Subgroups — C₃×C₅×#3200 #14276234

Order 1920.

820 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#485	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#482	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#468	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#450	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#448	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3200	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
19	C₃×C₅×#127	—	2	1	no	—
20	C₃×C₅×#124	—	2	1	no	—
21	C₃×C₅×#124	—	2	1	no	—
22	C₃×C₅×#123	—	2	1	no	—
23	C₃×C₅×#123	—	2	1	no	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₃×C₅×#121	C₂²	1	2	yes	—
27	C₃×C₅×#121	C₂²	1	2	yes	—
28	C₃×C₅×#120	—	2	1	no	—
29	C₃×C₅×#120	—	2	1	no	—
30	C₃×C₅×#117	C₂²	1	1	yes	characteristic
31	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×#107	C₂²	1	2	yes	complemented
33	C₃×C₅×#106	C₂²	1	2	yes	complemented
34	C₃×C₅×#103	C₂²	1	2	yes	complemented
35	C₃×C₅×#103	C₂²	1	2	yes	complemented
36	C₃×C₅×#102	C₂²	1	2	yes	—
37	C₃×C₅×#102	C₂²	1	2	yes	—
38	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
39	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
40	C₃×#3200	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#535	C₂×C₃	1	1	yes	characteristic
43	C₅×#485	C₂×C₃	1	2	yes	complemented
44	C₅×#482	C₂×C₃	1	2	yes	complemented
45	C₅×#468	C₂×C₃	1	2	yes	complemented
46	C₅×#465	C₂×C₃	1	2	yes	complemented
47	C₅×#450	C₂×C₃	1	2	yes	complemented
48	C₅×#448	C₂×C₃	1	2	yes	complemented
49	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂⁴×C₃×C₅	—	2	1	no	—
51	C₃×C₅×#41	—	4	1	no	—
52	C₃×C₅×#41	—	4	1	no	—
53	C₂×C₃×C₅×Q₈	—	2	1	no	—
54	C₂×C₃×C₅×Q₈	—	4	1	no	—
55	C₂×C₃×C₅×Q₈	—	4	1	no	—
56	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
57	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
58	C₂×C₃×C₅×D₄	—	2	2	no	—
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	—	4	1	no	—
62	C₂×C₃×C₅×D₄	—	4	1	no	—
63	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
65	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
66	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	—	2	1	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₃×C₅×SD₁₆	—	4	2	no	—
72	C₃×C₅×SD₁₆	—	4	2	no	—
73	C₃×C₅×M₁₆	—	4	1	no	—
74	C₂×C₃×C₅×C₈	—	4	1	no	—
75	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
76	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
77	C₃×C₅×C₄⋊C₄	—	2	2	no	—
78	C₃×C₅×C₄⋊C₄	—	2	2	no	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
81	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
82	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
87	C₃×C₄²×C₅	—	2	1	no	—
88	C₃×C₄²×C₅	—	2	1	no	—
89	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#535	C₂×C₅	1	1	yes	characteristic
91	C₃×#485	C₂×C₅	1	2	yes	complemented
92	C₃×#482	C₂×C₅	1	2	yes	complemented
93	C₃×#468	C₂×C₅	1	2	yes	complemented
94	C₃×#465	C₂×C₅	1	2	yes	complemented
95	C₃×#450	C₂×C₅	1	2	yes	complemented
96	C₃×#448	C₂×C₅	1	2	yes	complemented
97	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
102	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
103	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
105	C₅×C₄⋊Q₈	—	2	1	no	—
106	C₅×#127	—	2	1	no	—
107	C₅×#124	—	2	1	no	—
108	C₅×#124	—	2	1	no	—
109	C₅×#123	—	2	1	no	—
110	C₅×#123	—	2	1	no	—
111	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
112	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
113	C₅×#121	C₂²×C₃	1	2	yes	—
114	C₅×#121	C₂²×C₃	1	2	yes	—
115	C₅×#120	—	2	1	no	—
116	C₅×#120	—	2	1	no	—
117	C₅×#117	C₂²×C₃	1	1	yes	characteristic
118	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
119	C₅×#107	C₂²×C₃	1	2	yes	complemented
120	C₅×#106	C₂²×C₃	1	2	yes	complemented
