Subgroups — C₅×#79038 #14413912

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5126	C₂	1	2	yes	maximal
4	C₅×Dic₃×M₁₆	C₂	1	2	yes	maximal, complemented
5	C₅×#4924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4835	C₂	1	4	yes	maximal, complemented
7	C₅×#4833	C₂	1	4	yes	maximal, complemented
8	C₅×#2920	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₄	1	2	yes	—
10	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₄	1	2	yes	—
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	C₂²	1	2	yes	—
16	C₄²×C₅×D₃	C₄	1	2	yes	—
17	C₄²×C₅×D₃	C₄	1	2	yes	—
18	C₄²×C₅×D₃	C₂²	1	2	yes	—
19	C₄²×C₅×D₃	C₂²	1	2	yes	—
20	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
21	C₅×(C₂×D₃)⋊C₈	C₂²	1	8	yes	—
22	C₅×#815	C₂²	1	4	yes	complemented
23	C₅×C₈×Dic₃	C₂²	1	4	yes	complemented
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
25	#79038	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂²×C₄²×C₅	—	3	1	no	—
27	C₅×#432	—	3	4	no	—
28	C₅×#431	—	3	4	no	—
29	C₅×#423	—	3	1	no	—
30	C₅×#423	D₃	1	1	yes	characteristic, complemented
31	C₅×#407	—	3	2	no	—
32	C₄×C₅×M₁₆	—	3	2	no	—
33	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
38	C₂×C₄×C₅×D₃	—	2	2	no	—
39	C₂×C₄×C₅×D₃	—	2	2	no	—
40	C₂×C₄×C₅×D₃	—	2	8	no	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
42	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
43	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
44	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
45	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
46	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
47	C₃×C₅×M₁₆	—	2	4	no	—
48	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
49	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂³	1	2	yes	—
52	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
53	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
54	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
55	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
56	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
57	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
58	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
59	C₅×#208	—	2	4	no	—
60	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
61	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic
62	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
63	#5126	C₂×C₅	1	2	yes	—
64	Dic₃×M₁₆	C₂×C₅	1	2	yes	complemented
65	#4924	C₂×C₅	1	1	yes	characteristic, complemented
66	#4835	C₂×C₅	1	4	yes	complemented
67	#4833	C₂×C₅	1	4	yes	complemented
68	C₂³×C₄×C₅	—	3	2	no	—
69	C₂³×C₄×C₅	—	3	1	no	—
70	C₂×C₅×M₁₆	—	3	2	no	—
71	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
72	C₂×C₄²×C₅	—	3	2	no	—
73	C₂×C₄²×C₅	—	3	1	no	—
74	C₂×C₄²×C₅	—	3	2	no	—
75	C₂×C₄²×C₅	—	3	2	no	—
76	C₂×C₄²×C₅	—	3	2	no	—
77	C₂×C₄²×C₅	—	3	2	no	—
78	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
79	C₅×C₄⋊C₈	—	3	4	no	—
80	C₅×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
81	C₅×C₂²⋊C₈	—	3	8	no	—
82	C₅×#97	—	3	4	no	—
83	C₄×C₅×C₈	—	3	4	no	—
84	#2920	—	3	1	no	Sylow
85	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₅×D₃	—	2	2	no	—
87	C₂²×C₅×D₃	—	2	4	no	—
88	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	#41	1	2	yes	—
94	C₂×C₃×C₄×C₅	#41	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
96	C₂×C₅×Dic₃	—	2	2	no	—
97	C₂×C₅×Dic₃	—	2	4	no	—
98	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
99	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
100	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
