Subgroups — C₃×C₅×#3220 #14276254

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 516 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×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#490	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×#459	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#447	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3220	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
16	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
17	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
18	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic
20	C₃×C₅×#127	C₂²	1	1	yes	characteristic
21	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
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×#121	—	2	2	no	—
27	C₃×C₅×#121	—	2	2	no	—
28	C₃×C₅×#121	C₂²	1	2	yes	—
29	C₃×C₅×#120	—	2	2	no	—
30	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
31	C₃×C₅×#117	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
33	C₃×C₅×#103	C₂²	1	2	yes	complemented
34	C₃×C₅×#102	C₂²	1	2	yes	—
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₃×C₅×#102	C₂²	1	2	yes	complemented
37	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3220	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#540	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#496	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#493	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#490	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×#459	C₂×C₃	1	2	yes	complemented
49	C₅×#449	C₂×C₃	1	2	yes	complemented
50	C₅×#447	C₂×C₃	1	2	yes	complemented
51	C₅×#433	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂⁴×C₃×C₅	—	2	1	no	—
53	C₃×C₅×#41	—	4	2	no	—
54	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	—	2	1	no	—
58	C₂×C₃×C₅×D₄	—	2	2	no	—
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	4	2	no	—
62	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
63	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	—	2	1	no	—
67	C₂²×C₃×C₄×C₅	—	2	2	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₃×C₅×SD₁₆	—	4	2	no	—
70	C₃×C₅×D₈	—	4	2	no	—
71	C₃×C₅×D₈	—	4	2	no	—
72	C₃×C₅×D₈	—	4	2	no	—
73	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
74	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
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×#535	C₂×C₅	1	1	yes	characteristic, complemented
87	C₃×#496	C₂×C₅	1	1	yes	characteristic, complemented
88	C₃×#493	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#490	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×#459	C₂×C₅	1	2	yes	complemented
93	C₃×#449	C₂×C₅	1	2	yes	complemented
94	C₃×#447	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×D₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
99	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
100	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
101	C₂×C₅×D₈	C₂²×C₃	1	2	yes	complemented
102	C₅×#127	C₂²×C₃	1	1	yes	characteristic
103	C₅×#127	C₂²×C₃	1	1	yes	characteristic
104	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
105	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
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×#121	—	2	2	no	—
110	C₅×#121	—	2	2	no	—
111	C₅×#121	C₂²×C₃	1	2	yes	—
112	C₅×#120	—	2	2	no	—
113	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
114	C₅×#117	C₂²×C₃	1	1	yes	characteristic
115	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
116	C₅×#103	C₂²×C₃	1	2	yes	complemented
117	C₅×#102	C₂²×C₃	1	2	yes	—
118	C₅×#102	C₂²×C₃	1	2	yes	—
119	C₅×#102	C₂²×C₃	1	2	yes	complemented
120	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
