Subgroups — C₅×#10851 #11933571

Order 1280.

978 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×#2285	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#339	C₂	1	4	yes	maximal
5	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
6	C₂×C₅×#117	C₂²	1	2	yes	—
7	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
8	C₂²×C₄²×C₅	C₂²	1	2	yes	—
9	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₄×C₅×M₁₆	—	2	2	no	—
11	C₄×C₅×M₁₆	C₄	1	4	yes	complemented
12	C₂×C₅×#97	—	2	1	no	—
13	C₂×C₄×C₅×C₈	—	2	1	no	—
14	C₅×#384	C₄	1	2	yes	complemented
15	C₅×#382	C₄	1	2	yes	complemented
16	C₅×#380	—	2	1	no	—
17	C₅×#380	—	2	1	no	—
18	C₄×C₅×C₄⋊C₄	—	2	2	no	—
19	C₄×C₅×C₄⋊C₄	—	2	1	no	—
20	C₄×C₅×C₄⋊C₄	—	2	1	no	—
21	C₄×C₅×C₄⋊C₄	C₄	1	4	yes	complemented
22	C₂×C₅×#95	—	2	1	no	—
23	C₅×#339	—	2	8	no	—
24	#10851	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₄×C₅	—	2	2	no	—
26	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
29	C₂×C₅×M₁₆	—	2	2	no	—
30	C₂×C₅×M₁₆	—	2	2	no	—
31	C₂×C₅×M₁₆	—	2	2	no	—
32	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
33	C₂×C₅×M₁₆	D₄	1	4	yes	—
34	C₂×C₅×M₁₆	Q₈	1	4	yes	—
35	C₂²×C₅×C₈	—	2	2	no	—
36	C₅×#117	—	2	4	no	—
37	C₅×#117	—	2	4	no	—
38	C₂×C₅×C₄⋊C₄	—	2	8	no	—
39	C₂×C₅×C₄⋊C₄	—	2	4	no	—
40	C₂×C₅×C₄⋊C₄	—	2	2	no	—
41	C₂×C₅×C₄⋊C₄	—	2	2	no	—
42	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
43	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
44	C₂×C₄²×C₅	—	2	4	no	—
45	C₂×C₄²×C₅	—	2	4	no	—
46	C₂×C₄²×C₅	—	2	2	no	—
47	C₂×C₄²×C₅	—	2	2	no	—
48	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₅	D₄	1	2	yes	—
54	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₅	Q₈	1	2	yes	—
57	C₅×#97	—	2	4	no	—
58	C₄×C₅×C₈	—	2	4	no	—
59	C₅×#95	—	2	4	no	—
60	C₅×#95	—	2	2	no	—
61	C₅×#95	—	2	2	no	—
62	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
63	#2285	C₂×C₅	1	1	yes	characteristic
64	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
65	C₂×#339	C₂×C₅	1	4	yes	—
66	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₅	—	2	4	no	—
68	C₂²×C₄×C₅	—	2	8	no	—
69	C₂²×C₄×C₅	—	2	4	no	—
70	C₂²×C₄×C₅	—	2	4	no	—
71	C₂²×C₄×C₅	—	4	2	no	—
72	C₂²×C₄×C₅	—	4	4	no	—
73	C₂²×C₄×C₅	—	4	2	no	—
74	C₂²×C₄×C₅	—	4	2	no	—
75	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
77	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
82	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
83	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₅	#41	1	2	yes	—
92	C₂²×C₄×C₅	#41	1	2	yes	—
93	C₅×M₁₆	—	2	4	no	—
94	C₅×M₁₆	—	2	4	no	—
95	C₅×M₁₆	—	2	4	no	—
96	C₅×M₁₆	C₄⋊C₄	1	8	yes	complemented
97	C₂×C₅×C₈	—	2	4	no	—
98	C₂×C₅×C₈	—	2	4	no	—
99	C₂×C₅×C₈	—	2	4	no	—
100	C₅×C₄⋊C₄	—	2	16	no	—
101	C₅×C₄⋊C₄	—	2	8	no	—
102	C₅×C₄⋊C₄	—	4	4	no	—
103	C₅×C₄⋊C₄	—	4	4	no	—
104	C₅×C₂²⋊C₄	—	4	2	no	—
105	C₅×C₂²⋊C₄	—	4	2	no	—
106	C₄²×C₅	—	2	8	no	—
107	C₄²×C₅	—	4	4	no	—
