Subgroups — C₃×C₅×#3305 #14276339

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#482	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#466	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#416	C₂	1	2	yes	maximal, complemented
12	C₅×#3305	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
16	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#127	—	2	1	no	—
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic
20	C₃×C₅×#124	—	2	2	no	—
21	C₃×C₅×#121	—	2	1	no	—
22	C₃×C₅×#121	—	2	2	no	—
23	C₃×C₅×#121	C₂²	1	2	yes	—
24	C₃×C₅×#121	C₂²	1	2	yes	—
25	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₄×C₅×D₄	—	2	1	no	—
27	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₃×C₅×#117	—	2	1	no	—
30	C₃×C₅×#117	C₂²	1	2	yes	—
31	C₃×C₅×#107	C₂²	1	2	yes	—
32	C₃×C₅×#106	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×#103	C₂²	1	2	yes	—
35	C₃×C₅×#103	C₂²	1	1	yes	characteristic
36	C₃×C₅×#102	C₂²	1	2	yes	—
37	C₃×C₅×#102	C₂²	1	2	yes	—
38	C₃×C₅×#102	C₂²	1	1	yes	characteristic
39	C₃×C₅×#102	C₂²	1	2	yes	—
40	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
41	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₃×#3305	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#555	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#550	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#482	C₂×C₃	1	2	yes	complemented
47	C₅×#477	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#466	C₂×C₃	1	2	yes	complemented
49	C₅×#459	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#449	C₂×C₃	1	2	yes	complemented
51	C₄×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#416	C₂×C₃	1	2	yes	complemented
54	C₃×C₅×#41	—	2	4	no	—
55	C₃×C₅×#41	—	4	2	no	—
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
62	C₂×C₃×C₅×D₄	—	2	1	no	—
63	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
66	C₂²×C₃×C₄×C₅	—	2	1	no	—
67	C₂²×C₃×C₄×C₅	—	2	2	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
69	C₃×C₅×SD₁₆	—	2	2	no	—
70	C₃×C₅×D₈	—	4	2	no	—
71	C₂×C₃×C₅×C₈	—	4	2	no	—
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₃×C₅×C₄⋊C₄	—	2	1	no	—
76	C₃×C₅×C₄⋊C₄	—	2	1	no	—
77	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
78	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
82	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
86	C₃×C₄²×C₅	—	2	2	no	—
87	C₃×C₄²×C₅	—	2	1	no	—
88	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₃×#555	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#550	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#482	C₂×C₅	1	2	yes	complemented
93	C₃×#477	C₂×C₅	1	1	yes	characteristic, complemented
94	C₃×#466	C₂×C₅	1	2	yes	complemented
95	C₃×#459	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#449	C₂×C₅	1	2	yes	complemented
97	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#416	C₂×C₅	1	2	yes	complemented
100	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
101	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
103	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
104	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₅×#127	—	2	1	no	—
106	C₅×#127	C₂²×C₃	1	1	yes	characteristic
107	C₅×#124	—	2	2	no	—
108	C₅×#121	—	2	1	no	—
109	C₅×#121	—	2	2	no	—
110	C₅×#121	C₂²×C₃	1	2	yes	—
111	C₅×#121	C₂²×C₃	1	2	yes	—
112	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
113	C₄×C₅×D₄	—	2	1	no	—
114	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
115	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
