Subgroups — C₅×#71994 #14294655

Order 1920.

744 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	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#208	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#208	C₂	1	1	yes	maximal, characteristic
4	C₅×#4558	C₂	1	4	yes	maximal, complemented
5	C₅×#1738	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₅×M₁₆	—	2	2	no	—
8	C₂×C₃×C₅×M₁₆	—	2	1	no	—
9	C₂×C₃×C₅×M₁₆	C₄	1	4	yes	—
10	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×C₈	—	2	1	no	—
12	C₂×C₅×#208	—	2	2	no	—
13	C₂×C₅×#208	—	2	2	no	—
14	C₂×C₅×#208	—	2	1	no	—
15	C₂×C₅×#208	—	2	2	no	—
16	C₂×C₅×#208	C₄	1	4	yes	—
17	C₂×C₅×#208	C₄	1	2	yes	—
18	C₂×C₅×#208	C₄	1	2	yes	—
19	C₂×C₅×#208	C₂²	1	2	yes	—
20	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
21	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
22	#71994	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂²×C₅×M₁₆	—	3	1	no	—
24	C₂²×C₅×M₁₆	—	3	1	no	—
25	C₂²×C₅×M₁₆	D₃	1	1	yes	characteristic
26	C₅×#341	—	3	4	no	—
27	C₂⁴×C₃×C₅	Q₈	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
33	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	Q₈	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₃×C₅×M₁₆	—	2	4	no	—
39	C₃×C₅×M₁₆	—	2	2	no	—
40	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	—
41	C₂×C₃×C₅×C₈	—	2	4	no	—
42	C₂×C₃×C₅×C₈	—	2	2	no	—
43	C₅×#208	—	2	4	no	—
44	C₅×#208	—	2	4	no	—
45	C₅×#208	—	2	4	no	—
46	C₅×#208	—	2	2	no	—
47	C₅×#208	C₂×C₄	1	4	yes	—
48	C₂×C₅×C₃⋊C₈	—	2	4	no	—
49	C₂×C₅×C₃⋊C₈	—	2	2	no	—
50	C₂×C₅×C₃⋊C₈	—	2	2	no	—
51	C₂×C₅×C₃⋊C₈	—	2	2	no	—
52	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	—
53	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic
54	C₂²×#208	C₂×C₅	1	1	yes	characteristic
55	C₂²×#208	C₂×C₅	1	1	yes	characteristic
56	#4558	C₂×C₅	1	4	yes	complemented
57	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
58	C₂×C₅×M₁₆	—	2	2	no	—
59	C₂×C₅×M₁₆	—	2	1	no	—
60	C₂×C₅×M₁₆	—	3	2	no	—
61	C₂×C₅×M₁₆	—	3	2	no	—
62	C₂×C₅×M₁₆	—	3	4	no	—
63	C₂×C₅×M₁₆	—	3	2	no	—
64	C₂×C₅×M₁₆	—	6	2	no	—
65	C₂×C₅×M₁₆	—	6	2	no	—
66	C₂×C₅×M₁₆	—	6	2	no	—
67	C₂×C₅×M₁₆	—	6	1	no	—
68	C₂×C₅×M₁₆	Dic₃	1	4	yes	—
69	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
70	C₂²×C₅×C₈	—	2	1	no	—
71	C₂²×C₅×C₈	—	3	2	no	—
72	C₂²×C₅×C₈	—	6	1	no	—
73	#1738	—	3	1	no	Sylow
74	C₂³×C₃×C₅	—	4	2	no	—
75	C₂³×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
76	C₂³×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
77	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
78	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
79	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
81	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
82	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₃×C₅×C₈	—	2	4	no	—
99	C₅×C₃⋊C₈	—	2	4	no	—
100	C₅×C₃⋊C₈	—	2	4	no	—
101	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
102	C₂×C₃×M₁₆	—	2	2	no	—
103	C₂×C₃×M₁₆	—	2	1	no	—
104	C₂×C₃×M₁₆	C₄×C₅	1	4	yes	—
105	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
106	C₂²×C₃×C₈	—	2	1	no	—
107	C₂×#208	—	2	2	no	—
108	C₂×#208	—	2	2	no	—
109	C₂×#208	—	2	1	no	—
110	C₂×#208	—	2	2	no	—
111	C₂×#208	C₄×C₅	1	4	yes	—
