Subgroups — C₃×C₅×#3218 #14276252

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#497	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#491	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#462	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#461	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#451	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#448	C₂	1	2	yes	maximal
9	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3218	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
14	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
15	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₃×C₅×#126	—	2	1	no	—
19	C₃×C₅×#125	C₂²	1	1	yes	characteristic
20	C₃×C₅×#124	C₂²	1	1	yes	characteristic
21	C₃×C₅×#123	—	2	1	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#121	C₂²	1	1	yes	characteristic
24	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
25	C₃×C₄×C₅×D₄	—	2	1	no	—
26	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₃×C₅×#117	—	2	1	no	—
28	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
29	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
30	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
32	C₃×C₅×#103	C₂²	1	4	yes	—
33	C₃×C₅×#103	C₂²	1	4	yes	—
34	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₃×C₅×#97	C₂²	1	2	yes	—
36	C₃×#3218	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#529	C₂×C₃	1	1	yes	characteristic
39	C₅×#497	C₂×C₃	1	2	yes	complemented
40	C₅×#491	C₂×C₃	1	2	yes	complemented
41	C₅×#462	C₂×C₃	1	2	yes	complemented
42	C₅×#461	C₂×C₃	1	2	yes	complemented
43	C₅×#451	C₂×C₃	1	2	yes	complemented
44	C₅×#448	C₂×C₃	1	2	yes	—
45	C₅×#432	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₃×C₅×Q₈	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	—	4	4	no	—
48	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
50	C₂×C₃×C₅×D₄	—	2	1	no	—
51	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	—	2	2	no	—
53	C₂²×C₃×C₄×C₅	—	2	1	no	—
54	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₃×C₅×Q₁₆	—	4	4	no	—
58	C₃×C₅×SD₁₆	—	4	4	no	—
59	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
60	C₃×C₅×C₄⋊C₄	—	2	2	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	—	2	2	no	—
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	—	2	1	no	—
65	C₃×C₅×C₄⋊C₄	—	2	1	no	—
66	C₃×C₅×C₄⋊C₄	—	2	1	no	—
67	C₃×C₅×C₄⋊C₄	—	2	1	no	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
71	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
75	C₃×C₄²×C₅	—	2	1	no	—
76	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
77	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
78	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
81	C₃×#529	C₂×C₅	1	1	yes	characteristic
82	C₃×#497	C₂×C₅	1	2	yes	complemented
83	C₃×#491	C₂×C₅	1	2	yes	complemented
84	C₃×#462	C₂×C₅	1	2	yes	complemented
85	C₃×#461	C₂×C₅	1	2	yes	complemented
86	C₃×#451	C₂×C₅	1	2	yes	complemented
87	C₃×#448	C₂×C₅	1	2	yes	—
88	C₃×#432	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
90	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	—
91	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
92	C₅×C₄⋊Q₈	—	2	1	no	—
93	C₅×C₄⋊Q₈	—	2	1	no	—
94	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
95	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
96	C₅×#126	—	2	1	no	—
97	C₅×#125	C₂²×C₃	1	1	yes	characteristic
98	C₅×#124	C₂²×C₃	1	1	yes	characteristic
99	C₅×#123	—	2	1	no	—
100	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
101	C₅×#121	C₂²×C₃	1	1	yes	characteristic
102	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
103	C₄×C₅×D₄	—	2	1	no	—
104	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
105	C₅×#117	—	2	1	no	—
106	C₂×C₅×C₄⋊C₄	—	2	1	no	—