121	C₅×#103	C₂²×C₃	1	2	yes	complemented
122	C₅×#103	C₂²×C₃	1	2	yes	complemented
123	C₅×#102	C₂²×C₃	1	2	yes	—
124	C₅×#102	C₂²×C₃	1	2	yes	—
125	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
126	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
127	#3200	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
128	C₂³×C₃×C₅	—	2	2	no	—
129	C₂³×C₃×C₅	—	4	2	no	—
130	C₂³×C₃×C₅	—	8	2	no	—
131	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×Q₈	—	2	2	no	—
136	C₃×C₅×Q₈	—	4	1	no	—
137	C₃×C₅×Q₈	—	4	2	no	—
138	C₃×C₅×D₄	—	2	2	no	—
139	C₃×C₅×D₄	—	2	2	no	—
140	C₃×C₅×D₄	—	4	1	no	—
141	C₃×C₅×D₄	—	4	1	no	—
142	C₃×C₅×D₄	—	4	1	no	—
143	C₃×C₅×D₄	—	4	2	no	—
144	C₃×C₅×D₄	—	8	2	no	—
145	C₃×C₅×D₄	—	8	2	no	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	4	2	no	—
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
160	C₃×C₅×C₈	—	2	2	no	—
161	C₃×C₅×C₈	—	2	2	no	—
162	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
163	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
164	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
166	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
167	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
168	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
169	C₃×C₄⋊Q₈	—	2	1	no	—
170	C₃×#127	—	2	1	no	—
171	C₃×#124	—	2	1	no	—
172	C₃×#124	—	2	1	no	—
173	C₃×#123	—	2	1	no	—
174	C₃×#123	—	2	1	no	—
175	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
176	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
177	C₃×#121	C₂²×C₅	1	2	yes	—
178	C₃×#121	C₂²×C₅	1	2	yes	—
179	C₃×#120	—	2	1	no	—
180	C₃×#120	—	2	1	no	—
181	C₃×#117	C₂²×C₅	1	1	yes	characteristic
182	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₃×#107	C₂²×C₅	1	2	yes	complemented
184	C₃×#106	C₂²×C₅	1	2	yes	complemented
185	C₃×#103	C₂²×C₅	1	2	yes	complemented
186	C₃×#103	C₂²×C₅	1	2	yes	complemented
187	C₃×#102	C₂²×C₅	1	2	yes	—
188	C₃×#102	C₂²×C₅	1	2	yes	—
189	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
190	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
191	C₂⁴×C₅	—	2	1	no	—
192	C₅×#41	—	4	1	no	—
193	C₅×#41	—	4	1	no	—
194	C₂×C₅×Q₈	—	2	1	no	—
195	C₂×C₅×Q₈	—	4	1	no	—
196	C₂×C₅×Q₈	—	4	1	no	—
197	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
198	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
199	C₂×C₅×D₄	—	2	2	no	—
200	C₂×C₅×D₄	—	2	2	no	—
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	—	4	1	no	—
203	C₂×C₅×D₄	—	4	1	no	—
204	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
205	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
206	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
207	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
208	C₂²×C₄×C₅	—	2	1	no	—
209	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
212	C₅×SD₁₆	—	4	2	no	—
213	C₅×SD₁₆	—	4	2	no	—
214	C₅×M₁₆	—	4	1	no	—
215	C₂×C₅×C₈	—	4	1	no	—
216	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
217	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
218	C₅×C₄⋊C₄	—	2	2	no	—
219	C₅×C₄⋊C₄	—	2	2	no	—
220	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
221	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
222	C₅×C₂²⋊C₄	—	2	1	no	—
223	C₅×C₂²⋊C₄	—	2	1	no	—
224	C₅×C₂²⋊C₄	—	2	2	no	—
225	C₅×C₂²⋊C₄	—	2	2	no	—
226	C₅×C₂²⋊C₄	—	2	2	no	—
227	C₅×C₂²⋊C₄	—	2	2	no	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	—	2	1	no	—
230	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
231	#535	C₂×C₃×C₅	1	1	yes	characteristic
232	#485	C₂×C₃×C₅	1	2	yes	complemented
233	#482	C₂×C₃×C₅	1	2	yes	complemented
234	#468	C₂×C₃×C₅	1	2	yes	complemented
235	#465	C₂×C₃×C₅	1	2	yes	complemented
236	#450	C₂×C₃×C₅	1	2	yes	complemented
237	#448	C₂×C₃×C₅	1	2	yes	complemented
