Subgroups — C₃×C₅×#3197 #14276231

Order 1920.

836 conjugacy classes of subgroups.

The subgroup lattice has 476 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×#470	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#469	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#468	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	C₃×C₅×#407	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3197	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	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×M₁₆	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	2	yes	complemented
28	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#106	C₂²	1	1	yes	characteristic, 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×#3197	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×#470	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#469	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#468	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	C₅×#407	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	C₃×C₅×M₁₆	—	4	1	no	—
65	C₃×C₅×M₁₆	—	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×#470	C₂×C₅	1	1	yes	characteristic, complemented
83	C₃×#469	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×#468	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	C₃×#407	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	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×M₁₆	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	2	yes	complemented
105	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₅×#106	C₂²×C₃	1	1	yes	characteristic, 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	#3197	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	—	4	1	no	—
116	C₂³×C₃×C₅	—	4	2	no	—
117	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
118	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
119	C₃×C₅×Q₈	—	2	2	no	—
120	C₃×C₅×Q₈	—	2	2	no	—
121	C₃×C₅×D₄	—	2	2	no	—
122	C₃×C₅×D₄	—	2	2	no	—
123	C₃×C₅×D₄	—	4	4	no	—
124	C₃×C₅×D₄	—	4	4	no	—
125	C₃×C₅×D₄	—	4	4	no	—
126	C₂×C₃×C₄×C₅	—	2	1	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	—	2	2	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	—	4	1	no	—
134	C₂×C₃×C₄×C₅	—	4	2	no	—
135	C₂×C₃×C₄×C₅	—	4	4	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₃×C₅×C₈	—	2	1	no	—
140	C₃×C₅×C₈	—	2	2	no	—
141	C₃×C₅×C₈	—	2	1	no	—
142	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
143	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
145	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
146	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
147	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
148	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
149	C₃×#123	—	2	2	no	—
150	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
151	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
152	C₃×#121	C₂²×C₅	1	2	yes	—
153	C₃×#121	C₂²×C₅	1	2	yes	—
154	C₃×#120	—	2	2	no	—
155	C₃×C₄×D₄	—	2	2	no	—
156	C₃×C₄×D₄	—	2	2	no	—
157	C₃×#117	C₂²×C₅	1	2	yes	—
158	C₃×#107	C₂²×C₅	1	2	yes	complemented
159	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
160	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
161	C₃×#103	C₂²×C₅	1	2	yes	complemented
162	C₃×#103	C₂²×C₅	1	2	yes	complemented
163	C₃×#102	C₂²×C₅	1	2	yes	complemented
164	C₃×#102	C₂²×C₅	1	2	yes	complemented
165	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
166	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
167	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
168	C₅×#41	—	4	2	no	—
169	C₅×#41	—	4	2	no	—
