Subgroups — C₃×C₅×#3252 #14276286

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#479	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#477	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#470	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#468	C₂	1	2	yes	maximal
8	C₃×C₅×#464	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3252	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#126	—	2	1	no	—
19	C₃×C₅×#125	—	2	1	no	—
20	C₃×C₅×#125	C₂²	1	1	yes	characteristic
21	C₃×C₅×#124	C₂²	1	1	yes	characteristic
22	C₃×C₅×#123	—	2	1	no	—
23	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#121	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×Q₈	—	2	1	no	—
28	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
30	C₃×C₄×C₅×D₄	—	2	1	no	—
31	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₃×C₅×#117	—	2	1	no	—
33	C₃×C₅×#117	—	2	1	no	—
34	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
35	C₃×C₅×#107	C₂²	1	2	yes	—
36	C₃×C₅×#106	C₂²	1	2	yes	—
37	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
40	C₃×C₅×#103	C₂²	1	2	yes	—
41	C₃×C₅×#103	C₂²	1	2	yes	—
42	C₃×C₅×#103	C₂²	1	2	yes	—
43	C₃×C₅×#102	C₂²	1	2	yes	—
44	C₃×#3252	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#529	C₂×C₃	1	1	yes	characteristic
47	C₅×#479	C₂×C₃	1	2	yes	complemented
48	C₅×#477	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#470	C₂×C₃	1	2	yes	complemented
51	C₅×#468	C₂×C₃	1	2	yes	—
52	C₅×#464	C₂×C₃	1	2	yes	complemented
53	C₅×#462	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#461	C₂×C₃	1	1	yes	characteristic, complemented
55	C₅×#423	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₃×C₅×Q₁₆	—	4	2	no	—
66	C₃×C₅×SD₁₆	—	4	2	no	—
67	C₃×C₅×M₁₆	—	4	2	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	—	2	1	no	—
71	C₃×C₅×C₄⋊C₄	—	2	1	no	—
72	C₃×C₅×C₄⋊C₄	—	2	1	no	—
73	C₃×C₅×C₄⋊C₄	—	2	1	no	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	—	2	1	no	—
76	C₃×C₅×C₄⋊C₄	—	2	2	no	—
77	C₃×C₅×C₄⋊C₄	—	2	2	no	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
82	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₅	—	2	1	no	—
89	C₃×C₄²×C₅	—	2	2	no	—
90	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
91	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
92	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
95	C₃×#529	C₂×C₅	1	1	yes	characteristic
96	C₃×#479	C₂×C₅	1	2	yes	complemented
97	C₃×#477	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#470	C₂×C₅	1	2	yes	complemented
100	C₃×#468	C₂×C₅	1	2	yes	—
101	C₃×#464	C₂×C₅	1	2	yes	complemented
102	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
103	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
104	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
106	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
107	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
108	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
109	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
110	C₅×#126	—	2	1	no	—
111	C₅×#125	—	2	1	no	—
112	C₅×#125	C₂²×C₃	1	1	yes	characteristic
113	C₅×#124	C₂²×C₃	1	1	yes	characteristic
114	C₅×#123	—	2	1	no	—
115	C₅×C₂²⋊Q₈	—	2	1	no	—
116	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
117	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
118	C₅×#121	C₂²×C₃	1	1	yes	characteristic
119	C₄×C₅×Q₈	—	2	1	no	—
120	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
121	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
122	C₄×C₅×D₄	—	2	1	no	—
123	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
124	C₅×#117	—	2	1	no	—
125	C₅×#117	—	2	1	no	—
126	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
127	C₅×#107	C₂²×C₃	1	2	yes	—
128	C₅×#106	C₂²×C₃	1	2	yes	—
129	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
130	C₅×C₄⋊C₈	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×#103	C₂²×C₃	1	2	yes	—
135	C₅×#102	C₂²×C₃	1	2	yes	—
136	#3252	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
139	C₃×C₅×Q₈	—	2	2	no	—
140	C₃×C₅×Q₈	—	2	1	no	—
141	C₃×C₅×Q₈	—	2	1	no	—
142	C₃×C₅×Q₈	—	2	2	no	—
143	C₃×C₅×Q₈	—	4	2	no	—
144	C₃×C₅×D₄	—	2	1	no	—
145	C₃×C₅×D₄	—	2	1	no	—
