Subgroups — C₅×#8097 #11930817

Order 1280.

700 conjugacy classes of subgroups.

The subgroup lattice has 386 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×#423	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
4	C₅×#1303	C₂	1	4	yes	maximal, complemented
5	C₂²×C₅×M₁₆	—	2	1	no	—
6	C₂×C₅×#117	—	2	1	no	—
7	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₅×#432	—	2	1	no	—
9	C₅×#432	C₄	1	2	yes	complemented
10	C₅×#431	—	2	1	no	—
11	C₅×#431	C₂²	1	2	yes	—
12	C₅×#423	—	2	1	no	—
13	C₅×#423	—	2	1	no	—
14	C₅×#423	C₄	1	2	yes	complemented
15	C₅×#423	C₄	1	2	yes	complemented
16	C₅×#423	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₈	—	2	1	no	—
18	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	complemented
19	C₅×#407	—	2	1	no	—
20	C₄×C₅×M₁₆	—	2	1	no	—
21	C₄×C₅×C₄⋊C₄	—	2	1	no	—
22	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
24	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	—
25	C₅×#376	C₄	1	2	yes	—
26	C₄³×C₅	—	2	1	no	—
27	#8097	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
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	—	4	4	no	—
35	C₂²×C₅×C₈	—	2	2	no	—
36	C₅×#117	—	2	8	no	—
37	C₂×C₅×C₄⋊C₄	—	2	2	no	—
38	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
39	C₂×C₄²×C₅	—	2	2	no	—
40	C₂×C₄²×C₅	—	2	2	no	—
41	C₂×C₄²×C₅	—	2	2	no	—
42	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
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	D₄	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	Q₈	1	1	yes	characteristic
52	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
53	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₅×C₄⋊C₈	—	2	2	no	—
55	C₅×C₄⋊C₈	—	2	2	no	—
56	C₅×C₄⋊C₈	—	2	2	no	—
57	C₅×C₄⋊C₈	—	2	2	no	—
58	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
59	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
60	C₅×C₂²⋊C₈	—	2	2	no	—
61	C₅×C₂²⋊C₈	—	2	2	no	—
62	C₅×#97	—	2	2	no	—
63	C₄×C₅×C₈	—	2	2	no	—
64	C₅×#95	—	2	2	no	—
65	C₅×#95	C₂×C₄	1	4	yes	—
66	#2920	C₂×C₅	1	1	yes	characteristic
67	C₂×#423	C₂×C₅	1	1	yes	characteristic
68	C₄×#117	C₂×C₅	1	1	yes	characteristic
69	#1303	C₂×C₅	1	4	yes	complemented
70	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₅	—	2	4	no	—
72	C₂²×C₄×C₅	—	2	2	no	—
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	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
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	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₅×M₁₆	—	4	4	no	—
95	C₅×M₁₆	—	4	4	no	—
96	C₅×M₁₆	—	4	4	no	—
97	C₂×C₅×C₈	—	2	4	no	—
98	C₂×C₅×C₈	—	2	4	no	—
99	C₂×C₅×C₈	—	4	4	no	—
100	C₅×C₄⋊C₄	—	2	8	no	—
101	C₅×C₂²⋊C₄	—	2	8	no	—
102	C₄²×C₅	—	2	8	no	—
103	C₄²×C₅	—	4	4	no	—
104	C₄²×C₅	—	4	2	no	—
105	C₄²×C₅	—	4	2	no	—
106	C₄²×C₅	C₄²	1	1	yes	characteristic
107	C₄²×C₅	C₄²	1	1	yes	characteristic
108	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
122	C₂²×M₁₆	—	2	1	no	—
123	C₂×#117	—	2	1	no	—
124	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
125	#432	—	2	1	no	—
126	#432	C₄×C₅	1	2	yes	complemented
127	#431	—	2	1	no	—
128	#431	C₂²×C₅	1	2	yes	—
129	#423	—	2	1	no	—
130	#423	—	2	1	no	—
131	#423	C₄×C₅	1	2	yes	complemented
132	#423	C₄×C₅	1	2	yes	complemented
133	#423	C₂²×C₅	1	2	yes	—
134	C₂×C₄⋊C₈	—	2	1	no	—
135	C₂×C₄⋊C₈	C₄×C₅	1	2	yes	complemented
136	#407	—	2	1	no	—
137	C₄×M₁₆	—	2	1	no	—
138	C₄×C₄⋊C₄	—	2	1	no	—
139	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
140	C₄×C₂²⋊C₄	—	2	1	no	—
141	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	—