112	C₂×#208	C₄×C₅	1	2	yes	—
113	C₂×#208	C₄×C₅	1	2	yes	—
114	C₂×#208	C₂²×C₅	1	2	yes	—
115	C₂²×C₃⋊C₈	—	2	1	no	—
116	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
117	C₂⁴×C₅	Dic₆	1	1	yes	characteristic
118	C₂²×C₄×C₅	Dic₆	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
120	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
122	C₂²×C₄×C₅	D₁₂	1	2	yes	—
123	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
124	C₂²×C₄×C₅	#67	1	2	yes	—
125	C₂²×C₄×C₅	#67	1	1	yes	characteristic
126	C₂²×C₄×C₅	#67	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
128	C₅×M₁₆	—	2	4	no	—
129	C₅×M₁₆	—	2	2	no	—
130	C₅×M₁₆	—	3	4	no	—
131	C₅×M₁₆	—	6	4	no	—
132	C₅×M₁₆	—	6	4	no	—
133	C₅×M₁₆	—	6	4	no	—
134	C₅×M₁₆	—	6	2	no	—
135	C₅×M₁₆	C₂×Dic₃	1	4	yes	—
136	C₂×C₅×C₈	—	2	4	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	3	4	no	—
139	C₂×C₅×C₈	—	6	4	no	—
140	C₂×C₅×C₈	—	6	2	no	—
141	C₂×C₅×C₈	—	6	2	no	—
142	C₂×C₅×C₈	—	6	2	no	—
143	C₂²×M₁₆	—	3	1	no	—
144	C₂²×M₁₆	—	3	1	no	—
145	C₂²×M₁₆	C₅×D₃	1	1	yes	characteristic
146	#341	—	3	4	no	—
147	C₂²×C₃×C₅	—	2	2	no	—
148	C₂²×C₃×C₅	—	2	2	no	—
149	C₂²×C₃×C₅	—	2	2	no	—
150	C₂²×C₃×C₅	—	4	2	no	—
151	C₂²×C₃×C₅	—	4	2	no	—
152	C₂²×C₃×C₅	#95	1	2	yes	—
153	C₂²×C₃×C₅	#95	1	2	yes	—
154	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₃×C₄×C₅	#95	1	2	yes	—
158	C₃×C₄×C₅	#95	1	2	yes	—
159	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
160	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂⁴×C₃	C₅×Q₈	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
165	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
168	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
169	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
172	C₂²×C₃×C₄	C₅×Q₈	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₃×M₁₆	—	2	4	no	—
175	C₃×M₁₆	—	2	2	no	—
176	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	—
177	C₂×C₃×C₈	—	2	4	no	—
178	C₂×C₃×C₈	—	2	2	no	—
179	#208	—	2	4	no	—
180	#208	—	2	4	no	—
181	#208	—	2	4	no	—
182	#208	—	2	2	no	—
183	#208	C₂×C₄×C₅	1	4	yes	—
184	C₂×C₃⋊C₈	—	2	4	no	—
185	C₂×C₃⋊C₈	—	2	2	no	—
186	C₂×C₃⋊C₈	—	2	2	no	—
187	C₂×C₃⋊C₈	—	2	2	no	—
188	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	—
189	C₂³×C₅	—	4	2	no	—
190	C₂³×C₅	Dic₃⋊C₄	1	1	yes	characteristic
191	C₂³×C₅	Dic₃⋊C₄	1	1	yes	characteristic
192	C₂³×C₅	Dic₃⋊C₄	1	2	yes	—
193	C₂³×C₅	C₄⋊Dic₃	1	2	yes	—
194	C₂³×C₅	C₂×Dic₆	1	1	yes	characteristic
195	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
196	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
197	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
198	C₂×C₄×C₅	Dic₃⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₅	Dic₃⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₅	C₄⋊Dic₃	1	2	yes	—
201	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
202	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
203	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
204	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
205	C₂×C₄×C₅	#217	1	2	yes	—
206	C₂×C₄×C₅	#217	1	2	yes	—
207	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
213	C₅×C₈	—	2	4	no	—
214	C₅×C₈	—	6	4	no	—
215	C₅×C₈	—	6	4	no	—
216	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	2	1	no	—
