Subgroups — C₃×C₅×#3298 #14276332

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₄×Q₈	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×#483	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#475	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×#448	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	C₂×C₃×C₅×#103	C₂	1	2	yes	maximal, complemented
12	C₅×#3298	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	—	2	1	no	—
14	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
17	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
18	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
19	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×#123	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
23	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₃×C₅×#121	C₂²	1	2	yes	—
26	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×D₄	—	2	1	no	—
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
31	C₃×C₅×#106	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	2	yes	—
37	C₃×C₅×#103	C₂²	1	2	yes	—
38	C₃×C₅×#103	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×#3298	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×D₄×Q₈	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×#483	C₂×C₃	1	2	yes	complemented
47	C₅×#475	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×#448	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	C₂×C₅×#103	C₂×C₃	1	2	yes	complemented
54	C₃×C₅×#41	—	4	4	no	—
55	C₂×C₃×C₅×Q₈	—	2	2	no	—
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	—	2	4	no	—
58	C₂×C₃×C₅×Q₈	—	4	2	no	—
59	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	—	2	2	no	—
65	C₂²×C₃×C₄×C₅	—	2	2	no	—
66	C₂²×C₃×C₄×C₅	—	2	1	no	—
67	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
68	C₃×C₅×SD₁₆	—	2	2	no	—
69	C₃×C₅×SD₁₆	—	4	2	no	—
70	C₂×C₃×C₅×C₈	—	4	2	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
78	C₃×C₅×C₄⋊C₄	—	2	2	no	—
79	C₃×C₅×C₄⋊C₄	—	2	1	no	—
80	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
87	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
88	C₃×C₄²×C₅	—	2	1	no	—
89	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×#547	C₂×C₅	1	1	yes	characteristic
92	C₃×#487	C₂×C₅	1	1	yes	characteristic, complemented
93	C₃×#483	C₂×C₅	1	2	yes	complemented
94	C₃×#475	C₂×C₅	1	1	yes	characteristic, complemented
95	C₃×#465	C₂×C₅	1	2	yes	complemented
96	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#448	C₂×C₅	1	2	yes	complemented
98	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×C₃×#103	C₂×C₅	1	2	yes	complemented
101	C₂×C₅×#41	—	2	1	no	—
102	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
103	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
105	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
106	C₅×C₄⋊Q₈	—	2	1	no	—
107	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
108	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
109	C₅×#123	—	2	2	no	—
110	C₅×C₂²⋊Q₈	—	2	1	no	—
111	C₅×C₂²⋊Q₈	—	2	2	no	—
112	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
113	C₅×#121	C₂²×C₃	1	2	yes	—
114	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
115	C₄×C₅×D₄	—	2	1	no	—
116	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
119	C₅×#106	C₂²×C₃	1	1	yes	characteristic
120	C₅×#106	C₂²×C₃	1	2	yes	—
121	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
122	C₅×#103	C₂²×C₃	1	1	yes	characteristic
123	C₅×#103	C₂²×C₃	1	2	yes	—
124	C₅×#103	C₂²×C₃	1	2	yes	—
125	C₅×#103	C₂²×C₃	1	2	yes	—
126	C₅×#103	C₂²×C₃	1	2	yes	—
127	C₅×#102	C₂²×C₃	1	1	yes	characteristic
128	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
129	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
130	#3298	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
133	C₃×C₅×Q₈	—	2	1	no	—
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×Q₈	—	2	2	no	—
136	C₃×C₅×Q₈	—	4	4	no	—
137	C₃×C₅×Q₈	—	4	2	no	—
138	C₃×C₅×Q₈	#41	1	2	yes	complemented
139	C₃×C₅×D₄	—	2	1	no	—
140	C₃×C₅×D₄	—	2	1	no	—
141	C₃×C₅×D₄	—	4	4	no	—
142	C₃×C₅×D₄	SD₁₆	1	4	yes	complemented
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	2	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	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	4	4	no	—