121	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
123	#3220	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
124	C₂³×C₃×C₅	—	2	2	no	—
125	C₂³×C₃×C₅	—	2	1	no	—
126	C₂³×C₃×C₅	—	2	1	no	—
127	C₂³×C₃×C₅	—	2	1	no	—
128	C₂³×C₃×C₅	—	4	2	no	—
129	C₂³×C₃×C₅	—	8	2	no	—
130	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
131	C₃×C₅×Q₈	—	2	2	no	—
132	C₃×C₅×D₄	—	2	2	no	—
133	C₃×C₅×D₄	—	2	2	no	—
134	C₃×C₅×D₄	—	2	2	no	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₃×C₅×D₄	—	2	2	no	—
137	C₃×C₅×D₄	—	4	2	no	—
138	C₃×C₅×D₄	—	4	2	no	—
139	C₃×C₅×D₄	—	8	2	no	—
140	C₃×C₅×D₄	—	8	2	no	—
141	C₃×C₅×D₄	—	8	2	no	—
142	C₃×C₅×D₄	—	8	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	4	2	no	—
147	C₂×C₃×C₄×C₅	—	8	2	no	—
148	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
152	C₃×C₅×C₈	—	2	2	no	—
153	C₃×C₅×C₈	—	2	2	no	—
154	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
155	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
157	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
158	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
159	C₂×C₃×D₈	C₂²×C₅	1	2	yes	complemented
160	C₃×#127	C₂²×C₅	1	1	yes	characteristic
161	C₃×#127	C₂²×C₅	1	1	yes	characteristic
162	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
163	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
164	C₃×#124	C₂²×C₅	1	1	yes	characteristic
165	C₃×#124	C₂²×C₅	1	1	yes	characteristic
166	C₃×#123	—	2	2	no	—
167	C₃×#121	—	2	2	no	—
168	C₃×#121	—	2	2	no	—
169	C₃×#121	C₂²×C₅	1	2	yes	—
170	C₃×#120	—	2	2	no	—
171	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
172	C₃×#117	C₂²×C₅	1	1	yes	characteristic
173	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
174	C₃×#103	C₂²×C₅	1	2	yes	complemented
175	C₃×#102	C₂²×C₅	1	2	yes	—
176	C₃×#102	C₂²×C₅	1	2	yes	—
177	C₃×#102	C₂²×C₅	1	2	yes	complemented
178	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
179	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
180	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₂⁴×C₅	—	2	1	no	—
182	C₅×#41	—	4	2	no	—
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	1	no	—
187	C₂×C₅×D₄	—	2	2	no	—
188	C₂×C₅×D₄	—	2	2	no	—
189	C₂×C₅×D₄	—	2	2	no	—
190	C₂×C₅×D₄	—	4	2	no	—
191	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
192	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	2	2	no	—
197	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
198	C₅×SD₁₆	—	4	2	no	—
199	C₅×D₈	—	4	2	no	—
200	C₅×D₈	—	4	2	no	—
201	C₅×D₈	—	4	2	no	—
202	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
203	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
204	C₅×C₄⋊C₄	—	2	2	no	—
205	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
206	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
207	C₅×C₂²⋊C₄	—	2	2	no	—
208	C₅×C₂²⋊C₄	—	2	2	no	—
209	C₅×C₂²⋊C₄	—	2	2	no	—
210	C₅×C₂²⋊C₄	—	2	2	no	—
211	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
212	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
213	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
214	#540	C₂×C₃×C₅	1	1	yes	characteristic, complemented
215	#535	C₂×C₃×C₅	1	1	yes	characteristic, complemented
216	#496	C₂×C₃×C₅	1	1	yes	characteristic, complemented
217	#493	C₂×C₃×C₅	1	1	yes	characteristic, complemented
218	#490	C₂×C₃×C₅	1	1	yes	characteristic, complemented
219	#488	C₂×C₃×C₅	1	1	yes	characteristic, complemented
220	#463	C₂×C₃×C₅	1	2	yes	complemented
221	#459	C₂×C₃×C₅	1	2	yes	complemented
222	#449	C₂×C₃×C₅	1	2	yes	complemented
223	#447	C₂×C₃×C₅	1	2	yes	complemented
224	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
225	C₂²×C₃×C₅	—	2	1	no	—
226	C₂²×C₃×C₅	—	2	2	no	—
