Subgroups — C₃×C₅×#3221 #14276255

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#491	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#463	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#461	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#448	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3221	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
19	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×#127	C₂²	1	1	yes	characteristic
22	C₃×C₅×#125	C₂²	1	1	yes	characteristic
23	C₃×C₅×#124	C₂²	1	1	yes	characteristic
24	C₃×C₅×#124	C₂²	1	1	yes	characteristic
25	C₃×C₅×#123	—	2	2	no	—
26	C₃×C₅×#123	—	2	2	no	—
27	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
28	C₃×C₅×#121	—	2	2	no	—
29	C₃×C₅×#121	C₂²	1	2	yes	—
30	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
31	C₃×C₅×#117	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
33	C₃×C₅×#103	C₂²	1	2	yes	—
34	C₃×C₅×#103	C₂²	1	2	yes	—
35	C₃×C₅×#103	C₂²	1	2	yes	—
36	C₃×C₅×#102	C₂²	1	2	yes	—
37	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₃×C₅×#97	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₃×#3221	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#540	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#496	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#492	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#491	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#488	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#463	C₂×C₃	1	2	yes	complemented
48	C₅×#461	C₂×C₃	1	2	yes	complemented
49	C₅×#449	C₂×C₃	1	2	yes	complemented
50	C₅×#448	C₂×C₃	1	2	yes	complemented
51	C₅×#433	C₂×C₃	1	1	yes	characteristic, complemented
52	C₃×C₅×#41	—	4	2	no	—
53	C₂×C₃×C₅×Q₈	—	2	1	no	—
54	C₂×C₃×C₅×Q₈	—	4	2	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×D₄	—	2	1	no	—
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
62	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂²×C₃×C₄×C₅	—	2	1	no	—
65	C₂²×C₃×C₄×C₅	—	2	2	no	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₅×SD₁₆	—	4	2	no	—
68	C₃×C₅×SD₁₆	—	4	2	no	—
69	C₃×C₅×SD₁₆	—	4	2	no	—
70	C₃×C₅×D₈	—	4	2	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
75	C₃×C₅×C₄⋊C₄	—	2	2	no	—
76	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
77	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
78	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
79	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
80	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
81	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
82	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
83	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₃×#540	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
87	C₃×#496	C₂×C₅	1	1	yes	characteristic, complemented
88	C₃×#492	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#491	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#488	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×#463	C₂×C₅	1	2	yes	complemented
92	C₃×#461	C₂×C₅	1	2	yes	complemented
93	C₃×#449	C₂×C₅	1	2	yes	complemented
94	C₃×#448	C₂×C₅	1	2	yes	complemented
95	C₃×#433	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
97	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
99	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
100	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