146	C₃×C₅×D₄	—	4	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	1	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	—	2	1	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	4	1	no	—
156	C₂×C₃×C₄×C₅	—	4	2	no	—
157	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
163	C₃×C₅×C₈	—	2	2	no	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
166	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
167	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
168	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
169	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
170	C₃×#126	—	2	1	no	—
171	C₃×#125	—	2	1	no	—
172	C₃×#125	C₂²×C₅	1	1	yes	characteristic
173	C₃×#124	C₂²×C₅	1	1	yes	characteristic
174	C₃×#123	—	2	1	no	—
175	C₃×C₂²⋊Q₈	—	2	1	no	—
176	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
177	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
178	C₃×#121	C₂²×C₅	1	1	yes	characteristic
179	C₃×C₄×Q₈	—	2	1	no	—
180	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
181	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
182	C₃×C₄×D₄	—	2	1	no	—
183	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
184	C₃×#117	—	2	1	no	—
185	C₃×#117	—	2	1	no	—
186	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
187	C₃×#107	C₂²×C₅	1	2	yes	—
188	C₃×#106	C₂²×C₅	1	2	yes	—
189	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
190	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
191	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
192	C₃×#103	C₂²×C₅	1	2	yes	—
193	C₃×#103	C₂²×C₅	1	2	yes	—
194	C₃×#103	C₂²×C₅	1	2	yes	—
195	C₃×#102	C₂²×C₅	1	2	yes	—
196	C₂×C₅×Q₈	—	2	1	no	—
197	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
199	C₂×C₅×D₄	—	2	1	no	—
200	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
201	C₂²×C₄×C₅	—	2	1	no	—
202	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₅×Q₁₆	—	4	2	no	—
206	C₅×SD₁₆	—	4	2	no	—
207	C₅×M₁₆	—	4	2	no	—
208	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
209	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	2	2	no	—
217	C₅×C₄⋊C₄	—	2	2	no	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
220	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
221	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
222	C₅×C₂²⋊C₄	—	2	2	no	—
223	C₅×C₂²⋊C₄	—	2	1	no	—
224	C₅×C₂²⋊C₄	—	2	1	no	—
225	C₅×C₂²⋊C₄	—	2	1	no	—
226	C₅×C₂²⋊C₄	—	2	1	no	—
227	C₅×C₂²⋊C₄	—	2	1	no	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	—	2	2	no	—
230	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
231	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
232	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
233	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
234	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	#529	C₂×C₃×C₅	1	1	yes	characteristic
236	#479	C₂×C₃×C₅	1	2	yes	complemented
237	#477	C₂×C₃×C₅	1	1	yes	characteristic, complemented
238	#476	C₂×C₃×C₅	1	1	yes	characteristic, complemented
239	#470	C₂×C₃×C₅	1	2	yes	complemented
240	#468	C₂×C₃×C₅	1	2	yes	—
241	#464	C₂×C₃×C₅	1	2	yes	complemented
242	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
243	#461	C₂×C₃×C₅	1	1	yes	characteristic, complemented
244	#423	C₂×C₃×C₅	1	1	yes	characteristic, complemented
245	C₂²×C₃×C₅	—	2	1	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	4	1	no	—
249	C₂²×C₃×C₅	—	4	1	no	—
250	C₂²×C₃×C₅	—	4	1	no	—
251	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
252	C₃×C₄×C₅	—	2	1	no	—
253	C₃×C₄×C₅	—	2	1	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	1	no	—
256	C₃×C₄×C₅	—	4	1	no	—
257	C₃×C₄×C₅	—	4	2	no	—
258	C₃×C₄×C₅	—	4	1	no	—
259	C₃×C₄×C₅	—	4	1	no	—
260	C₃×C₄×C₅	—	4	2	no	—
261	C₃×C₄×C₅	#137	1	2	yes	—
262	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
263	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
264	C₂×C₃×Q₈	—	2	1	no	—
265	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
267	C₂×C₃×D₄	—	2	1	no	—
268	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
269	C₂²×C₃×C₄	—	2	1	no	—
270	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
271	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
273	C₃×Q₁₆	—	4	2	no	—
274	C₃×SD₁₆	—	4	2	no	—