101	C₄×C₅×D₃	—	2	4	no	—
102	C₄×C₅×D₃	—	2	4	no	—
103	C₄×C₅×D₃	—	2	4	no	—
104	C₄×C₅×D₃	—	2	2	no	—
105	C₄×C₅×D₃	—	2	2	no	—
106	C₄×C₅×D₃	—	2	4	no	—
107	C₄×C₅×D₃	M₁₆	1	8	yes	complemented
108	C₃×C₅×C₈	—	2	4	no	—
109	C₅×C₃⋊C₈	—	2	4	no	—
110	C₂²×C₄×D₃	C₄×C₅	1	2	yes	—
111	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
112	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
113	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
114	C₂×C₄×Dic₃	C₄×C₅	1	2	yes	—
115	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
116	C₂×#208	C₂²×C₅	1	2	yes	—
117	C₄²×D₃	C₄×C₅	1	2	yes	—
118	C₄²×D₃	C₄×C₅	1	2	yes	—
119	C₄²×D₃	C₂²×C₅	1	2	yes	—
120	C₄²×D₃	C₂²×C₅	1	2	yes	—
121	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
122	(C₂×D₃)⋊C₈	C₂²×C₅	1	8	yes	—
123	#815	C₂²×C₅	1	4	yes	complemented
124	C₈×Dic₃	C₂²×C₅	1	4	yes	complemented
125	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
126	C₂⁴×C₅	—	3	1	no	—
127	C₂²×C₄×C₅	—	3	2	no	—
128	C₂²×C₄×C₅	—	3	2	no	—
129	C₂²×C₄×C₅	—	3	1	no	—
130	C₂²×C₄×C₅	—	3	2	no	—
131	C₂²×C₄×C₅	—	3	2	no	—
132	C₂²×C₄×C₅	—	3	2	no	—
133	C₂²×C₄×C₅	—	3	2	no	—
134	C₂²×C₄×C₅	—	3	2	no	—
135	C₂²×C₄×C₅	—	6	8	no	—
136	C₂²×C₄×C₅	—	6	2	no	—
137	C₂²×C₄×C₅	—	6	2	no	—
138	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
139	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
140	C₅×M₁₆	—	2	4	no	—
141	C₅×M₁₆	—	6	4	no	—
142	C₂×C₅×C₈	—	3	4	no	—
143	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
144	C₄²×C₅	—	3	2	no	—
145	C₄²×C₅	—	3	2	no	—
146	C₄²×C₅	—	3	2	no	—
147	C₄²×C₅	—	3	2	no	—
148	C₄²×C₅	—	3	2	no	—
149	C₄²×C₅	—	3	1	no	—
150	C₄²×C₅	—	3	1	no	—
151	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
152	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
153	C₄²×C₅	C₂²×D₃	1	2	yes	—
154	C₂²×C₄²	—	3	1	no	—
155	#432	—	3	4	no	—
156	#431	—	3	4	no	—
157	#423	—	3	1	no	—
158	#423	C₅×D₃	1	1	yes	characteristic, complemented
159	#407	—	3	2	no	—
160	C₄×M₁₆	—	3	2	no	—
161	C₂²×C₃×C₅	—	2	2	no	—
162	C₂²×C₃×C₅	#117	1	2	yes	—
163	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₅×D₃	—	2	8	no	—
165	C₂×C₅×D₃	—	2	2	no	—
166	C₂×C₅×D₃	—	2	2	no	—
167	C₂×C₅×D₃	C₂×M₁₆	1	4	yes	—
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	#117	1	2	yes	—
170	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	—
171	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
172	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
173	C₅×Dic₃	—	2	2	no	—
174	C₅×Dic₃	—	2	2	no	—
175	C₅×Dic₃	C₂×M₁₆	1	4	yes	—
176	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
178	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
179	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
180	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
181	C₂×C₄×D₃	—	2	2	no	—
182	C₂×C₄×D₃	—	2	2	no	—
183	C₂×C₄×D₃	—	2	8	no	—
184	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
185	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
186	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
187	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
188	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
189	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
190	C₃×M₁₆	—	2	4	no	—
191	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
192	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
193	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
194	C₃×C₄²	C₂³×C₅	1	2	yes	—
195	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
196	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