101	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
102	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
103	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
104	C₅×#127	C₂²×C₃	1	1	yes	characteristic
105	C₅×#125	C₂²×C₃	1	1	yes	characteristic
106	C₅×#124	C₂²×C₃	1	1	yes	characteristic
107	C₅×#124	C₂²×C₃	1	1	yes	characteristic
108	C₅×#123	—	2	2	no	—
109	C₅×#123	—	2	2	no	—
110	C₅×C₂²⋊Q₈	—	2	2	no	—
111	C₅×#121	—	2	2	no	—
112	C₅×#121	C₂²×C₃	1	2	yes	—
113	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
114	C₅×#117	C₂²×C₃	1	1	yes	characteristic
115	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
116	C₅×#103	C₂²×C₃	1	2	yes	—
117	C₅×#103	C₂²×C₃	1	2	yes	—
118	C₅×#103	C₂²×C₃	1	2	yes	—
119	C₅×#102	C₂²×C₃	1	2	yes	—
120	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
121	C₅×#97	C₂²×C₃	1	1	yes	characteristic
122	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
123	#3221	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
124	C₂³×C₃×C₅	—	2	1	no	—
125	C₂³×C₃×C₅	—	2	2	no	—
126	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
127	C₃×C₅×Q₈	—	2	2	no	—
128	C₃×C₅×Q₈	—	2	2	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	—	4	2	no	—
131	C₃×C₅×D₄	—	2	2	no	—
132	C₃×C₅×D₄	—	2	2	no	—
133	C₃×C₅×D₄	—	2	2	no	—
134	C₃×C₅×D₄	—	4	2	no	—
135	C₃×C₅×D₄	—	8	2	no	—
136	C₃×C₅×D₄	—	8	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	1	no	—
141	C₂×C₃×C₄×C₅	—	2	1	no	—
142	C₂×C₃×C₄×C₅	—	4	2	no	—
143	C₂×C₃×C₄×C₅	—	4	2	no	—
144	C₂×C₃×C₄×C₅	—	8	2	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₃×C₅×C₈	—	2	2	no	—
150	C₃×C₅×C₈	—	2	2	no	—
151	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
152	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
154	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
155	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
156	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
157	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
158	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
159	C₃×#127	C₂²×C₅	1	1	yes	characteristic
160	C₃×#125	C₂²×C₅	1	1	yes	characteristic
161	C₃×#124	C₂²×C₅	1	1	yes	characteristic
162	C₃×#124	C₂²×C₅	1	1	yes	characteristic
163	C₃×#123	—	2	2	no	—
164	C₃×#123	—	2	2	no	—
165	C₃×C₂²⋊Q₈	—	2	2	no	—
166	C₃×#121	—	2	2	no	—
167	C₃×#121	C₂²×C₅	1	2	yes	—
168	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
169	C₃×#117	C₂²×C₅	1	1	yes	characteristic
170	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
171	C₃×#103	C₂²×C₅	1	2	yes	—
172	C₃×#103	C₂²×C₅	1	2	yes	—
173	C₃×#103	C₂²×C₅	1	2	yes	—
174	C₃×#102	C₂²×C₅	1	2	yes	—
175	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
176	C₃×#97	C₂²×C₅	1	1	yes	characteristic
177	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
178	C₅×#41	—	4	2	no	—
179	C₂×C₅×Q₈	—	2	1	no	—
180	C₂×C₅×Q₈	—	4	2	no	—
181	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₅×D₄	—	2	1	no	—
185	C₂×C₅×D₄	—	2	2	no	—
186	C₂×C₅×D₄	—	2	2	no	—
187	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
188	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	2	no	—
192	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
193	C₅×SD₁₆	—	4	2	no	—
194	C₅×SD₁₆	—	4	2	no	—
195	C₅×SD₁₆	—	4	2	no	—
196	C₅×D₈	—	4	2	no	—
197	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
198	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
