Subgroups — C₃×C₅×#3191 #14276225

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#525	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#485	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#482	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#452	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3191	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#123	—	2	2	no	—
19	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₃×C₅×#121	C₂²	1	2	yes	—
22	C₃×C₅×#121	C₂²	1	2	yes	—
23	C₃×C₅×#120	—	2	2	no	—
24	C₃×C₄×C₅×D₄	—	2	2	no	—
25	C₃×C₄×C₅×D₄	—	2	2	no	—
26	C₃×C₅×#117	C₂²	1	2	yes	—
27	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#106	C₂²	1	2	yes	complemented
30	C₃×C₅×#103	C₂²	1	2	yes	complemented
31	C₃×C₅×#103	C₂²	1	2	yes	complemented
32	C₃×C₅×#102	C₂²	1	2	yes	complemented
33	C₃×C₅×#102	C₂²	1	2	yes	complemented
34	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₃×#3191	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#525	C₂×C₃	1	2	yes	complemented
38	C₅×#485	C₂×C₃	1	2	yes	complemented
39	C₅×#482	C₂×C₃	1	2	yes	complemented
40	C₅×#467	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#466	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#465	C₂×C₃	1	2	yes	complemented
43	C₅×#452	C₂×C₃	1	2	yes	complemented
44	C₅×#449	C₂×C₃	1	2	yes	complemented
45	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
47	C₃×C₅×#41	—	4	2	no	—
48	C₃×C₅×#41	—	4	2	no	—
49	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
50	C₂×C₃×C₅×D₄	—	2	2	no	—
51	C₂×C₃×C₅×D₄	—	2	2	no	—
52	C₂×C₃×C₅×D₄	—	2	2	no	—
53	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂²×C₃×C₄×C₅	—	4	1	no	—
56	C₂²×C₃×C₄×C₅	—	4	1	no	—
57	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₃×C₅×Q₁₆	—	4	1	no	—
62	C₃×C₅×SD₁₆	—	4	2	no	—
63	C₃×C₅×D₈	—	4	1	no	—
64	C₂×C₃×C₅×C₈	—	4	1	no	—
65	C₂×C₃×C₅×C₈	—	4	1	no	—
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	—	2	2	no	—
70	C₃×C₅×C₄⋊C₄	—	2	2	no	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₃×C₄²×C₅	—	2	2	no	—
79	C₃×#525	C₂×C₅	1	2	yes	complemented
80	C₃×#485	C₂×C₅	1	2	yes	complemented
81	C₃×#482	C₂×C₅	1	2	yes	complemented
82	C₃×#467	C₂×C₅	1	1	yes	characteristic, complemented
83	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×#465	C₂×C₅	1	2	yes	complemented
85	C₃×#452	C₂×C₅	1	2	yes	complemented
86	C₃×#449	C₂×C₅	1	2	yes	complemented
87	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
89	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
91	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
92	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
93	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
95	C₅×#123	—	2	2	no	—
96	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
97	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
98	C₅×#121	C₂²×C₃	1	2	yes	—
99	C₅×#121	C₂²×C₃	1	2	yes	—
100	C₅×#120	—	2	2	no	—
101	C₄×C₅×D₄	—	2	2	no	—
102	C₄×C₅×D₄	—	2	2	no	—
103	C₅×#117	C₂²×C₃	1	2	yes	—
104	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
105	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₅×#106	C₂²×C₃	1	2	yes	complemented
107	C₅×#103	C₂²×C₃	1	2	yes	complemented
108	C₅×#103	C₂²×C₃	1	2	yes	complemented
109	C₅×#102	C₂²×C₃	1	2	yes	complemented
110	C₅×#102	C₂²×C₃	1	2	yes	complemented
111	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
112	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
113	#3191	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	—	4	1	no	—