108	C₄²×C₅	—	4	4	no	—
109	C₄²×C₅	C₄²	1	2	yes	—
110	C₄²×C₅	C₄²	1	2	yes	—
111	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
112	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
113	C₄²×C₅	C₄⋊C₄	1	2	yes	—
114	C₄²×C₅	C₄⋊C₄	1	2	yes	—
115	C₄²×C₅	C₄⋊C₄	1	2	yes	—
116	C₄²×C₅	C₄⋊C₄	1	2	yes	—
117	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
118	C₂×#117	C₂²×C₅	1	2	yes	—
119	C₂²×C₄⋊C₄	—	2	1	no	—
120	C₂²×C₄²	C₂²×C₅	1	2	yes	—
121	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
122	C₄×M₁₆	—	2	2	no	—
123	C₄×M₁₆	C₄×C₅	1	4	yes	complemented
124	C₂×#97	—	2	1	no	—
125	C₂×C₄×C₈	—	2	1	no	—
126	#384	C₄×C₅	1	2	yes	complemented
127	#382	C₄×C₅	1	2	yes	complemented
128	#380	—	2	1	no	—
129	#380	—	2	1	no	—
130	C₄×C₄⋊C₄	—	2	2	no	—
131	C₄×C₄⋊C₄	—	2	1	no	—
132	C₄×C₄⋊C₄	—	2	1	no	—
133	C₄×C₄⋊C₄	C₄×C₅	1	4	yes	complemented
134	C₂×#95	—	2	1	no	—
135	#339	—	2	8	no	—
136	C₂³×C₅	—	2	2	no	—
137	C₂³×C₅	—	2	2	no	—
138	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂³×C₅	#124	1	1	yes	characteristic
142	C₂³×C₅	#124	1	1	yes	characteristic
143	C₂³×C₅	#127	1	1	yes	characteristic
144	C₂³×C₅	C₄⋊Q₈	1	1	yes	characteristic
145	C₂×C₄×C₅	—	2	2	no	—
146	C₂×C₄×C₅	—	2	2	no	—
147	C₂×C₄×C₅	—	2	2	no	—
148	C₂×C₄×C₅	—	2	4	no	—
149	C₂×C₄×C₅	—	2	4	no	—
150	C₂×C₄×C₅	—	2	8	no	—
151	C₂×C₄×C₅	—	4	2	no	—
152	C₂×C₄×C₅	—	4	2	no	—
153	C₂×C₄×C₅	—	4	8	no	—
154	C₂×C₄×C₅	—	4	8	no	—
155	C₂×C₄×C₅	—	4	4	no	—
156	C₂×C₄×C₅	—	4	4	no	—
157	C₂×C₄×C₅	—	4	4	no	—
158	C₂×C₄×C₅	—	4	4	no	—
159	C₂×C₄×C₅	—	4	4	no	—
160	C₂×C₄×C₅	#95	1	2	yes	—
161	C₂×C₄×C₅	#95	1	2	yes	—
162	C₂×C₄×C₅	#95	1	2	yes	—
163	C₂×C₄×C₅	#95	1	2	yes	—
164	C₂×C₄×C₅	#104	1	4	yes	—
165	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₅	#117	1	2	yes	—
171	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
174	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
175	C₂×C₄×C₅	#121	1	2	yes	—
176	C₂×C₄×C₅	#121	1	2	yes	—
177	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₅	#125	1	2	yes	—
180	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
181	C₅×C₈	—	2	8	no	—
182	C₂³×C₄	—	2	2	no	—
183	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
184	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
185	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₂×M₁₆	—	2	2	no	—
187	C₂×M₁₆	—	2	2	no	—
188	C₂×M₁₆	—	2	2	no	—
189	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
190	C₂×M₁₆	C₅×D₄	1	4	yes	—
191	C₂×M₁₆	C₅×Q₈	1	4	yes	—
192	C₂²×C₈	—	2	2	no	—
193	#117	—	2	4	no	—
194	#117	—	2	4	no	—
195	C₂×C₄⋊C₄	—	2	8	no	—
196	C₂×C₄⋊C₄	—	2	4	no	—
197	C₂×C₄⋊C₄	—	2	2	no	—
198	C₂×C₄⋊C₄	—	2	2	no	—
199	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
200	C₂×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₄²	—	2	4	no	—
202	C₂×C₄²	—	2	4	no	—
203	C₂×C₄²	—	2	2	no	—
204	C₂×C₄²	—	2	2	no	—
205	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