151	C₂×C₃×C₄×C₅	—	4	4	no	—
152	C₂×C₃×C₄×C₅	—	4	2	no	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
157	C₃×C₅×C₈	—	2	1	no	—
158	C₃×C₅×C₈	—	2	1	no	—
159	C₃×C₅×C₈	—	2	2	no	—
160	C₂×C₃×#41	—	2	1	no	—
161	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
162	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
164	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
165	C₃×C₄⋊Q₈	—	2	1	no	—
166	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
167	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
168	C₃×#123	—	2	2	no	—
169	C₃×C₂²⋊Q₈	—	2	1	no	—
170	C₃×C₂²⋊Q₈	—	2	2	no	—
171	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
172	C₃×#121	C₂²×C₅	1	2	yes	—
173	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
174	C₃×C₄×D₄	—	2	1	no	—
175	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
176	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
178	C₃×#106	C₂²×C₅	1	1	yes	characteristic
179	C₃×#106	C₂²×C₅	1	2	yes	—
180	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
181	C₃×#103	C₂²×C₅	1	1	yes	characteristic
182	C₃×#103	C₂²×C₅	1	2	yes	—
183	C₃×#103	C₂²×C₅	1	2	yes	—
184	C₃×#103	C₂²×C₅	1	2	yes	—
185	C₃×#103	C₂²×C₅	1	2	yes	—
186	C₃×#102	C₂²×C₅	1	1	yes	characteristic
187	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
188	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
189	C₅×#41	—	4	4	no	—
190	C₂×C₅×Q₈	—	2	2	no	—
191	C₂×C₅×Q₈	—	2	1	no	—
192	C₂×C₅×Q₈	—	2	4	no	—
193	C₂×C₅×Q₈	—	4	2	no	—
194	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
195	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₅×D₄	—	2	2	no	—
197	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
198	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
199	C₂²×C₄×C₅	—	2	2	no	—
200	C₂²×C₄×C₅	—	2	2	no	—
201	C₂²×C₄×C₅	—	2	1	no	—
202	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
203	C₅×SD₁₆	—	2	2	no	—
204	C₅×SD₁₆	—	4	2	no	—
205	C₂×C₅×C₈	—	4	2	no	—
206	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
208	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
209	C₅×C₄⋊C₄	—	2	2	no	—
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	2	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
216	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
217	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
218	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
219	C₅×C₂²⋊C₄	—	2	2	no	—
220	C₅×C₂²⋊C₄	—	2	1	no	—
221	C₅×C₂²⋊C₄	—	2	2	no	—
222	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
223	C₄²×C₅	—	2	1	no	—
224	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
225	D₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
226	#547	C₂×C₃×C₅	1	1	yes	characteristic
227	#487	C₂×C₃×C₅	1	1	yes	characteristic, complemented
228	#483	C₂×C₃×C₅	1	2	yes	complemented
229	#475	C₂×C₃×C₅	1	1	yes	characteristic, complemented
230	#465	C₂×C₃×C₅	1	2	yes	complemented
231	#461	C₂×C₃×C₅	1	1	yes	characteristic, complemented
232	#448	C₂×C₃×C₅	1	2	yes	complemented
233	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
234	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	C₂×#103	C₂×C₃×C₅	1	2	yes	complemented
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	C₂×SD₁₆	1	4	yes	—
242	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
243	C₃×C₄×C₅	—	2	2	no	—
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	2	no	—
249	C₃×C₄×C₅	—	4	1	no	—
250	C₃×C₄×C₅	C₂×SD₁₆	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	—	4	4	no	—
254	C₂×C₃×Q₈	—	2	2	no	—
255	C₂×C₃×Q₈	—	2	1	no	—
256	C₂×C₃×Q₈	—	2	4	no	—
257	C₂×C₃×Q₈	—	4	2	no	—
258	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
259	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₃×D₄	—	2	2	no	—
261	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
262	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
263	C₂²×C₃×C₄	—	2	2	no	—
264	C₂²×C₃×C₄	—	2	2	no	—
265	C₂²×C₃×C₄	—	2	1	no	—
266	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
267	C₃×SD₁₆	—	2	2	no	—
268	C₃×SD₁₆	—	4	2	no	—
269	C₂×C₃×C₈	—	4	2	no	—
270	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
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	—	2	1	no	—
277	C₃×C₄⋊C₄	—	2	2	no	—