116	C₅×#117	—	2	1	no	—
117	C₅×#117	C₂²×C₃	1	2	yes	—
118	C₅×#107	C₂²×C₃	1	2	yes	—
119	C₅×#106	C₂²×C₃	1	1	yes	characteristic
120	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
121	C₅×#103	C₂²×C₃	1	1	yes	characteristic
122	C₅×#103	C₂²×C₃	1	2	yes	—
123	C₅×#102	C₂²×C₃	1	2	yes	—
124	C₅×#102	C₂²×C₃	1	2	yes	—
125	C₅×#102	C₂²×C₃	1	1	yes	characteristic
126	C₅×#102	C₂²×C₃	1	2	yes	—
127	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
128	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
129	#3305	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
130	C₂³×C₃×C₅	—	2	1	no	—
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
133	C₃×C₅×Q₈	—	2	1	no	—
134	C₃×C₅×Q₈	—	8	1	no	—
135	C₃×C₅×Q₈	#41	1	2	yes	—
136	C₃×C₅×D₄	—	2	2	no	—
137	C₃×C₅×D₄	—	2	1	no	—
138	C₃×C₅×D₄	—	2	2	no	—
139	C₃×C₅×D₄	—	2	1	no	—
140	C₃×C₅×D₄	—	2	2	no	—
141	C₃×C₅×D₄	—	4	4	no	—
142	C₃×C₅×D₄	—	4	2	no	—
143	C₃×C₅×D₄	—	8	1	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	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	4	4	no	—
153	C₂×C₃×C₄×C₅	—	4	2	no	—
154	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
158	C₃×C₅×C₈	—	2	1	no	—
159	C₃×C₅×C₈	—	2	1	no	—
160	C₃×C₅×C₈	—	2	2	no	—
161	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
162	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
164	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
165	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
166	C₃×#127	—	2	1	no	—
167	C₃×#127	C₂²×C₅	1	1	yes	characteristic
168	C₃×#124	—	2	2	no	—
169	C₃×#121	—	2	1	no	—
170	C₃×#121	—	2	2	no	—
171	C₃×#121	C₂²×C₅	1	2	yes	—
172	C₃×#121	C₂²×C₅	1	2	yes	—
173	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
174	C₃×C₄×D₄	—	2	1	no	—
175	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
176	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
177	C₃×#117	—	2	1	no	—
178	C₃×#117	C₂²×C₅	1	2	yes	—
179	C₃×#107	C₂²×C₅	1	2	yes	—
180	C₃×#106	C₂²×C₅	1	1	yes	characteristic
181	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
182	C₃×#103	C₂²×C₅	1	1	yes	characteristic
183	C₃×#103	C₂²×C₅	1	2	yes	—
184	C₃×#102	C₂²×C₅	1	2	yes	—
185	C₃×#102	C₂²×C₅	1	2	yes	—
186	C₃×#102	C₂²×C₅	1	1	yes	characteristic
187	C₃×#102	C₂²×C₅	1	2	yes	—
188	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
189	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
190	C₅×#41	—	2	4	no	—
191	C₅×#41	—	4	2	no	—
192	C₂×C₅×Q₈	—	2	1	no	—
193	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₅×D₄	—	2	2	no	—
195	C₂×C₅×D₄	—	2	2	no	—
196	C₂×C₅×D₄	—	2	2	no	—
197	C₂×C₅×D₄	—	2	1	no	—
198	C₂×C₅×D₄	—	2	1	no	—
199	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
200	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
202	C₂²×C₄×C₅	—	2	1	no	—
203	C₂²×C₄×C₅	—	2	2	no	—
204	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
205	C₅×SD₁₆	—	2	2	no	—
206	C₅×D₈	—	4	2	no	—
207	C₂×C₅×C₈	—	4	2	no	—
208	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
210	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
214	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
215	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
216	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
217	C₅×C₂²⋊C₄	—	2	2	no	—
218	C₅×C₂²⋊C₄	—	2	2	no	—
219	C₅×C₂²⋊C₄	—	2	2	no	—
220	C₅×C₂²⋊C₄	—	2	1	no	—
221	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
222	C₄²×C₅	—	2	2	no	—
223	C₄²×C₅	—	2	1	no	—
224	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
