Subgroups — C₃×C₅×#3302 #14276336

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#485	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#467	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#452	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×#3302	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	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×#126	—	2	2	no	—
20	C₃×C₅×#124	—	2	1	no	—
21	C₃×C₅×#123	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₃×C₅×#121	—	2	1	no	—
25	C₃×C₄×C₅×Q₈	—	2	1	no	—
26	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₃×C₅×#117	C₂²	1	2	yes	—
30	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
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	2	yes	—
36	C₃×C₅×#103	C₂²	1	1	yes	characteristic
37	C₃×C₅×#103	C₂²	1	2	yes	—
38	C₃×C₅×#102	C₂²	1	2	yes	—
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×#3302	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#547	C₂×C₃	1	1	yes	characteristic
45	C₅×#487	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#485	C₂×C₃	1	2	yes	complemented
47	C₅×#474	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#467	C₂×C₃	1	2	yes	complemented
49	C₅×#462	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#452	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×Q₈	C₂³	1	2	yes	—
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	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	—	2	2	no	—
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₃×C₅×Q₁₆	—	4	2	no	—
66	C₃×C₅×SD₁₆	—	2	2	no	—
67	C₂×C₃×C₅×C₈	—	4	2	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	—	2	1	no	—
72	C₃×C₅×C₄⋊C₄	—	2	2	no	—
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	—	2	1	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	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×#556	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#547	C₂×C₅	1	1	yes	characteristic
91	C₃×#487	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#485	C₂×C₅	1	2	yes	complemented
93	C₃×#474	C₂×C₅	1	1	yes	characteristic, complemented
94	C₃×#467	C₂×C₅	1	2	yes	complemented
95	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#452	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×Q₁₆	C₂²×C₃	1	2	yes	—
102	C₂×C₅×SD₁₆	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×#126	—	2	2	no	—
107	C₅×#124	—	2	1	no	—
108	C₅×#123	—	2	2	no	—
109	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
110	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
111	C₅×#121	—	2	1	no	—
112	C₄×C₅×Q₈	—	2	1	no	—
113	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
114	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
115	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
116	C₅×#117	C₂²×C₃	1	2	yes	—
117	C₂×C₅×C₄⋊C₄	—	2	1	no	—
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	2	yes	—
122	C₅×#103	C₂²×C₃	1	2	yes	—
123	C₅×#103	C₂²×C₃	1	1	yes	characteristic
124	C₅×#103	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	#3302	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
130	C₂³×C₃×C₅	—	2	1	no	—
131	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
132	C₃×C₅×Q₈	—	2	1	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	2	1	no	—
135	C₃×C₅×Q₈	—	2	2	no	—
136	C₃×C₅×Q₈	—	4	2	no	—
137	C₃×C₅×D₄	—	2	2	no	—
138	C₃×C₅×D₄	—	2	1	no	—
139	C₃×C₅×D₄	—	4	4	no	—
140	C₃×C₅×D₄	#41	1	2	yes	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	4	4	no	—
149	C₂×C₃×C₄×C₅	—	4	2	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₃×C₅×C₈	—	2	1	no	—
155	C₃×C₅×C₈	—	2	1	no	—
156	C₃×C₅×C₈	—	2	2	no	—
157	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
158	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
159	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
160	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
161	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
162	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
163	C₃×#126	—	2	2	no	—
