Subgroups — C₅×#10870 #11933590

Order 1280.

774 conjugacy classes of subgroups.

The subgroup lattice has 410 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×#107	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×#107	—	2	1	no	—
15	C₂×C₅×#107	—	2	1	no	—
16	C₂×C₅×#107	—	2	2	no	—
17	C₂×C₅×#107	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	#10870	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×#107	—	2	4	no	—
64	C₅×#107	—	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×#107	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×#107	—	2	1	no	—
135	C₂×#107	—	2	1	no	—
136	C₂×#107	—	2	2	no	—
137	C₂×#107	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	2	no	—
145	C₂³×C₅	—	2	2	no	—
146	C₂³×C₅	#117	1	1	yes	characteristic
147	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
148	C₂³×C₅	C₄×Q₈	1	1	yes	characteristic
149	C₂³×C₅	#121	1	1	yes	characteristic
150	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂³×C₅	#124	1	1	yes	characteristic
152	C₂³×C₅	#125	1	1	yes	characteristic
153	C₂×C₄×C₅	—	2	4	no	—
154	C₂×C₄×C₅	—	4	2	no	—
155	C₂×C₄×C₅	—	4	2	no	—
156	C₂×C₄×C₅	—	4	4	no	—
157	C₂×C₄×C₅	—	8	4	no	—
158	C₂×C₄×C₅	—	8	4	no	—
159	C₂×C₄×C₅	—	8	4	no	—
160	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₅	C₂×C₂²⋊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	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₅	#117	1	1	yes	characteristic
170	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₅	#121	1	1	yes	characteristic
177	C₂×C₄×C₅	#121	1	1	yes	characteristic
178	C₂×C₄×C₅	#121	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂×C₄×C₅	#124	1	1	yes	characteristic
183	C₂×C₄×C₅	#125	1	1	yes	characteristic
184	C₂×C₄×C₅	#127	1	1	yes	characteristic
185	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
187	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
188	C₅×C₈	—	2	4	no	—
189	C₅×C₈	—	4	4	no	—
190	C₅×C₈	#95	1	4	yes	—
191	C₅×C₈	#95	1	4	yes	—
192	C₂³×C₄	—	2	2	no	—
193	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
194	C₂×M₁₆	—	2	1	no	—
195	C₂×M₁₆	—	2	1	no	—
196	C₂×M₁₆	—	2	1	no	—
197	C₂×M₁₆	—	2	2	no	—
198	C₂×M₁₆	—	2	2	no	—
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	—	2	2	no	—
201	C₂×M₁₆	—	2	2	no	—
202	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
203	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
204	C₂×M₁₆	C₅×D₄	1	2	yes	—
205	C₂×M₁₆	C₅×Q₈	1	2	yes	—
206	C₂²×C₈	—	2	1	no	—
207	C₂²×C₈	—	2	2	no	—
208	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
209	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
210	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
211	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
212	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
213	C₂²×C₈	C₅×D₄	1	2	yes	—
214	C₂²×C₈	C₅×D₄	1	2	yes	—
215	C₂²×C₈	C₅×Q₈	1	2	yes	—
216	#117	—	2	1	no	—
217	#117	—	2	1	no	—
218	#117	C₂×C₄×C₅	1	2	yes	—
219	#117	C₅×Q₈	1	2	yes	—
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	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
226	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	C₂×C₄²	—	2	1	no	—
229	#108	—	2	8	no	—
230	#107	—	2	4	no	—
231	#107	—	2	4	no	—
232	#97	—	2	4	no	—
233	C₄×C₈	—	2	4	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	—	2	1	no	—
239	C₂²×C₅	—	2	1	no	—
240	C₂²×C₅	—	2	1	no	—
241	C₂²×C₅	—	2	1	no	—
242	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
243	C₂²×C₅	#380	1	1	yes	characteristic
244	C₂²×C₅	#382	1	1	yes	characteristic
245	C₂²×C₅	#389	1	1	yes	characteristic
246	C₂²×C₅	#389	1	1	yes	characteristic
247	C₂²×C₅	#390	1	1	yes	characteristic
248	C₂²×C₅	#391	1	1	yes	characteristic
249	C₂²×C₅	#472	1	2	yes	—
250	C₂²×C₅	#473	1	2	yes	—
251	C₄×C₅	—	4	4	no	—
252	C₄×C₅	—	8	4	no	—
253	C₄×C₅	C₂×#95	1	1	yes	characteristic
254	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
255	C₄×C₅	#380	1	1	yes	characteristic
256	C₄×C₅	#384	1	1	yes	characteristic
257	C₄×C₅	#389	1	1	yes	characteristic
258	C₄×C₅	#389	1	1	yes	characteristic
259	C₄×C₅	#390	1	1	yes	characteristic
260	C₄×C₅	#391	1	1	yes	characteristic
261	C₂⁴	C₅×#41	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	8	4	no	—
267	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
278	C₂²×C₄	C₅×#41	1	1	yes	characteristic
279	C₂²×C₄	C₅×#41	1	1	yes	characteristic