170	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
171	C₂×C₅×D₄	—	2	2	no	—
172	C₂×C₅×D₄	—	2	2	no	—
173	C₂×C₅×D₄	—	2	2	no	—
174	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
175	C₂²×C₄×C₅	—	2	2	no	—
176	C₂²×C₄×C₅	—	4	1	no	—
177	C₂²×C₄×C₅	—	4	1	no	—
178	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
180	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
181	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
182	C₅×Q₁₆	—	4	1	no	—
183	C₅×SD₁₆	—	4	2	no	—
184	C₅×D₈	—	4	1	no	—
185	C₅×M₁₆	—	4	1	no	—
186	C₅×M₁₆	—	4	1	no	—
187	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
189	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
193	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
194	C₅×C₂²⋊C₄	—	2	2	no	—
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	C₄²×C₅	—	2	2	no	—
200	#525	C₂×C₃×C₅	1	2	yes	complemented
201	#485	C₂×C₃×C₅	1	2	yes	complemented
202	#482	C₂×C₃×C₅	1	2	yes	complemented
203	#470	C₂×C₃×C₅	1	1	yes	characteristic, complemented
204	#469	C₂×C₃×C₅	1	1	yes	characteristic, complemented
205	#468	C₂×C₃×C₅	1	2	yes	complemented
206	#452	C₂×C₃×C₅	1	2	yes	complemented
207	#449	C₂×C₃×C₅	1	2	yes	complemented
208	#407	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	—	2	1	no	—
211	C₂²×C₃×C₅	—	2	2	no	—
212	C₂²×C₃×C₅	—	2	2	no	—
213	C₂²×C₃×C₅	—	2	2	no	—
214	C₂²×C₃×C₅	—	4	4	no	—
215	C₂²×C₃×C₅	—	4	2	no	—
216	C₂²×C₃×C₅	—	4	2	no	—
217	C₂²×C₃×C₅	—	4	2	no	—
218	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
219	C₃×C₄×C₅	—	2	2	no	—
220	C₃×C₄×C₅	—	2	1	no	—
221	C₃×C₄×C₅	—	4	2	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×C₄×C₅	—	4	2	no	—
224	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
225	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
227	C₃×#41	—	4	2	no	—
228	C₃×#41	—	4	2	no	—
229	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
230	C₂×C₃×D₄	—	2	2	no	—
231	C₂×C₃×D₄	—	2	2	no	—
232	C₂×C₃×D₄	—	2	2	no	—
233	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
234	C₂²×C₃×C₄	—	2	2	no	—
235	C₂²×C₃×C₄	—	4	1	no	—
236	C₂²×C₃×C₄	—	4	1	no	—
237	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
239	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
240	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
241	C₃×Q₁₆	—	4	1	no	—
242	C₃×SD₁₆	—	4	2	no	—
243	C₃×D₈	—	4	1	no	—
244	C₃×M₁₆	—	4	1	no	—
245	C₃×M₁₆	—	4	1	no	—
246	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
247	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
248	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
249	C₃×C₄⋊C₄	—	2	2	no	—
250	C₃×C₄⋊C₄	—	2	2	no	—
251	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
252	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
253	C₃×C₂²⋊C₄	—	2	2	no	—
254	C₃×C₂²⋊C₄	—	2	2	no	—
255	C₃×C₂²⋊C₄	—	2	2	no	—
256	C₃×C₂²⋊C₄	—	2	2	no	—
257	C₃×C₂²⋊C₄	—	2	2	no	—
258	C₃×C₄²	—	2	2	no	—
259	C₂³×C₅	—	2	2	no	—
260	C₂³×C₅	—	4	1	no	—
261	C₂³×C₅	—	4	2	no	—
262	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
263	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
264	C₅×Q₈	—	2	2	no	—
265	C₅×Q₈	—	2	2	no	—
266	C₅×D₄	—	2	2	no	—
267	C₅×D₄	—	2	2	no	—
268	C₅×D₄	—	4	4	no	—
269	C₅×D₄	—	4	4	no	—
270	C₅×D₄	—	4	4	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	4	1	no	—
279	C₂×C₄×C₅	—	4	2	no	—
280	C₂×C₄×C₅	—	4	4	no	—
281	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
282	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
284	C₅×C₈	—	2	1	no	—
285	C₅×C₈	—	2	2	no	—
286	C₅×C₈	—	2	1	no	—
287	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
288	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
