106	—	2	1	no	—
15	C₂×C₅×#106	—	2	1	no	—
16	C₂×C₅×#106	—	2	2	no	—
17	C₂×C₅×#106	C₄	1	4	yes	complemented
18	C₅×#405	—	2	2	no	—
19	C₅×#405	C₄	1	4	yes	complemented
20	C₂×C₅×#97	—	2	1	no	—
21	C₂×C₄×C₅×C₈	—	2	1	no	—
22	C₅×#343	—	2	4	no	—
23	C₅×#340	—	2	4	no	—
24	#10869	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₄×C₅	—	2	2	no	—
26	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
27	C₂×C₅×M₁₆	—	2	1	no	—
28	C₂×C₅×M₁₆	—	2	1	no	—
29	C₂×C₅×M₁₆	—	2	1	no	—
30	C₂×C₅×M₁₆	—	2	2	no	—
31	C₂×C₅×M₁₆	—	2	2	no	—
32	C₂×C₅×M₁₆	—	2	2	no	—
33	C₂×C₅×M₁₆	—	2	2	no	—
34	C₂×C₅×M₁₆	—	2	2	no	—
35	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
36	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
37	C₂×C₅×M₁₆	D₄	1	2	yes	—
38	C₂×C₅×M₁₆	Q₈	1	2	yes	—
39	C₂²×C₅×C₈	—	2	1	no	—
40	C₂²×C₅×C₈	—	2	2	no	—
41	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
43	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
44	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
45	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
46	C₂²×C₅×C₈	D₄	1	2	yes	—
47	C₂²×C₅×C₈	D₄	1	2	yes	—
48	C₂²×C₅×C₈	Q₈	1	2	yes	—
49	C₅×#117	—	2	1	no	—
50	C₅×#117	—	2	1	no	—
51	C₅×#117	C₂×C₄	1	2	yes	—
52	C₅×#117	Q₈	1	2	yes	—
53	C₂×C₅×C₄⋊C₄	—	2	2	no	—
54	C₂×C₅×C₄⋊C₄	—	2	2	no	—
55	C₂×C₅×C₄⋊C₄	—	2	2	no	—
56	C₂×C₅×C₄⋊C₄	—	2	2	no	—
57	C₂×C₅×C₄⋊C₄	—	2	2	no	—
58	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
59	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
60	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
61	C₂×C₄²×C₅	—	2	1	no	—
62	C₅×#108	—	2	8	no	—
63	C₅×#106	—	2	4	no	—
64	C₅×#106	—	2	4	no	—
65	C₅×#97	—	2	4	no	—
66	C₄×C₅×C₈	—	2	4	no	—
67	C₂²×#108	C₂×C₅	1	1	yes	characteristic
68	C₂²×#106	C₂×C₅	1	1	yes	characteristic
69	C₂×#405	C₂×C₅	1	1	yes	characteristic
70	C₂×#343	C₂×C₅	1	2	yes	—
71	#1736	C₂×C₅	1	2	yes	—
72	C₂⁴×C₅	#41	1	1	yes	characteristic
73	C₂²×C₄×C₅	—	2	2	no	—
74	C₂²×C₄×C₅	—	2	4	no	—
75	C₂²×C₄×C₅	—	4	2	no	—
76	C₂²×C₄×C₅	—	4	2	no	—
77	C₂²×C₄×C₅	—	8	4	no	—
78	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₅	#41	1	1	yes	characteristic
90	C₂²×C₄×C₅	#41	1	1	yes	characteristic
91	C₂²×C₄×C₅	#41	1	1	yes	characteristic
92	C₅×M₁₆	—	2	2	no	—
93	C₅×M₁₆	—	2	2	no	—
94	C₅×M₁₆	—	2	2	no	—
95	C₅×M₁₆	—	2	4	no	—
96	C₅×M₁₆	—	2	4	no	—
97	C₅×M₁₆	—	4	2	no	—
98	C₅×M₁₆	—	4	2	no	—
99	C₅×M₁₆	C₄⋊C₄	1	4	yes	—
100	C₂×C₅×C₈	—	2	2	no	—
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	—	2	4	no	—
104	C₂×C₅×C₈	—	4	2	no	—
105	C₂×C₅×C₈	—	4	2	no	—
106	C₂×C₅×C₈	C₄²	1	4	yes	—
107	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
108	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
109	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
110	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
111	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
112	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
113	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
114	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
115	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
116	C₅×C₄⋊C₄	—	2	2	no	—
117	C₅×C₄⋊C₄	—	2	4	no	—
118	C₅×C₄⋊C₄	—	2	4	no	—
119	C₅×C₄⋊C₄	—	4	2	no	—
120	C₅×C₄⋊C₄	—	4	2	no	—
121	C₅×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
122	C₅×C₂²⋊C₄	—	2	2	no	—
123	C₅×C₂²⋊C₄	—	2	2	no	—
124	C₄²×C₅	—	2	2	no	—
125	C₄²×C₅	—	2	2	no	—
126	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
127	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
128	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
129	C₂×#117	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
131	C₂×#108	—	2	2	no	—
132	C₂×#108	—	2	2	no	—
133	C₂×#108	C₄×C₅	1	4	yes	complemented
134	C₂×#106	—	2	1	no	—
135	C₂×#106	—	2	1	no	—
136	C₂×#106	—	2	2	no	—
137	C₂×#106	C₄×C₅	1	4	yes	complemented
138	#405	—	2	2	no	—
139	#405	C₄×C₅	1	4	yes	complemented
140	C₂×#97	—	2	1	no	—
141	C₂×C₄×C₈	—	2	1	no	—
142	#343	—	2	4	no	—