227	C₂²×C₃×C₅	—	4	1	no	—
228	C₂²×C₃×C₅	—	4	1	no	—
229	C₂²×C₃×C₅	—	4	1	no	—
230	C₂²×C₃×C₅	—	4	2	no	—
231	C₂²×C₃×C₅	—	4	2	no	—
232	C₂²×C₃×C₅	—	4	2	no	—
233	C₂²×C₃×C₅	—	4	2	no	—
234	C₂²×C₃×C₅	—	4	2	no	—
235	C₂²×C₃×C₅	—	4	2	no	—
236	C₂²×C₃×C₅	—	8	4	no	—
237	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
238	C₃×C₄×C₅	—	2	1	no	—
239	C₃×C₄×C₅	—	2	2	no	—
240	C₃×C₄×C₅	—	2	2	no	—
241	C₃×C₄×C₅	—	4	1	no	—
242	C₃×C₄×C₅	—	4	2	no	—
243	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
244	C₂⁴×C₃	—	2	1	no	—
245	C₃×#41	—	4	2	no	—
246	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
247	C₂×C₃×D₄	—	2	1	no	—
248	C₂×C₃×D₄	—	2	2	no	—
249	C₂×C₃×D₄	—	2	1	no	—
250	C₂×C₃×D₄	—	2	2	no	—
251	C₂×C₃×D₄	—	2	2	no	—
252	C₂×C₃×D₄	—	2	2	no	—
253	C₂×C₃×D₄	—	4	2	no	—
254	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
255	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
258	C₂²×C₃×C₄	—	2	1	no	—
259	C₂²×C₃×C₄	—	2	2	no	—
260	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
261	C₃×SD₁₆	—	4	2	no	—
262	C₃×D₈	—	4	2	no	—
263	C₃×D₈	—	4	2	no	—
264	C₃×D₈	—	4	2	no	—
265	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
266	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
267	C₃×C₄⋊C₄	—	2	2	no	—
268	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
269	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
270	C₃×C₂²⋊C₄	—	2	2	no	—
271	C₃×C₂²⋊C₄	—	2	2	no	—
272	C₃×C₂²⋊C₄	—	2	2	no	—
273	C₃×C₂²⋊C₄	—	2	2	no	—
274	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
275	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
276	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
277	C₂³×C₅	—	2	2	no	—
278	C₂³×C₅	—	2	1	no	—
279	C₂³×C₅	—	2	1	no	—
280	C₂³×C₅	—	2	1	no	—
281	C₂³×C₅	—	4	2	no	—
282	C₂³×C₅	—	8	2	no	—
283	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
284	C₅×Q₈	—	2	2	no	—
285	C₅×D₄	—	2	2	no	—
286	C₅×D₄	—	2	2	no	—
287	C₅×D₄	—	2	2	no	—
288	C₅×D₄	—	2	2	no	—
289	C₅×D₄	—	2	2	no	—
290	C₅×D₄	—	4	2	no	—
291	C₅×D₄	—	4	2	no	—
292	C₅×D₄	—	8	2	no	—
293	C₅×D₄	—	8	2	no	—
294	C₅×D₄	—	8	2	no	—
295	C₅×D₄	—	8	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	4	2	no	—
300	C₂×C₄×C₅	—	8	2	no	—
301	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
302	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
303	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
305	C₅×C₈	—	2	2	no	—
306	C₅×C₈	—	2	2	no	—
307	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
308	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
309	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
310	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
311	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
312	C₂×D₈	C₂²×C₃×C₅	1	2	yes	complemented
313	#127	C₂²×C₃×C₅	1	1	yes	characteristic
314	#127	C₂²×C₃×C₅	1	1	yes	characteristic
315	#127	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
316	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
317	#124	C₂²×C₃×C₅	1	1	yes	characteristic
318	#124	C₂²×C₃×C₅	1	1	yes	characteristic
319	#123	—	2	2	no	—
320	#121	—	2	2	no	—
321	#121	—	2	2	no	—
322	#121	C₂²×C₃×C₅	1	2	yes	—
323	#120	—	2	2	no	—
324	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
325	#117	C₂²×C₃×C₅	1	1	yes	characteristic
326	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
327	#103	C₂²×C₃×C₅	1	2	yes	complemented
328	#102	C₂²×C₃×C₅	1	2	yes	—
329	#102	C₂²×C₃×C₅	1	2	yes	—
330	#102	C₂²×C₃×C₅	1	2	yes	complemented
331	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
332	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
333	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
334	C₂×C₃×C₅	—	4	1	no	—
335	C₂×C₃×C₅	—	8	1	no	—
