Subgroups — C₅×#83898 #14417629

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₅×#5827	C₂	1	2	yes	maximal, complemented
3	C₅×#5232	C₂	1	2	yes	maximal, complemented
4	C₅×Dic₃×Q₁₆	C₂	1	2	yes	maximal, complemented
5	C₅×#5164	C₂	1	4	yes	maximal, complemented
6	C₅×Dic₃×D₈	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#818	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5101	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2951	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₃×C₅×#135	C₄	1	8	yes	complemented
12	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₅×Q₈×Dic₃	C₂²	1	4	yes	—
17	C₅×D₄×Dic₃	—	2	4	no	—
18	C₅×D₄×Dic₃	C₂²	1	4	yes	—
19	C₅×#926	—	2	2	no	—
20	C₅×#926	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊Dic₃	—	2	2	no	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
23	C₂×C₅×#208	C₂²	1	1	yes	characteristic
24	C₅×#835	C₂²	1	4	yes	—
25	C₅×#832	C₂²	1	4	yes	—
26	C₅×#818	C₂²	1	2	yes	—
27	C₅×#818	C₂²	1	2	yes	—
28	C₅×#815	C₂²	1	2	yes	—
29	C₅×C₈×Dic₃	C₂²	1	2	yes	—
30	#83898	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#135	D₃	1	1	yes	characteristic
32	C₅×#520	—	3	2	no	—
33	C₅×#440	—	3	4	no	—
34	C₄×C₅×Q₁₆	—	3	2	no	—
35	C₄×C₅×D₈	—	3	2	no	—
36	C₂×C₅×#107	—	3	1	no	—
37	C₅×#417	—	3	2	no	—
38	C₅×#405	—	3	1	no	—
39	C₃×C₅×#41	—	2	4	no	—
40	C₃×C₅×#41	C₂×C₄	1	8	yes	complemented
41	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	—	2	2	no	—
47	C₂²×C₅×Dic₃	—	2	4	no	—
48	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
49	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
50	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
51	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
52	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₅×#217	—	2	4	no	—
55	C₅×#217	D₄	1	2	yes	—
56	C₅×C₄⋊Dic₃	—	2	2	no	—
57	C₅×C₄⋊Dic₃	—	2	4	no	—
58	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
59	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
60	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
61	C₄×C₅×Dic₃	—	2	4	no	—
62	C₄×C₅×Dic₃	C₂³	1	2	yes	—
63	C₅×#208	—	2	2	no	—
64	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
65	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic
66	#5827	C₂×C₅	1	2	yes	complemented
67	#5232	C₂×C₅	1	2	yes	complemented
68	Dic₃×Q₁₆	C₂×C₅	1	2	yes	complemented
69	#5164	C₂×C₅	1	4	yes	complemented
70	Dic₃×D₈	C₂×C₅	1	2	yes	complemented
71	C₂×#818	C₂×C₅	1	1	yes	characteristic, complemented
72	#5101	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×C₅×#41	C₂×D₃	1	2	yes	—
74	C₅×#135	Dic₃	1	8	yes	complemented
75	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
76	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
77	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
78	C₂×C₅×M₁₆	—	3	1	no	—
79	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
80	C₄×C₅×Q₈	—	3	4	no	—
81	C₄×C₅×D₄	—	3	4	no	—
82	C₄×C₅×D₄	—	6	4	no	—
83	C₅×#117	—	3	1	no	—
84	C₅×#117	—	6	2	no	—
85	C₂×C₅×C₄⋊C₄	—	3	2	no	—
86	C₂×C₅×C₄⋊C₄	—	6	2	no	—
87	C₅×#107	—	3	2	no	—
88	C₅×#107	—	3	2	no	—
89	C₅×#103	—	3	4	no	—
90	C₅×#102	—	3	4	no	—
91	C₅×#97	—	3	2	no	—
92	C₄×C₅×C₈	—	3	2	no	—
93	#2951	—	3	1	no	Sylow
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
96	C₃×C₅×Q₈	—	2	2	no	—
97	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
98	C₃×C₅×D₄	—	2	8	no	—
99	C₃×C₅×D₄	—	2	2	no	—
100	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	8	no	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₂×C₅×Dic₃	—	2	4	no	—
108	C₂×C₅×Dic₃	—	8	4	no	—
109	C₂×C₅×Dic₃	—	8	2	no	—
110	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