225	#555	C₂×C₃×C₅	1	1	yes	characteristic, complemented
226	#550	C₂×C₃×C₅	1	1	yes	characteristic, complemented
227	#486	C₂×C₃×C₅	1	1	yes	characteristic, complemented
228	#482	C₂×C₃×C₅	1	2	yes	complemented
229	#477	C₂×C₃×C₅	1	1	yes	characteristic, complemented
230	#466	C₂×C₃×C₅	1	2	yes	complemented
231	#459	C₂×C₃×C₅	1	1	yes	characteristic, complemented
232	#449	C₂×C₃×C₅	1	2	yes	complemented
233	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
234	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	#416	C₂×C₃×C₅	1	2	yes	complemented
236	C₂²×C₃×C₅	—	2	2	no	—
237	C₂²×C₃×C₅	—	2	2	no	—
238	C₂²×C₃×C₅	—	2	2	no	—
239	C₂²×C₃×C₅	—	4	2	no	—
240	C₂²×C₃×C₅	—	4	1	no	—
241	C₂²×C₃×C₅	—	4	1	no	—
242	C₂²×C₃×C₅	—	4	2	no	—
243	C₂²×C₃×C₅	—	4	2	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₃×C₄×C₅	—	2	2	no	—
247	C₃×C₄×C₅	—	2	2	no	—
248	C₃×C₄×C₅	—	2	1	no	—
249	C₃×C₄×C₅	—	4	1	no	—
250	C₃×C₄×C₅	—	4	1	no	—
251	C₃×C₄×C₅	—	4	2	no	—
252	C₃×C₄×C₅	#135	1	2	yes	—
253	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
254	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
255	C₃×#41	—	2	4	no	—
256	C₃×#41	—	4	2	no	—
257	C₂×C₃×Q₈	—	2	1	no	—
258	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₃×D₄	—	2	2	no	—
260	C₂×C₃×D₄	—	2	2	no	—
261	C₂×C₃×D₄	—	2	2	no	—
262	C₂×C₃×D₄	—	2	1	no	—
263	C₂×C₃×D₄	—	2	1	no	—
264	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
265	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
266	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
267	C₂²×C₃×C₄	—	2	1	no	—
268	C₂²×C₃×C₄	—	2	2	no	—
269	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
270	C₃×SD₁₆	—	2	2	no	—
271	C₃×D₈	—	4	2	no	—
272	C₂×C₃×C₈	—	4	2	no	—
273	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
275	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
276	C₃×C₄⋊C₄	—	2	1	no	—
277	C₃×C₄⋊C₄	—	2	1	no	—
278	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
279	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
280	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
281	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
282	C₃×C₂²⋊C₄	—	2	2	no	—
283	C₃×C₂²⋊C₄	—	2	2	no	—
284	C₃×C₂²⋊C₄	—	2	2	no	—
285	C₃×C₂²⋊C₄	—	2	1	no	—
286	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
287	C₃×C₄²	—	2	2	no	—
288	C₃×C₄²	—	2	1	no	—
289	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
290	C₂³×C₅	—	2	1	no	—
291	C₂³×C₅	—	2	2	no	—
292	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
293	C₅×Q₈	—	2	1	no	—
294	C₅×Q₈	—	8	1	no	—
295	C₅×Q₈	C₃×#41	1	2	yes	—
296	C₅×D₄	—	2	2	no	—
297	C₅×D₄	—	2	1	no	—
298	C₅×D₄	—	2	2	no	—
299	C₅×D₄	—	2	1	no	—
300	C₅×D₄	—	2	2	no	—
301	C₅×D₄	—	4	4	no	—
302	C₅×D₄	—	4	2	no	—
303	C₅×D₄	—	8	1	no	—
304	C₅×D₄	—	8	2	no	—
305	C₅×D₄	—	8	2	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	4	4	no	—
313	C₂×C₄×C₅	—	4	2	no	—
314	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
315	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
318	C₅×C₈	—	2	1	no	—
319	C₅×C₈	—	2	1	no	—
320	C₅×C₈	—	2	2	no	—
321	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
322	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
323	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
324	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
325	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
326	#127	—	2	1	no	—
327	#127	C₂²×C₃×C₅	1	1	yes	characteristic
328	#124	—	2	2	no	—
329	#121	—	2	1	no	—
330	#121	—	2	2	no	—
331	#121	C₂²×C₃×C₅	1	2	yes	—
332	#121	C₂²×C₃×C₅	1	2	yes	—