275	C₃×M₁₆	—	4	2	no	—
276	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
277	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
278	C₃×C₄⋊C₄	—	2	1	no	—
279	C₃×C₄⋊C₄	—	2	1	no	—
280	C₃×C₄⋊C₄	—	2	1	no	—
281	C₃×C₄⋊C₄	—	2	1	no	—
282	C₃×C₄⋊C₄	—	2	1	no	—
283	C₃×C₄⋊C₄	—	2	1	no	—
284	C₃×C₄⋊C₄	—	2	2	no	—
285	C₃×C₄⋊C₄	—	2	2	no	—
286	C₃×C₄⋊C₄	—	2	1	no	—
287	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
288	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
289	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
290	C₃×C₂²⋊C₄	—	2	2	no	—
291	C₃×C₂²⋊C₄	—	2	1	no	—
292	C₃×C₂²⋊C₄	—	2	1	no	—
293	C₃×C₂²⋊C₄	—	2	1	no	—
294	C₃×C₂²⋊C₄	—	2	1	no	—
295	C₃×C₂²⋊C₄	—	2	1	no	—
296	C₃×C₄²	—	2	1	no	—
297	C₃×C₄²	—	2	2	no	—
298	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
299	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
300	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
301	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
302	C₂³×C₅	—	2	1	no	—
303	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
304	C₅×Q₈	—	2	2	no	—
305	C₅×Q₈	—	2	1	no	—
306	C₅×Q₈	—	2	1	no	—
307	C₅×Q₈	—	2	2	no	—
308	C₅×Q₈	—	4	2	no	—
309	C₅×D₄	—	2	1	no	—
310	C₅×D₄	—	2	1	no	—
311	C₅×D₄	—	4	2	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	2	no	—
322	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
328	C₅×C₈	—	2	2	no	—
329	C₅×C₈	—	2	2	no	—
330	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
331	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
332	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
333	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
334	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
335	#126	—	2	1	no	—
336	#125	—	2	1	no	—
337	#125	C₂²×C₃×C₅	1	1	yes	characteristic
338	#124	C₂²×C₃×C₅	1	1	yes	characteristic
339	#123	—	2	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
342	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
343	#121	C₂²×C₃×C₅	1	1	yes	characteristic
344	C₄×Q₈	—	2	1	no	—
345	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
346	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
349	#117	—	2	1	no	—
350	#117	—	2	1	no	—
351	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
352	#107	C₂²×C₃×C₅	1	2	yes	—
353	#106	C₂²×C₃×C₅	1	2	yes	—
354	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
355	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
356	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
357	#103	C₂²×C₃×C₅	1	2	yes	—
358	#103	C₂²×C₃×C₅	1	2	yes	—
359	#103	C₂²×C₃×C₅	1	2	yes	—
360	#102	C₂²×C₃×C₅	1	2	yes	—
361	C₂×C₃×C₅	—	4	1	no	—
362	C₂×C₃×C₅	—	8	1	no	—
363	C₂×C₃×C₅	#537	1	1	yes	characteristic
364	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
365	C₂×C₃×C₅	#575	1	1	yes	characteristic
366	C₂³×C₃	—	2	1	no	—
367	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
368	C₃×Q₈	—	2	2	no	—
369	C₃×Q₈	—	2	1	no	—
370	C₃×Q₈	—	2	1	no	—
371	C₃×Q₈	—	2	2	no	—
372	C₃×Q₈	—	4	2	no	—
373	C₃×D₄	—	2	1	no	—
374	C₃×D₄	—	2	1	no	—
375	C₃×D₄	—	4	2	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	4	1	no	—
385	C₂×C₃×C₄	—	4	2	no	—
386	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
392	C₃×C₈	—	2	2	no	—
393	C₃×C₈	—	2	2	no	—
394	C₂²×C₅	—	2	1	no	—
395	C₂²×C₅	—	2	1	no	—
396	C₂²×C₅	—	2	1	no	—
397	C₂²×C₅	—	4	1	no	—
398	C₂²×C₅	—	4	1	no	—
399	C₂²×C₅	—	4	1	no	—
400	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
401	C₄×C₅	—	2	1	no	—
402	C₄×C₅	—	2	1	no	—
403	C₄×C₅	—	2	1	no	—
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	4	1	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	—	4	2	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	4	2	no	—
410	C₄×C₅	C₃×#137	1	2	yes	—
411	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
412	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
415	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
420	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
421	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
422	Q₁₆	—	4	2	no	—
423	SD₁₆	—	4	2	no	—
424	M₁₆	—	4	2	no	—
425	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
426	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