336	C₂×C₃×C₅	—	8	2	no	—
337	C₂×C₃×C₅	—	8	1	no	—
338	C₂×C₃×C₅	—	8	1	no	—
339	C₂×C₃×C₅	#535	1	1	yes	characteristic
340	C₂×C₃×C₅	#576	1	2	yes	—
341	C₂³×C₃	—	2	2	no	—
342	C₂³×C₃	—	2	1	no	—
343	C₂³×C₃	—	2	1	no	—
344	C₂³×C₃	—	2	1	no	—
345	C₂³×C₃	—	4	2	no	—
346	C₂³×C₃	—	8	2	no	—
347	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
348	C₃×Q₈	—	2	2	no	—
349	C₃×D₄	—	2	2	no	—
350	C₃×D₄	—	2	2	no	—
351	C₃×D₄	—	2	2	no	—
352	C₃×D₄	—	2	2	no	—
353	C₃×D₄	—	2	2	no	—
354	C₃×D₄	—	4	2	no	—
355	C₃×D₄	—	4	2	no	—
356	C₃×D₄	—	8	2	no	—
357	C₃×D₄	—	8	2	no	—
358	C₃×D₄	—	8	2	no	—
359	C₃×D₄	—	8	2	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	4	2	no	—
364	C₂×C₃×C₄	—	8	2	no	—
365	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
366	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
367	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
369	C₃×C₈	—	2	2	no	—
370	C₃×C₈	—	2	2	no	—
371	C₂²×C₅	—	2	2	no	—
372	C₂²×C₅	—	2	1	no	—
373	C₂²×C₅	—	4	2	no	—
374	C₂²×C₅	—	4	2	no	—
375	C₂²×C₅	—	4	2	no	—
376	C₂²×C₅	—	4	2	no	—
377	C₂²×C₅	—	4	2	no	—
378	C₂²×C₅	—	4	1	no	—
379	C₂²×C₅	—	4	1	no	—
380	C₂²×C₅	—	4	1	no	—
381	C₂²×C₅	—	4	2	no	—
382	C₂²×C₅	—	8	4	no	—
383	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
384	C₄×C₅	—	2	2	no	—
385	C₄×C₅	—	2	2	no	—
386	C₄×C₅	—	2	1	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	—	4	1	no	—
389	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
390	C₂⁴	—	2	1	no	—
391	#41	—	4	2	no	—
392	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
401	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
402	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
403	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
407	SD₁₆	—	4	2	no	—
408	D₈	—	4	2	no	—
409	D₈	—	4	2	no	—
410	D₈	—	4	2	no	—
411	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
412	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
415	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
421	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
422	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
423	C₃×C₅	#3220	1	1	yes	characteristic, direct product factor, Hall
424	C₂²×C₃	—	2	1	no	—
425	C₂²×C₃	—	2	2	no	—
426	C₂²×C₃	—	4	1	no	—
427	C₂²×C₃	—	4	1	no	—
428	C₂²×C₃	—	4	1	no	—
429	C₂²×C₃	—	4	2	no	—
430	C₂²×C₃	—	4	2	no	—
431	C₂²×C₃	—	4	2	no	—
432	C₂²×C₃	—	4	2	no	—
433	C₂²×C₃	—	4	2	no	—
434	C₂²×C₃	—	4	2	no	—
435	C₂²×C₃	—	8	4	no	—
436	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
437	C₃×C₄	—	2	1	no	—
438	C₃×C₄	—	2	2	no	—
439	C₃×C₄	—	2	2	no	—
440	C₃×C₄	—	4	1	no	—
441	C₃×C₄	—	4	2	no	—
442	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
443	C₂×C₅	—	4	1	no	—
444	C₂×C₅	—	8	1	no	—
445	C₂×C₅	—	8	1	no	—
446	C₂×C₅	—	8	2	no	—
447	C₂×C₅	—	8	1	no	—
448	C₂×C₅	C₃×#535	1	1	yes	characteristic
449	C₂×C₅	C₃×#576	1	2	yes	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	1	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
457	Q₈	—	2	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	2	no	—
465	D₄	—	8	2	no	—
466	D₄	—	8	2	no	—
467	D₄	—	8	2	no	—
468	D₄	—	8	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	8	2	no	—
474	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
475	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
476	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
477	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₂×C₃	—	4	1	no	—
481	C₂×C₃	—	8	1	no	—
482	C₂×C₃	—	8	1	no	—
483	C₂×C₃	—	8	1	no	—
484	C₂×C₃	—	8	2	no	—
485	C₂×C₃	C₅×#535	1	1	yes	characteristic
486	C₂×C₃	C₅×#576	1	2	yes	—
487	C₅	C₃×#3220	1	1	yes	characteristic, direct product factor, Sylow
488	C₂²	—	2	1	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	8	4	no	—