219	C₂×M₁₆	—	3	2	no	—
220	C₂×M₁₆	—	3	2	no	—
221	C₂×M₁₆	—	3	4	no	—
222	C₂×M₁₆	—	3	2	no	—
223	C₂×M₁₆	—	6	2	no	—
224	C₂×M₁₆	—	6	2	no	—
225	C₂×M₁₆	—	6	2	no	—
226	C₂×M₁₆	—	6	1	no	—
227	C₂×M₁₆	C₅×Dic₃	1	4	yes	—
228	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	3	2	no	—
231	C₂²×C₈	—	6	1	no	—
232	C₂×C₃×C₅	—	2	2	no	—
233	C₂×C₃×C₅	—	2	2	no	—
234	C₂×C₃×C₅	—	2	1	no	—
235	C₂×C₃×C₅	—	2	1	no	—
236	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
237	C₂×C₃×C₅	#430	1	2	yes	—
238	C₂³×C₃	—	4	2	no	—
239	C₂³×C₃	C₅×C₄⋊C₄	1	1	yes	characteristic
240	C₂³×C₃	C₅×C₄⋊C₄	1	1	yes	characteristic
241	C₂³×C₃	C₅×C₄⋊C₄	1	2	yes	—
242	C₂³×C₃	C₅×C₄⋊C₄	1	2	yes	—
243	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
244	C₂×C₃×C₄	C₄²×C₅	1	2	yes	—
245	C₂×C₃×C₄	C₄²×C₅	1	2	yes	—
246	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
247	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
248	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
249	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
250	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
251	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
252	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
253	C₂×C₃×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
256	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
262	C₃×C₈	—	2	4	no	—
263	C₃⋊C₈	—	2	4	no	—
264	C₃⋊C₈	—	2	4	no	—
265	C₂²×C₅	—	2	2	no	—
266	C₂²×C₅	—	2	2	no	—
267	C₂²×C₅	—	2	2	no	—
268	C₂²×C₅	—	4	2	no	—
269	C₂²×C₅	—	4	2	no	—
270	C₂²×C₅	C₃⋊#95	1	2	yes	—
271	C₂²×C₅	C₃⋊#95	1	2	yes	—
272	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
273	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
274	C₂²×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
275	C₄×C₅	C₃⋊#95	1	2	yes	—
276	C₄×C₅	C₃⋊#95	1	2	yes	—
277	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
278	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
279	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
280	C₄×C₅	C₂×#217	1	1	yes	characteristic
281	C₂⁴	C₅×Dic₆	1	1	yes	characteristic
282	C₂²×C₄	C₅×Dic₆	1	1	yes	characteristic
283	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
284	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
285	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
286	C₂²×C₄	C₅×D₁₂	1	2	yes	—
287	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
288	C₂²×C₄	C₅×#67	1	1	yes	characteristic
289	C₂²×C₄	C₅×#67	1	1	yes	characteristic
290	C₂²×C₄	C₅×#67	1	2	yes	—
291	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
292	M₁₆	—	2	4	no	—
293	M₁₆	—	2	2	no	—
294	M₁₆	—	3	4	no	—
295	M₁₆	—	6	4	no	—
296	M₁₆	—	6	4	no	—
297	M₁₆	—	6	4	no	—
298	M₁₆	—	6	2	no	—
299	M₁₆	C₂×C₅×Dic₃	1	4	yes	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	3	4	no	—
303	C₂×C₈	—	6	4	no	—
304	C₂×C₈	—	6	2	no	—
305	C₂×C₈	—	6	2	no	—
306	C₂×C₈	—	6	2	no	—
307	C₃×C₅	#1738	1	1	yes	characteristic, complemented, Hall
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	4	2	no	—
312	C₂²×C₃	—	4	2	no	—
313	C₂²×C₃	C₅×#95	1	2	yes	—
314	C₂²×C₃	C₅×#95	1	2	yes	—
315	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
316	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