206	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
207	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
208	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
209	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
210	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
211	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
212	C₂×C₄²	C₅×D₄	1	2	yes	—
213	C₂×C₄²	C₅×Q₈	1	2	yes	—
214	#97	—	2	4	no	—
215	C₄×C₈	—	2	4	no	—
216	#95	—	2	4	no	—
217	#95	—	2	2	no	—
218	#95	—	2	2	no	—
219	C₂²×C₅	—	2	2	no	—
220	C₂²×C₅	—	2	2	no	—
221	C₂²×C₅	—	2	2	no	—
222	C₂²×C₅	—	2	2	no	—
223	C₂²×C₅	—	2	1	no	—
224	C₂²×C₅	—	2	1	no	—
225	C₂²×C₅	—	2	1	no	—
226	C₂²×C₅	—	2	1	no	—
227	C₂²×C₅	C₂×#95	1	1	yes	characteristic
228	C₂²×C₅	#382	1	1	yes	characteristic
229	C₂²×C₅	#384	1	1	yes	characteristic
230	C₂²×C₅	#390	1	1	yes	characteristic
231	C₂²×C₅	#390	1	1	yes	characteristic
232	C₂²×C₅	#391	1	1	yes	characteristic
233	C₂²×C₅	#391	1	1	yes	characteristic
234	C₂²×C₅	C₂×#104	1	2	yes	—
235	C₂²×C₅	#421	1	2	yes	—
236	C₄×C₅	—	2	2	no	—
237	C₄×C₅	—	2	2	no	—
238	C₄×C₅	—	2	2	no	—
239	C₄×C₅	—	4	8	no	—
240	C₄×C₅	—	8	4	no	—
241	C₄×C₅	#339	1	4	yes	complemented
242	C₄×C₅	C₄×C₄⋊C₄	1	2	yes	—
243	C₄×C₅	#380	1	2	yes	—
244	C₄×C₅	#389	1	2	yes	—
245	C₄×C₅	#389	1	2	yes	—
246	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	—	4	4	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
259	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
260	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
262	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
263	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₄×C₅	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	2	yes	—
269	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
271	C₂²×C₄	C₅×#41	1	2	yes	—
272	C₂²×C₄	C₅×#41	1	2	yes	—
273	M₁₆	—	2	4	no	—
274	M₁₆	—	2	4	no	—
275	M₁₆	—	2	4	no	—
276	M₁₆	C₅×C₄⋊C₄	1	8	yes	complemented
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₄⋊C₄	—	2	16	no	—
281	C₄⋊C₄	—	2	8	no	—
282	C₄⋊C₄	—	4	4	no	—
283	C₄⋊C₄	—	4	4	no	—
284	C₂²⋊C₄	—	4	2	no	—
285	C₂²⋊C₄	—	4	2	no	—
286	C₄²	—	2	8	no	—
287	C₄²	—	4	4	no	—
288	C₄²	—	4	4	no	—
289	C₄²	C₄²×C₅	1	2	yes	—
290	C₄²	C₄²×C₅	1	2	yes	—
291	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
292	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
293	C₄²	C₅×C₄⋊C₄	1	2	yes	—
294	C₄²	C₅×C₄⋊C₄	1	2	yes	—
295	C₄²	C₅×C₄⋊C₄	1	2	yes	—
296	C₄²	C₅×C₄⋊C₄	1	2	yes	—
297	C₂×C₅	—	2	1	no	—
298	C₂×C₅	—	2	1	no	—
299	C₂×C₅	—	2	1	no	—
300	C₂×C₅	—	2	1	no	—
301	C₂×C₅	C₄⋊#95	1	1	yes	characteristic
302	C₂×C₅	C₂×#339	1	1	yes	characteristic
303	C₂×C₅	#1733	1	1	yes	characteristic
304	C₂×C₅	#1980	1	2	yes	—
305	C₂×C₅	#1986	1	2	yes	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	2	no	—
308	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