107	C₂×C₅×C₄⋊C₄	—	2	1	no	—
108	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
109	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
110	C₅×#103	C₂²×C₃	1	4	yes	—
111	C₅×#103	C₂²×C₃	1	4	yes	—
112	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
113	C₅×#97	C₂²×C₃	1	2	yes	—
114	#3218	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
115	C₂³×C₃×C₅	—	2	1	no	—
116	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
117	C₃×C₅×Q₈	—	2	4	no	—
118	C₃×C₅×Q₈	—	2	2	no	—
119	C₃×C₅×Q₈	—	2	4	no	—
120	C₃×C₅×Q₈	—	4	4	no	—
121	C₃×C₅×D₄	—	2	2	no	—
122	C₃×C₅×D₄	—	4	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	1	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	—	2	1	no	—
129	C₂×C₃×C₄×C₅	—	2	4	no	—
130	C₂×C₃×C₄×C₅	—	4	4	no	—
131	C₂×C₃×C₄×C₅	—	4	2	no	—
132	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₃×C₅×C₈	—	2	4	no	—
139	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
140	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	—
141	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
142	C₃×C₄⋊Q₈	—	2	1	no	—
143	C₃×C₄⋊Q₈	—	2	1	no	—
144	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
145	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
146	C₃×#126	—	2	1	no	—
147	C₃×#125	C₂²×C₅	1	1	yes	characteristic
148	C₃×#124	C₂²×C₅	1	1	yes	characteristic
149	C₃×#123	—	2	1	no	—
150	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
151	C₃×#121	C₂²×C₅	1	1	yes	characteristic
152	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
153	C₃×C₄×D₄	—	2	1	no	—
154	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
155	C₃×#117	—	2	1	no	—
156	C₂×C₃×C₄⋊C₄	—	2	1	no	—
157	C₂×C₃×C₄⋊C₄	—	2	1	no	—
158	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
159	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
160	C₃×#103	C₂²×C₅	1	4	yes	—
161	C₃×#103	C₂²×C₅	1	4	yes	—
162	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
163	C₃×#97	C₂²×C₅	1	2	yes	—
164	C₂×C₅×Q₈	—	2	2	no	—
165	C₂×C₅×Q₈	—	4	4	no	—
166	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
167	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	—	2	2	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
175	C₅×Q₁₆	—	4	4	no	—
176	C₅×SD₁₆	—	4	4	no	—
177	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
178	C₅×C₄⋊C₄	—	2	2	no	—
179	C₅×C₄⋊C₄	—	2	2	no	—
180	C₅×C₄⋊C₄	—	2	2	no	—
181	C₅×C₄⋊C₄	—	2	2	no	—
182	C₅×C₄⋊C₄	—	2	1	no	—
183	C₅×C₄⋊C₄	—	2	1	no	—
184	C₅×C₄⋊C₄	—	2	1	no	—
185	C₅×C₄⋊C₄	—	2	1	no	—
186	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
187	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
188	C₅×C₂²⋊C₄	—	2	1	no	—
189	C₅×C₂²⋊C₄	—	2	1	no	—
190	C₅×C₂²⋊C₄	—	2	1	no	—
191	C₅×C₂²⋊C₄	—	2	1	no	—
192	C₅×C₂²⋊C₄	—	2	1	no	—
193	C₄²×C₅	—	2	1	no	—
194	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
195	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
196	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
197	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
199	#529	C₂×C₃×C₅	1	1	yes	characteristic
200	#497	C₂×C₃×C₅	1	2	yes	complemented
201	#491	C₂×C₃×C₅	1	2	yes	complemented
202	#462	C₂×C₃×C₅	1	2	yes	complemented
203	#461	C₂×C₃×C₅	1	2	yes	complemented
204	#451	C₂×C₃×C₅	1	2	yes	complemented
205	#448	C₂×C₃×C₅	1	2	yes	—
206	#432	C₂×C₃×C₅	1	1	yes	characteristic, complemented
207	C₂²×C₃×C₅	—	2	1	no	—
208	C₂²×C₃×C₅	—	2	1	no	—
209	C₂²×C₃×C₅	—	4	1	no	—
210	C₂²×C₃×C₅	—	4	1	no	—
211	C₂²×C₃×C₅	—	4	1	no	—
212	C₂²×C₃×C₅	#137	1	2	yes	—
213	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₃×C₄×C₅	—	2	1	no	—
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×C₄×C₅	—	2	1	no	—
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	—	4	4	no	—
219	C₃×C₄×C₅	—	4	1	no	—
220	C₃×C₄×C₅	—	4	1	no	—