117	C₂³×C₃×C₅	—	4	1	no	—
118	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
119	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
120	C₃×C₅×Q₈	—	2	2	no	—
121	C₃×C₅×Q₈	—	2	2	no	—
122	C₃×C₅×D₄	—	2	2	no	—
123	C₃×C₅×D₄	—	2	2	no	—
124	C₃×C₅×D₄	—	4	4	no	—
125	C₃×C₅×D₄	—	4	4	no	—
126	C₃×C₅×D₄	—	4	4	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	—	2	1	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	4	1	no	—
135	C₂×C₃×C₄×C₅	—	4	2	no	—
136	C₂×C₃×C₄×C₅	—	4	4	no	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₃×C₅×C₈	—	2	1	no	—
141	C₃×C₅×C₈	—	2	2	no	—
142	C₃×C₅×C₈	—	2	1	no	—
143	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
144	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
146	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
147	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
149	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
150	C₃×#123	—	2	2	no	—
151	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
152	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
153	C₃×#121	C₂²×C₅	1	2	yes	—
154	C₃×#121	C₂²×C₅	1	2	yes	—
155	C₃×#120	—	2	2	no	—
156	C₃×C₄×D₄	—	2	2	no	—
157	C₃×C₄×D₄	—	2	2	no	—
158	C₃×#117	C₂²×C₅	1	2	yes	—
159	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
160	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
161	C₃×#106	C₂²×C₅	1	2	yes	complemented
162	C₃×#103	C₂²×C₅	1	2	yes	complemented
163	C₃×#103	C₂²×C₅	1	2	yes	complemented
164	C₃×#102	C₂²×C₅	1	2	yes	complemented
165	C₃×#102	C₂²×C₅	1	2	yes	complemented
166	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
167	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
168	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
169	C₅×#41	—	4	2	no	—
170	C₅×#41	—	4	2	no	—
171	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
172	C₂×C₅×D₄	—	2	2	no	—
173	C₂×C₅×D₄	—	2	2	no	—
174	C₂×C₅×D₄	—	2	2	no	—
175	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
176	C₂²×C₄×C₅	—	2	2	no	—
177	C₂²×C₄×C₅	—	4	1	no	—
178	C₂²×C₄×C₅	—	4	1	no	—
179	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
181	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
182	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
183	C₅×Q₁₆	—	4	1	no	—
184	C₅×SD₁₆	—	4	2	no	—
185	C₅×D₈	—	4	1	no	—
186	C₂×C₅×C₈	—	4	1	no	—
187	C₂×C₅×C₈	—	4	1	no	—
188	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
190	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	2	no	—
193	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
194	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
195	C₅×C₂²⋊C₄	—	2	2	no	—
196	C₅×C₂²⋊C₄	—	2	2	no	—
197	C₅×C₂²⋊C₄	—	2	2	no	—
198	C₅×C₂²⋊C₄	—	2	2	no	—
199	C₅×C₂²⋊C₄	—	2	2	no	—
200	C₄²×C₅	—	2	2	no	—
201	#525	C₂×C₃×C₅	1	2	yes	complemented
202	#485	C₂×C₃×C₅	1	2	yes	complemented
203	#482	C₂×C₃×C₅	1	2	yes	complemented
204	#467	C₂×C₃×C₅	1	1	yes	characteristic, complemented
205	#466	C₂×C₃×C₅	1	1	yes	characteristic, complemented
206	#465	C₂×C₃×C₅	1	2	yes	complemented
207	#452	C₂×C₃×C₅	1	2	yes	complemented
208	#449	C₂×C₃×C₅	1	2	yes	complemented
209	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
210	C₂²×C₃×C₅	—	2	1	no	—
211	C₂²×C₃×C₅	—	2	1	no	—
212	C₂²×C₃×C₅	—	2	2	no	—
213	C₂²×C₃×C₅	—	2	2	no	—
214	C₂²×C₃×C₅	—	2	2	no	—
215	C₂²×C₃×C₅	—	4	4	no	—
216	C₂²×C₃×C₅	—	4	2	no	—
217	C₂²×C₃×C₅	—	4	2	no	—
218	C₂²×C₃×C₅	—	4	2	no	—
219	C₂²×C₃×C₅	#135	1	2	yes	—
220	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₃×C₄×C₅	—	2	2	no	—
