Subgroups — C₃×C₅×#3303 #14276337

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 524 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×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#485	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×D₈	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×#3303	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	2	yes	—
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×#124	—	2	2	no	—
20	C₃×C₅×#123	—	2	2	no	—
21	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₃×C₅×#121	—	2	1	no	—
23	C₃×C₅×#121	—	2	1	no	—
24	C₃×C₅×#121	C₂²	1	2	yes	—
25	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₅×#117	—	2	1	no	—
29	C₃×C₅×#117	C₂²	1	2	yes	—
30	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
31	C₃×C₅×#107	C₂²	1	1	yes	characteristic
32	C₃×C₅×#106	C₂²	1	2	yes	—
33	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×#103	C₂²	1	2	yes	—
35	C₃×C₅×#103	C₂²	1	2	yes	—
36	C₃×C₅×#103	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	1	yes	characteristic
40	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
41	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₃×#3303	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#555	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#487	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#485	C₂×C₃	1	2	yes	complemented
47	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#465	C₂×C₃	1	2	yes	complemented
49	C₅×#461	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#449	C₂×C₃	1	2	yes	complemented
51	C₄×C₅×D₈	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	2	yes	—
58	C₂×C₃×C₅×D₄	—	2	2	no	—
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂²×C₃×C₄×C₅	—	2	2	no	—
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₃×C₅×SD₁₆	—	4	2	no	—
68	C₃×C₅×D₈	—	2	2	no	—
69	C₂×C₃×C₅×C₈	—	4	2	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	—	2	1	no	—
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
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	—	2	1	no	—
86	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
87	C₃×C₄²×C₅	—	2	2	no	—
88	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₃×#555	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×#487	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#485	C₂×C₅	1	2	yes	complemented
93	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
94	C₃×#465	C₂×C₅	1	2	yes	complemented
95	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#449	C₂×C₅	1	2	yes	complemented
97	C₃×C₄×D₈	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	2	yes	—
102	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
103	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
104	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
106	C₅×#124	—	2	2	no	—
107	C₅×#123	—	2	2	no	—
108	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
109	C₅×#121	—	2	1	no	—
110	C₅×#121	—	2	1	no	—
111	C₅×#121	C₂²×C₃	1	2	yes	—
112	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
113	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
114	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
115	C₅×#117	—	2	1	no	—
116	C₅×#117	C₂²×C₃	1	2	yes	—
117	C₂×C₅×C₄⋊C₄	—	2	1	no	—
118	C₅×#107	C₂²×C₃	1	1	yes	characteristic
119	C₅×#106	C₂²×C₃	1	2	yes	—
120	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
121	C₅×#103	C₂²×C₃	1	2	yes	—
122	C₅×#103	C₂²×C₃	1	2	yes	—
123	C₅×#103	C₂²×C₃	1	2	yes	—
124	C₅×#102	C₂²×C₃	1	1	yes	characteristic
125	C₅×#102	C₂²×C₃	1	2	yes	—
126	C₅×#102	C₂²×C₃	1	1	yes	characteristic
127	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
128	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
129	#3303	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
130	C₂³×C₃×C₅	—	2	1	no	—
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×Q₈	—	8	1	no	—
136	C₃×C₅×D₄	—	2	2	no	—
137	C₃×C₅×D₄	—	2	1	no	—
138	C₃×C₅×D₄	—	2	1	no	—
139	C₃×C₅×D₄	—	2	1	no	—
140	C₃×C₅×D₄	—	4	4	no	—
141	C₃×C₅×D₄	—	8	2	no	—
142	C₃×C₅×D₄	#41	1	2	yes	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	4	4	no	—
150	C₂×C₃×C₄×C₅	—	4	2	no	—
151	C₂×C₃×C₄×C₅	—	4	2	no	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₃×C₅×C₈	—	2	1	no	—
