Subgroups — C₃×C₅×#3219 #14276253

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#491	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#464	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#463	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#452	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3219	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic
20	C₃×C₅×#126	—	2	1	no	—
21	C₃×C₅×#125	C₂²	1	1	yes	characteristic
22	C₃×C₅×#124	C₂²	1	2	yes	—
23	C₃×C₅×#124	C₂²	1	1	yes	characteristic
24	C₃×C₅×#123	—	2	1	no	—
25	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#121	—	2	1	no	—
27	C₃×C₅×#121	—	2	1	no	—
28	C₃×C₅×#121	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₅×D₄	—	2	1	no	—
31	C₃×C₄×C₅×D₄	—	2	1	no	—
32	C₃×C₄×C₅×D₄	—	2	1	no	—
33	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₃×C₅×#117	—	2	1	no	—
35	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
37	C₃×C₅×#103	C₂²	1	2	yes	—
38	C₃×C₅×#103	C₂²	1	2	yes	—
39	C₃×C₅×#102	C₂²	1	2	yes	—
40	C₃×C₅×#102	C₂²	1	2	yes	—
41	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
42	C₃×C₅×#97	C₂²	1	1	yes	characteristic
43	C₃×C₅×#97	C₂²	1	1	yes	characteristic
44	C₃×#3219	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#496	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#491	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#490	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#464	C₂×C₃	1	2	yes	complemented
52	C₅×#463	C₂×C₃	1	2	yes	complemented
53	C₅×#452	C₂×C₃	1	2	yes	complemented
54	C₅×#449	C₂×C₃	1	2	yes	complemented
55	C₅×#432	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×C₅×#41	—	4	2	no	—
57	C₃×C₅×#41	—	4	2	no	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	2	1	no	—
63	C₂×C₃×C₅×D₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₃×C₅×Q₁₆	—	4	2	no	—
72	C₃×C₅×SD₁₆	—	4	2	no	—
73	C₃×C₅×SD₁₆	—	4	2	no	—
74	C₃×C₅×D₈	—	4	2	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	1	no	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	—	2	1	no	—
80	C₃×C₅×C₄⋊C₄	—	2	1	no	—
81	C₃×C₅×C₄⋊C₄	—	2	1	no	—
82	C₃×C₅×C₄⋊C₄	—	2	1	no	—
83	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
89	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
90	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
91	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₃×C₄²×C₅	—	2	1	no	—
93	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
94	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
95	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
96	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
97	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#496	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#491	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#490	C₂×C₅	1	1	yes	characteristic, complemented
103	C₃×#464	C₂×C₅	1	2	yes	complemented
104	C₃×#463	C₂×C₅	1	2	yes	complemented
105	C₃×#452	C₂×C₅	1	2	yes	complemented
106	C₃×#449	C₂×C₅	1	2	yes	complemented
107	C₃×#432	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
109	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
110	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
111	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
112	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
113	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
114	C₅×#127	C₂²×C₃	1	1	yes	characteristic
115	C₅×#126	—	2	1	no	—
116	C₅×#125	C₂²×C₃	1	1	yes	characteristic
117	C₅×#124	C₂²×C₃	1	2	yes	—
118	C₅×#124	C₂²×C₃	1	1	yes	characteristic
119	C₅×#123	—	2	1	no	—
120	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
121	C₅×#121	—	2	1	no	—