278	C₃×C₄⋊C₄	—	2	1	no	—
279	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
280	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
281	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
282	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
283	C₃×C₂²⋊C₄	—	2	2	no	—
284	C₃×C₂²⋊C₄	—	2	1	no	—
285	C₃×C₂²⋊C₄	—	2	2	no	—
286	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
287	C₃×C₄²	—	2	1	no	—
288	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
291	C₅×Q₈	—	2	1	no	—
292	C₅×Q₈	—	2	2	no	—
293	C₅×Q₈	—	2	2	no	—
294	C₅×Q₈	—	4	4	no	—
295	C₅×Q₈	—	4	2	no	—
296	C₅×Q₈	C₃×#41	1	2	yes	complemented
297	C₅×D₄	—	2	1	no	—
298	C₅×D₄	—	2	1	no	—
299	C₅×D₄	—	4	4	no	—
300	C₅×D₄	C₃×SD₁₆	1	4	yes	complemented
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	4	4	no	—
309	C₂×C₄×C₅	—	4	4	no	—
310	C₂×C₄×C₅	—	4	2	no	—
311	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
313	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
315	C₅×C₈	—	2	1	no	—
316	C₅×C₈	—	2	1	no	—
317	C₅×C₈	—	2	2	no	—
318	C₂×#41	—	2	1	no	—
319	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
320	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
321	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
322	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
323	C₄⋊Q₈	—	2	1	no	—
324	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
325	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
326	#123	—	2	2	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	2	no	—
329	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
330	#121	C₂²×C₃×C₅	1	2	yes	—
331	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
334	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
336	#106	C₂²×C₃×C₅	1	1	yes	characteristic
337	#106	C₂²×C₃×C₅	1	2	yes	—
338	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
339	#103	C₂²×C₃×C₅	1	1	yes	characteristic
340	#103	C₂²×C₃×C₅	1	2	yes	—
341	#103	C₂²×C₃×C₅	1	2	yes	—
342	#103	C₂²×C₃×C₅	1	2	yes	—
343	#103	C₂²×C₃×C₅	1	2	yes	—
344	#102	C₂²×C₃×C₅	1	1	yes	characteristic
345	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
346	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
347	C₂×C₃×C₅	—	2	4	no	—
348	C₂×C₃×C₅	—	8	1	no	—
349	C₂×C₃×C₅	#546	1	1	yes	characteristic
350	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
351	C₂×C₃×C₅	#578	1	1	yes	characteristic
352	C₂³×C₃	—	2	1	no	—
353	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
354	C₃×Q₈	—	2	1	no	—
355	C₃×Q₈	—	2	2	no	—
356	C₃×Q₈	—	2	2	no	—
357	C₃×Q₈	—	4	4	no	—
358	C₃×Q₈	—	4	2	no	—
359	C₃×Q₈	C₅×#41	1	2	yes	complemented
360	C₃×D₄	—	2	1	no	—
361	C₃×D₄	—	2	1	no	—
362	C₃×D₄	—	4	4	no	—
363	C₃×D₄	C₅×SD₁₆	1	4	yes	complemented
364	C₂×C₃×C₄	—	2	1	no	—
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	4	no	—
373	C₂×C₃×C₄	—	4	2	no	—
374	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
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	—	4	1	no	—
384	C₂²×C₅	—	4	1	no	—
385	C₂²×C₅	—	4	1	no	—
386	C₂²×C₅	C₂×C₃×SD₁₆	1	4	yes	—
387	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
388	C₄×C₅	—	2	1	no	—
389	C₄×C₅	—	2	2	no	—
390	C₄×C₅	—	2	2	no	—
391	C₄×C₅	—	4	1	no	—
392	C₄×C₅	—	4	2	no	—
393	C₄×C₅	—	4	1	no	—
394	C₄×C₅	—	4	2	no	—
395	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
396	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
397	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
398	#41	—	4	4	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	4	2	no	—
403	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
404	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
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	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
412	SD₁₆	—	2	2	no	—
413	SD₁₆	—	4	2	no	—
414	C₂×C₈	—	4	2	no	—
415	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
416	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
417	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
425	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
426	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
427	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
432	C₄²	—	2	1	no	—
433	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