142	#376	C₄×C₅	1	2	yes	—
143	C₄³	—	2	1	no	—
144	C₂³×C₅	—	2	2	no	—
145	C₂³×C₅	—	2	2	no	—
146	C₂³×C₅	—	4	1	no	—
147	C₂³×C₅	#95	1	1	yes	characteristic
148	C₂³×C₅	#95	1	1	yes	characteristic
149	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₅	—	2	2	no	—
151	C₂×C₄×C₅	—	2	2	no	—
152	C₂×C₄×C₅	—	2	2	no	—
153	C₂×C₄×C₅	—	2	2	no	—
154	C₂×C₄×C₅	—	2	2	no	—
155	C₂×C₄×C₅	—	2	2	no	—
156	C₂×C₄×C₅	—	2	2	no	—
157	C₂×C₄×C₅	—	2	1	no	—
158	C₂×C₄×C₅	—	2	1	no	—
159	C₂×C₄×C₅	—	2	1	no	—
160	C₂×C₄×C₅	—	2	1	no	—
161	C₂×C₄×C₅	—	2	2	no	—
162	C₂×C₄×C₅	—	2	2	no	—
163	C₂×C₄×C₅	—	2	2	no	—
164	C₂×C₄×C₅	—	2	2	no	—
165	C₂×C₄×C₅	—	2	8	no	—
166	C₂×C₄×C₅	—	4	1	no	—
167	C₂×C₄×C₅	—	4	1	no	—
168	C₂×C₄×C₅	—	4	1	no	—
169	C₂×C₄×C₅	—	4	4	no	—
170	C₂×C₄×C₅	—	4	4	no	—
171	C₂×C₄×C₅	#95	1	1	yes	characteristic
172	C₂×C₄×C₅	#95	1	1	yes	characteristic
173	C₂×C₄×C₅	#95	1	1	yes	characteristic
174	C₂×C₄×C₅	#95	1	1	yes	characteristic
175	C₂×C₄×C₅	#95	1	1	yes	characteristic
176	C₂×C₄×C₅	#95	1	1	yes	characteristic
177	C₂×C₄×C₅	#104	1	4	yes	—
178	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
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	AGL(1,ℤ/8)	1	2	yes	—
185	C₂×C₄×C₅	#137	1	2	yes	—
186	C₅×C₈	—	4	4	no	—
187	C₅×C₈	—	4	4	no	—
188	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
189	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
190	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
191	C₂×M₁₆	—	2	2	no	—
192	C₂×M₁₆	—	2	2	no	—
193	C₂×M₁₆	—	2	2	no	—
194	C₂×M₁₆	—	4	4	no	—
195	C₂²×C₈	—	2	2	no	—
196	#117	—	2	8	no	—
197	C₂×C₄⋊C₄	—	2	2	no	—
198	C₂×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₄²	—	2	2	no	—
200	C₂×C₄²	—	2	2	no	—
201	C₂×C₄²	—	2	2	no	—
202	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
203	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
204	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
206	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
207	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
208	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
209	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
210	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
211	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
212	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
213	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
214	C₄⋊C₈	—	2	2	no	—
215	C₄⋊C₈	—	2	2	no	—
216	C₄⋊C₈	—	2	2	no	—
217	C₄⋊C₈	—	2	2	no	—
218	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
219	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
220	C₂²⋊C₈	—	2	2	no	—
221	C₂²⋊C₈	—	2	2	no	—
222	#97	—	2	2	no	—
223	C₄×C₈	—	2	2	no	—
224	#95	—	2	2	no	—
225	#95	C₂×C₄×C₅	1	4	yes	—
226	C₂²×C₅	—	2	1	no	—
227	C₂²×C₅	—	2	1	no	—
228	C₂²×C₅	—	2	1	no	—
229	C₂²×C₅	—	2	1	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	2	1	no	—
232	C₂²×C₅	—	2	1	no	—
233	C₂²×C₅	—	4	4	no	—
234	C₂²×C₅	#339	1	2	yes	—
235	C₂²×C₅	C₂×#95	1	1	yes	characteristic
236	C₂²×C₅	#417	1	2	yes	—
237	C₄×C₅	—	2	1	no	—
238	C₄×C₅	—	2	1	no	—
239	C₄×C₅	—	2	1	no	—
240	C₄×C₅	—	2	1	no	—
241	C₄×C₅	—	2	1	no	—
242	C₄×C₅	—	2	1	no	—
243	C₄×C₅	—	2	1	no	—
244	C₄×C₅	—	4	8	no	—
245	C₄×C₅	#339	1	2	yes	—
246	C₄×C₅	#344	1	2	yes	—
247	C₄×C₅	#418	1	1	yes	characteristic
248	C₄×C₅	#419	1	1	yes	characteristic
249	C₄×C₅	C₂×#104	1	2	yes	—
250	C₄×C₅	#428	1	2	yes	—
251	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
258	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