222	C₃×C₄×C₅	—	2	1	no	—
223	C₃×C₄×C₅	—	4	2	no	—
224	C₃×C₄×C₅	—	4	2	no	—
225	C₃×C₄×C₅	—	4	2	no	—
226	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
227	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
229	C₃×#41	—	4	2	no	—
230	C₃×#41	—	4	2	no	—
231	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
232	C₂×C₃×D₄	—	2	2	no	—
233	C₂×C₃×D₄	—	2	2	no	—
234	C₂×C₃×D₄	—	2	2	no	—
235	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
236	C₂²×C₃×C₄	—	2	2	no	—
237	C₂²×C₃×C₄	—	4	1	no	—
238	C₂²×C₃×C₄	—	4	1	no	—
239	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
241	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
242	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
243	C₃×Q₁₆	—	4	1	no	—
244	C₃×SD₁₆	—	4	2	no	—
245	C₃×D₈	—	4	1	no	—
246	C₂×C₃×C₈	—	4	1	no	—
247	C₂×C₃×C₈	—	4	1	no	—
248	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
249	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
250	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
251	C₃×C₄⋊C₄	—	2	2	no	—
252	C₃×C₄⋊C₄	—	2	2	no	—
253	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
254	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
255	C₃×C₂²⋊C₄	—	2	2	no	—
256	C₃×C₂²⋊C₄	—	2	2	no	—
257	C₃×C₂²⋊C₄	—	2	2	no	—
258	C₃×C₂²⋊C₄	—	2	2	no	—
259	C₃×C₂²⋊C₄	—	2	2	no	—
260	C₃×C₄²	—	2	2	no	—
261	C₂³×C₅	—	2	2	no	—
262	C₂³×C₅	—	2	2	no	—
263	C₂³×C₅	—	4	1	no	—
264	C₂³×C₅	—	4	1	no	—
265	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
266	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
267	C₅×Q₈	—	2	2	no	—
268	C₅×Q₈	—	2	2	no	—
269	C₅×D₄	—	2	2	no	—
270	C₅×D₄	—	2	2	no	—
271	C₅×D₄	—	4	4	no	—
272	C₅×D₄	—	4	4	no	—
273	C₅×D₄	—	4	4	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	4	1	no	—
282	C₂×C₄×C₅	—	4	2	no	—
283	C₂×C₄×C₅	—	4	4	no	—
284	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
285	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
287	C₅×C₈	—	2	1	no	—
288	C₅×C₈	—	2	2	no	—
289	C₅×C₈	—	2	1	no	—
290	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
291	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
292	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
293	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
294	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
295	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
296	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
297	#123	—	2	2	no	—
298	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
299	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
300	#121	C₂²×C₃×C₅	1	2	yes	—
301	#121	C₂²×C₃×C₅	1	2	yes	—
302	#120	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	#117	C₂²×C₃×C₅	1	2	yes	—
306	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
307	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
308	#106	C₂²×C₃×C₅	1	2	yes	complemented
309	#103	C₂²×C₃×C₅	1	2	yes	complemented
310	#103	C₂²×C₃×C₅	1	2	yes	complemented
311	#102	C₂²×C₃×C₅	1	2	yes	complemented
312	#102	C₂²×C₃×C₅	1	2	yes	complemented
313	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
314	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
315	C₂×C₃×C₅	—	2	2	no	—
316	C₂×C₃×C₅	—	4	2	no	—
317	C₂×C₃×C₅	—	8	2	no	—
318	C₂×C₃×C₅	#534	1	1	yes	characteristic
319	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
320	C₂×C₃×C₅	#575	1	1	yes	characteristic
321	C₂³×C₃	—	2	2	no	—
322	C₂³×C₃	—	2	2	no	—
323	C₂³×C₃	—	4	1	no	—
324	C₂³×C₃	—	4	1	no	—