238	#408	C₂×C₃×C₅	1	1	yes	characteristic, complemented
239	C₂²×C₃×C₅	—	2	1	no	—
240	C₂²×C₃×C₅	—	2	1	no	—
241	C₂²×C₃×C₅	—	2	1	no	—
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	—	2	2	no	—
244	C₂²×C₃×C₅	—	2	2	no	—
245	C₂²×C₃×C₅	—	4	2	no	—
246	C₂²×C₃×C₅	—	4	2	no	—
247	C₂²×C₃×C₅	—	4	2	no	—
248	C₂²×C₃×C₅	—	8	4	no	—
249	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₃×C₄×C₅	—	2	1	no	—
251	C₃×C₄×C₅	—	2	1	no	—
252	C₃×C₄×C₅	—	2	1	no	—
253	C₃×C₄×C₅	—	4	2	no	—
254	C₃×C₄×C₅	—	4	2	no	—
255	C₃×C₄×C₅	—	4	2	no	—
256	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
257	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
258	C₂⁴×C₃	—	2	1	no	—
259	C₃×#41	—	4	1	no	—
260	C₃×#41	—	4	1	no	—
261	C₂×C₃×Q₈	—	2	1	no	—
262	C₂×C₃×Q₈	—	4	1	no	—
263	C₂×C₃×Q₈	—	4	1	no	—
264	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
265	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
266	C₂×C₃×D₄	—	2	2	no	—
267	C₂×C₃×D₄	—	2	2	no	—
268	C₂×C₃×D₄	—	2	1	no	—
269	C₂×C₃×D₄	—	4	1	no	—
270	C₂×C₃×D₄	—	4	1	no	—
271	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
272	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
273	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
274	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
275	C₂²×C₃×C₄	—	2	1	no	—
276	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
279	C₃×SD₁₆	—	4	2	no	—
280	C₃×SD₁₆	—	4	2	no	—
281	C₃×M₁₆	—	4	1	no	—
282	C₂×C₃×C₈	—	4	1	no	—
283	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
284	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
285	C₃×C₄⋊C₄	—	2	2	no	—
286	C₃×C₄⋊C₄	—	2	2	no	—
287	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
288	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
289	C₃×C₂²⋊C₄	—	2	1	no	—
290	C₃×C₂²⋊C₄	—	2	1	no	—
291	C₃×C₂²⋊C₄	—	2	2	no	—
292	C₃×C₂²⋊C₄	—	2	2	no	—
293	C₃×C₂²⋊C₄	—	2	2	no	—
294	C₃×C₂²⋊C₄	—	2	2	no	—
295	C₃×C₄²	—	2	1	no	—
296	C₃×C₄²	—	2	1	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	—	4	2	no	—
299	C₂³×C₅	—	8	2	no	—
300	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
301	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
302	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
303	C₅×Q₈	—	2	2	no	—
304	C₅×Q₈	—	2	2	no	—
305	C₅×Q₈	—	4	1	no	—
306	C₅×Q₈	—	4	2	no	—
307	C₅×D₄	—	2	2	no	—
308	C₅×D₄	—	2	2	no	—
309	C₅×D₄	—	4	1	no	—
310	C₅×D₄	—	4	1	no	—
311	C₅×D₄	—	4	1	no	—
312	C₅×D₄	—	4	2	no	—
313	C₅×D₄	—	8	2	no	—
314	C₅×D₄	—	8	2	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	4	2	no	—
325	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
329	C₅×C₈	—	2	2	no	—
330	C₅×C₈	—	2	2	no	—
331	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
332	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
333	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
334	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
335	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
336	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
337	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
338	C₄⋊Q₈	—	2	1	no	—
339	#127	—	2	1	no	—
340	#124	—	2	1	no	—
341	#124	—	2	1	no	—
342	#123	—	2	1	no	—
343	#123	—	2	1	no	—
344	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
345	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
346	#121	C₂²×C₃×C₅	1	2	yes	—
347	#121	C₂²×C₃×C₅	1	2	yes	—
348	#120	—	2	1	no	—
349	#120	—	2	1	no	—
350	#117	C₂²×C₃×C₅	1	1	yes	characteristic
351	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
352	#107	C₂²×C₃×C₅	1	2	yes	complemented
353	#106	C₂²×C₃×C₅	1	2	yes	complemented
354	#103	C₂²×C₃×C₅	1	2	yes	complemented
355	#103	C₂²×C₃×C₅	1	2	yes	complemented
356	#102	C₂²×C₃×C₅	1	2	yes	—
357	#102	C₂²×C₃×C₅	1	2	yes	—
358	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