309	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
310	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
311	C₂³	C₅×#124	1	1	yes	characteristic
312	C₂³	C₅×#124	1	1	yes	characteristic
313	C₂³	C₅×#127	1	1	yes	characteristic
314	C₂³	C₅×C₄⋊Q₈	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	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	8	no	—
324	C₂×C₄	—	4	8	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	C₅×#95	1	2	yes	—
331	C₂×C₄	C₅×#95	1	2	yes	—
332	C₂×C₄	C₅×#95	1	2	yes	—
333	C₂×C₄	C₅×#95	1	2	yes	—
334	C₂×C₄	C₅×#104	1	4	yes	—
335	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
336	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
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	C₅×#117	1	2	yes	—
341	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
342	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
343	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
344	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
345	C₂×C₄	C₅×#121	1	2	yes	—
346	C₂×C₄	C₅×#121	1	2	yes	—
347	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
348	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
349	C₂×C₄	C₅×#125	1	2	yes	—
350	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
351	C₈	—	2	8	no	—
352	C₅	#10851	1	1	yes	characteristic, direct product factor, Sylow
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	C₂×C₅×#95	1	1	yes	characteristic
362	C₂²	C₅×#382	1	1	yes	characteristic
363	C₂²	C₅×#384	1	1	yes	characteristic
364	C₂²	C₅×#390	1	1	yes	characteristic
365	C₂²	C₅×#390	1	1	yes	characteristic
366	C₂²	C₅×#391	1	1	yes	characteristic
367	C₂²	C₅×#391	1	1	yes	characteristic
368	C₂²	C₂×C₅×#104	1	2	yes	—
369	C₂²	C₅×#421	1	2	yes	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	4	8	no	—
374	C₄	—	8	4	no	—
375	C₄	C₅×#339	1	4	yes	complemented
376	C₄	C₄×C₅×C₄⋊C₄	1	2	yes	—
377	C₄	C₅×#380	1	2	yes	—
378	C₄	C₅×#389	1	2	yes	—
379	C₄	C₅×#389	1	2	yes	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	C₅×C₄⋊#95	1	1	yes	characteristic
385	C₂	C₂×C₅×#339	1	1	yes	characteristic
386	C₂	C₅×#1733	1	1	yes	characteristic
387	C₂	C₅×#1980	1	2	yes	—
388	C₂	C₅×#1986	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
11. C₄×C₅×M₁₆	C₄	semidirect
14. C₅×#384	C₄	semidirect
15. C₅×#382	C₄	semidirect
21. C₄×C₅×C₄⋊C₄	C₄	semidirect
24. #10851	C₅	direct (N × H)
96. C₅×M₁₆	C₄⋊C₄	semidirect
123. C₄×M₁₆	C₄×C₅	semidirect
126. #384	C₄×C₅	semidirect
127. #382	C₄×C₅	semidirect
133. C₄×C₄⋊C₄	C₄×C₅	semidirect
241. C₄×C₅	#339	semidirect
276. M₁₆	C₅×C₄⋊C₄	semidirect
352. C₅	#10851	direct (N × H)
375. C₄	C₅×#339	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×M₁₆	2
C₅×#2285	2
C₂×C₄×C₅×C₄⋊C₄	2
C₂×C₅×#339	2
#10851	5

Subgroups — C5×#10851 #11933571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10851 #11933571