Subgroups — C₃×C₅×#3208 #14276242

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#492	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#486	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#460	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#450	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3208	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×D₄	—	2	1	no	—
10	C₂²×C₃×C₅×D₄	—	2	1	no	—
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₂×C₃×C₅×SD₁₆	C₂²	1	8	yes	complemented
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₃×C₅×#127	—	2	1	no	—
16	C₃×C₅×#127	—	2	1	no	—
17	C₃×C₅×#127	C₂²	1	2	yes	—
18	C₃×C₅×#127	C₂²	1	2	yes	—
19	C₃×C₅×#125	—	2	1	no	—
20	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
21	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₃×C₄×C₅×Q₈	—	2	1	no	—
23	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
24	C₃×C₅×#117	—	2	1	no	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
27	C₃×C₅×#102	C₂²	1	8	yes	complemented
28	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
30	C₃×#3208	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic
33	C₅×#492	C₂×C₃	1	2	yes	complemented
34	C₅×#486	C₂×C₃	1	2	yes	complemented
35	C₅×#460	C₂×C₃	1	4	yes	complemented
36	C₅×#450	C₂×C₃	1	4	yes	complemented
37	C₅×#431	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂⁴×C₃×C₅	—	2	2	no	—
39	C₂×C₃×C₅×Q₈	—	2	1	no	—
40	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
41	C₂×C₃×C₅×D₄	—	2	2	no	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	—	4	4	no	—
47	C₂×C₃×C₅×D₄	—	4	4	no	—
48	C₂×C₃×C₅×D₄	—	4	4	no	—
49	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
50	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₃×C₅×SD₁₆	—	4	8	no	—
54	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
55	C₃×C₅×C₄⋊C₄	—	2	1	no	—
56	C₃×C₅×C₄⋊C₄	—	2	1	no	—
57	C₃×C₅×C₄⋊C₄	—	2	1	no	—
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
62	C₃×C₄²×C₅	—	2	2	no	—
63	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
64	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic
69	C₃×#492	C₂×C₅	1	2	yes	complemented
70	C₃×#486	C₂×C₅	1	2	yes	complemented
71	C₃×#460	C₂×C₅	1	4	yes	complemented
72	C₃×#450	C₂×C₅	1	4	yes	complemented
73	C₃×#431	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂²×C₅×D₄	—	2	1	no	—
75	C₂²×C₅×D₄	—	2	1	no	—
76	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
77	C₂×C₅×SD₁₆	C₂²×C₃	1	8	yes	complemented
78	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
79	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
80	C₅×#127	—	2	1	no	—
81	C₅×#127	—	2	1	no	—
82	C₅×#127	C₂²×C₃	1	2	yes	—
83	C₅×#127	C₂²×C₃	1	2	yes	—
84	C₅×#125	—	2	1	no	—
85	C₅×C₂²⋊Q₈	—	2	1	no	—
86	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
87	C₄×C₅×Q₈	—	2	1	no	—
88	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
89	C₅×#117	—	2	1	no	—
90	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
91	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
92	C₅×#102	C₂²×C₃	1	8	yes	complemented
93	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
94	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
95	#3208	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
96	C₂³×C₃×C₅	—	2	4	no	—
97	C₂³×C₃×C₅	—	4	4	no	—
98	C₂³×C₃×C₅	—	4	4	no	—
99	C₂³×C₃×C₅	—	4	4	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
101	C₃×C₅×Q₈	—	2	4	no	—
102	C₃×C₅×Q₈	—	4	2	no	—
103	C₃×C₅×D₄	—	2	8	no	—
104	C₃×C₅×D₄	—	4	4	no	—
105	C₃×C₅×D₄	—	4	4	no	—
106	C₃×C₅×D₄	—	4	4	no	—
107	C₃×C₅×D₄	—	4	4	no	—
108	C₃×C₅×D₄	—	4	4	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₃×C₅×C₈	—	2	4	no	—
121	C₂²×C₃×D₄	—	2	1	no	—
122	C₂²×C₃×D₄	—	2	1	no	—
123	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