359	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
360	C₂×C₃×C₅	—	4	1	no	—
361	C₂×C₃×C₅	—	4	1	no	—
362	C₂×C₃×C₅	—	4	1	no	—
363	C₂×C₃×C₅	—	8	2	no	—
364	C₂×C₃×C₅	#534	1	1	yes	characteristic
365	C₂×C₃×C₅	#577	1	2	yes	—
366	C₂³×C₃	—	2	2	no	—
367	C₂³×C₃	—	4	2	no	—
368	C₂³×C₃	—	8	2	no	—
369	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
371	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
372	C₃×Q₈	—	2	2	no	—
373	C₃×Q₈	—	2	2	no	—
374	C₃×Q₈	—	4	1	no	—
375	C₃×Q₈	—	4	2	no	—
376	C₃×D₄	—	2	2	no	—
377	C₃×D₄	—	2	2	no	—
378	C₃×D₄	—	4	1	no	—
379	C₃×D₄	—	4	1	no	—
380	C₃×D₄	—	4	1	no	—
381	C₃×D₄	—	4	2	no	—
382	C₃×D₄	—	8	2	no	—
383	C₃×D₄	—	8	2	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	4	2	no	—
394	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
396	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
397	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
398	C₃×C₈	—	2	2	no	—
399	C₃×C₈	—	2	2	no	—
400	C₂²×C₅	—	2	2	no	—
401	C₂²×C₅	—	2	2	no	—
402	C₂²×C₅	—	2	2	no	—
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	4	2	no	—
407	C₂²×C₅	—	4	2	no	—
408	C₂²×C₅	—	4	2	no	—
409	C₂²×C₅	—	8	4	no	—
410	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
411	C₄×C₅	—	2	1	no	—
412	C₄×C₅	—	2	1	no	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	4	2	no	—
415	C₄×C₅	—	4	2	no	—
416	C₄×C₅	—	4	2	no	—
417	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
418	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂⁴	—	2	1	no	—
420	#41	—	4	1	no	—
421	#41	—	4	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	4	1	no	—
424	C₂×Q₈	—	4	1	no	—
425	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
426	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
433	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
434	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
435	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
438	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
439	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
440	SD₁₆	—	4	2	no	—
441	SD₁₆	—	4	2	no	—
442	M₁₆	—	4	1	no	—
443	C₂×C₈	—	4	1	no	—
444	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
445	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
449	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
450	C₂²⋊C₄	—	2	1	no	—
451	C₂²⋊C₄	—	2	1	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₃×C₅	#3200	1	1	yes	characteristic, direct product factor, Hall
459	C₂²×C₃	—	2	1	no	—
460	C₂²×C₃	—	2	1	no	—
461	C₂²×C₃	—	2	1	no	—
462	C₂²×C₃	—	2	2	no	—
463	C₂²×C₃	—	2	2	no	—
464	C₂²×C₃	—	2	2	no	—
465	C₂²×C₃	—	4	2	no	—
466	C₂²×C₃	—	4	2	no	—
467	C₂²×C₃	—	4	2	no	—
468	C₂²×C₃	—	8	4	no	—
469	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
470	C₃×C₄	—	2	1	no	—
471	C₃×C₄	—	2	1	no	—
472	C₃×C₄	—	2	1	no	—
473	C₃×C₄	—	4	2	no	—
474	C₃×C₄	—	4	2	no	—
475	C₃×C₄	—	4	2	no	—
476	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
477	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂×C₅	—	4	1	no	—
479	C₂×C₅	—	4	1	no	—
480	C₂×C₅	—	4	1	no	—
481	C₂×C₅	—	8	2	no	—
482	C₂×C₅	C₃×#534	1	1	yes	characteristic
483	C₂×C₅	C₃×#577	1	2	yes	—
484	C₂³	—	2	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	8	2	no	—
487	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
488	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
489	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
490	Q₈	—	2	2	no	—
491	Q₈	—	2	2	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	2	2	no	—
496	D₄	—	4	1	no	—
497	D₄	—	4	1	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	2	no	—
500	D₄	—	8	2	no	—
501	D₄	—	8	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
513	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