199	C₅×C₄⋊C₄	—	2	2	no	—
200	C₅×C₄⋊C₄	—	2	2	no	—
201	C₅×C₄⋊C₄	—	2	2	no	—
202	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
203	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
204	C₅×C₂²⋊C₄	—	2	2	no	—
205	C₅×C₂²⋊C₄	—	2	2	no	—
206	C₅×C₂²⋊C₄	—	2	2	no	—
207	C₅×C₂²⋊C₄	—	2	2	no	—
208	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
209	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
210	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
211	#540	C₂×C₃×C₅	1	1	yes	characteristic, complemented
212	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
213	#496	C₂×C₃×C₅	1	1	yes	characteristic, complemented
214	#492	C₂×C₃×C₅	1	1	yes	characteristic, complemented
215	#491	C₂×C₃×C₅	1	1	yes	characteristic, complemented
216	#488	C₂×C₃×C₅	1	1	yes	characteristic, complemented
217	#463	C₂×C₃×C₅	1	2	yes	complemented
218	#461	C₂×C₃×C₅	1	2	yes	complemented
219	#449	C₂×C₃×C₅	1	2	yes	complemented
220	#448	C₂×C₃×C₅	1	2	yes	complemented
221	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
222	C₂²×C₃×C₅	—	2	1	no	—
223	C₂²×C₃×C₅	—	2	2	no	—
224	C₂²×C₃×C₅	—	4	1	no	—
225	C₂²×C₃×C₅	—	4	2	no	—
226	C₂²×C₃×C₅	—	4	2	no	—
227	C₂²×C₃×C₅	—	4	2	no	—
228	C₂²×C₃×C₅	—	4	2	no	—
229	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₃×C₄×C₅	—	2	1	no	—
231	C₃×C₄×C₅	—	2	2	no	—
232	C₃×C₄×C₅	—	2	2	no	—
233	C₃×C₄×C₅	—	4	1	no	—
234	C₃×C₄×C₅	—	4	1	no	—
235	C₃×C₄×C₅	—	4	1	no	—
236	C₃×C₄×C₅	—	4	2	no	—
237	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
238	C₃×#41	—	4	2	no	—
239	C₂×C₃×Q₈	—	2	1	no	—
240	C₂×C₃×Q₈	—	4	2	no	—
241	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
242	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
243	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
244	C₂×C₃×D₄	—	2	1	no	—
245	C₂×C₃×D₄	—	2	2	no	—
246	C₂×C₃×D₄	—	2	2	no	—
247	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
248	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
249	C₂²×C₃×C₄	—	2	1	no	—
250	C₂²×C₃×C₄	—	2	1	no	—
251	C₂²×C₃×C₄	—	2	2	no	—
252	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
253	C₃×SD₁₆	—	4	2	no	—
254	C₃×SD₁₆	—	4	2	no	—
255	C₃×SD₁₆	—	4	2	no	—
256	C₃×D₈	—	4	2	no	—
257	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
258	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
259	C₃×C₄⋊C₄	—	2	2	no	—
260	C₃×C₄⋊C₄	—	2	2	no	—
261	C₃×C₄⋊C₄	—	2	2	no	—
262	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
263	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
264	C₃×C₂²⋊C₄	—	2	2	no	—
265	C₃×C₂²⋊C₄	—	2	2	no	—
266	C₃×C₂²⋊C₄	—	2	2	no	—
267	C₃×C₂²⋊C₄	—	2	2	no	—
268	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
269	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
270	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
271	C₂³×C₅	—	2	1	no	—
272	C₂³×C₅	—	2	2	no	—
273	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
274	C₅×Q₈	—	2	2	no	—
275	C₅×Q₈	—	2	2	no	—
276	C₅×Q₈	—	2	2	no	—
277	C₅×Q₈	—	4	2	no	—
278	C₅×D₄	—	2	2	no	—
279	C₅×D₄	—	2	2	no	—
280	C₅×D₄	—	2	2	no	—
281	C₅×D₄	—	4	2	no	—
282	C₅×D₄	—	8	2	no	—
283	C₅×D₄	—	8	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	4	2	no	—
290	C₂×C₄×C₅	—	4	2	no	—
291	C₂×C₄×C₅	—	8	2	no	—
292	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
293	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
294	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