280	C₂²×C₄	C₅×#41	1	1	yes	characteristic
281	M₁₆	—	2	2	no	—
282	M₁₆	—	2	2	no	—
283	M₁₆	—	2	2	no	—
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	—	4	2	no	—
287	M₁₆	—	4	2	no	—
288	M₁₆	C₅×C₄⋊C₄	1	4	yes	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₂×C₈	C₄²×C₅	1	4	yes	—
296	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
297	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
298	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
299	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
300	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
301	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
302	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
303	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
304	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₂×C₅	—	2	1	no	—
316	C₂×C₅	—	2	1	no	—
317	C₂×C₅	—	2	1	no	—
318	C₂×C₅	—	2	1	no	—
319	C₂×C₅	C₄⋊#95	1	1	yes	characteristic
320	C₂×C₅	#1816	1	2	yes	—
321	C₂×C₅	#1952	1	2	yes	—
322	C₂×C₅	#1978	1	1	yes	characteristic
323	C₂×C₅	#1979	1	1	yes	characteristic
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	C₅×#117	1	1	yes	characteristic
327	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
328	C₂³	C₄×C₅×Q₈	1	1	yes	characteristic
329	C₂³	C₅×#121	1	1	yes	characteristic
330	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
331	C₂³	C₅×#124	1	1	yes	characteristic
332	C₂³	C₅×#125	1	1	yes	characteristic
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	8	4	no	—
338	C₂×C₄	—	8	4	no	—
339	C₂×C₄	—	8	4	no	—
340	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
341	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
342	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
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	C₅×#117	1	1	yes	characteristic
350	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
351	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
352	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
353	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
354	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
355	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
356	C₂×C₄	C₅×#121	1	1	yes	characteristic
357	C₂×C₄	C₅×#121	1	1	yes	characteristic
358	C₂×C₄	C₅×#121	1	1	yes	characteristic
359	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
360	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
361	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
362	C₂×C₄	C₅×#124	1	1	yes	characteristic
363	C₂×C₄	C₅×#125	1	1	yes	characteristic
364	C₂×C₄	C₅×#127	1	1	yes	characteristic
365	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
366	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
367	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
368	C₈	—	2	4	no	—
369	C₈	—	4	4	no	—
370	C₈	C₅×#95	1	4	yes	—
371	C₈	C₅×#95	1	4	yes	—
372	C₅	#10870	1	1	yes	characteristic, direct product factor, Sylow
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
382	C₂²	C₅×#380	1	1	yes	characteristic
383	C₂²	C₅×#382	1	1	yes	characteristic
384	C₂²	C₅×#389	1	1	yes	characteristic
385	C₂²	C₅×#389	1	1	yes	characteristic
386	C₂²	C₅×#390	1	1	yes	characteristic
387	C₂²	C₅×#391	1	1	yes	characteristic
388	C₂²	C₅×#472	1	2	yes	—
389	C₂²	C₅×#473	1	2	yes	—
390	C₄	—	4	4	no	—
391	C₄	—	8	4	no	—
392	C₄	C₂×C₅×#95	1	1	yes	characteristic
393	C₄	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
394	C₄	C₅×#380	1	1	yes	characteristic
395	C₄	C₅×#384	1	1	yes	characteristic
396	C₄	C₅×#389	1	1	yes	characteristic
397	C₄	C₅×#389	1	1	yes	characteristic
398	C₄	C₅×#390	1	1	yes	characteristic
399	C₄	C₅×#391	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	C₅×C₄⋊#95	1	1	yes	characteristic
405	C₂	C₅×#1816	1	2	yes	—
406	C₂	C₅×#1952	1	2	yes	—
407	C₂	C₅×#1978	1	1	yes	characteristic
408	C₂	C₅×#1979	1	1	yes	characteristic

	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×#107	C₄	semidirect
19. C₅×#405	C₄	semidirect
24. #10870	C₅	direct (N × H)
133. C₂×#108	C₄×C₅	semidirect
137. C₂×#107	C₄×C₅	semidirect
139. #405	C₄×C₅	semidirect
372. C₅	#10870	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×#107	2
C₂×C₅×#405	2
C₂×C₅×#343	2
C₅×#1736	2
#10870	5

Subgroups — C5×#10870 #11933590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10870 #11933590