515	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
516	C₈	—	2	2	no	—
517	C₈	—	2	2	no	—
518	C₂×C₃	—	4	1	no	—
519	C₂×C₃	—	4	1	no	—
520	C₂×C₃	—	4	1	no	—
521	C₂×C₃	—	8	2	no	—
522	C₂×C₃	C₅×#534	1	1	yes	characteristic
523	C₂×C₃	C₅×#577	1	2	yes	—
524	C₅	C₃×#3200	1	1	yes	characteristic, direct product factor, Sylow
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	8	4	no	—
535	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	2	no	—
542	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
543	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
544	C₃	C₅×#3200	1	1	yes	characteristic, direct product factor, Sylow
545	C₂	—	4	1	no	—
546	C₂	—	4	1	no	—
547	C₂	—	4	1	no	—
548	C₂	—	8	2	no	—
549	C₂	C₃×C₅×#534	1	1	yes	characteristic
550	C₂	C₃×C₅×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#536	C₂	semidirect
3. C₃×C₅×#485	C₂	semidirect
4. C₃×C₅×#482	C₂	semidirect
5. C₃×C₅×#468	C₂	semidirect
6. C₃×C₅×#465	C₂	semidirect
7. C₃×C₅×#450	C₂	semidirect
8. C₃×C₅×#448	C₂	semidirect
9. C₃×C₅×#408	C₂	semidirect
10. C₅×#3200	C₃	direct (N × H)
12. C₂²×C₃×C₅×Q₈	C₂²	semidirect
16. C₂×C₃×C₅×M₁₆	C₂²	semidirect
17. C₂²×C₃×C₅×C₈	C₂²	semidirect
25. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
31. C₃×C₅×#117	C₂²	semidirect
32. C₃×C₅×#107	C₂²	semidirect
33. C₃×C₅×#106	C₂²	semidirect
34. C₃×C₅×#103	C₂²	semidirect
35. C₃×C₅×#103	C₂²	semidirect
39. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
40. C₃×#3200	C₅	direct (N × H)
41. C₅×#536	C₂×C₃	semidirect
43. C₅×#485	C₂×C₃	semidirect
44. C₅×#482	C₂×C₃	semidirect
45. C₅×#468	C₂×C₃	semidirect
46. C₅×#465	C₂×C₃	semidirect
47. C₅×#450	C₂×C₃	semidirect
48. C₅×#448	C₂×C₃	semidirect
49. C₅×#408	C₂×C₃	semidirect
89. C₃×#536	C₂×C₅	semidirect
91. C₃×#485	C₂×C₅	semidirect
92. C₃×#482	C₂×C₅	semidirect
93. C₃×#468	C₂×C₅	semidirect
94. C₃×#465	C₂×C₅	semidirect
95. C₃×#450	C₂×C₅	semidirect
96. C₃×#448	C₂×C₅	semidirect
97. C₃×#408	C₂×C₅	semidirect
99. C₂²×C₅×Q₈	C₂²×C₃	semidirect
103. C₂×C₅×M₁₆	C₂²×C₃	semidirect
104. C₂²×C₅×C₈	C₂²×C₃	semidirect
112. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
118. C₅×#117	C₂²×C₃	semidirect
119. C₅×#107	C₂²×C₃	semidirect
120. C₅×#106	C₂²×C₃	semidirect
121. C₅×#103	C₂²×C₃	semidirect
122. C₅×#103	C₂²×C₃	semidirect
126. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
127. #3200	C₃×C₅	direct (N × H)
163. C₂²×C₃×Q₈	C₂²×C₅	semidirect
167. C₂×C₃×M₁₆	C₂²×C₅	semidirect
168. C₂²×C₃×C₈	C₂²×C₅	semidirect
176. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
182. C₃×#117	C₂²×C₅	semidirect
183. C₃×#107	C₂²×C₅	semidirect
184. C₃×#106	C₂²×C₅	semidirect
185. C₃×#103	C₂²×C₅	semidirect
186. C₃×#103	C₂²×C₅	semidirect
190. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
230. #536	C₂×C₃×C₅	semidirect
232. #485	C₂×C₃×C₅	semidirect
233. #482	C₂×C₃×C₅	semidirect
234. #468	C₂×C₃×C₅	semidirect
235. #465	C₂×C₃×C₅	semidirect
236. #450	C₂×C₃×C₅	semidirect
237. #448	C₂×C₃×C₅	semidirect
238. #408	C₂×C₃×C₅	semidirect
332. C₂²×Q₈	C₂²×C₃×C₅	semidirect
336. C₂×M₁₆	C₂²×C₃×C₅	semidirect
337. C₂²×C₈	C₂²×C₃×C₅	semidirect
345. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
351. #117	C₂²×C₃×C₅	semidirect
352. #107	C₂²×C₃×C₅	semidirect
353. #106	C₂²×C₃×C₅	semidirect
354. #103	C₂²×C₃×C₅	semidirect
355. #103	C₂²×C₃×C₅	semidirect
359. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
458. C₃×C₅	#3200	direct (N × H)
524. C₅	C₃×#3200	direct (N × H)
544. C₃	C₅×#3200	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×#536	2
C₃×C₅×#535	2
C₃×C₅×#485	2
C₃×C₅×#482	2
C₃×C₅×#468	2
C₃×C₅×#465	2
C₃×C₅×#450	2
C₃×C₅×#448	2
C₃×C₅×#408	2
C₅×#3200	3
C₃×#3200	5

Subgroups — C3×C5×#3200 #14276234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3200 #14276234