296	C₅×C₈	—	2	2	no	—
297	C₅×C₈	—	2	2	no	—
298	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
300	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
301	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
302	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
303	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
304	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
305	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
306	#127	C₂²×C₃×C₅	1	1	yes	characteristic
307	#125	C₂²×C₃×C₅	1	1	yes	characteristic
308	#124	C₂²×C₃×C₅	1	1	yes	characteristic
309	#124	C₂²×C₃×C₅	1	1	yes	characteristic
310	#123	—	2	2	no	—
311	#123	—	2	2	no	—
312	C₂²⋊Q₈	—	2	2	no	—
313	#121	—	2	2	no	—
314	#121	C₂²×C₃×C₅	1	2	yes	—
315	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
316	#117	C₂²×C₃×C₅	1	1	yes	characteristic
317	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
318	#103	C₂²×C₃×C₅	1	2	yes	—
319	#103	C₂²×C₃×C₅	1	2	yes	—
320	#103	C₂²×C₃×C₅	1	2	yes	—
321	#102	C₂²×C₃×C₅	1	2	yes	—
322	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
323	#97	C₂²×C₃×C₅	1	1	yes	characteristic
324	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
325	C₂×C₃×C₅	—	4	1	no	—
326	C₂×C₃×C₅	—	8	1	no	—
327	C₂×C₃×C₅	—	8	2	no	—
328	C₂×C₃×C₅	#535	1	1	yes	characteristic
329	C₂×C₃×C₅	#577	1	2	yes	—
330	C₂³×C₃	—	2	1	no	—
331	C₂³×C₃	—	2	2	no	—
332	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
333	C₃×Q₈	—	2	2	no	—
334	C₃×Q₈	—	2	2	no	—
335	C₃×Q₈	—	2	2	no	—
336	C₃×Q₈	—	4	2	no	—
337	C₃×D₄	—	2	2	no	—
338	C₃×D₄	—	2	2	no	—
339	C₃×D₄	—	2	2	no	—
340	C₃×D₄	—	4	2	no	—
341	C₃×D₄	—	8	2	no	—
342	C₃×D₄	—	8	2	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	1	no	—
346	C₂×C₃×C₄	—	2	1	no	—
347	C₂×C₃×C₄	—	2	1	no	—
348	C₂×C₃×C₄	—	4	2	no	—
349	C₂×C₃×C₄	—	4	2	no	—
350	C₂×C₃×C₄	—	8	2	no	—
351	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
352	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
353	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
355	C₃×C₈	—	2	2	no	—
356	C₃×C₈	—	2	2	no	—
357	C₂²×C₅	—	2	2	no	—
358	C₂²×C₅	—	2	1	no	—
359	C₂²×C₅	—	4	2	no	—
360	C₂²×C₅	—	4	2	no	—
361	C₂²×C₅	—	4	2	no	—
362	C₂²×C₅	—	4	1	no	—
363	C₂²×C₅	—	4	2	no	—
364	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
365	C₄×C₅	—	2	2	no	—
366	C₄×C₅	—	2	2	no	—
367	C₄×C₅	—	2	1	no	—
368	C₄×C₅	—	4	2	no	—
369	C₄×C₅	—	4	1	no	—
370	C₄×C₅	—	4	1	no	—
371	C₄×C₅	—	4	1	no	—
372	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
373	#41	—	4	2	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	4	2	no	—
376	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
377	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
378	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
383	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
388	SD₁₆	—	4	2	no	—
389	SD₁₆	—	4	2	no	—
390	SD₁₆	—	4	2	no	—
391	D₈	—	4	2	no	—
392	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
393	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
398	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
404	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
405	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
406	C₃×C₅	#3221	1	1	yes	characteristic, direct product factor, Hall
407	C₂²×C₃	—	2	1	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	4	1	no	—
410	C₂²×C₃	—	4	2	no	—