325	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
326	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
327	C₃×Q₈	—	2	2	no	—
328	C₃×Q₈	—	2	2	no	—
329	C₃×D₄	—	2	2	no	—
330	C₃×D₄	—	2	2	no	—
331	C₃×D₄	—	4	4	no	—
332	C₃×D₄	—	4	4	no	—
333	C₃×D₄	—	4	4	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	1	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	4	1	no	—
342	C₂×C₃×C₄	—	4	2	no	—
343	C₂×C₃×C₄	—	4	4	no	—
344	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
345	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
347	C₃×C₈	—	2	1	no	—
348	C₃×C₈	—	2	2	no	—
349	C₃×C₈	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	2	2	no	—
353	C₂²×C₅	—	2	2	no	—
354	C₂²×C₅	—	2	2	no	—
355	C₂²×C₅	—	4	4	no	—
356	C₂²×C₅	—	4	2	no	—
357	C₂²×C₅	—	4	2	no	—
358	C₂²×C₅	—	4	2	no	—
359	C₂²×C₅	C₃×#135	1	2	yes	—
360	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
361	C₄×C₅	—	2	2	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	—	4	2	no	—
364	C₄×C₅	—	4	2	no	—
365	C₄×C₅	—	4	2	no	—
366	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
367	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
369	#41	—	4	2	no	—
370	#41	—	4	2	no	—
371	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
380	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
381	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
382	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
383	Q₁₆	—	4	1	no	—
384	SD₁₆	—	4	2	no	—
385	D₈	—	4	1	no	—
386	C₂×C₈	—	4	1	no	—
387	C₂×C₈	—	4	1	no	—
388	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
389	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
390	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
394	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₃×C₅	#3191	1	1	yes	characteristic, direct product factor, Hall
402	C₂²×C₃	—	2	1	no	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	2	2	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	2	no	—
407	C₂²×C₃	—	4	4	no	—
408	C₂²×C₃	—	4	2	no	—
409	C₂²×C₃	—	4	2	no	—
410	C₂²×C₃	—	4	2	no	—
411	C₂²×C₃	C₅×#135	1	2	yes	—
412	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	4	2	no	—
416	C₃×C₄	—	4	2	no	—
417	C₃×C₄	—	4	2	no	—
418	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
419	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂×C₅	—	2	2	no	—
421	C₂×C₅	—	4	2	no	—
422	C₂×C₅	—	8	2	no	—
423	C₂×C₅	C₃×#534	1	1	yes	characteristic
424	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
425	C₂×C₅	C₃×#575	1	1	yes	characteristic
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
431	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
432	Q₈	—	2	2	no	—
433	Q₈	—	2	2	no	—
434	D₄	—	2	2	no	—
435	D₄	—	2	2	no	—
436	D₄	—	4	4	no	—
437	D₄	—	4	4	no	—
438	D₄	—	4	4	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
450	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
451	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
452	C₈	—	2	1	no	—
453	C₈	—	2	2	no	—
454	C₈	—	2	1	no	—
455	C₂×C₃	—	2	2	no	—
456	C₂×C₃	—	4	2	no	—
457	C₂×C₃	—	8	2	no	—
458	C₂×C₃	C₅×#534	1	1	yes	characteristic
459	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
460	C₂×C₃	C₅×#575	1	1	yes	characteristic
461	C₅	C₃×#3191	1	1	yes	characteristic, direct product factor, Sylow
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	C₃×C₅×#135	1	2	yes	—
472	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	1	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
479	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