317	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
318	C₃×C₄	C₅×#95	1	2	yes	—
319	C₃×C₄	C₅×#95	1	2	yes	—
320	C₃×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
321	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
322	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
323	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	—	2	2	no	—
326	C₂×C₅	—	2	1	no	—
327	C₂×C₅	—	2	1	no	—
328	C₂×C₅	#5124	1	2	yes	—
329	C₂×C₅	C₂×C₃⋊#95	1	1	yes	characteristic
330	C₂³	—	4	2	no	—
331	C₂³	C₅×Dic₃⋊C₄	1	1	yes	characteristic
332	C₂³	C₅×Dic₃⋊C₄	1	1	yes	characteristic
333	C₂³	C₅×Dic₃⋊C₄	1	2	yes	—
334	C₂³	C₅×C₄⋊Dic₃	1	2	yes	—
335	C₂³	C₂×C₅×Dic₆	1	1	yes	characteristic
336	C₂×C₄	C₄×C₅×Dic₃	1	2	yes	—
337	C₂×C₄	C₄×C₅×Dic₃	1	2	yes	—
338	C₂×C₄	C₅×Dic₃⋊C₄	1	2	yes	—
339	C₂×C₄	C₅×Dic₃⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₅×Dic₃⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₅×C₄⋊Dic₃	1	2	yes	—
342	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
343	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
344	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
345	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
346	C₂×C₄	C₅×#217	1	2	yes	—
347	C₂×C₄	C₅×#217	1	2	yes	—
348	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
350	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
351	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
352	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
353	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
354	C₈	—	2	4	no	—
355	C₈	—	6	4	no	—
356	C₈	—	6	4	no	—
357	C₂×C₃	—	2	1	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	2	2	no	—
360	C₂×C₃	—	2	2	no	—
361	C₂×C₃	C₂×C₅×#95	1	1	yes	characteristic
362	C₂×C₃	C₅×#430	1	2	yes	—
363	C₅	#71994	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	C₅×C₃⋊#95	1	2	yes	—
370	C₂²	C₅×C₃⋊#95	1	2	yes	—
371	C₂²	C₂×C₅×Dic₃⋊C₄	1	1	yes	characteristic
372	C₂²	C₂×C₅×Dic₃⋊C₄	1	1	yes	characteristic
373	C₂²	C₂×C₅×C₄⋊Dic₃	1	1	yes	characteristic
374	C₄	C₅×C₃⋊#95	1	2	yes	—
375	C₄	C₅×C₃⋊#95	1	2	yes	—
376	C₄	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
377	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
378	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
379	C₄	C₂×C₅×#217	1	1	yes	characteristic
380	C₃	C₅×#1738	1	1	yes	characteristic, complemented, Sylow
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	2	no	—
384	C₂	—	2	2	no	—
385	C₂	C₅×#5124	1	2	yes	—
386	C₂	C₂×C₅×C₃⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator	C₃×C₄	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂⁴×C₃×C₅	Q₈
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂²×C₅×M₁₆	D₃
hypocenter	C₃	C₅×#1738
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₂²×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
4. C₅×#4558	C₂	semidirect
22. #71994	C₅	direct (N × H)
56. #4558	C₂×C₅	semidirect
307. C₃×C₅	#1738	semidirect
363. C₅	#71994	direct (N × H)
380. C₃	C₅×#1738	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×M₁₆	2
C₂²×C₅×#208	2
C₅×#4558	2
C₅×#1738	3
#71994	5

Subgroups — C5×#71994 #14294655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71994 #14294655