124	C₂×C₃×SD₁₆	C₂²×C₅	1	8	yes	complemented
125	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
126	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
127	C₃×#127	—	2	1	no	—
128	C₃×#127	—	2	1	no	—
129	C₃×#127	C₂²×C₅	1	2	yes	—
130	C₃×#127	C₂²×C₅	1	2	yes	—
131	C₃×#125	—	2	1	no	—
132	C₃×C₂²⋊Q₈	—	2	1	no	—
133	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
134	C₃×C₄×Q₈	—	2	1	no	—
135	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
136	C₃×#117	—	2	1	no	—
137	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
138	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
139	C₃×#102	C₂²×C₅	1	8	yes	complemented
140	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
141	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
142	C₂⁴×C₅	—	2	2	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
145	C₂×C₅×D₄	—	2	2	no	—
146	C₂×C₅×D₄	—	2	2	no	—
147	C₂×C₅×D₄	—	2	2	no	—
148	C₂×C₅×D₄	—	2	2	no	—
149	C₂×C₅×D₄	—	2	2	no	—
150	C₂×C₅×D₄	—	4	4	no	—
151	C₂×C₅×D₄	—	4	4	no	—
152	C₂×C₅×D₄	—	4	4	no	—
153	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
154	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
157	C₅×SD₁₆	—	4	8	no	—
158	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	—	2	2	no	—
163	C₅×C₄⋊C₄	—	2	2	no	—
164	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
165	C₅×C₂²⋊C₄	—	2	2	no	—
166	C₄²×C₅	—	2	2	no	—
167	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
168	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
169	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
170	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
171	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
172	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic
173	#492	C₂×C₃×C₅	1	2	yes	complemented
174	#486	C₂×C₃×C₅	1	2	yes	complemented
175	#460	C₂×C₃×C₅	1	4	yes	complemented
176	#450	C₂×C₃×C₅	1	4	yes	complemented
177	#431	C₂×C₃×C₅	1	1	yes	characteristic, complemented
178	C₂²×C₃×C₅	—	2	1	no	—
179	C₂²×C₃×C₅	—	2	1	no	—
180	C₂²×C₃×C₅	—	4	4	no	—
181	C₂²×C₃×C₅	—	4	4	no	—
182	C₂²×C₃×C₅	—	4	4	no	—
183	C₂²×C₃×C₅	—	8	8	no	—
184	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
185	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
186	C₃×C₄×C₅	—	2	1	no	—
187	C₃×C₄×C₅	—	2	1	no	—
188	C₃×C₄×C₅	—	4	2	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
191	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
192	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
193	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
194	C₂⁴×C₃	—	2	2	no	—
195	C₂×C₃×Q₈	—	2	1	no	—
196	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
197	C₂×C₃×D₄	—	2	2	no	—
198	C₂×C₃×D₄	—	2	2	no	—
199	C₂×C₃×D₄	—	2	2	no	—
200	C₂×C₃×D₄	—	2	2	no	—
201	C₂×C₃×D₄	—	2	2	no	—
202	C₂×C₃×D₄	—	4	4	no	—
203	C₂×C₃×D₄	—	4	4	no	—
204	C₂×C₃×D₄	—	4	4	no	—
205	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
206	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₃×SD₁₆	—	4	8	no	—
210	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
211	C₃×C₄⋊C₄	—	2	1	no	—
212	C₃×C₄⋊C₄	—	2	1	no	—
213	C₃×C₄⋊C₄	—	2	1	no	—
214	C₃×C₄⋊C₄	—	2	2	no	—
215	C₃×C₄⋊C₄	—	2	2	no	—
216	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
217	C₃×C₂²⋊C₄	—	2	2	no	—
218	C₃×C₄²	—	2	2	no	—
219	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
220	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
221	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
222	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
223	C₂³×C₅	—	2	4	no	—
224	C₂³×C₅	—	4	4	no	—
225	C₂³×C₅	—	4	4	no	—
226	C₂³×C₅	—	4	4	no	—
227	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
228	C₅×Q₈	—	2	4	no	—
229	C₅×Q₈	—	4	2	no	—
230	C₅×D₄	—	2	8	no	—
231	C₅×D₄	—	4	4	no	—
232	C₅×D₄	—	4	4	no	—