164	C₃×#124	—	2	1	no	—
165	C₃×#123	—	2	2	no	—
166	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
167	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
168	C₃×#121	—	2	1	no	—
169	C₃×C₄×Q₈	—	2	1	no	—
170	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
171	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
172	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
173	C₃×#117	C₂²×C₅	1	2	yes	—
174	C₂×C₃×C₄⋊C₄	—	2	1	no	—
175	C₃×#107	C₂²×C₅	1	2	yes	—
176	C₃×#106	C₂²×C₅	1	1	yes	characteristic
177	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
178	C₃×#103	C₂²×C₅	1	2	yes	—
179	C₃×#103	C₂²×C₅	1	2	yes	—
180	C₃×#103	C₂²×C₅	1	1	yes	characteristic
181	C₃×#103	C₂²×C₅	1	2	yes	—
182	C₃×#102	C₂²×C₅	1	1	yes	characteristic
183	C₃×#102	C₂²×C₅	1	2	yes	—
184	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
185	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
186	C₅×#41	—	2	4	no	—
187	C₅×#41	—	4	2	no	—
188	C₂×C₅×Q₈	—	2	1	no	—
189	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
191	C₂×C₅×D₄	—	2	2	no	—
192	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
193	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	2	2	no	—
196	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
197	C₅×Q₁₆	—	4	2	no	—
198	C₅×SD₁₆	—	2	2	no	—
199	C₂×C₅×C₈	—	4	2	no	—
200	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
202	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	2	no	—
205	C₅×C₄⋊C₄	—	2	2	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
210	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
211	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
212	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
213	C₅×C₂²⋊C₄	—	2	2	no	—
214	C₅×C₂²⋊C₄	—	2	2	no	—
215	C₅×C₂²⋊C₄	—	2	2	no	—
216	C₅×C₂²⋊C₄	—	2	1	no	—
217	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
218	C₄²×C₅	—	2	2	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
221	#556	C₂×C₃×C₅	1	1	yes	characteristic, complemented
222	#547	C₂×C₃×C₅	1	1	yes	characteristic
223	#487	C₂×C₃×C₅	1	1	yes	characteristic, complemented
224	#485	C₂×C₃×C₅	1	2	yes	complemented
225	#474	C₂×C₃×C₅	1	1	yes	characteristic, complemented
226	#467	C₂×C₃×C₅	1	2	yes	complemented
227	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
228	#452	C₂×C₃×C₅	1	2	yes	complemented
229	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
230	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
231	#416	C₂×C₃×C₅	1	2	yes	complemented
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	—	2	2	no	—
234	C₂²×C₃×C₅	—	2	2	no	—
235	C₂²×C₃×C₅	—	2	2	no	—
236	C₂²×C₃×C₅	—	4	1	no	—
237	C₂²×C₃×C₅	—	4	1	no	—
238	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
239	C₃×C₄×C₅	—	2	2	no	—
240	C₃×C₄×C₅	—	2	1	no	—
241	C₃×C₄×C₅	—	4	2	no	—
242	C₃×C₄×C₅	—	4	1	no	—
243	C₃×C₄×C₅	—	4	1	no	—
244	C₃×C₄×C₅	—	4	2	no	—
245	C₃×C₄×C₅	—	4	1	no	—
246	C₃×C₄×C₅	#135	1	2	yes	—
247	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
248	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
249	C₃×#41	—	2	4	no	—
250	C₃×#41	—	4	2	no	—
251	C₂×C₃×Q₈	—	2	1	no	—
252	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
253	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
254	C₂×C₃×D₄	—	2	2	no	—
255	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
256	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
257	C₂²×C₃×C₄	—	2	1	no	—
258	C₂²×C₃×C₄	—	2	2	no	—
259	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
260	C₃×Q₁₆	—	4	2	no	—
261	C₃×SD₁₆	—	2	2	no	—
262	C₂×C₃×C₈	—	4	2	no	—
263	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
264	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
265	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
266	C₃×C₄⋊C₄	—	2	1	no	—
267	C₃×C₄⋊C₄	—	2	2	no	—
268	C₃×C₄⋊C₄	—	2	2	no	—
269	C₃×C₄⋊C₄	—	2	1	no	—
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₄⋊C₄	—	2	1	no	—
272	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
273	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