500	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
501	C₄	—	2	1	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	1	no	—
505	C₄	—	4	2	no	—
506	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
507	C₃	C₅×#3220	1	1	yes	characteristic, direct product factor, Sylow
508	C₂	—	4	1	no	—
509	C₂	—	8	1	no	—
510	C₂	—	8	1	no	—
511	C₂	—	8	1	no	—
512	C₂	—	8	2	no	—
513	C₂	C₃×C₅×#535	1	1	yes	characteristic
514	C₂	C₃×C₅×#576	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×#535	C₂	semidirect
3. C₃×C₅×#496	C₂	semidirect
4. C₃×C₅×#493	C₂	semidirect
5. C₃×C₅×#490	C₂	semidirect
6. C₃×C₅×#488	C₂	semidirect
7. C₃×C₅×#463	C₂	semidirect
8. C₃×C₅×#459	C₂	semidirect
9. C₃×C₅×#449	C₂	semidirect
10. C₃×C₅×#447	C₂	semidirect
11. C₃×C₅×#433	C₂	semidirect
12. C₅×#3220	C₃	direct (N × H)
15. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
18. C₂×C₃×C₅×D₈	C₂²	semidirect
21. C₃×C₅×#127	C₂²	semidirect
22. C₃×C₅×#125	C₂²	semidirect
30. C₃×C₄×C₅×D₄	C₂²	semidirect
32. C₃×C₅×C₄⋊C₈	C₂²	semidirect
33. C₃×C₅×#103	C₂²	semidirect
36. C₃×C₅×#102	C₂²	semidirect
38. C₃×C₅×#97	C₂²	semidirect
39. C₃×C₄×C₅×C₈	C₂²	semidirect
40. C₃×#3220	C₅	direct (N × H)
41. C₅×#540	C₂×C₃	semidirect
42. C₅×#535	C₂×C₃	semidirect
43. C₅×#496	C₂×C₃	semidirect
44. C₅×#493	C₂×C₃	semidirect
45. C₅×#490	C₂×C₃	semidirect
46. C₅×#488	C₂×C₃	semidirect
47. C₅×#463	C₂×C₃	semidirect
48. C₅×#459	C₂×C₃	semidirect
49. C₅×#449	C₂×C₃	semidirect
50. C₅×#447	C₂×C₃	semidirect
51. C₅×#433	C₂×C₃	semidirect
85. C₃×#540	C₂×C₅	semidirect
86. C₃×#535	C₂×C₅	semidirect
87. C₃×#496	C₂×C₅	semidirect
88. C₃×#493	C₂×C₅	semidirect
89. C₃×#490	C₂×C₅	semidirect
90. C₃×#488	C₂×C₅	semidirect
91. C₃×#463	C₂×C₅	semidirect
92. C₃×#459	C₂×C₅	semidirect
93. C₃×#449	C₂×C₅	semidirect
94. C₃×#447	C₂×C₅	semidirect
95. C₃×#433	C₂×C₅	semidirect
98. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
101. C₂×C₅×D₈	C₂²×C₃	semidirect
104. C₅×#127	C₂²×C₃	semidirect
105. C₅×#125	C₂²×C₃	semidirect
113. C₄×C₅×D₄	C₂²×C₃	semidirect
115. C₅×C₄⋊C₈	C₂²×C₃	semidirect
116. C₅×#103	C₂²×C₃	semidirect
119. C₅×#102	C₂²×C₃	semidirect
121. C₅×#97	C₂²×C₃	semidirect
122. C₄×C₅×C₈	C₂²×C₃	semidirect
123. #3220	C₃×C₅	direct (N × H)
156. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
159. C₂×C₃×D₈	C₂²×C₅	semidirect
162. C₃×#127	C₂²×C₅	semidirect
163. C₃×#125	C₂²×C₅	semidirect
171. C₃×C₄×D₄	C₂²×C₅	semidirect
173. C₃×C₄⋊C₈	C₂²×C₅	semidirect
174. C₃×#103	C₂²×C₅	semidirect
177. C₃×#102	C₂²×C₅	semidirect
179. C₃×#97	C₂²×C₅	semidirect
180. C₃×C₄×C₈	C₂²×C₅	semidirect
214. #540	C₂×C₃×C₅	semidirect
215. #535	C₂×C₃×C₅	semidirect
216. #496	C₂×C₃×C₅	semidirect
217. #493	C₂×C₃×C₅	semidirect
218. #490	C₂×C₃×C₅	semidirect
219. #488	C₂×C₃×C₅	semidirect
220. #463	C₂×C₃×C₅	semidirect
221. #459	C₂×C₃×C₅	semidirect
222. #449	C₂×C₃×C₅	semidirect
223. #447	C₂×C₃×C₅	semidirect
224. #433	C₂×C₃×C₅	semidirect
309. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
312. C₂×D₈	C₂²×C₃×C₅	semidirect
315. #127	C₂²×C₃×C₅	semidirect
316. #125	C₂²×C₃×C₅	semidirect
324. C₄×D₄	C₂²×C₃×C₅	semidirect
326. C₄⋊C₈	C₂²×C₃×C₅	semidirect
327. #103	C₂²×C₃×C₅	semidirect
330. #102	C₂²×C₃×C₅	semidirect
332. #97	C₂²×C₃×C₅	semidirect
333. C₄×C₈	C₂²×C₃×C₅	semidirect
423. C₃×C₅	#3220	direct (N × H)
487. C₅	C₃×#3220	direct (N × H)
507. C₃	C₅×#3220	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×#535	2
C₃×C₅×#496	2
C₃×C₅×#493	2
C₃×C₅×#490	2
C₃×C₅×#488	2
C₃×C₅×#463	2
C₃×C₅×#459	2
C₃×C₅×#449	2
C₃×C₅×#447	2
C₃×C₅×#433	2
C₅×#3220	3
C₃×#3220	5

Subgroups — C3×C5×#3220 #14276254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3220 #14276254