122	C₅×#121	—	2	1	no	—
123	C₅×#121	C₂²×C₃	1	1	yes	characteristic
124	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
125	C₄×C₅×D₄	—	2	1	no	—
126	C₄×C₅×D₄	—	2	1	no	—
127	C₄×C₅×D₄	—	2	1	no	—
128	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
129	C₅×#117	—	2	1	no	—
130	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
131	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
132	C₅×#103	C₂²×C₃	1	2	yes	—
133	C₅×#103	C₂²×C₃	1	2	yes	—
134	C₅×#102	C₂²×C₃	1	2	yes	—
135	C₅×#102	C₂²×C₃	1	2	yes	—
136	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
137	C₅×#97	C₂²×C₃	1	1	yes	characteristic
138	C₅×#97	C₂²×C₃	1	1	yes	characteristic
139	#3219	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
140	C₂³×C₃×C₅	—	2	1	no	—
141	C₂³×C₃×C₅	—	2	2	no	—
142	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
143	C₃×C₅×Q₈	—	2	2	no	—
144	C₃×C₅×Q₈	—	2	2	no	—
145	C₃×C₅×Q₈	—	2	2	no	—
146	C₃×C₅×D₄	—	2	2	no	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	—	2	2	no	—
149	C₃×C₅×D₄	—	4	2	no	—
150	C₃×C₅×D₄	—	4	2	no	—
151	C₃×C₅×D₄	—	4	2	no	—
152	C₃×C₅×D₄	—	4	4	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	1	no	—
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	2	2	no	—
158	C₂×C₃×C₄×C₅	—	4	1	no	—
159	C₂×C₃×C₄×C₅	—	4	1	no	—
160	C₂×C₃×C₄×C₅	—	4	2	no	—
161	C₂×C₃×C₄×C₅	—	4	4	no	—
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
168	C₃×C₅×C₈	—	2	2	no	—
169	C₃×C₅×C₈	—	2	2	no	—
170	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
171	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
172	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
173	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
174	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
175	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
176	C₃×#127	C₂²×C₅	1	1	yes	characteristic
177	C₃×#126	—	2	1	no	—
178	C₃×#125	C₂²×C₅	1	1	yes	characteristic
179	C₃×#124	C₂²×C₅	1	2	yes	—
180	C₃×#124	C₂²×C₅	1	1	yes	characteristic
181	C₃×#123	—	2	1	no	—
182	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
183	C₃×#121	—	2	1	no	—
184	C₃×#121	—	2	1	no	—
185	C₃×#121	C₂²×C₅	1	1	yes	characteristic
186	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
187	C₃×C₄×D₄	—	2	1	no	—
188	C₃×C₄×D₄	—	2	1	no	—
189	C₃×C₄×D₄	—	2	1	no	—
190	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
191	C₃×#117	—	2	1	no	—
192	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
193	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
194	C₃×#103	C₂²×C₅	1	2	yes	—
195	C₃×#103	C₂²×C₅	1	2	yes	—
196	C₃×#102	C₂²×C₅	1	2	yes	—
197	C₃×#102	C₂²×C₅	1	2	yes	—
198	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
199	C₃×#97	C₂²×C₅	1	1	yes	characteristic
200	C₃×#97	C₂²×C₅	1	1	yes	characteristic
201	C₅×#41	—	4	2	no	—
202	C₅×#41	—	4	2	no	—
203	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
205	C₂×C₅×D₄	—	2	1	no	—
206	C₂×C₅×D₄	—	2	2	no	—
207	C₂×C₅×D₄	—	2	1	no	—
208	C₂×C₅×D₄	—	2	1	no	—
209	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
211	C₂²×C₄×C₅	—	2	1	no	—
212	C₂²×C₄×C₅	—	2	2	no	—
213	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
216	C₅×Q₁₆	—	4	2	no	—
217	C₅×SD₁₆	—	4	2	no	—
218	C₅×SD₁₆	—	4	2	no	—
219	C₅×D₈	—	4	2	no	—
220	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
221	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	2	1	no	—
224	C₅×C₄⋊C₄	—	2	1	no	—
225	C₅×C₄⋊C₄	—	2	1	no	—
226	C₅×C₄⋊C₄	—	2	1	no	—
227	C₅×C₄⋊C₄	—	2	1	no	—
228	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
229	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
230	C₅×C₂²⋊C₄	—	2	1	no	—
231	C₅×C₂²⋊C₄	—	2	1	no	—
232	C₅×C₂²⋊C₄	—	2	1	no	—