411	C₂²×C₃	—	4	2	no	—
412	C₂²×C₃	—	4	2	no	—
413	C₂²×C₃	—	4	2	no	—
414	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	4	1	no	—
419	C₃×C₄	—	4	1	no	—
420	C₃×C₄	—	4	1	no	—
421	C₃×C₄	—	4	2	no	—
422	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
423	C₂×C₅	—	4	1	no	—
424	C₂×C₅	—	8	2	no	—
425	C₂×C₅	—	8	1	no	—
426	C₂×C₅	C₃×#535	1	1	yes	characteristic
427	C₂×C₅	C₃×#577	1	2	yes	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	2	no	—
430	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
431	Q₈	—	2	2	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	2	2	no	—
434	Q₈	—	4	2	no	—
435	D₄	—	2	2	no	—
436	D₄	—	2	2	no	—
437	D₄	—	2	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	8	2	no	—
440	D₄	—	8	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	8	2	no	—
449	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
450	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
451	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
452	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₂×C₃	—	4	1	no	—
456	C₂×C₃	—	8	1	no	—
457	C₂×C₃	—	8	2	no	—
458	C₂×C₃	C₅×#535	1	1	yes	characteristic
459	C₂×C₃	C₅×#577	1	2	yes	—
460	C₅	C₃×#3221	1	1	yes	characteristic, direct product factor, Sylow
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
477	C₃	C₅×#3221	1	1	yes	characteristic, direct product factor, Sylow
478	C₂	—	4	1	no	—
479	C₂	—	8	1	no	—
480	C₂	—	8	2	no	—
481	C₂	C₃×C₅×#535	1	1	yes	characteristic
482	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
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#540	C₂	semidirect
2. C₃×C₅×#536	C₂	semidirect
3. C₃×C₅×#496	C₂	semidirect
4. C₃×C₅×#492	C₂	semidirect
5. C₃×C₅×#491	C₂	semidirect
6. C₃×C₅×#488	C₂	semidirect
7. C₃×C₅×#463	C₂	semidirect
8. C₃×C₅×#461	C₂	semidirect
9. C₃×C₅×#449	C₂	semidirect
10. C₃×C₅×#448	C₂	semidirect
11. C₃×C₅×#433	C₂	semidirect
12. C₅×#3221	C₃	direct (N × H)
40. C₃×#3221	C₅	direct (N × H)
41. C₅×#540	C₂×C₃	semidirect
42. C₅×#536	C₂×C₃	semidirect
43. C₅×#496	C₂×C₃	semidirect
44. C₅×#492	C₂×C₃	semidirect
45. C₅×#491	C₂×C₃	semidirect
46. C₅×#488	C₂×C₃	semidirect
47. C₅×#463	C₂×C₃	semidirect
48. C₅×#461	C₂×C₃	semidirect
49. C₅×#449	C₂×C₃	semidirect
50. C₅×#448	C₂×C₃	semidirect
51. C₅×#433	C₂×C₃	semidirect
85. C₃×#540	C₂×C₅	semidirect
86. C₃×#536	C₂×C₅	semidirect
87. C₃×#496	C₂×C₅	semidirect
88. C₃×#492	C₂×C₅	semidirect
89. C₃×#491	C₂×C₅	semidirect
90. C₃×#488	C₂×C₅	semidirect
91. C₃×#463	C₂×C₅	semidirect
92. C₃×#461	C₂×C₅	semidirect
93. C₃×#449	C₂×C₅	semidirect
94. C₃×#448	C₂×C₅	semidirect
95. C₃×#433	C₂×C₅	semidirect
123. #3221	C₃×C₅	direct (N × H)
211. #540	C₂×C₃×C₅	semidirect
212. #536	C₂×C₃×C₅	semidirect
213. #496	C₂×C₃×C₅	semidirect
214. #492	C₂×C₃×C₅	semidirect
215. #491	C₂×C₃×C₅	semidirect
216. #488	C₂×C₃×C₅	semidirect
217. #463	C₂×C₃×C₅	semidirect
218. #461	C₂×C₃×C₅	semidirect
219. #449	C₂×C₃×C₅	semidirect
220. #448	C₂×C₃×C₅	semidirect
221. #433	C₂×C₃×C₅	semidirect
406. C₃×C₅	#3221	direct (N × H)
460. C₅	C₃×#3221	direct (N × H)
477. C₃	C₅×#3221	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×#540	2
C₃×C₅×#536	2
C₃×C₅×#496	2
C₃×C₅×#492	2
C₃×C₅×#491	2
C₃×C₅×#488	2
C₃×C₅×#463	2
C₃×C₅×#461	2
C₃×C₅×#449	2
C₃×C₅×#448	2
C₃×C₅×#433	2
C₅×#3221	3
C₃×#3221	5

Subgroups — C3×C5×#3221 #14276255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3221 #14276255