111	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
112	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
113	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
114	C₅×C₃⋊C₈	—	2	2	no	—
115	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
116	C₃×#135	C₄×C₅	1	8	yes	complemented
117	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
119	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
121	Q₈×Dic₃	C₂²×C₅	1	4	yes	—
122	D₄×Dic₃	—	2	4	no	—
123	D₄×Dic₃	C₂²×C₅	1	4	yes	—
124	#926	—	2	2	no	—
125	#926	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₄⋊Dic₃	—	2	2	no	—
127	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
128	C₂×#208	C₂²×C₅	1	1	yes	characteristic
129	#835	C₂²×C₅	1	4	yes	—
130	#832	C₂²×C₅	1	4	yes	—
131	#818	C₂²×C₅	1	2	yes	—
132	#818	C₂²×C₅	1	2	yes	—
133	#815	C₂²×C₅	1	2	yes	—
134	C₈×Dic₃	C₂²×C₅	1	2	yes	—
135	C₅×#41	—	2	4	no	—
136	C₅×#41	C₂×Dic₃	1	8	yes	complemented
137	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
138	C₂×C₅×D₄	—	2	2	no	—
139	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	—	6	4	no	—
142	C₂²×C₄×C₅	—	6	2	no	—
143	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₅×Q₁₆	C₂×Dic₃	1	4	yes	complemented
145	C₅×SD₁₆	C₂×Dic₃	1	8	yes	complemented
146	C₅×D₈	C₂×Dic₃	1	4	yes	complemented
147	C₅×M₁₆	—	6	2	no	—
148	C₂×C₅×C₈	—	3	2	no	—
149	C₂×C₅×C₈	C₂×Dic₃	1	4	yes	complemented
150	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
152	C₅×C₄⋊C₄	—	3	1	no	—
153	C₅×C₄⋊C₄	—	3	1	no	—
154	C₅×C₄⋊C₄	—	3	4	no	—
155	C₅×C₄⋊C₄	—	6	4	no	—
156	C₅×C₄⋊C₄	—	6	2	no	—
157	C₅×C₂²⋊C₄	—	3	2	no	—
158	C₅×C₂²⋊C₄	—	6	4	no	—
159	C₄²×C₅	—	3	2	no	—
160	C₄²×C₅	—	6	4	no	—
161	C₂×#135	C₅×D₃	1	1	yes	characteristic
162	#520	—	3	2	no	—
163	#440	—	3	4	no	—
164	C₄×Q₁₆	—	3	2	no	—
165	C₄×D₈	—	3	2	no	—
166	C₂×#107	—	3	1	no	—
167	#417	—	3	2	no	—
168	#405	—	3	1	no	—
169	C₂²×C₃×C₅	—	2	1	no	—
170	C₂²×C₃×C₅	—	2	1	no	—
171	C₂²×C₃×C₅	—	2	4	no	—
172	C₂²×C₃×C₅	—	4	2	no	—
173	C₂²×C₃×C₅	—	4	2	no	—
174	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
175	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
176	C₃×C₄×C₅	—	2	4	no	—
177	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
178	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
179	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
180	C₅×Dic₃	—	2	2	no	—
181	C₅×Dic₃	—	2	2	no	—
182	C₅×Dic₃	—	4	4	no	—
183	C₃×#41	—	2	4	no	—
184	C₃×#41	C₂×C₄×C₅	1	8	yes	complemented
185	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
186	C₂×C₃×D₄	—	2	2	no	—
187	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
188	C₂²×C₃×C₄	—	2	2	no	—
189	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
190	C₂²×Dic₃	—	2	2	no	—
191	C₂²×Dic₃	—	2	4	no	—
192	C₃×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
193	C₃×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
194	C₃×D₈	C₂×C₄×C₅	1	4	yes	complemented
195	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
196	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
197	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
198	#217	—	2	4	no	—
199	#217	C₅×D₄	1	2	yes	—
200	C₄⋊Dic₃	—	2	2	no	—
201	C₄⋊Dic₃	—	2	4	no	—
202	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
203	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
204	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
205	C₄×Dic₃	—	2	4	no	—
206	C₄×Dic₃	C₂³×C₅	1	2	yes	—
207	#208	—	2	2	no	—
208	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
211	C₅×Q₈	—	2	2	no	—
212	C₅×Q₈	C₂²×Dic₃	1	4	yes	—
213	C₅×D₄	—	2	8	no	—
214	C₅×D₄	—	2	2	no	—