233	C₅×D₄	—	4	4	no	—
234	C₅×D₄	—	4	4	no	—
235	C₅×D₄	—	4	4	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	C₃×SD₁₆	1	4	yes	complemented
241	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
247	C₅×C₈	—	2	4	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
251	C₂×SD₁₆	C₂²×C₃×C₅	1	8	yes	complemented
252	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
253	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
254	#127	—	2	1	no	—
255	#127	—	2	1	no	—
256	#127	C₂²×C₃×C₅	1	2	yes	—
257	#127	C₂²×C₃×C₅	1	2	yes	—
258	#125	—	2	1	no	—
259	C₂²⋊Q₈	—	2	1	no	—
260	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
263	#117	—	2	1	no	—
264	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
266	#102	C₂²×C₃×C₅	1	8	yes	complemented
267	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
268	C₄×C₈	C₂²×C₃×C₅	1	2	yes	complemented
269	C₂×C₃×C₅	—	2	2	no	—
270	C₂×C₃×C₅	—	8	4	no	—
271	C₂×C₃×C₅	#535	1	1	yes	characteristic
272	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
273	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₂³×C₃	—	2	4	no	—
275	C₂³×C₃	—	4	4	no	—
276	C₂³×C₃	—	4	4	no	—
277	C₂³×C₃	—	4	4	no	—
278	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
279	C₃×Q₈	—	2	4	no	—
280	C₃×Q₈	—	4	2	no	—
281	C₃×D₄	—	2	8	no	—
282	C₃×D₄	—	4	4	no	—
283	C₃×D₄	—	4	4	no	—
284	C₃×D₄	—	4	4	no	—
285	C₃×D₄	—	4	4	no	—
286	C₃×D₄	—	4	4	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	complemented
292	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
298	C₃×C₈	—	2	4	no	—
299	C₂²×C₅	—	2	1	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	4	4	no	—
302	C₂²×C₅	—	4	4	no	—
303	C₂²×C₅	—	4	4	no	—
304	C₂²×C₅	—	8	8	no	—
305	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
306	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	4	2	no	—
310	C₄×C₅	—	4	2	no	—
311	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
312	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
313	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
314	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
315	C₂⁴	—	2	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	—	4	4	no	—
326	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
327	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
328	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
329	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
330	SD₁₆	—	4	8	no	—
331	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
341	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
342	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
343	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
344	C₃×C₅	#3208	1	1	yes	characteristic, direct product factor, Hall
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	4	4	no	—
348	C₂²×C₃	—	4	4	no	—
349	C₂²×C₃	—	4	4	no	—
350	C₂²×C₃	—	8	8	no	—
351	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
352	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	4	2	no	—
356	C₃×C₄	—	4	2	no	—
357	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
358	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
359	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
360	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
361	C₂×C₅	—	2	2	no	—
362	C₂×C₅	—	8	4	no	—
363	C₂×C₅	C₃×#535	1	1	yes	characteristic
364	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
365	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
366	C₂³	—	2	4	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	4	no	—
369	C₂³	—	4	4	no	—
370	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
371	Q₈	—	2	4	no	—
372	Q₈	—	4	2	no	—
373	D₄	—	2	8	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	4	no	—