333	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
336	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
337	#117	—	2	1	no	—
338	#117	C₂²×C₃×C₅	1	2	yes	—
339	#107	C₂²×C₃×C₅	1	2	yes	—
340	#106	C₂²×C₃×C₅	1	1	yes	characteristic
341	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
342	#103	C₂²×C₃×C₅	1	1	yes	characteristic
343	#103	C₂²×C₃×C₅	1	2	yes	—
344	#102	C₂²×C₃×C₅	1	2	yes	—
345	#102	C₂²×C₃×C₅	1	2	yes	—
346	#102	C₂²×C₃×C₅	1	1	yes	characteristic
347	#102	C₂²×C₃×C₅	1	2	yes	—
348	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
349	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
350	C₂×C₃×C₅	—	4	2	no	—
351	C₂×C₃×C₅	—	8	2	no	—
352	C₂×C₃×C₅	—	8	1	no	—
353	C₂×C₃×C₅	#546	1	1	yes	characteristic
354	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
355	C₂×C₃×C₅	#576	1	1	yes	characteristic
356	C₂³×C₃	—	2	1	no	—
357	C₂³×C₃	—	2	2	no	—
358	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
359	C₃×Q₈	—	2	1	no	—
360	C₃×Q₈	—	8	1	no	—
361	C₃×Q₈	C₅×#41	1	2	yes	—
362	C₃×D₄	—	2	2	no	—
363	C₃×D₄	—	2	1	no	—
364	C₃×D₄	—	2	2	no	—
365	C₃×D₄	—	2	1	no	—
366	C₃×D₄	—	2	2	no	—
367	C₃×D₄	—	4	4	no	—
368	C₃×D₄	—	4	2	no	—
369	C₃×D₄	—	8	1	no	—
370	C₃×D₄	—	8	2	no	—
371	C₃×D₄	—	8	2	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	4	4	no	—
379	C₂×C₃×C₄	—	4	2	no	—
380	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
381	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
384	C₃×C₈	—	2	1	no	—
385	C₃×C₈	—	2	1	no	—
386	C₃×C₈	—	2	2	no	—
387	C₂²×C₅	—	2	2	no	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	2	2	no	—
390	C₂²×C₅	—	4	1	no	—
391	C₂²×C₅	—	4	2	no	—
392	C₂²×C₅	—	4	2	no	—
393	C₂²×C₅	—	4	1	no	—
394	C₂²×C₅	—	4	2	no	—
395	C₂²×C₅	—	4	1	no	—
396	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
397	C₄×C₅	—	2	1	no	—
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	2	2	no	—
400	C₄×C₅	—	4	1	no	—
401	C₄×C₅	—	4	1	no	—
402	C₄×C₅	—	4	2	no	—
403	C₄×C₅	C₃×#135	1	2	yes	—
404	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
405	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
406	#41	—	2	4	no	—
407	#41	—	4	2	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
416	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
417	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
421	SD₁₆	—	2	2	no	—
422	D₈	—	4	2	no	—
423	C₂×C₈	—	4	2	no	—
424	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
425	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
426	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
430	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
431	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
432	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	1	no	—
440	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
441	C₃×C₅	#3305	1	1	yes	characteristic, direct product factor, Hall
442	C₂²×C₃	—	2	2	no	—
443	C₂²×C₃	—	2	2	no	—
444	C₂²×C₃	—	2	2	no	—
445	C₂²×C₃	—	4	2	no	—
446	C₂²×C₃	—	4	1	no	—
447	C₂²×C₃	—	4	1	no	—
448	C₂²×C₃	—	4	2	no	—
449	C₂²×C₃	—	4	2	no	—
450	C₂²×C₃	—	4	1	no	—
451	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	2	1	no	—
455	C₃×C₄	—	4	1	no	—
456	C₃×C₄	—	4	1	no	—
457	C₃×C₄	—	4	2	no	—
458	C₃×C₄	C₅×#135	1	2	yes	—
459	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
460	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂×C₅	—	4	2	no	—
462	C₂×C₅	—	8	1	no	—
463	C₂×C₅	—	8	2	no	—
464	C₂×C₅	C₃×#546	1	1	yes	characteristic
465	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