157	C₃×C₅×C₈	—	2	1	no	—
158	C₃×C₅×C₈	—	2	2	no	—
159	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
160	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
161	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
162	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
163	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
164	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
165	C₃×#124	—	2	2	no	—
166	C₃×#123	—	2	2	no	—
167	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
168	C₃×#121	—	2	1	no	—
169	C₃×#121	—	2	1	no	—
170	C₃×#121	C₂²×C₅	1	2	yes	—
171	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
172	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
173	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
174	C₃×#117	—	2	1	no	—
175	C₃×#117	C₂²×C₅	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	—	2	1	no	—
177	C₃×#107	C₂²×C₅	1	1	yes	characteristic
178	C₃×#106	C₂²×C₅	1	2	yes	—
179	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
180	C₃×#103	C₂²×C₅	1	2	yes	—
181	C₃×#103	C₂²×C₅	1	2	yes	—
182	C₃×#103	C₂²×C₅	1	2	yes	—
183	C₃×#102	C₂²×C₅	1	1	yes	characteristic
184	C₃×#102	C₂²×C₅	1	2	yes	—
185	C₃×#102	C₂²×C₅	1	1	yes	characteristic
186	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
187	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
188	C₅×#41	—	2	4	no	—
189	C₅×#41	—	4	2	no	—
190	C₂×C₅×Q₈	—	2	1	no	—
191	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
192	C₂×C₅×D₄	—	2	2	no	—
193	C₂×C₅×D₄	—	2	2	no	—
194	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
195	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
197	C₂²×C₄×C₅	—	2	1	no	—
198	C₂²×C₄×C₅	—	2	2	no	—
199	C₂²×C₄×C₅	—	2	1	no	—
200	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
201	C₅×SD₁₆	—	4	2	no	—
202	C₅×D₈	—	2	2	no	—
203	C₂×C₅×C₈	—	4	2	no	—
204	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
206	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	2	2	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
212	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
213	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
214	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
215	C₅×C₂²⋊C₄	—	2	2	no	—
216	C₅×C₂²⋊C₄	—	2	2	no	—
217	C₅×C₂²⋊C₄	—	2	2	no	—
218	C₅×C₂²⋊C₄	—	2	1	no	—
219	C₅×C₂²⋊C₄	—	2	1	no	—
220	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
221	C₄²×C₅	—	2	2	no	—
222	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
223	#555	C₂×C₃×C₅	1	1	yes	characteristic, complemented
224	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
225	#487	C₂×C₃×C₅	1	1	yes	characteristic, complemented
226	#485	C₂×C₃×C₅	1	2	yes	complemented
227	#476	C₂×C₃×C₅	1	1	yes	characteristic, complemented
228	#465	C₂×C₃×C₅	1	2	yes	complemented
229	#461	C₂×C₃×C₅	1	1	yes	characteristic, complemented
230	#449	C₂×C₃×C₅	1	2	yes	complemented
231	C₄×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
232	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
233	#416	C₂×C₃×C₅	1	2	yes	complemented
234	C₂²×C₃×C₅	—	2	2	no	—
235	C₂²×C₃×C₅	—	2	2	no	—
236	C₂²×C₃×C₅	—	2	2	no	—
237	C₂²×C₃×C₅	—	2	2	no	—
238	C₂²×C₃×C₅	—	4	1	no	—
239	C₂²×C₃×C₅	—	4	1	no	—
240	C₂²×C₃×C₅	—	4	1	no	—
241	C₂²×C₃×C₅	—	4	1	no	—
242	C₂²×C₃×C₅	—	4	1	no	—
243	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₃×C₄×C₅	—	2	2	no	—
245	C₃×C₄×C₅	—	2	1	no	—
246	C₃×C₄×C₅	—	4	2	no	—
247	C₃×C₄×C₅	—	4	1	no	—
248	C₃×C₄×C₅	—	4	1	no	—
249	C₃×C₄×C₅	—	4	2	no	—
250	C₃×C₄×C₅	#135	1	2	yes	—
251	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
252	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
253	C₃×#41	—	2	4	no	—
254	C₃×#41	—	4	2	no	—
255	C₂×C₃×Q₈	—	2	1	no	—
256	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
257	C₂×C₃×D₄	—	2	2	no	—
258	C₂×C₃×D₄	—	2	2	no	—
259	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
260	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
261	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₃×C₄	—	2	1	no	—
263	C₂²×C₃×C₄	—	2	2	no	—
264	C₂²×C₃×C₄	—	2	1	no	—
265	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
266	C₃×SD₁₆	—	4	2	no	—
267	C₃×D₈	—	2	2	no	—
268	C₂×C₃×C₈	—	4	2	no	—
269	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