221	C₃×C₄×C₅	—	4	1	no	—
222	C₃×C₄×C₅	#137	1	2	yes	—
223	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
224	C₂×C₃×Q₈	—	2	2	no	—
225	C₂×C₃×Q₈	—	4	4	no	—
226	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
227	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
228	C₂×C₃×D₄	—	2	1	no	—
229	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
230	C₂²×C₃×C₄	—	2	2	no	—
231	C₂²×C₃×C₄	—	2	1	no	—
232	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
235	C₃×Q₁₆	—	4	4	no	—
236	C₃×SD₁₆	—	4	4	no	—
237	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
238	C₃×C₄⋊C₄	—	2	2	no	—
239	C₃×C₄⋊C₄	—	2	2	no	—
240	C₃×C₄⋊C₄	—	2	2	no	—
241	C₃×C₄⋊C₄	—	2	2	no	—
242	C₃×C₄⋊C₄	—	2	1	no	—
243	C₃×C₄⋊C₄	—	2	1	no	—
244	C₃×C₄⋊C₄	—	2	1	no	—
245	C₃×C₄⋊C₄	—	2	1	no	—
246	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
247	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
248	C₃×C₂²⋊C₄	—	2	1	no	—
249	C₃×C₂²⋊C₄	—	2	1	no	—
250	C₃×C₂²⋊C₄	—	2	1	no	—
251	C₃×C₂²⋊C₄	—	2	1	no	—
252	C₃×C₂²⋊C₄	—	2	1	no	—
253	C₃×C₄²	—	2	1	no	—
254	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
255	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
256	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
257	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
258	C₂³×C₅	—	2	1	no	—
259	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
260	C₅×Q₈	—	2	4	no	—
261	C₅×Q₈	—	2	2	no	—
262	C₅×Q₈	—	2	4	no	—
263	C₅×Q₈	—	4	4	no	—
264	C₅×D₄	—	2	2	no	—
265	C₅×D₄	—	4	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	4	no	—
273	C₂×C₄×C₅	—	4	4	no	—
274	C₂×C₄×C₅	—	4	2	no	—
275	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
281	C₅×C₈	—	2	4	no	—
282	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
283	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	—
284	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
288	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
289	#126	—	2	1	no	—
290	#125	C₂²×C₃×C₅	1	1	yes	characteristic
291	#124	C₂²×C₃×C₅	1	1	yes	characteristic
292	#123	—	2	1	no	—
293	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
294	#121	C₂²×C₃×C₅	1	1	yes	characteristic
295	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
298	#117	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
302	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
303	#103	C₂²×C₃×C₅	1	4	yes	—
304	#103	C₂²×C₃×C₅	1	4	yes	—
305	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
306	#97	C₂²×C₃×C₅	1	2	yes	—
307	C₂×C₃×C₅	—	2	2	no	—
308	C₂×C₃×C₅	—	8	1	no	—
309	C₂×C₃×C₅	#535	1	1	yes	characteristic
310	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
311	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
312	C₂³×C₃	—	2	1	no	—
313	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
314	C₃×Q₈	—	2	4	no	—
315	C₃×Q₈	—	2	2	no	—
316	C₃×Q₈	—	2	4	no	—
317	C₃×Q₈	—	4	4	no	—
318	C₃×D₄	—	2	2	no	—
319	C₃×D₄	—	4	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	4	no	—
327	C₂×C₃×C₄	—	4	4	no	—
328	C₂×C₃×C₄	—	4	2	no	—
329	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
335	C₃×C₈	—	2	4	no	—
336	C₂²×C₅	—	2	1	no	—
337	C₂²×C₅	—	2	1	no	—
338	C₂²×C₅	—	4	1	no	—
339	C₂²×C₅	—	4	1	no	—
340	C₂²×C₅	—	4	1	no	—
341	C₂²×C₅	C₃×#137	1	2	yes	—
342	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
343	C₄×C₅	—	2	1	no	—
344	C₄×C₅	—	2	1	no	—
345	C₄×C₅	—	2	1	no	—
346	C₄×C₅	—	2	1	no	—
347	C₄×C₅	—	4	1	no	—
348	C₄×C₅	—	4	1	no	—
349	C₄×C₅	—	4	4	no	—
350	C₄×C₅	—	4	1	no	—
351	C₄×C₅	C₃×#137	1	2	yes	—
352	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
356	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
364	Q₁₆	—	4	4	no	—
365	SD₁₆	—	4	4	no	—
366	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