289	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
290	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
291	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
292	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
293	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
294	#123	—	2	2	no	—
295	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
296	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
297	#121	C₂²×C₃×C₅	1	2	yes	—
298	#121	C₂²×C₃×C₅	1	2	yes	—
299	#120	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	#117	C₂²×C₃×C₅	1	2	yes	—
303	#107	C₂²×C₃×C₅	1	2	yes	complemented
304	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
305	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
306	#103	C₂²×C₃×C₅	1	2	yes	complemented
307	#103	C₂²×C₃×C₅	1	2	yes	complemented
308	#102	C₂²×C₃×C₅	1	2	yes	complemented
309	#102	C₂²×C₃×C₅	1	2	yes	complemented
310	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
311	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
312	C₂×C₃×C₅	—	4	2	no	—
313	C₂×C₃×C₅	—	4	1	no	—
314	C₂×C₃×C₅	—	8	2	no	—
315	C₂×C₃×C₅	#534	1	1	yes	characteristic
316	C₂×C₃×C₅	#575	1	2	yes	—
317	C₂³×C₃	—	2	2	no	—
318	C₂³×C₃	—	4	1	no	—
319	C₂³×C₃	—	4	2	no	—
320	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
321	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
322	C₃×Q₈	—	2	2	no	—
323	C₃×Q₈	—	2	2	no	—
324	C₃×D₄	—	2	2	no	—
325	C₃×D₄	—	2	2	no	—
326	C₃×D₄	—	4	4	no	—
327	C₃×D₄	—	4	4	no	—
328	C₃×D₄	—	4	4	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	4	1	no	—
337	C₂×C₃×C₄	—	4	2	no	—
338	C₂×C₃×C₄	—	4	4	no	—
339	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
340	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
342	C₃×C₈	—	2	1	no	—
343	C₃×C₈	—	2	2	no	—
344	C₃×C₈	—	2	1	no	—
345	C₂²×C₅	—	2	2	no	—
346	C₂²×C₅	—	2	2	no	—
347	C₂²×C₅	—	2	2	no	—
348	C₂²×C₅	—	2	2	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	4	4	no	—
351	C₂²×C₅	—	4	2	no	—
352	C₂²×C₅	—	4	2	no	—
353	C₂²×C₅	—	4	2	no	—
354	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	1	no	—
357	C₄×C₅	—	4	2	no	—
358	C₄×C₅	—	4	2	no	—
359	C₄×C₅	—	4	2	no	—
360	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
361	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
363	#41	—	4	2	no	—
364	#41	—	4	2	no	—
365	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	4	1	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
374	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
375	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
376	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
377	Q₁₆	—	4	1	no	—
378	SD₁₆	—	4	2	no	—
379	D₈	—	4	1	no	—
380	M₁₆	—	4	1	no	—
381	M₁₆	—	4	1	no	—
382	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
383	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
384	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
388	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₃×C₅	#3197	1	1	yes	characteristic, direct product factor, Hall
396	C₂²×C₃	—	2	2	no	—
397	C₂²×C₃	—	2	1	no	—
398	C₂²×C₃	—	2	2	no	—
399	C₂²×C₃	—	2	2	no	—
400	C₂²×C₃	—	2	2	no	—
401	C₂²×C₃	—	4	4	no	—
402	C₂²×C₃	—	4	2	no	—
403	C₂²×C₃	—	4	2	no	—
404	C₂²×C₃	—	4	2	no	—
405	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
406	C₃×C₄	—	2	2	no	—
407	C₃×C₄	—	2	1	no	—
408	C₃×C₄	—	4	2	no	—
409	C₃×C₄	—	4	2	no	—
410	C₃×C₄	—	4	2	no	—
411	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
412	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂×C₅	—	4	1	no	—
414	C₂×C₅	—	4	2	no	—
415	C₂×C₅	—	8	2	no	—
416	C₂×C₅	C₃×#534	1	1	yes	characteristic