480	C₃	C₅×#3191	1	1	yes	characteristic, direct product factor, Sylow
481	C₂	—	2	2	no	—
482	C₂	—	4	2	no	—
483	C₂	—	8	2	no	—
484	C₂	C₃×C₅×#534	1	1	yes	characteristic
485	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
486	C₂	C₃×C₅×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂³×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#525	C₂	semidirect
2. C₃×C₅×#485	C₂	semidirect
3. C₃×C₅×#482	C₂	semidirect
4. C₃×C₅×#467	C₂	semidirect
5. C₃×C₅×#466	C₂	semidirect
6. C₃×C₅×#465	C₂	semidirect
7. C₃×C₅×#452	C₂	semidirect
8. C₃×C₅×#449	C₂	semidirect
9. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
10. C₅×#3191	C₃	direct (N × H)
13. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
14. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
15. C₂×C₃×C₅×D₈	C₂²	semidirect
27. C₃×C₅×#107	C₂²	semidirect
28. C₃×C₅×#107	C₂²	semidirect
29. C₃×C₅×#106	C₂²	semidirect
30. C₃×C₅×#103	C₂²	semidirect
31. C₃×C₅×#103	C₂²	semidirect
32. C₃×C₅×#102	C₂²	semidirect
33. C₃×C₅×#102	C₂²	semidirect
36. C₃×#3191	C₅	direct (N × H)
37. C₅×#525	C₂×C₃	semidirect
38. C₅×#485	C₂×C₃	semidirect
39. C₅×#482	C₂×C₃	semidirect
40. C₅×#467	C₂×C₃	semidirect
41. C₅×#466	C₂×C₃	semidirect
42. C₅×#465	C₂×C₃	semidirect
43. C₅×#452	C₂×C₃	semidirect
44. C₅×#449	C₂×C₃	semidirect
45. C₂×C₅×C₂²⋊C₈	C₂×C₃	semidirect
79. C₃×#525	C₂×C₅	semidirect
80. C₃×#485	C₂×C₅	semidirect
81. C₃×#482	C₂×C₅	semidirect
82. C₃×#467	C₂×C₅	semidirect
83. C₃×#466	C₂×C₅	semidirect
84. C₃×#465	C₂×C₅	semidirect
85. C₃×#452	C₂×C₅	semidirect
86. C₃×#449	C₂×C₅	semidirect
87. C₂×C₃×C₂²⋊C₈	C₂×C₅	semidirect
90. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
91. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
92. C₂×C₅×D₈	C₂²×C₃	semidirect
104. C₅×#107	C₂²×C₃	semidirect
105. C₅×#107	C₂²×C₃	semidirect
106. C₅×#106	C₂²×C₃	semidirect
107. C₅×#103	C₂²×C₃	semidirect
108. C₅×#103	C₂²×C₃	semidirect
109. C₅×#102	C₂²×C₃	semidirect
110. C₅×#102	C₂²×C₃	semidirect
113. #3191	C₃×C₅	direct (N × H)
145. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
146. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
147. C₂×C₃×D₈	C₂²×C₅	semidirect
159. C₃×#107	C₂²×C₅	semidirect
160. C₃×#107	C₂²×C₅	semidirect
161. C₃×#106	C₂²×C₅	semidirect
162. C₃×#103	C₂²×C₅	semidirect
163. C₃×#103	C₂²×C₅	semidirect
164. C₃×#102	C₂²×C₅	semidirect
165. C₃×#102	C₂²×C₅	semidirect
201. #525	C₂×C₃×C₅	semidirect
202. #485	C₂×C₃×C₅	semidirect
203. #482	C₂×C₃×C₅	semidirect
204. #467	C₂×C₃×C₅	semidirect
205. #466	C₂×C₃×C₅	semidirect
206. #465	C₂×C₃×C₅	semidirect
207. #452	C₂×C₃×C₅	semidirect
208. #449	C₂×C₃×C₅	semidirect
209. C₂×C₂²⋊C₈	C₂×C₃×C₅	semidirect
292. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
293. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
294. C₂×D₈	C₂²×C₃×C₅	semidirect
306. #107	C₂²×C₃×C₅	semidirect
307. #107	C₂²×C₃×C₅	semidirect
308. #106	C₂²×C₃×C₅	semidirect
309. #103	C₂²×C₃×C₅	semidirect
310. #103	C₂²×C₃×C₅	semidirect
311. #102	C₂²×C₃×C₅	semidirect
312. #102	C₂²×C₃×C₅	semidirect
401. C₃×C₅	#3191	direct (N × H)
461. C₅	C₃×#3191	direct (N × H)
480. C₃	C₅×#3191	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×#525	2
C₃×C₅×#485	2
C₃×C₅×#482	2
C₃×C₅×#467	2
C₃×C₅×#466	2
C₃×C₅×#465	2
C₃×C₅×#452	2
C₃×C₅×#449	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₅×#3191	3
C₃×#3191	5

Subgroups — C3×C5×#3191 #14276225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3191 #14276225