376	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
384	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
385	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
386	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
387	C₃×C₅	#3218	1	1	yes	characteristic, direct product factor, Hall
388	C₂²×C₃	—	2	1	no	—
389	C₂²×C₃	—	2	1	no	—
390	C₂²×C₃	—	4	1	no	—
391	C₂²×C₃	—	4	1	no	—
392	C₂²×C₃	—	4	1	no	—
393	C₂²×C₃	C₅×#137	1	2	yes	—
394	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
395	C₃×C₄	—	2	1	no	—
396	C₃×C₄	—	2	1	no	—
397	C₃×C₄	—	2	1	no	—
398	C₃×C₄	—	2	1	no	—
399	C₃×C₄	—	4	4	no	—
400	C₃×C₄	—	4	1	no	—
401	C₃×C₄	—	4	1	no	—
402	C₃×C₄	—	4	1	no	—
403	C₃×C₄	C₅×#137	1	2	yes	—
404	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
405	C₂×C₅	—	2	2	no	—
406	C₂×C₅	—	8	1	no	—
407	C₂×C₅	C₃×#535	1	1	yes	characteristic
408	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
409	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
410	C₂³	—	2	1	no	—
411	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
412	Q₈	—	2	4	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	2	4	no	—
415	Q₈	—	4	4	no	—
416	D₄	—	2	2	no	—
417	D₄	—	4	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
428	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
429	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
430	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
431	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
432	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
433	C₈	—	2	4	no	—
434	C₂×C₃	—	2	2	no	—
435	C₂×C₃	—	8	1	no	—
436	C₂×C₃	C₅×#535	1	1	yes	characteristic
437	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
438	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
439	C₅	C₃×#3218	1	1	yes	characteristic, direct product factor, Sylow
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	C₃×C₅×#137	1	2	yes	—
446	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	1	no	—
455	C₄	C₃×C₅×#137	1	2	yes	—
456	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
457	C₃	C₅×#3218	1	1	yes	characteristic, direct product factor, Sylow
458	C₂	—	2	2	no	—
459	C₂	—	8	1	no	—
460	C₂	C₃×C₅×#535	1	1	yes	characteristic
461	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
462	C₂	C₂×C₃×C₅×#137	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. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₃×C₅×#497	C₂	semidirect
4. C₃×C₅×#491	C₂	semidirect
5. C₃×C₅×#462	C₂	semidirect
6. C₃×C₅×#461	C₂	semidirect
7. C₃×C₅×#451	C₂	semidirect
9. C₃×C₅×#432	C₂	semidirect
10. C₅×#3218	C₃	direct (N × H)
36. C₃×#3218	C₅	direct (N × H)
37. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
39. C₅×#497	C₂×C₃	semidirect
40. C₅×#491	C₂×C₃	semidirect
41. C₅×#462	C₂×C₃	semidirect
42. C₅×#461	C₂×C₃	semidirect
43. C₅×#451	C₂×C₃	semidirect
45. C₅×#432	C₂×C₃	semidirect
80. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
82. C₃×#497	C₂×C₅	semidirect
83. C₃×#491	C₂×C₅	semidirect
84. C₃×#462	C₂×C₅	semidirect
85. C₃×#461	C₂×C₅	semidirect
86. C₃×#451	C₂×C₅	semidirect
88. C₃×#432	C₂×C₅	semidirect
114. #3218	C₃×C₅	direct (N × H)
198. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
200. #497	C₂×C₃×C₅	semidirect
201. #491	C₂×C₃×C₅	semidirect
202. #462	C₂×C₃×C₅	semidirect
203. #461	C₂×C₃×C₅	semidirect
204. #451	C₂×C₃×C₅	semidirect
206. #432	C₂×C₃×C₅	semidirect
387. C₃×C₅	#3218	direct (N × H)
439. C₅	C₃×#3218	direct (N × H)
457. C₃	C₅×#3218	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×C₄⋊Q₈	2
C₃×C₅×#529	2
C₃×C₅×#497	2
C₃×C₅×#491	2
C₃×C₅×#462	2
C₃×C₅×#461	2
C₃×C₅×#451	2
C₃×C₅×#448	2
C₃×C₅×#432	2
C₅×#3218	3
C₃×#3218	5

Subgroups — C3×C5×#3218 #14276252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3218 #14276252