270	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
272	C₃×C₄⋊C₄	—	2	1	no	—
273	C₃×C₄⋊C₄	—	2	2	no	—
274	C₃×C₄⋊C₄	—	2	1	no	—
275	C₃×C₄⋊C₄	—	2	1	no	—
276	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
277	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
278	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
279	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
280	C₃×C₂²⋊C₄	—	2	2	no	—
281	C₃×C₂²⋊C₄	—	2	2	no	—
282	C₃×C₂²⋊C₄	—	2	2	no	—
283	C₃×C₂²⋊C₄	—	2	1	no	—
284	C₃×C₂²⋊C₄	—	2	1	no	—
285	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
286	C₃×C₄²	—	2	2	no	—
287	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
291	C₅×Q₈	—	2	2	no	—
292	C₅×Q₈	—	2	2	no	—
293	C₅×Q₈	—	8	1	no	—
294	C₅×D₄	—	2	2	no	—
295	C₅×D₄	—	2	1	no	—
296	C₅×D₄	—	2	1	no	—
297	C₅×D₄	—	2	1	no	—
298	C₅×D₄	—	4	4	no	—
299	C₅×D₄	—	8	2	no	—
300	C₅×D₄	C₃×#41	1	2	yes	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	4	4	no	—
308	C₂×C₄×C₅	—	4	2	no	—
309	C₂×C₄×C₅	—	4	2	no	—
310	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
311	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
314	C₅×C₈	—	2	1	no	—
315	C₅×C₈	—	2	1	no	—
316	C₅×C₈	—	2	2	no	—
317	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
318	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
319	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
320	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
321	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
322	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
323	#124	—	2	2	no	—
324	#123	—	2	2	no	—
325	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
326	#121	—	2	1	no	—
327	#121	—	2	1	no	—
328	#121	C₂²×C₃×C₅	1	2	yes	—
329	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
330	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
331	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
332	#117	—	2	1	no	—
333	#117	C₂²×C₃×C₅	1	2	yes	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	#107	C₂²×C₃×C₅	1	1	yes	characteristic
336	#106	C₂²×C₃×C₅	1	2	yes	—
337	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
338	#103	C₂²×C₃×C₅	1	2	yes	—
339	#103	C₂²×C₃×C₅	1	2	yes	—
340	#103	C₂²×C₃×C₅	1	2	yes	—
341	#102	C₂²×C₃×C₅	1	1	yes	characteristic
342	#102	C₂²×C₃×C₅	1	2	yes	—
343	#102	C₂²×C₃×C₅	1	1	yes	characteristic
344	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
345	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
346	C₂×C₃×C₅	—	4	2	no	—
347	C₂×C₃×C₅	—	4	2	no	—
348	C₂×C₃×C₅	—	8	1	no	—
349	C₂×C₃×C₅	#546	1	1	yes	characteristic
350	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
351	C₂×C₃×C₅	#577	1	1	yes	characteristic
352	C₂³×C₃	—	2	1	no	—
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
355	C₃×Q₈	—	2	2	no	—
356	C₃×Q₈	—	2	2	no	—
357	C₃×Q₈	—	8	1	no	—
358	C₃×D₄	—	2	2	no	—
359	C₃×D₄	—	2	1	no	—
360	C₃×D₄	—	2	1	no	—
361	C₃×D₄	—	2	1	no	—
362	C₃×D₄	—	4	4	no	—
363	C₃×D₄	—	8	2	no	—
364	C₃×D₄	C₅×#41	1	2	yes	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	4	4	no	—
372	C₂×C₃×C₄	—	4	2	no	—
373	C₂×C₃×C₄	—	4	2	no	—
374	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
375	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
378	C₃×C₈	—	2	1	no	—
379	C₃×C₈	—	2	1	no	—
380	C₃×C₈	—	2	2	no	—
381	C₂²×C₅	—	2	2	no	—
382	C₂²×C₅	—	2	2	no	—
383	C₂²×C₅	—	2	2	no	—
384	C₂²×C₅	—	2	2	no	—
385	C₂²×C₅	—	4	1	no	—
386	C₂²×C₅	—	4	1	no	—
387	C₂²×C₅	—	4	1	no	—
388	C₂²×C₅	—	4	1	no	—
389	C₂²×C₅	—	4	1	no	—
390	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
391	C₄×C₅	—	2	1	no	—
392	C₄×C₅	—	2	2	no	—
393	C₄×C₅	—	4	1	no	—
394	C₄×C₅	—	4	1	no	—
395	C₄×C₅	—	4	2	no	—
396	C₄×C₅	—	4	2	no	—
397	C₄×C₅	C₃×#135	1	2	yes	—
398	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
399	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
400	#41	—	2	4	no	—
401	#41	—	4	2	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
407	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
408	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
413	SD₁₆	—	4	2	no	—
414	D₈	—	2	2	no	—
415	C₂×C₈	—	4	2	no	—
416	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
417	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
418	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