233	C₅×C₂²⋊C₄	—	2	2	no	—
234	C₅×C₂²⋊C₄	—	2	2	no	—
235	C₅×C₂²⋊C₄	—	2	1	no	—
236	C₅×C₂²⋊C₄	—	2	1	no	—
237	C₄²×C₅	—	2	1	no	—
238	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
239	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
240	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
241	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
242	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
243	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
244	#497	C₂×C₃×C₅	1	1	yes	characteristic, complemented
245	#496	C₂×C₃×C₅	1	1	yes	characteristic, complemented
246	#491	C₂×C₃×C₅	1	1	yes	characteristic, complemented
247	#490	C₂×C₃×C₅	1	1	yes	characteristic, complemented
248	#464	C₂×C₃×C₅	1	2	yes	complemented
249	#463	C₂×C₃×C₅	1	2	yes	complemented
250	#452	C₂×C₃×C₅	1	2	yes	complemented
251	#449	C₂×C₃×C₅	1	2	yes	complemented
252	#432	C₂×C₃×C₅	1	1	yes	characteristic, complemented
253	C₂²×C₃×C₅	—	2	1	no	—
254	C₂²×C₃×C₅	—	2	1	no	—
255	C₂²×C₃×C₅	—	2	1	no	—
256	C₂²×C₃×C₅	—	4	2	no	—
257	C₂²×C₃×C₅	—	4	1	no	—
258	C₂²×C₃×C₅	—	4	1	no	—
259	C₂²×C₃×C₅	—	4	2	no	—
260	C₂²×C₃×C₅	—	4	2	no	—
261	C₂²×C₃×C₅	—	4	1	no	—
262	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
263	C₃×C₄×C₅	—	2	1	no	—
264	C₃×C₄×C₅	—	2	1	no	—
265	C₃×C₄×C₅	—	2	1	no	—
266	C₃×C₄×C₅	—	2	1	no	—
267	C₃×C₄×C₅	—	2	1	no	—
268	C₃×C₄×C₅	—	4	2	no	—
269	C₃×C₄×C₅	—	4	1	no	—
270	C₃×C₄×C₅	—	4	1	no	—
271	C₃×C₄×C₅	—	4	1	no	—
272	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
273	C₃×#41	—	4	2	no	—
274	C₃×#41	—	4	2	no	—
275	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
276	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₃×D₄	—	2	1	no	—
278	C₂×C₃×D₄	—	2	2	no	—
279	C₂×C₃×D₄	—	2	1	no	—
280	C₂×C₃×D₄	—	2	1	no	—
281	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
282	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
283	C₂²×C₃×C₄	—	2	1	no	—
284	C₂²×C₃×C₄	—	2	2	no	—
285	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
286	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
287	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
288	C₃×Q₁₆	—	4	2	no	—
289	C₃×SD₁₆	—	4	2	no	—
290	C₃×SD₁₆	—	4	2	no	—
291	C₃×D₈	—	4	2	no	—
292	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
293	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
294	C₃×C₄⋊C₄	—	2	1	no	—
295	C₃×C₄⋊C₄	—	2	1	no	—
296	C₃×C₄⋊C₄	—	2	1	no	—
297	C₃×C₄⋊C₄	—	2	1	no	—
298	C₃×C₄⋊C₄	—	2	1	no	—
299	C₃×C₄⋊C₄	—	2	1	no	—
300	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
301	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
302	C₃×C₂²⋊C₄	—	2	1	no	—
303	C₃×C₂²⋊C₄	—	2	1	no	—
304	C₃×C₂²⋊C₄	—	2	1	no	—
305	C₃×C₂²⋊C₄	—	2	2	no	—
306	C₃×C₂²⋊C₄	—	2	2	no	—
307	C₃×C₂²⋊C₄	—	2	1	no	—
308	C₃×C₂²⋊C₄	—	2	1	no	—
309	C₃×C₄²	—	2	1	no	—
310	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
311	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
312	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
313	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
314	C₂³×C₅	—	2	1	no	—
315	C₂³×C₅	—	2	2	no	—
316	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
317	C₅×Q₈	—	2	2	no	—
318	C₅×Q₈	—	2	2	no	—
319	C₅×Q₈	—	2	2	no	—
320	C₅×D₄	—	2	2	no	—
321	C₅×D₄	—	2	2	no	—
322	C₅×D₄	—	2	2	no	—
323	C₅×D₄	—	4	2	no	—
324	C₅×D₄	—	4	2	no	—
325	C₅×D₄	—	4	2	no	—
326	C₅×D₄	—	4	4	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	4	1	no	—
334	C₂×C₄×C₅	—	4	2	no	—
335	C₂×C₄×C₅	—	4	4	no	—
336	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
340	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
342	C₅×C₈	—	2	2	no	—
343	C₅×C₈	—	2	2	no	—
344	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