417	C₂×C₅	C₃×#575	1	2	yes	—
418	C₂³	—	2	2	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	2	no	—
421	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
422	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
423	Q₈	—	2	2	no	—
424	Q₈	—	2	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	4	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
441	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
442	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
443	C₈	—	2	1	no	—
444	C₈	—	2	2	no	—
445	C₈	—	2	1	no	—
446	C₂×C₃	—	4	2	no	—
447	C₂×C₃	—	4	1	no	—
448	C₂×C₃	—	8	2	no	—
449	C₂×C₃	C₅×#534	1	1	yes	characteristic
450	C₂×C₃	C₅×#575	1	2	yes	—
451	C₅	C₃×#3197	1	1	yes	characteristic, direct product factor, Sylow
452	C₂²	—	2	2	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	1	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	2	no	—
467	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
468	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
469	C₃	C₅×#3197	1	1	yes	characteristic, direct product factor, Sylow
470	C₂	—	4	2	no	—
471	C₂	—	4	1	no	—
472	C₂	—	8	2	no	—
473	C₂	C₃×C₅×#534	1	1	yes	characteristic
474	C₂	C₃×C₅×#575	1	2	yes	—

	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×#470	C₂	semidirect
5. C₃×C₅×#469	C₂	semidirect
6. C₃×C₅×#468	C₂	semidirect
7. C₃×C₅×#452	C₂	semidirect
8. C₃×C₅×#449	C₂	semidirect
9. C₃×C₅×#407	C₂	semidirect
10. C₅×#3197	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×#106	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×#3197	C₅	direct (N × H)
37. C₅×#525	C₂×C₃	semidirect
38. C₅×#485	C₂×C₃	semidirect
39. C₅×#482	C₂×C₃	semidirect
40. C₅×#470	C₂×C₃	semidirect
41. C₅×#469	C₂×C₃	semidirect
42. C₅×#468	C₂×C₃	semidirect
43. C₅×#452	C₂×C₃	semidirect
44. C₅×#449	C₂×C₃	semidirect
45. C₅×#407	C₂×C₃	semidirect
79. C₃×#525	C₂×C₅	semidirect
80. C₃×#485	C₂×C₅	semidirect
81. C₃×#482	C₂×C₅	semidirect
82. C₃×#470	C₂×C₅	semidirect
83. C₃×#469	C₂×C₅	semidirect
84. C₃×#468	C₂×C₅	semidirect
85. C₃×#452	C₂×C₅	semidirect
86. C₃×#449	C₂×C₅	semidirect
87. C₃×#407	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×#106	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. #3197	C₃×C₅	direct (N × H)
144. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
145. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
146. C₂×C₃×D₈	C₂²×C₅	semidirect
158. C₃×#107	C₂²×C₅	semidirect
159. C₃×#106	C₂²×C₅	semidirect
160. C₃×#106	C₂²×C₅	semidirect
161. C₃×#103	C₂²×C₅	semidirect
162. C₃×#103	C₂²×C₅	semidirect
163. C₃×#102	C₂²×C₅	semidirect
164. C₃×#102	C₂²×C₅	semidirect
200. #525	C₂×C₃×C₅	semidirect
201. #485	C₂×C₃×C₅	semidirect
202. #482	C₂×C₃×C₅	semidirect
203. #470	C₂×C₃×C₅	semidirect
204. #469	C₂×C₃×C₅	semidirect
205. #468	C₂×C₃×C₅	semidirect
206. #452	C₂×C₃×C₅	semidirect
207. #449	C₂×C₃×C₅	semidirect
208. #407	C₂×C₃×C₅	semidirect
289. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
290. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
291. C₂×D₈	C₂²×C₃×C₅	semidirect
303. #107	C₂²×C₃×C₅	semidirect
304. #106	C₂²×C₃×C₅	semidirect
305. #106	C₂²×C₃×C₅	semidirect
306. #103	C₂²×C₃×C₅	semidirect
307. #103	C₂²×C₃×C₅	semidirect
308. #102	C₂²×C₃×C₅	semidirect
309. #102	C₂²×C₃×C₅	semidirect
395. C₃×C₅	#3197	direct (N × H)
451. C₅	C₃×#3197	direct (N × H)
469. C₃	C₅×#3197	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×#470	2
C₃×C₅×#469	2
C₃×C₅×#468	2
C₃×C₅×#452	2
C₃×C₅×#449	2
C₃×C₅×#407	2
C₅×#3197	3
C₃×#3197	5

Subgroups — C3×C5×#3197 #14276231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3197 #14276231