197	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
198	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
199	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
200	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
201	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
202	#208	—	2	4	no	—
203	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
204	C₂³×C₅	—	3	2	no	—
205	C₂³×C₅	—	6	4	no	—
206	C₂³×C₅	—	6	2	no	—
207	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	3	2	no	—
210	C₂×C₄×C₅	—	3	8	no	—
211	C₂×C₄×C₅	—	3	2	no	—
212	C₂×C₄×C₅	—	3	2	no	—
213	C₂×C₄×C₅	—	6	4	no	—
214	C₂×C₄×C₅	—	6	4	no	—
215	C₂×C₄×C₅	—	6	4	no	—
216	C₂×C₄×C₅	—	6	2	no	—
217	C₂×C₄×C₅	—	6	4	no	—
218	C₂×C₄×C₅	—	6	4	no	—
219	C₂×C₄×C₅	—	6	2	no	—
220	C₂×C₄×C₅	—	6	2	no	—
221	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
222	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
224	C₂×C₄×C₅	#237	1	2	yes	—
225	C₂×C₄×C₅	#239	1	2	yes	—
226	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
227	C₅×C₈	—	2	4	no	—
228	C₅×C₈	—	6	4	no	—
229	C₂³×C₄	—	3	2	no	—
230	C₂³×C₄	—	3	1	no	—
231	C₂×M₁₆	—	3	2	no	—
232	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
233	C₂×C₄²	—	3	2	no	—
234	C₂×C₄²	—	3	1	no	—
235	C₂×C₄²	—	3	2	no	—
236	C₂×C₄²	—	3	2	no	—
237	C₂×C₄²	—	3	2	no	—
238	C₂×C₄²	—	3	2	no	—
239	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
240	C₄⋊C₈	—	3	4	no	—
241	C₄⋊C₈	C₂×C₅×D₃	1	4	yes	complemented
242	C₂²⋊C₈	—	3	8	no	—
243	#97	—	3	4	no	—
244	C₄×C₈	—	3	4	no	—
245	C₂×C₃×C₅	—	2	2	no	—
246	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
248	C₅×D₃	—	2	4	no	—
249	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
250	C₂²×D₃	—	2	2	no	—
251	C₂²×D₃	—	2	4	no	—
252	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
255	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
257	C₂×C₃×C₄	C₅×#41	1	2	yes	—
258	C₂×C₃×C₄	C₅×#41	1	2	yes	—
259	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
260	C₂×Dic₃	—	2	2	no	—
261	C₂×Dic₃	—	2	4	no	—
262	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
263	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
264	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
265	C₄×D₃	—	2	4	no	—
266	C₄×D₃	—	2	4	no	—
267	C₄×D₃	—	2	4	no	—
268	C₄×D₃	—	2	2	no	—
269	C₄×D₃	—	2	2	no	—
270	C₄×D₃	—	2	4	no	—
271	C₄×D₃	C₅×M₁₆	1	8	yes	complemented
272	C₃×C₈	—	2	4	no	—
273	C₃⋊C₈	—	2	4	no	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	3	4	no	—
276	C₂²×C₅	—	6	8	no	—
277	C₂²×C₅	—	6	2	no	—
278	C₂²×C₅	—	6	2	no	—
279	C₂²×C₅	#892	1	2	yes	—
280	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
281	C₄×C₅	—	2	2	no	—
282	C₄×C₅	—	3	4	no	—
283	C₄×C₅	—	6	2	no	—
284	C₄×C₅	—	6	2	no	—
285	C₄×C₅	#892	1	2	yes	—
286	C₄×C₅	D₃×M₁₆	1	4	yes	—
287	C₄×C₅	C₂×#237	1	1	yes	characteristic
288	C₄×C₅	C₂×#239	1	1	yes	characteristic
289	C₂⁴	—	3	1	no	—
290	C₂²×C₄	—	3	2	no	—
291	C₂²×C₄	—	3	2	no	—
292	C₂²×C₄	—	3	1	no	—
293	C₂²×C₄	—	3	2	no	—
294	C₂²×C₄	—	3	2	no	—
295	C₂²×C₄	—	3	2	no	—
296	C₂²×C₄	—	3	2	no	—
297	C₂²×C₄	—	3	2	no	—
298	C₂²×C₄	—	6	8	no	—
299	C₂²×C₄	—	6	2	no	—
300	C₂²×C₄	—	6	2	no	—
301	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
302	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
303	M₁₆	—	2	4	no	—
304	M₁₆	—	6	4	no	—
305	C₂×C₈	—	3	4	no	—
306	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
307	C₄²	—	3	2	no	—
308	C₄²	—	3	2	no	—
309	C₄²	—	3	2	no	—
310	C₄²	—	3	2	no	—
311	C₄²	—	3	2	no	—
312	C₄²	—	3	1	no	—
313	C₄²	—	3	1	no	—
314	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