345	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
346	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
347	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
348	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
349	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
350	#127	C₂²×C₃×C₅	1	1	yes	characteristic
351	#126	—	2	1	no	—
352	#125	C₂²×C₃×C₅	1	1	yes	characteristic
353	#124	C₂²×C₃×C₅	1	1	yes	characteristic
354	#124	C₂²×C₃×C₅	1	2	yes	—
355	#123	—	2	1	no	—
356	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
357	#121	—	2	1	no	—
358	#121	—	2	1	no	—
359	#121	C₂²×C₃×C₅	1	1	yes	characteristic
360	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
365	#117	—	2	1	no	—
366	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
367	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
368	#103	C₂²×C₃×C₅	1	2	yes	—
369	#103	C₂²×C₃×C₅	1	2	yes	—
370	#102	C₂²×C₃×C₅	1	2	yes	—
371	#102	C₂²×C₃×C₅	1	2	yes	—
372	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
373	#97	C₂²×C₃×C₅	1	1	yes	characteristic
374	#97	C₂²×C₃×C₅	1	1	yes	characteristic
375	C₂×C₃×C₅	—	4	1	no	—
376	C₂×C₃×C₅	—	8	2	no	—
377	C₂×C₃×C₅	—	8	1	no	—
378	C₂×C₃×C₅	#535	1	1	yes	characteristic
379	C₂×C₃×C₅	#575	1	1	yes	characteristic
380	C₂×C₃×C₅	#575	1	1	yes	characteristic
381	C₂³×C₃	—	2	1	no	—
382	C₂³×C₃	—	2	2	no	—
383	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
384	C₃×Q₈	—	2	2	no	—
385	C₃×Q₈	—	2	2	no	—
386	C₃×Q₈	—	2	2	no	—
387	C₃×D₄	—	2	2	no	—
388	C₃×D₄	—	2	2	no	—
389	C₃×D₄	—	2	2	no	—
390	C₃×D₄	—	4	2	no	—
391	C₃×D₄	—	4	2	no	—
392	C₃×D₄	—	4	2	no	—
393	C₃×D₄	—	4	4	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	4	1	no	—
400	C₂×C₃×C₄	—	4	1	no	—
401	C₂×C₃×C₄	—	4	2	no	—
402	C₂×C₃×C₄	—	4	4	no	—
403	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
407	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
408	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
409	C₃×C₈	—	2	2	no	—
410	C₃×C₈	—	2	2	no	—
411	C₂²×C₅	—	2	1	no	—
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	4	1	no	—
415	C₂²×C₅	—	4	2	no	—
416	C₂²×C₅	—	4	2	no	—
417	C₂²×C₅	—	4	1	no	—
418	C₂²×C₅	—	4	2	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
421	C₄×C₅	—	2	1	no	—
422	C₄×C₅	—	2	1	no	—
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	—	4	1	no	—
427	C₄×C₅	—	4	1	no	—
428	C₄×C₅	—	4	2	no	—
429	C₄×C₅	—	4	1	no	—
430	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
431	#41	—	4	2	no	—
432	#41	—	4	2	no	—
433	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
434	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
440	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
444	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
445	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
446	Q₁₆	—	4	2	no	—
447	SD₁₆	—	4	2	no	—
448	SD₁₆	—	4	2	no	—
449	D₈	—	4	2	no	—
450	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
451	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
459	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
469	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
470	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
471	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
472	C₃×C₅	#3219	1	1	yes	characteristic, direct product factor, Hall
473	C₂²×C₃	—	2	1	no	—
474	C₂²×C₃	—	2	1	no	—
475	C₂²×C₃	—	2	1	no	—
476	C₂²×C₃	—	4	2	no	—
477	C₂²×C₃	—	4	1	no	—
478	C₂²×C₃	—	4	1	no	—
479	C₂²×C₃	—	4	2	no	—
480	C₂²×C₃	—	4	2	no	—
481	C₂²×C₃	—	4	1	no	—
482	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
483	C₃×C₄	—	2	1	no	—
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	2	1	no	—