466	C₂×C₅	C₃×#576	1	1	yes	characteristic
467	C₂³	—	2	1	no	—
468	C₂³	—	2	2	no	—
469	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
470	Q₈	—	2	1	no	—
471	Q₈	—	8	1	no	—
472	Q₈	C₃×C₅×#41	1	2	yes	—
473	D₄	—	2	1	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	1	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	2	no	—
478	D₄	—	4	4	no	—
479	D₄	—	4	2	no	—
480	D₄	—	8	1	no	—
481	D₄	—	8	2	no	—
482	D₄	—	8	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
492	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
493	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
494	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
495	C₈	—	2	1	no	—
496	C₈	—	2	1	no	—
497	C₈	—	2	2	no	—
498	C₂×C₃	—	4	2	no	—
499	C₂×C₃	—	8	2	no	—
500	C₂×C₃	—	8	1	no	—
501	C₂×C₃	C₅×#546	1	1	yes	characteristic
502	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
503	C₂×C₃	C₅×#576	1	1	yes	characteristic
504	C₅	C₃×#3305	1	1	yes	characteristic, direct product factor, Sylow
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	1	no	—
514	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	2	no	—
521	C₄	C₃×C₅×#135	1	2	yes	—
522	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
523	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
524	C₃	C₅×#3305	1	1	yes	characteristic, direct product factor, Sylow
525	C₂	—	4	2	no	—
526	C₂	—	8	2	no	—
527	C₂	—	8	1	no	—
528	C₂	C₃×C₅×#546	1	1	yes	characteristic
529	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
530	C₂	C₃×C₅×#576	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 ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#555	C₂	semidirect
2. C₃×C₅×#550	C₂	semidirect
3. C₃×C₅×#486	C₂	semidirect
4. C₃×C₅×#482	C₂	semidirect
5. C₃×C₅×#477	C₂	semidirect
6. C₃×C₅×#466	C₂	semidirect
7. C₃×C₅×#459	C₂	semidirect
8. C₃×C₅×#449	C₂	semidirect
9. C₃×C₄×C₅×SD₁₆	C₂	semidirect
10. C₃×C₅×C₈×D₄	C₂	semidirect
11. C₃×C₅×#416	C₂	semidirect
12. C₅×#3305	C₃	direct (N × H)
42. C₃×#3305	C₅	direct (N × H)
43. C₅×#555	C₂×C₃	semidirect
44. C₅×#550	C₂×C₃	semidirect
45. C₅×#486	C₂×C₃	semidirect
46. C₅×#482	C₂×C₃	semidirect
47. C₅×#477	C₂×C₃	semidirect
48. C₅×#466	C₂×C₃	semidirect
49. C₅×#459	C₂×C₃	semidirect
50. C₅×#449	C₂×C₃	semidirect
51. C₄×C₅×SD₁₆	C₂×C₃	semidirect
52. C₅×C₈×D₄	C₂×C₃	semidirect
53. C₅×#416	C₂×C₃	semidirect
89. C₃×#555	C₂×C₅	semidirect
90. C₃×#550	C₂×C₅	semidirect
91. C₃×#486	C₂×C₅	semidirect
92. C₃×#482	C₂×C₅	semidirect
93. C₃×#477	C₂×C₅	semidirect
94. C₃×#466	C₂×C₅	semidirect
95. C₃×#459	C₂×C₅	semidirect
96. C₃×#449	C₂×C₅	semidirect
97. C₃×C₄×SD₁₆	C₂×C₅	semidirect
98. C₃×C₈×D₄	C₂×C₅	semidirect
99. C₃×#416	C₂×C₅	semidirect
129. #3305	C₃×C₅	direct (N × H)
225. #555	C₂×C₃×C₅	semidirect
226. #550	C₂×C₃×C₅	semidirect
227. #486	C₂×C₃×C₅	semidirect
228. #482	C₂×C₃×C₅	semidirect
229. #477	C₂×C₃×C₅	semidirect
230. #466	C₂×C₃×C₅	semidirect
231. #459	C₂×C₃×C₅	semidirect
232. #449	C₂×C₃×C₅	semidirect
233. C₄×SD₁₆	C₂×C₃×C₅	semidirect
234. C₈×D₄	C₂×C₃×C₅	semidirect
235. #416	C₂×C₃×C₅	semidirect
441. C₃×C₅	#3305	direct (N × H)
504. C₅	C₃×#3305	direct (N × H)
524. C₃	C₅×#3305	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×#555	2
C₃×C₅×#550	2
C₃×C₅×#486	2
C₃×C₅×#482	2
C₃×C₅×#477	2
C₃×C₅×#466	2
C₃×C₅×#459	2
C₃×C₅×#449	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×C₈×D₄	2
C₃×C₅×#416	2
C₅×#3305	3
C₃×#3305	5

Subgroups — C3×C5×#3305 #14276339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3305 #14276339