143	#340	—	2	4	no	—
144	C₂³×C₅	—	2	4	no	—
145	C₂³×C₅	#117	1	1	yes	characteristic
146	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
147	C₂³×C₅	C₄×Q₈	1	1	yes	characteristic
148	C₂³×C₅	#121	1	1	yes	characteristic
149	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂³×C₅	#124	1	1	yes	characteristic
151	C₂³×C₅	#125	1	1	yes	characteristic
152	C₂×C₄×C₅	—	2	4	no	—
153	C₂×C₄×C₅	—	4	4	no	—
154	C₂×C₄×C₅	—	4	4	no	—
155	C₂×C₄×C₅	—	8	4	no	—
156	C₂×C₄×C₅	—	8	4	no	—
157	C₂×C₄×C₅	—	8	4	no	—
158	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₅	#117	1	1	yes	characteristic
168	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₅	#121	1	1	yes	characteristic
175	C₂×C₄×C₅	#121	1	1	yes	characteristic
176	C₂×C₄×C₅	#121	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₅	#124	1	1	yes	characteristic
181	C₂×C₄×C₅	#125	1	1	yes	characteristic
182	C₂×C₄×C₅	#127	1	1	yes	characteristic
183	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
184	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
186	C₅×C₈	—	2	4	no	—
187	C₅×C₈	—	4	4	no	—
188	C₅×C₈	#95	1	4	yes	—
189	C₅×C₈	#95	1	4	yes	—
190	C₂³×C₄	—	2	2	no	—
191	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₂×M₁₆	—	2	1	no	—
193	C₂×M₁₆	—	2	1	no	—
194	C₂×M₁₆	—	2	1	no	—
195	C₂×M₁₆	—	2	2	no	—
196	C₂×M₁₆	—	2	2	no	—
197	C₂×M₁₆	—	2	2	no	—
198	C₂×M₁₆	—	2	2	no	—
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
201	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
202	C₂×M₁₆	C₅×D₄	1	2	yes	—
203	C₂×M₁₆	C₅×Q₈	1	2	yes	—
204	C₂²×C₈	—	2	1	no	—
205	C₂²×C₈	—	2	2	no	—
206	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
207	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
208	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
209	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
210	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
211	C₂²×C₈	C₅×D₄	1	2	yes	—
212	C₂²×C₈	C₅×D₄	1	2	yes	—
213	C₂²×C₈	C₅×Q₈	1	2	yes	—
214	#117	—	2	1	no	—
215	#117	—	2	1	no	—
216	#117	C₂×C₄×C₅	1	2	yes	—
217	#117	C₅×Q₈	1	2	yes	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
224	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
225	C₂×C₂²⋊C₄	—	2	1	no	—
226	C₂×C₄²	—	2	1	no	—
227	#108	—	2	8	no	—
228	#106	—	2	4	no	—
229	#106	—	2	4	no	—
230	#97	—	2	4	no	—
231	C₄×C₈	—	2	4	no	—
232	C₂²×C₅	—	2	2	no	—
233	C₂²×C₅	—	2	2	no	—
234	C₂²×C₅	—	2	2	no	—
235	C₂²×C₅	—	2	2	no	—
236	C₂²×C₅	—	2	2	no	—
237	C₂²×C₅	—	2	2	no	—
238	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
239	C₂²×C₅	#380	1	1	yes	characteristic
240	C₂²×C₅	#382	1	1	yes	characteristic
241	C₂²×C₅	#389	1	1	yes	characteristic
242	C₂²×C₅	#389	1	1	yes	characteristic
243	C₂²×C₅	#390	1	1	yes	characteristic
244	C₂²×C₅	#391	1	1	yes	characteristic
245	C₂²×C₅	#471	1	4	yes	—
246	C₄×C₅	—	4	4	no	—
247	C₄×C₅	—	8	4	no	—
248	C₄×C₅	C₂×#95	1	1	yes	characteristic
249	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
250	C₄×C₅	#380	1	1	yes	characteristic
251	C₄×C₅	#384	1	1	yes	characteristic
252	C₄×C₅	#389	1	1	yes	characteristic
253	C₄×C₅	#389	1	1	yes	characteristic
254	C₄×C₅	#390	1	1	yes	characteristic
255	C₄×C₅	#391	1	1	yes	characteristic
256	C₂⁴	C₅×#41	1	1	yes	characteristic
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	8	4	no	—
262	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
263	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
273	C₂²×C₄	C₅×#41	1	1	yes	characteristic
274	C₂²×C₄	C₅×#41	1	1	yes	characteristic
275	C₂²×C₄	C₅×#41	1	1	yes	characteristic
276	M₁₆	—	2	2	no	—
277	M₁₆	—	2	2	no	—
278	M₁₆	—	2	2	no	—
279	M₁₆	—	2	4	no	—
280	M₁₆	—	2	4	no	—
281	M₁₆	—	4	2	no	—
282	M₁₆	—	4	2	no	—
283	M₁₆	C₅×C₄⋊C₄	1	4	yes	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	4	2	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	C₄²×C₅	1	4	yes	—
291	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
292	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