215	C₅×D₄	C₂²×Dic₃	1	4	yes	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	8	no	—
218	C₂×C₄×C₅	—	3	2	no	—
219	C₂×C₄×C₅	—	3	2	no	—
220	C₂×C₄×C₅	—	6	4	no	—
221	C₂×C₄×C₅	—	24	4	no	—
222	C₂×C₄×C₅	—	24	2	no	—
223	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	#237	1	2	yes	—
225	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
226	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
227	C₅×C₈	—	6	2	no	—
228	C₅×C₈	C₂²×Dic₃	1	2	yes	—
229	C₅×C₈	C₂²×Dic₃	1	2	yes	—
230	C₂×#41	C₂×C₅×D₃	1	2	yes	—
231	#135	C₅×Dic₃	1	8	yes	complemented
232	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
233	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
234	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
235	C₂×M₁₆	—	3	1	no	—
236	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
237	C₄×Q₈	—	3	4	no	—
238	C₄×D₄	—	3	4	no	—
239	C₄×D₄	—	6	4	no	—
240	#117	—	3	1	no	—
241	#117	—	6	2	no	—
242	C₂×C₄⋊C₄	—	3	2	no	—
243	C₂×C₄⋊C₄	—	6	2	no	—
244	#107	—	3	2	no	—
245	#107	—	3	2	no	—
246	#103	—	3	4	no	—
247	#102	—	3	4	no	—
248	#97	—	3	2	no	—
249	C₄×C₈	—	3	2	no	—
250	C₂×C₃×C₅	—	2	2	no	—
251	C₂×C₃×C₅	—	4	4	no	—
252	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂×C₃×C₅	#576	1	1	yes	characteristic
254	C₂×C₃×C₅	#578	1	1	yes	characteristic
255	C₂³×C₃	—	2	2	no	—
256	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
257	C₃×Q₈	—	2	2	no	—
258	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
259	C₃×D₄	—	2	8	no	—
260	C₃×D₄	—	2	2	no	—
261	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	8	no	—
264	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
265	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₅×#41	1	2	yes	—
267	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
268	C₂×Dic₃	—	2	4	no	—
269	C₂×Dic₃	—	8	4	no	—
270	C₂×Dic₃	—	8	2	no	—
271	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
272	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
273	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
274	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
275	C₃⋊C₈	—	2	2	no	—
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	1	no	—
278	C₂²×C₅	—	2	4	no	—
279	C₂²×C₅	—	4	2	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	D₄×Dic₃	1	2	yes	—
282	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
283	C₄×C₅	—	2	4	no	—
284	C₄×C₅	—	6	2	no	—
285	C₄×C₅	—	6	2	no	—
286	C₄×C₅	—	12	4	no	—
287	C₄×C₅	D₄×Dic₃	1	2	yes	—
288	C₄×C₅	C₂×#237	1	1	yes	characteristic
289	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
290	#41	—	2	4	no	—
291	#41	C₂×C₅×Dic₃	1	8	yes	complemented
292	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	6	4	no	—
297	C₂²×C₄	—	6	2	no	—
298	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
299	Q₁₆	C₂×C₅×Dic₃	1	4	yes	complemented
300	SD₁₆	C₂×C₅×Dic₃	1	8	yes	complemented
301	D₈	C₂×C₅×Dic₃	1	4	yes	complemented
302	M₁₆	—	6	2	no	—
303	C₂×C₈	—	3	2	no	—
304	C₂×C₈	C₂×C₅×Dic₃	1	4	yes	complemented
305	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
306	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
307	C₄⋊C₄	—	3	1	no	—
308	C₄⋊C₄	—	3	1	no	—
309	C₄⋊C₄	—	3	4	no	—
310	C₄⋊C₄	—	6	4	no	—
311	C₄⋊C₄	—	6	2	no	—
312	C₂²⋊C₄	—	3	2	no	—
313	C₂²⋊C₄	—	6	4	no	—
314	C₄²	—	3	2	no	—
315	C₄²	—	6	4	no	—
316	C₃×C₅	#2951	1	1	yes	characteristic, complemented, Hall
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	—	2	4	no	—
320	C₂²×C₃	—	4	2	no	—
321	C₂²×C₃	—	4	2	no	—
322	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
323	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
324	C₃×C₄	—	2	4	no	—
325	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