315	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
316	C₄²	C₂²×C₅×D₃	1	2	yes	—
317	C₃×C₅	#2920	1	1	yes	characteristic, complemented, Hall
318	C₂²×C₃	—	2	2	no	—
319	C₂²×C₃	C₅×#117	1	2	yes	—
320	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
321	C₂×D₃	—	2	8	no	—
322	C₂×D₃	—	2	2	no	—
323	C₂×D₃	—	2	2	no	—
324	C₂×D₃	C₂×C₅×M₁₆	1	4	yes	—
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	C₅×#117	1	2	yes	—
327	C₃×C₄	C₂×C₅×M₁₆	1	4	yes	—
328	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
329	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
330	Dic₃	—	2	2	no	—
331	Dic₃	—	2	2	no	—
332	Dic₃	C₂×C₅×M₁₆	1	4	yes	—
333	C₂×C₅	—	2	2	no	—
334	C₂×C₅	—	6	4	no	—
335	C₂×C₅	C₂×#892	1	1	yes	characteristic
336	C₂×C₅	C₂×D₃×M₁₆	1	2	yes	—
337	C₂³	—	3	2	no	—
338	C₂³	—	6	4	no	—
339	C₂³	—	6	2	no	—
340	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	3	2	no	—
343	C₂×C₄	—	3	8	no	—
344	C₂×C₄	—	3	2	no	—
345	C₂×C₄	—	3	2	no	—
346	C₂×C₄	—	6	4	no	—
347	C₂×C₄	—	6	4	no	—
348	C₂×C₄	—	6	4	no	—
349	C₂×C₄	—	6	2	no	—
350	C₂×C₄	—	6	4	no	—
351	C₂×C₄	—	6	4	no	—
352	C₂×C₄	—	6	2	no	—
353	C₂×C₄	—	6	2	no	—
354	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
355	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
357	C₂×C₄	C₅×#237	1	2	yes	—
358	C₂×C₄	C₅×#239	1	2	yes	—
359	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
360	C₈	—	2	4	no	—
361	C₈	—	6	4	no	—
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
364	C₂×C₃	C₂²×C₅×M₁₆	1	2	yes	—
365	D₃	—	2	4	no	—
366	C₅	#79038	1	1	yes	characteristic, direct product factor, Sylow
367	C₂²	—	2	2	no	—
368	C₂²	—	3	4	no	—
369	C₂²	—	6	8	no	—
370	C₂²	—	6	2	no	—
371	C₂²	—	6	2	no	—
372	C₂²	C₅×#892	1	2	yes	—
373	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
374	C₄	—	2	2	no	—
375	C₄	—	3	4	no	—
376	C₄	—	6	2	no	—
377	C₄	—	6	2	no	—
378	C₄	C₅×#892	1	2	yes	—
379	C₄	C₅×D₃×M₁₆	1	4	yes	—
380	C₄	C₂×C₅×#237	1	1	yes	characteristic
381	C₄	C₂×C₅×#239	1	1	yes	characteristic
382	C₃	C₅×#2920	1	1	yes	characteristic, complemented, Sylow
383	C₂	—	2	2	no	—
384	C₂	—	6	4	no	—
385	C₂	C₂×C₅×#892	1	1	yes	characteristic
386	C₂	C₂×C₅×D₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#423	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#423	D₃
hypocenter	C₃	C₅×#2920
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#423

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#423	C₂	semidirect
4. C₅×Dic₃×M₁₆	C₂	semidirect
5. C₅×#4924	C₂	semidirect
6. C₅×#4835	C₂	semidirect
7. C₅×#4833	C₂	semidirect
20. C₃×C₅×C₄⋊C₈	C₂²	semidirect
22. C₅×#815	C₂²	semidirect
23. C₅×C₈×Dic₃	C₂²	semidirect
24. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
25. #79038	C₅	direct (N × H)
30. C₅×#423	D₃	semidirect
62. C₃×#423	C₂×C₅	semidirect
64. Dic₃×M₁₆	C₂×C₅	semidirect
65. #4924	C₂×C₅	semidirect
66. #4835	C₂×C₅	semidirect
67. #4833	C₂×C₅	semidirect
80. C₅×C₄⋊C₈	C₂×D₃	semidirect
107. C₄×C₅×D₃	M₁₆	semidirect
121. C₃×C₄⋊C₈	C₂²×C₅	semidirect
123. #815	C₂²×C₅	semidirect
124. C₈×Dic₃	C₂²×C₅	semidirect
125. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
158. #423	C₅×D₃	semidirect
241. C₄⋊C₈	C₂×C₅×D₃	semidirect
271. C₄×D₃	C₅×M₁₆	semidirect
317. C₃×C₅	#2920	semidirect
366. C₅	#79038	direct (N × H)
382. C₃	C₅×#2920	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₅×D₃	2
C₃×C₅×#423	2
C₅×#5126	2
C₅×Dic₃×M₁₆	2
C₅×#4924	2
C₅×#4835	2
C₅×#4833	2
C₅×#2920	3
#79038	5

Subgroups — C5×#79038 #14413912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79038 #14413912