424	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
425	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
426	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
433	C₄²	—	2	2	no	—
434	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
435	C₃×C₅	#3303	1	1	yes	characteristic, direct product factor, Hall
436	C₂²×C₃	—	2	2	no	—
437	C₂²×C₃	—	2	2	no	—
438	C₂²×C₃	—	2	2	no	—
439	C₂²×C₃	—	2	2	no	—
440	C₂²×C₃	—	4	1	no	—
441	C₂²×C₃	—	4	1	no	—
442	C₂²×C₃	—	4	1	no	—
443	C₂²×C₃	—	4	1	no	—
444	C₂²×C₃	—	4	1	no	—
445	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
446	C₃×C₄	—	2	2	no	—
447	C₃×C₄	—	2	1	no	—
448	C₃×C₄	—	4	2	no	—
449	C₃×C₄	—	4	1	no	—
450	C₃×C₄	—	4	1	no	—
451	C₃×C₄	—	4	2	no	—
452	C₃×C₄	C₅×#135	1	2	yes	—
453	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
454	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
455	C₂×C₅	—	4	2	no	—
456	C₂×C₅	—	4	2	no	—
457	C₂×C₅	—	8	1	no	—
458	C₂×C₅	C₃×#546	1	1	yes	characteristic
459	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
460	C₂×C₅	C₃×#577	1	1	yes	characteristic
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
464	Q₈	—	2	2	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	8	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	1	no	—
469	D₄	—	2	1	no	—
470	D₄	—	2	2	no	—
471	D₄	—	4	4	no	—
472	D₄	—	8	2	no	—
473	D₄	C₃×C₅×#41	1	2	yes	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
484	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
485	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
486	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
487	C₈	—	2	1	no	—
488	C₈	—	2	1	no	—
489	C₈	—	2	2	no	—
490	C₂×C₃	—	4	2	no	—
491	C₂×C₃	—	4	2	no	—
492	C₂×C₃	—	8	1	no	—
493	C₂×C₃	C₅×#546	1	1	yes	characteristic
494	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
495	C₂×C₃	C₅×#577	1	1	yes	characteristic
496	C₅	C₃×#3303	1	1	yes	characteristic, direct product factor, Sylow
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	2	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	C₃×C₅×#135	1	2	yes	—
514	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
515	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
516	C₃	C₅×#3303	1	1	yes	characteristic, direct product factor, Sylow
517	C₂	—	4	2	no	—
518	C₂	—	4	2	no	—
519	C₂	—	8	1	no	—
520	C₂	C₃×C₅×#546	1	1	yes	characteristic
521	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
522	C₂	C₃×C₅×#577	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×#547	C₂	semidirect
3. C₃×C₅×#487	C₂	semidirect
4. C₃×C₅×#485	C₂	semidirect
5. C₃×C₅×#476	C₂	semidirect
6. C₃×C₅×#465	C₂	semidirect
7. C₃×C₅×#461	C₂	semidirect
8. C₃×C₅×#449	C₂	semidirect
9. C₃×C₄×C₅×D₈	C₂	semidirect
10. C₃×C₅×C₈×D₄	C₂	semidirect
11. C₃×C₅×#416	C₂	semidirect
12. C₅×#3303	C₃	direct (N × H)
42. C₃×#3303	C₅	direct (N × H)
43. C₅×#555	C₂×C₃	semidirect
44. C₅×#547	C₂×C₃	semidirect
45. C₅×#487	C₂×C₃	semidirect
46. C₅×#485	C₂×C₃	semidirect
47. C₅×#476	C₂×C₃	semidirect
48. C₅×#465	C₂×C₃	semidirect
49. C₅×#461	C₂×C₃	semidirect
50. C₅×#449	C₂×C₃	semidirect
51. C₄×C₅×D₈	C₂×C₃	semidirect
52. C₅×C₈×D₄	C₂×C₃	semidirect
53. C₅×#416	C₂×C₃	semidirect
89. C₃×#555	C₂×C₅	semidirect
90. C₃×#547	C₂×C₅	semidirect
91. C₃×#487	C₂×C₅	semidirect
92. C₃×#485	C₂×C₅	semidirect
93. C₃×#476	C₂×C₅	semidirect
94. C₃×#465	C₂×C₅	semidirect
95. C₃×#461	C₂×C₅	semidirect
96. C₃×#449	C₂×C₅	semidirect
97. C₃×C₄×D₈	C₂×C₅	semidirect
98. C₃×C₈×D₄	C₂×C₅	semidirect
99. C₃×#416	C₂×C₅	semidirect
129. #3303	C₃×C₅	direct (N × H)
223. #555	C₂×C₃×C₅	semidirect
224. #547	C₂×C₃×C₅	semidirect
225. #487	C₂×C₃×C₅	semidirect
226. #485	C₂×C₃×C₅	semidirect
227. #476	C₂×C₃×C₅	semidirect
228. #465	C₂×C₃×C₅	semidirect
229. #461	C₂×C₃×C₅	semidirect
230. #449	C₂×C₃×C₅	semidirect
231. C₄×D₈	C₂×C₃×C₅	semidirect
232. C₈×D₄	C₂×C₃×C₅	semidirect
233. #416	C₂×C₃×C₅	semidirect
435. C₃×C₅	#3303	direct (N × H)
496. C₅	C₃×#3303	direct (N × H)
516. C₃	C₅×#3303	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×#547	2
C₃×C₅×#487	2
C₃×C₅×#485	2
C₃×C₅×#476	2
C₃×C₅×#465	2
C₃×C₅×#461	2
C₃×C₅×#449	2
C₃×C₄×C₅×D₈	2
C₃×C₅×C₈×D₄	2
C₃×C₅×#416	2
C₅×#3303	3
C₃×#3303	5

Subgroups — C3×C5×#3303 #14276337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3303 #14276337