376	D₄	—	4	4	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	C₃×C₅×SD₁₆	1	4	yes	complemented
384	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
385	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
386	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
387	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
388	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
389	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
390	C₈	—	2	4	no	—
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	—	8	4	no	—
393	C₂×C₃	C₅×#535	1	1	yes	characteristic
394	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
395	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₅	C₃×#3208	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	8	8	no	—
403	C₂²	C₂×C₃×C₅×SD₁₆	1	2	yes	—
404	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	C₂×C₃×C₅×SD₁₆	1	2	yes	—
410	C₄	C₂×C₃×C₅×SD₁₆	1	2	yes	—
411	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
412	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
413	C₃	C₅×#3208	1	1	yes	characteristic, direct product factor, Sylow
414	C₂	—	2	2	no	—
415	C₂	—	8	4	no	—
416	C₂	C₃×C₅×#535	1	1	yes	characteristic
417	C₂	C₂²×C₃×C₅×SD₁₆	1	1	yes	characteristic
418	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#533	C₂	semidirect
3. C₃×C₅×#492	C₂	semidirect
4. C₃×C₅×#486	C₂	semidirect
5. C₃×C₅×#460	C₂	semidirect
6. C₃×C₅×#450	C₂	semidirect
7. C₃×C₅×#431	C₂	semidirect
8. C₅×#3208	C₃	direct (N × H)
12. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
13. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
14. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
23. C₃×C₄×C₅×Q₈	C₂²	semidirect
26. C₃×C₅×C₄⋊C₈	C₂²	semidirect
27. C₃×C₅×#102	C₂²	semidirect
29. C₃×C₄×C₅×C₈	C₂²	semidirect
30. C₃×#3208	C₅	direct (N × H)
31. C₅×#533	C₂×C₃	semidirect
33. C₅×#492	C₂×C₃	semidirect
34. C₅×#486	C₂×C₃	semidirect
35. C₅×#460	C₂×C₃	semidirect
36. C₅×#450	C₂×C₃	semidirect
37. C₅×#431	C₂×C₃	semidirect
67. C₃×#533	C₂×C₅	semidirect
69. C₃×#492	C₂×C₅	semidirect
70. C₃×#486	C₂×C₅	semidirect
71. C₃×#460	C₂×C₅	semidirect
72. C₃×#450	C₂×C₅	semidirect
73. C₃×#431	C₂×C₅	semidirect
77. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
78. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
79. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
88. C₄×C₅×Q₈	C₂²×C₃	semidirect
91. C₅×C₄⋊C₈	C₂²×C₃	semidirect
92. C₅×#102	C₂²×C₃	semidirect
94. C₄×C₅×C₈	C₂²×C₃	semidirect
95. #3208	C₃×C₅	direct (N × H)
113. C₂×C₃×C₄×C₅	SD₁₆	semidirect
124. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
125. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
126. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
135. C₃×C₄×Q₈	C₂²×C₅	semidirect
138. C₃×C₄⋊C₈	C₂²×C₅	semidirect
139. C₃×#102	C₂²×C₅	semidirect
141. C₃×C₄×C₈	C₂²×C₅	semidirect
171. #533	C₂×C₃×C₅	semidirect
173. #492	C₂×C₃×C₅	semidirect
174. #486	C₂×C₃×C₅	semidirect
175. #460	C₂×C₃×C₅	semidirect
176. #450	C₂×C₃×C₅	semidirect
177. #431	C₂×C₃×C₅	semidirect
240. C₂×C₄×C₅	C₃×SD₁₆	semidirect
251. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
252. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
253. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
262. C₄×Q₈	C₂²×C₃×C₅	semidirect
265. C₄⋊C₈	C₂²×C₃×C₅	semidirect
266. #102	C₂²×C₃×C₅	semidirect
268. C₄×C₈	C₂²×C₃×C₅	semidirect
291. C₂×C₃×C₄	C₅×SD₁₆	semidirect
344. C₃×C₅	#3208	direct (N × H)
383. C₂×C₄	C₃×C₅×SD₁₆	semidirect
396. C₅	C₃×#3208	direct (N × H)
413. C₃	C₅×#3208	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#533	2
C₂×C₃×C₅×#127	2
C₃×C₅×#492	2
C₃×C₅×#486	2
C₃×C₅×#460	2
C₃×C₅×#450	2
C₃×C₅×#431	2
C₅×#3208	3
C₃×#3208	5

Subgroups — C3×C5×#3208 #14276242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3208 #14276242