293	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
294	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
295	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
296	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
297	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
298	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
299	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₂×C₅	—	2	1	no	—
311	C₂×C₅	—	2	1	no	—
312	C₂×C₅	—	2	1	no	—
313	C₂×C₅	—	2	1	no	—
314	C₂×C₅	C₄⋊#95	1	1	yes	characteristic
315	C₂×C₅	#1815	1	2	yes	—
316	C₂×C₅	#1951	1	2	yes	—
317	C₂×C₅	#1977	1	2	yes	—
318	C₂³	—	2	4	no	—
319	C₂³	C₅×#117	1	1	yes	characteristic
320	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
321	C₂³	C₄×C₅×Q₈	1	1	yes	characteristic
322	C₂³	C₅×#121	1	1	yes	characteristic
323	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
324	C₂³	C₅×#124	1	1	yes	characteristic
325	C₂³	C₅×#125	1	1	yes	characteristic
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	8	4	no	—
330	C₂×C₄	—	8	4	no	—
331	C₂×C₄	—	8	4	no	—
332	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
333	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
338	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
339	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₅×#117	1	1	yes	characteristic
342	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
343	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
344	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
345	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
346	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
347	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
348	C₂×C₄	C₅×#121	1	1	yes	characteristic
349	C₂×C₄	C₅×#121	1	1	yes	characteristic
350	C₂×C₄	C₅×#121	1	1	yes	characteristic
351	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
352	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
353	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
354	C₂×C₄	C₅×#124	1	1	yes	characteristic
355	C₂×C₄	C₅×#125	1	1	yes	characteristic
356	C₂×C₄	C₅×#127	1	1	yes	characteristic
357	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
358	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
359	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
360	C₈	—	2	4	no	—
361	C₈	—	4	4	no	—
362	C₈	C₅×#95	1	4	yes	—
363	C₈	C₅×#95	1	4	yes	—
364	C₅	#10869	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
372	C₂²	C₅×#380	1	1	yes	characteristic
373	C₂²	C₅×#382	1	1	yes	characteristic
374	C₂²	C₅×#389	1	1	yes	characteristic
375	C₂²	C₅×#389	1	1	yes	characteristic
376	C₂²	C₅×#390	1	1	yes	characteristic
377	C₂²	C₅×#391	1	1	yes	characteristic
378	C₂²	C₅×#471	1	4	yes	—
379	C₄	—	4	4	no	—
380	C₄	—	8	4	no	—
381	C₄	C₂×C₅×#95	1	1	yes	characteristic
382	C₄	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
383	C₄	C₅×#380	1	1	yes	characteristic
384	C₄	C₅×#384	1	1	yes	characteristic
385	C₄	C₅×#389	1	1	yes	characteristic
386	C₄	C₅×#389	1	1	yes	characteristic
387	C₄	C₅×#390	1	1	yes	characteristic
388	C₄	C₅×#391	1	1	yes	characteristic
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	C₅×C₄⋊#95	1	1	yes	characteristic
394	C₂	C₅×#1815	1	2	yes	—
395	C₂	C₅×#1951	1	2	yes	—
396	C₂	C₅×#1977	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	#121
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
prime radical	C₂⁴×C₅	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₂×C₅×#108	C₄	semidirect
17. C₂×C₅×#106	C₄	semidirect
19. C₅×#405	C₄	semidirect
24. #10869	C₅	direct (N × H)
133. C₂×#108	C₄×C₅	semidirect
137. C₂×#106	C₄×C₅	semidirect
139. #405	C₄×C₅	semidirect
364. C₅	#10869	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×#108	2
C₂²×C₅×#106	2
C₂×C₅×#405	2
C₂×C₅×#343	2
C₅×#1736	2
#10869	5

Subgroups — C5×#10869 #11933589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10869 #11933589