274	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
275	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
276	C₃×C₂²⋊C₄	—	2	2	no	—
277	C₃×C₂²⋊C₄	—	2	2	no	—
278	C₃×C₂²⋊C₄	—	2	2	no	—
279	C₃×C₂²⋊C₄	—	2	1	no	—
280	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
281	C₃×C₄²	—	2	2	no	—
282	C₃×C₄²	—	2	1	no	—
283	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
286	C₅×Q₈	—	2	1	no	—
287	C₅×Q₈	—	2	2	no	—
288	C₅×Q₈	—	2	1	no	—
289	C₅×Q₈	—	2	2	no	—
290	C₅×Q₈	—	4	2	no	—
291	C₅×D₄	—	2	2	no	—
292	C₅×D₄	—	2	1	no	—
293	C₅×D₄	—	4	4	no	—
294	C₅×D₄	C₃×#41	1	2	yes	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	4	4	no	—
303	C₂×C₄×C₅	—	4	2	no	—
304	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
305	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
308	C₅×C₈	—	2	1	no	—
309	C₅×C₈	—	2	1	no	—
310	C₅×C₈	—	2	2	no	—
311	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
312	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
313	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
314	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
315	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
316	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
317	#126	—	2	2	no	—
318	#124	—	2	1	no	—
319	#123	—	2	2	no	—
320	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
321	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
322	#121	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
325	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
326	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
327	#117	C₂²×C₃×C₅	1	2	yes	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	#107	C₂²×C₃×C₅	1	2	yes	—
330	#106	C₂²×C₃×C₅	1	1	yes	characteristic
331	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
332	#103	C₂²×C₃×C₅	1	2	yes	—
333	#103	C₂²×C₃×C₅	1	2	yes	—
334	#103	C₂²×C₃×C₅	1	1	yes	characteristic
335	#103	C₂²×C₃×C₅	1	2	yes	—
336	#102	C₂²×C₃×C₅	1	1	yes	characteristic
337	#102	C₂²×C₃×C₅	1	2	yes	—
338	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
339	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
340	C₂×C₃×C₅	—	4	2	no	—
341	C₂×C₃×C₅	—	4	2	no	—
342	C₂×C₃×C₅	#546	1	1	yes	characteristic
343	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
344	C₂×C₃×C₅	#578	1	1	yes	characteristic
345	C₂³×C₃	—	2	1	no	—
346	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
347	C₃×Q₈	—	2	1	no	—
348	C₃×Q₈	—	2	2	no	—
349	C₃×Q₈	—	2	1	no	—
350	C₃×Q₈	—	2	2	no	—
351	C₃×Q₈	—	4	2	no	—
352	C₃×D₄	—	2	2	no	—
353	C₃×D₄	—	2	1	no	—
354	C₃×D₄	—	4	4	no	—
355	C₃×D₄	C₅×#41	1	2	yes	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	1	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	4	no	—
364	C₂×C₃×C₄	—	4	2	no	—
365	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
366	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
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	1	no	—
370	C₃×C₈	—	2	1	no	—
371	C₃×C₈	—	2	2	no	—
372	C₂²×C₅	—	2	2	no	—
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	—	2	2	no	—
375	C₂²×C₅	—	2	2	no	—
376	C₂²×C₅	—	4	1	no	—
377	C₂²×C₅	—	4	1	no	—
378	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	2	2	no	—
381	C₄×C₅	—	4	1	no	—
382	C₄×C₅	—	4	2	no	—
383	C₄×C₅	—	4	1	no	—
384	C₄×C₅	—	4	2	no	—
385	C₄×C₅	—	4	1	no	—
386	C₄×C₅	C₃×#135	1	2	yes	—
387	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
388	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
389	#41	—	2	4	no	—
390	#41	—	4	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
393	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
396	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
400	Q₁₆	—	4	2	no	—
401	SD₁₆	—	2	2	no	—
402	C₂×C₈	—	4	2	no	—
403	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
404	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
405	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
413	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