326	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
327	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
328	Dic₃	—	2	2	no	—
329	Dic₃	—	2	2	no	—
330	Dic₃	—	4	4	no	—
331	C₂×C₅	—	2	2	no	—
332	C₂×C₅	—	4	4	no	—
333	C₂×C₅	#5769	1	1	yes	characteristic
334	C₂×C₅	#5771	1	1	yes	characteristic
335	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
336	C₂³	—	2	2	no	—
337	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
338	Q₈	—	2	2	no	—
339	Q₈	C₂²×C₅×Dic₃	1	4	yes	—
340	D₄	—	2	8	no	—
341	D₄	—	2	2	no	—
342	D₄	C₂²×C₅×Dic₃	1	4	yes	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	3	2	no	—
346	C₂×C₄	—	3	2	no	—
347	C₂×C₄	—	6	4	no	—
348	C₂×C₄	—	24	4	no	—
349	C₂×C₄	—	24	2	no	—
350	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
351	C₂×C₄	C₅×#237	1	2	yes	—
352	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
353	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
354	C₈	—	6	2	no	—
355	C₈	C₂²×C₅×Dic₃	1	2	yes	—
356	C₈	C₂²×C₅×Dic₃	1	2	yes	—
357	C₂×C₃	—	2	2	no	—
358	C₂×C₃	—	4	4	no	—
359	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
360	C₂×C₃	C₅×#576	1	1	yes	characteristic
361	C₂×C₃	C₅×#578	1	1	yes	characteristic
362	C₅	#83898	1	1	yes	characteristic, direct product factor, Sylow
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	C₅×D₄×Dic₃	1	2	yes	—
369	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
370	C₄	—	2	4	no	—
371	C₄	—	6	2	no	—
372	C₄	—	6	2	no	—
373	C₄	—	12	4	no	—
374	C₄	C₅×D₄×Dic₃	1	2	yes	—
375	C₄	C₂×C₅×#237	1	1	yes	characteristic
376	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
377	C₃	C₅×#2951	1	1	yes	characteristic, complemented, Sylow
378	C₂	—	2	2	no	—
379	C₂	—	4	4	no	—
380	C₂	C₅×#5769	1	1	yes	characteristic
381	C₂	C₅×#5771	1	1	yes	characteristic
382	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#135	D₃
hypocenter	C₃	C₅×#2951
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#135

Complements

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

N	H ≅ G/N	type
2. C₅×#5827	C₂	semidirect
3. C₅×#5232	C₂	semidirect
4. C₅×Dic₃×Q₁₆	C₂	semidirect
5. C₅×#5164	C₂	semidirect
6. C₅×Dic₃×D₈	C₂	semidirect
7. C₂×C₅×#818	C₂	semidirect
8. C₅×#5101	C₂	semidirect
11. C₃×C₅×#135	C₄	semidirect
30. #83898	C₅	direct (N × H)
40. C₃×C₅×#41	C₂×C₄	semidirect
48. C₃×C₅×Q₁₆	C₂×C₄	semidirect
49. C₃×C₅×SD₁₆	C₂×C₄	semidirect
50. C₃×C₅×D₈	C₂×C₄	semidirect
51. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
66. #5827	C₂×C₅	semidirect
67. #5232	C₂×C₅	semidirect
68. Dic₃×Q₁₆	C₂×C₅	semidirect
69. #5164	C₂×C₅	semidirect
70. Dic₃×D₈	C₂×C₅	semidirect
71. C₂×#818	C₂×C₅	semidirect
72. #5101	C₂×C₅	semidirect
74. C₅×#135	Dic₃	semidirect
116. C₃×#135	C₄×C₅	semidirect
136. C₅×#41	C₂×Dic₃	semidirect
144. C₅×Q₁₆	C₂×Dic₃	semidirect
145. C₅×SD₁₆	C₂×Dic₃	semidirect
146. C₅×D₈	C₂×Dic₃	semidirect
149. C₂×C₅×C₈	C₂×Dic₃	semidirect
184. C₃×#41	C₂×C₄×C₅	semidirect
192. C₃×Q₁₆	C₂×C₄×C₅	semidirect
193. C₃×SD₁₆	C₂×C₄×C₅	semidirect
194. C₃×D₈	C₂×C₄×C₅	semidirect
195. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
231. #135	C₅×Dic₃	semidirect
291. #41	C₂×C₅×Dic₃	semidirect
299. Q₁₆	C₂×C₅×Dic₃	semidirect
300. SD₁₆	C₂×C₅×Dic₃	semidirect
301. D₈	C₂×C₅×Dic₃	semidirect
304. C₂×C₈	C₂×C₅×Dic₃	semidirect
316. C₃×C₅	#2951	semidirect
362. C₅	#83898	direct (N × H)
377. C₃	C₅×#2951	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#135	2
C₅×#5827	2
C₅×#5232	2
C₅×Dic₃×Q₁₆	2
C₅×#5164	2
C₅×Dic₃×D₈	2
C₂×C₅×#818	2
C₅×#5101	2
C₅×#2951	3
#83898	5

Subgroups — C5×#83898 #14417629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83898 #14417629