437	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
438	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	2	no	—
447	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
448	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
449	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
450	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
451	C₃×C₅	#3252	1	1	yes	characteristic, direct product factor, Hall
452	C₂²×C₃	—	2	1	no	—
453	C₂²×C₃	—	2	1	no	—
454	C₂²×C₃	—	2	1	no	—
455	C₂²×C₃	—	4	1	no	—
456	C₂²×C₃	—	4	1	no	—
457	C₂²×C₃	—	4	1	no	—
458	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₃×C₄	—	2	1	no	—
460	C₃×C₄	—	2	1	no	—
461	C₃×C₄	—	2	1	no	—
462	C₃×C₄	—	2	1	no	—
463	C₃×C₄	—	4	1	no	—
464	C₃×C₄	—	4	2	no	—
465	C₃×C₄	—	4	1	no	—
466	C₃×C₄	—	4	1	no	—
467	C₃×C₄	—	4	2	no	—
468	C₃×C₄	C₅×#137	1	2	yes	—
469	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
470	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
471	C₂×C₅	—	4	1	no	—
472	C₂×C₅	—	8	1	no	—
473	C₂×C₅	C₃×#537	1	1	yes	characteristic
474	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
475	C₂×C₅	C₃×#575	1	1	yes	characteristic
476	C₂³	—	2	1	no	—
477	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
478	Q₈	—	2	2	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	2	2	no	—
482	Q₈	—	4	2	no	—
483	D₄	—	2	1	no	—
484	D₄	—	2	1	no	—
485	D₄	—	4	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
497	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
498	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
499	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
500	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
501	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₂×C₃	—	4	1	no	—
505	C₂×C₃	—	8	1	no	—
506	C₂×C₃	C₅×#537	1	1	yes	characteristic
507	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
508	C₂×C₃	C₅×#575	1	1	yes	characteristic
509	C₅	C₃×#3252	1	1	yes	characteristic, direct product factor, Sylow
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	1	no	—
516	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	2	no	—
526	C₄	C₃×C₅×#137	1	2	yes	—
527	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
528	C₄	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
529	C₃	C₅×#3252	1	1	yes	characteristic, direct product factor, Sylow
530	C₂	—	4	1	no	—
531	C₂	—	8	1	no	—
532	C₂	C₃×C₅×#537	1	1	yes	characteristic
533	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
534	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
prime radical	C₃×C₅×#121	C₂²
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×#533	C₂	semidirect
3. C₃×C₅×#479	C₂	semidirect
4. C₃×C₅×#477	C₂	semidirect
5. C₃×C₅×#476	C₂	semidirect
6. C₃×C₅×#470	C₂	semidirect
8. C₃×C₅×#464	C₂	semidirect
9. C₃×C₅×#462	C₂	semidirect
10. C₃×C₅×#461	C₂	semidirect
11. C₃×C₅×#423	C₂	semidirect
12. C₅×#3252	C₃	direct (N × H)
44. C₃×#3252	C₅	direct (N × H)
45. C₅×#533	C₂×C₃	semidirect
47. C₅×#479	C₂×C₃	semidirect
48. C₅×#477	C₂×C₃	semidirect
49. C₅×#476	C₂×C₃	semidirect
50. C₅×#470	C₂×C₃	semidirect
52. C₅×#464	C₂×C₃	semidirect
53. C₅×#462	C₂×C₃	semidirect
54. C₅×#461	C₂×C₃	semidirect
55. C₅×#423	C₂×C₃	semidirect
94. C₃×#533	C₂×C₅	semidirect
96. C₃×#479	C₂×C₅	semidirect
97. C₃×#477	C₂×C₅	semidirect
98. C₃×#476	C₂×C₅	semidirect
99. C₃×#470	C₂×C₅	semidirect
101. C₃×#464	C₂×C₅	semidirect
102. C₃×#462	C₂×C₅	semidirect
103. C₃×#461	C₂×C₅	semidirect
104. C₃×#423	C₂×C₅	semidirect
136. #3252	C₃×C₅	direct (N × H)
234. #533	C₂×C₃×C₅	semidirect
236. #479	C₂×C₃×C₅	semidirect
237. #477	C₂×C₃×C₅	semidirect
238. #476	C₂×C₃×C₅	semidirect
239. #470	C₂×C₃×C₅	semidirect
241. #464	C₂×C₃×C₅	semidirect
242. #462	C₂×C₃×C₅	semidirect
243. #461	C₂×C₃×C₅	semidirect
244. #423	C₂×C₃×C₅	semidirect
451. C₃×C₅	#3252	direct (N × H)
509. C₅	C₃×#3252	direct (N × H)
529. C₃	C₅×#3252	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×#533	2
C₃×C₅×#529	2
C₃×C₅×#479	2
C₃×C₅×#477	2
C₃×C₅×#476	2
C₃×C₅×#470	2
C₃×C₅×#468	2
C₃×C₅×#464	2
C₃×C₅×#462	2
C₃×C₅×#461	2
C₃×C₅×#423	2
C₅×#3252	3
C₃×#3252	5

Subgroups — C3×C5×#3252 #14276286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3252 #14276286