414	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
415	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	1	no	—
423	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
424	C₃×C₅	#3302	1	1	yes	characteristic, direct product factor, Hall
425	C₂²×C₃	—	2	2	no	—
426	C₂²×C₃	—	2	2	no	—
427	C₂²×C₃	—	2	2	no	—
428	C₂²×C₃	—	2	2	no	—
429	C₂²×C₃	—	4	1	no	—
430	C₂²×C₃	—	4	1	no	—
431	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	2	1	no	—
434	C₃×C₄	—	4	2	no	—
435	C₃×C₄	—	4	1	no	—
436	C₃×C₄	—	4	1	no	—
437	C₃×C₄	—	4	2	no	—
438	C₃×C₄	—	4	1	no	—
439	C₃×C₄	C₅×#135	1	2	yes	—
440	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
441	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
442	C₂×C₅	—	4	2	no	—
443	C₂×C₅	—	4	2	no	—
444	C₂×C₅	C₃×#546	1	1	yes	characteristic
445	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
446	C₂×C₅	C₃×#578	1	1	yes	characteristic
447	C₂³	—	2	1	no	—
448	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
449	Q₈	—	2	1	no	—
450	Q₈	—	2	2	no	—
451	Q₈	—	2	1	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	4	2	no	—
454	D₄	—	2	1	no	—
455	D₄	—	2	2	no	—
456	D₄	—	4	4	no	—
457	D₄	C₃×C₅×#41	1	2	yes	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
468	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
469	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
470	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
471	C₈	—	2	1	no	—
472	C₈	—	2	1	no	—
473	C₈	—	2	2	no	—
474	C₂×C₃	—	4	2	no	—
475	C₂×C₃	—	4	2	no	—
476	C₂×C₃	C₅×#546	1	1	yes	characteristic
477	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
478	C₂×C₃	C₅×#578	1	1	yes	characteristic
479	C₅	C₃×#3302	1	1	yes	characteristic, direct product factor, Sylow
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	1	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	1	no	—
494	C₄	C₃×C₅×#135	1	2	yes	—
495	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
496	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
497	C₃	C₅×#3302	1	1	yes	characteristic, direct product factor, Sylow
498	C₂	—	4	2	no	—
499	C₂	—	4	2	no	—
500	C₂	C₃×C₅×#546	1	1	yes	characteristic
501	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
502	C₂	C₃×C₅×#578	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×#547	C₂
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×#556	C₂	semidirect
3. C₃×C₅×#487	C₂	semidirect
4. C₃×C₅×#485	C₂	semidirect
5. C₃×C₅×#474	C₂	semidirect
6. C₃×C₅×#467	C₂	semidirect
7. C₃×C₅×#462	C₂	semidirect
8. C₃×C₅×#452	C₂	semidirect
9. C₃×C₄×C₅×SD₁₆	C₂	semidirect
10. C₃×C₅×C₈×D₄	C₂	semidirect
11. C₃×C₅×#416	C₂	semidirect
12. C₅×#3302	C₃	direct (N × H)
42. C₃×#3302	C₅	direct (N × H)
43. C₅×#556	C₂×C₃	semidirect
45. C₅×#487	C₂×C₃	semidirect
46. C₅×#485	C₂×C₃	semidirect
47. C₅×#474	C₂×C₃	semidirect
48. C₅×#467	C₂×C₃	semidirect
49. C₅×#462	C₂×C₃	semidirect
50. C₅×#452	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×#556	C₂×C₅	semidirect
91. C₃×#487	C₂×C₅	semidirect
92. C₃×#485	C₂×C₅	semidirect
93. C₃×#474	C₂×C₅	semidirect
94. C₃×#467	C₂×C₅	semidirect
95. C₃×#462	C₂×C₅	semidirect
96. C₃×#452	C₂×C₅	semidirect
97. C₃×C₄×SD₁₆	C₂×C₅	semidirect
98. C₃×C₈×D₄	C₂×C₅	semidirect
99. C₃×#416	C₂×C₅	semidirect
129. #3302	C₃×C₅	direct (N × H)
221. #556	C₂×C₃×C₅	semidirect
223. #487	C₂×C₃×C₅	semidirect
224. #485	C₂×C₃×C₅	semidirect
225. #474	C₂×C₃×C₅	semidirect
226. #467	C₂×C₃×C₅	semidirect
227. #462	C₂×C₃×C₅	semidirect
228. #452	C₂×C₃×C₅	semidirect
229. C₄×SD₁₆	C₂×C₃×C₅	semidirect
230. C₈×D₄	C₂×C₃×C₅	semidirect
231. #416	C₂×C₃×C₅	semidirect
424. C₃×C₅	#3302	direct (N × H)
479. C₅	C₃×#3302	direct (N × H)
497. C₃	C₅×#3302	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×#556	2
C₃×C₅×#547	2
C₃×C₅×#487	2
C₃×C₅×#485	2
C₃×C₅×#474	2
C₃×C₅×#467	2
C₃×C₅×#462	2
C₃×C₅×#452	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×C₈×D₄	2
C₃×C₅×#416	2
C₅×#3302	3
C₃×#3302	5

Subgroups — C3×C5×#3302 #14276336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3302 #14276336