486	C₃×C₄	—	2	1	no	—
487	C₃×C₄	—	2	1	no	—
488	C₃×C₄	—	4	2	no	—
489	C₃×C₄	—	4	1	no	—
490	C₃×C₄	—	4	1	no	—
491	C₃×C₄	—	4	1	no	—
492	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
493	C₂×C₅	—	4	1	no	—
494	C₂×C₅	—	8	1	no	—
495	C₂×C₅	—	8	2	no	—
496	C₂×C₅	C₃×#535	1	1	yes	characteristic
497	C₂×C₅	C₃×#575	1	1	yes	characteristic
498	C₂×C₅	C₃×#575	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	2	2	no	—
501	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
502	Q₈	—	2	2	no	—
503	Q₈	—	2	2	no	—
504	Q₈	—	2	2	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	2	no	—
507	D₄	—	2	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	4	no	—
511	D₄	—	4	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
522	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
523	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
524	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
525	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
526	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
527	C₈	—	2	2	no	—
528	C₈	—	2	2	no	—
529	C₂×C₃	—	4	1	no	—
530	C₂×C₃	—	8	2	no	—
531	C₂×C₃	—	8	1	no	—
532	C₂×C₃	C₅×#535	1	1	yes	characteristic
533	C₂×C₃	C₅×#575	1	1	yes	characteristic
534	C₂×C₃	C₅×#575	1	1	yes	characteristic
535	C₅	C₃×#3219	1	1	yes	characteristic, direct product factor, Sylow
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	1	no	—
545	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	4	2	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
556	C₃	C₅×#3219	1	1	yes	characteristic, direct product factor, Sylow
557	C₂	—	4	1	no	—
558	C₂	—	8	2	no	—
559	C₂	—	8	1	no	—
560	C₂	C₃×C₅×#535	1	1	yes	characteristic
561	C₂	C₃×C₅×#575	1	1	yes	characteristic
562	C₂	C₃×C₅×#575	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 ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₃×C₅×#529	C₂	semidirect
3. C₃×C₅×#497	C₂	semidirect
4. C₃×C₅×#496	C₂	semidirect
5. C₃×C₅×#491	C₂	semidirect
6. C₃×C₅×#490	C₂	semidirect
7. C₃×C₅×#464	C₂	semidirect
8. C₃×C₅×#463	C₂	semidirect
9. C₃×C₅×#452	C₂	semidirect
10. C₃×C₅×#449	C₂	semidirect
11. C₃×C₅×#432	C₂	semidirect
12. C₅×#3219	C₃	direct (N × H)
44. C₃×#3219	C₅	direct (N × H)
45. C₅×#532	C₂×C₃	semidirect
46. C₅×#529	C₂×C₃	semidirect
47. C₅×#497	C₂×C₃	semidirect
48. C₅×#496	C₂×C₃	semidirect
49. C₅×#491	C₂×C₃	semidirect
50. C₅×#490	C₂×C₃	semidirect
51. C₅×#464	C₂×C₃	semidirect
52. C₅×#463	C₂×C₃	semidirect
53. C₅×#452	C₂×C₃	semidirect
54. C₅×#449	C₂×C₃	semidirect
55. C₅×#432	C₂×C₃	semidirect
97. C₃×#532	C₂×C₅	semidirect
98. C₃×#529	C₂×C₅	semidirect
99. C₃×#497	C₂×C₅	semidirect
100. C₃×#496	C₂×C₅	semidirect
101. C₃×#491	C₂×C₅	semidirect
102. C₃×#490	C₂×C₅	semidirect
103. C₃×#464	C₂×C₅	semidirect
104. C₃×#463	C₂×C₅	semidirect
105. C₃×#452	C₂×C₅	semidirect
106. C₃×#449	C₂×C₅	semidirect
107. C₃×#432	C₂×C₅	semidirect
139. #3219	C₃×C₅	direct (N × H)
242. #532	C₂×C₃×C₅	semidirect
243. #529	C₂×C₃×C₅	semidirect
244. #497	C₂×C₃×C₅	semidirect
245. #496	C₂×C₃×C₅	semidirect
246. #491	C₂×C₃×C₅	semidirect
247. #490	C₂×C₃×C₅	semidirect
248. #464	C₂×C₃×C₅	semidirect
249. #463	C₂×C₃×C₅	semidirect
250. #452	C₂×C₃×C₅	semidirect
251. #449	C₂×C₃×C₅	semidirect
252. #432	C₂×C₃×C₅	semidirect
472. C₃×C₅	#3219	direct (N × H)
535. C₅	C₃×#3219	direct (N × H)
556. C₃	C₅×#3219	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×#532	2
C₃×C₅×#529	2
C₃×C₅×#497	2
C₃×C₅×#496	2
C₃×C₅×#491	2
C₃×C₅×#490	2
C₃×C₅×#464	2
C₃×C₅×#463	2
C₃×C₅×#452	2
C₃×C₅×#449	2
C₃×C₅×#432	2
C₅×#3219	3
C₃×#3219	5

Subgroups — C3×C5×#3219 #14276253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3219 #14276253