259	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₅	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	M₁₆	—	4	4	no	—
276	M₁₆	—	4	4	no	—
277	M₁₆	—	4	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	4	4	no	—
281	C₄⋊C₄	—	2	8	no	—
282	C₂²⋊C₄	—	2	8	no	—
283	C₄²	—	2	8	no	—
284	C₄²	—	4	4	no	—
285	C₄²	—	4	2	no	—
286	C₄²	—	4	2	no	—
287	C₄²	C₄²×C₅	1	1	yes	characteristic
288	C₄²	C₄²×C₅	1	1	yes	characteristic
289	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
290	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
291	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
292	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
293	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
294	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
295	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
296	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
297	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
298	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
299	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
300	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
301	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
302	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
303	C₂×C₅	—	2	2	no	—
304	C₂×C₅	—	2	2	no	—
305	C₂×C₅	—	4	1	no	—
306	C₂×C₅	C₂×#339	1	1	yes	characteristic
307	C₂×C₅	#1736	1	1	yes	characteristic
308	C₂×C₅	C₂×#344	1	1	yes	characteristic
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	4	1	no	—
312	C₂³	C₅×#95	1	1	yes	characteristic
313	C₂³	C₅×#95	1	1	yes	characteristic
314	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	C₅×#95	1	1	yes	characteristic
337	C₂×C₄	C₅×#95	1	1	yes	characteristic
338	C₂×C₄	C₅×#95	1	1	yes	characteristic
339	C₂×C₄	C₅×#95	1	1	yes	characteristic
340	C₂×C₄	C₅×#95	1	1	yes	characteristic
341	C₂×C₄	C₅×#95	1	1	yes	characteristic
342	C₂×C₄	C₅×#104	1	4	yes	—
343	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
344	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₂×C₅×C₂²⋊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×AGL(1,ℤ/8)	1	2	yes	—
350	C₂×C₄	C₅×#137	1	2	yes	—
351	C₈	—	4	4	no	—
352	C₈	—	4	4	no	—
353	C₅	#8097	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	4	4	no	—
362	C₂²	C₅×#339	1	2	yes	—
363	C₂²	C₂×C₅×#95	1	1	yes	characteristic
364	C₂²	C₅×#417	1	2	yes	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	8	no	—
373	C₄	C₅×#339	1	2	yes	—
374	C₄	C₅×#344	1	2	yes	—
375	C₄	C₅×#418	1	1	yes	characteristic
376	C₄	C₅×#419	1	1	yes	characteristic
377	C₄	C₂×C₅×#104	1	2	yes	—
378	C₄	C₅×#428	1	2	yes	—
379	C₂	—	2	2	no	—
380	C₂	—	2	2	no	—
381	C₂	—	4	1	no	—
382	C₂	C₂×C₅×#339	1	1	yes	characteristic
383	C₂	C₅×#1736	1	1	yes	characteristic
384	C₂	C₂×C₅×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle	C₂²×C₅	C₂×#95
prime radical	C₂⁴×C₅	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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×#1303	C₂	semidirect
9. C₅×#432	C₄	semidirect
14. C₅×#423	C₄	semidirect
15. C₅×#423	C₄	semidirect
18. C₂×C₅×C₄⋊C₈	C₄	semidirect
27. #8097	C₅	direct (N × H)
69. #1303	C₂×C₅	semidirect
126. #432	C₄×C₅	semidirect
131. #423	C₄×C₅	semidirect
132. #423	C₄×C₅	semidirect
135. C₂×C₄⋊C₈	C₄×C₅	semidirect
353. C₅	#8097	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×#423	2
C₄×C₅×#117	2
C₅×#1303	2
#8097	5

Subgroups — C5×#8097 #11930817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8097 #11930817