434	C₃×C₅	#3298	1	1	yes	characteristic, direct product factor, Hall
435	C₂²×C₃	—	2	2	no	—
436	C₂²×C₃	—	2	2	no	—
437	C₂²×C₃	—	4	1	no	—
438	C₂²×C₃	—	4	1	no	—
439	C₂²×C₃	—	4	1	no	—
440	C₂²×C₃	C₂×C₅×SD₁₆	1	4	yes	—
441	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
442	C₃×C₄	—	2	2	no	—
443	C₃×C₄	—	2	2	no	—
444	C₃×C₄	—	2	1	no	—
445	C₃×C₄	—	4	2	no	—
446	C₃×C₄	—	4	1	no	—
447	C₃×C₄	—	4	2	no	—
448	C₃×C₄	—	4	1	no	—
449	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
450	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
451	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×C₅	—	2	4	no	—
453	C₂×C₅	—	8	1	no	—
454	C₂×C₅	C₃×#546	1	1	yes	characteristic
455	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
456	C₂×C₅	C₃×#578	1	1	yes	characteristic
457	C₂³	—	2	1	no	—
458	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	4	4	no	—
463	Q₈	—	4	2	no	—
464	Q₈	C₃×C₅×#41	1	2	yes	complemented
465	D₄	—	2	1	no	—
466	D₄	—	2	1	no	—
467	D₄	—	4	4	no	—
468	D₄	C₃×C₅×SD₁₆	1	4	yes	complemented
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
480	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
481	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
482	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
483	C₈	—	2	1	no	—
484	C₈	—	2	1	no	—
485	C₈	—	2	2	no	—
486	C₂×C₃	—	2	4	no	—
487	C₂×C₃	—	8	1	no	—
488	C₂×C₃	C₅×#546	1	1	yes	characteristic
489	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
490	C₂×C₃	C₅×#578	1	1	yes	characteristic
491	C₅	C₃×#3298	1	1	yes	characteristic, direct product factor, Sylow
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	C₂×C₃×C₅×SD₁₆	1	4	yes	—
498	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	1	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	1	no	—
506	C₄	C₂×C₃×C₅×SD₁₆	1	2	yes	—
507	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
508	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
509	C₃	C₅×#3298	1	1	yes	characteristic, direct product factor, Sylow
510	C₂	—	2	4	no	—
511	C₂	—	8	1	no	—
512	C₂	C₃×C₅×#546	1	1	yes	characteristic
513	C₂	C₂²×C₃×C₅×SD₁₆	1	1	yes	characteristic
514	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×D₄×Q₈	C₂	semidirect
3. C₃×C₅×#487	C₂	semidirect
4. C₃×C₅×#483	C₂	semidirect
5. C₃×C₅×#475	C₂	semidirect
6. C₃×C₅×#465	C₂	semidirect
7. C₃×C₅×#461	C₂	semidirect
8. C₃×C₅×#448	C₂	semidirect
9. C₃×C₄×C₅×SD₁₆	C₂	semidirect
10. C₃×C₅×C₈×D₄	C₂	semidirect
11. C₂×C₃×C₅×#103	C₂	semidirect
12. C₅×#3298	C₃	direct (N × H)
42. C₃×#3298	C₅	direct (N × H)
43. C₅×D₄×Q₈	C₂×C₃	semidirect
45. C₅×#487	C₂×C₃	semidirect
46. C₅×#483	C₂×C₃	semidirect
47. C₅×#475	C₂×C₃	semidirect
48. C₅×#465	C₂×C₃	semidirect
49. C₅×#461	C₂×C₃	semidirect
50. C₅×#448	C₂×C₃	semidirect
51. C₄×C₅×SD₁₆	C₂×C₃	semidirect
52. C₅×C₈×D₄	C₂×C₃	semidirect
53. C₂×C₅×#103	C₂×C₃	semidirect
90. C₃×D₄×Q₈	C₂×C₅	semidirect
92. C₃×#487	C₂×C₅	semidirect
93. C₃×#483	C₂×C₅	semidirect
94. C₃×#475	C₂×C₅	semidirect
95. C₃×#465	C₂×C₅	semidirect
96. C₃×#461	C₂×C₅	semidirect
97. C₃×#448	C₂×C₅	semidirect
98. C₃×C₄×SD₁₆	C₂×C₅	semidirect
99. C₃×C₈×D₄	C₂×C₅	semidirect
100. C₂×C₃×#103	C₂×C₅	semidirect
130. #3298	C₃×C₅	direct (N × H)
138. C₃×C₅×Q₈	#41	semidirect
142. C₃×C₅×D₄	SD₁₆	semidirect
225. D₄×Q₈	C₂×C₃×C₅	semidirect
227. #487	C₂×C₃×C₅	semidirect
228. #483	C₂×C₃×C₅	semidirect
229. #475	C₂×C₃×C₅	semidirect
230. #465	C₂×C₃×C₅	semidirect
231. #461	C₂×C₃×C₅	semidirect
232. #448	C₂×C₃×C₅	semidirect
233. C₄×SD₁₆	C₂×C₃×C₅	semidirect
234. C₈×D₄	C₂×C₃×C₅	semidirect
235. C₂×#103	C₂×C₃×C₅	semidirect
296. C₅×Q₈	C₃×#41	semidirect
300. C₅×D₄	C₃×SD₁₆	semidirect
359. C₃×Q₈	C₅×#41	semidirect
363. C₃×D₄	C₅×SD₁₆	semidirect
434. C₃×C₅	#3298	direct (N × H)
464. Q₈	C₃×C₅×#41	semidirect
468. D₄	C₃×C₅×SD₁₆	semidirect
491. C₅	C₃×#3298	direct (N × H)
509. C₃	C₅×#3298	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×D₄×Q₈	2
C₃×C₅×#547	2
C₃×C₅×#487	2
C₃×C₅×#483	2
C₃×C₅×#475	2
C₃×C₅×#465	2
C₃×C₅×#461	2
C₃×C₅×#448	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×C₈×D₄	2
C₂×C₃×C₅×#103	2
C₅×#3298	3
C₃×#3298	5

Subgroups — C3×C5×#3298 #14276332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3298 #14276332