Subgroups — C₃×C₅×#3290 #14276324

Order 1920.

908 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#577	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#576	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#473	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#472	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#471	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#455	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#454	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3290	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×2₋¹⁺⁴	C₂²	1	2	yes	complemented
14	C₃×C₅×H(5,𝔽₂)	C₂²	1	2	yes	—
15	C₃×C₅×#137	—	2	2	no	—
16	C₃×C₅×#137	—	2	2	no	—
17	C₃×C₅×#137	C₂²	1	2	yes	—
18	C₃×C₅×#137	C₂²	1	2	yes	complemented
19	C₃×C₅×AGL(1,ℤ/8)	—	2	2	no	—
20	C₃×C₅×AGL(1,ℤ/8)	—	2	2	no	—
21	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
23	C₃×C₅×#135	—	2	1	no	—
24	C₃×C₅×#135	—	2	2	no	—
25	C₃×C₅×#135	—	2	1	no	—
26	C₃×C₅×#135	C₂²	1	1	yes	characteristic
27	C₃×C₅×#135	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
29	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₅×SD₁₆	—	2	2	no	—
31	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
32	C₂×C₃×C₅×D₈	—	2	1	no	—
33	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×#131	C₂²	1	1	yes	characteristic
35	C₃×C₅×#131	C₂²	1	2	yes	complemented
36	C₃×C₅×#131	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₅×#124	C₂²	1	2	yes	complemented
38	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×#104	C₂²	1	1	yes	characteristic
41	C₃×C₅×#104	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₅×#104	C₂²	1	2	yes	complemented
43	C₃×C₅×#101	C₂²	1	2	yes	complemented
44	C₃×C₅×#100	C₂²	1	2	yes	complemented
45	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
46	C₃×#3290	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
47	C₅×#578	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#577	C₂×C₃	1	2	yes	complemented
49	C₅×#576	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#495	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#473	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×#472	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#471	C₂×C₃	1	2	yes	complemented
54	C₅×#455	C₂×C₃	1	2	yes	complemented
55	C₅×#454	C₂×C₃	1	2	yes	complemented
56	C₅×#443	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#443	C₂×C₃	1	1	yes	characteristic, complemented
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	—	2	2	no	—
60	C₃×C₅×#41	—	2	2	no	—
61	C₃×C₅×#41	—	2	2	no	—
62	C₃×C₅×#41	—	4	2	no	—
63	C₃×C₅×#41	C₂³	1	1	yes	characteristic
64	C₃×C₅×#41	C₂³	1	2	yes	—
65	C₃×C₅×#41	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×Q₈	—	2	2	no	—
67	C₂×C₃×C₅×Q₈	—	2	2	no	—
68	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
69	C₂×C₃×C₅×D₄	—	2	2	no	—
70	C₂×C₃×C₅×D₄	—	2	2	no	—
71	C₂×C₃×C₅×D₄	—	4	2	no	—
72	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
73	C₃×C₅×Q₁₆	—	2	2	no	—
74	C₃×C₅×Q₁₆	—	2	2	no	—
75	C₃×C₅×Q₁₆	—	2	1	no	—
76	C₃×C₅×Q₁₆	—	2	1	no	—
77	C₃×C₅×Q₁₆	D₄	1	1	yes	characteristic
78	C₃×C₅×Q₁₆	D₄	1	1	yes	characteristic
79	C₃×C₅×SD₁₆	—	2	2	no	—
80	C₃×C₅×SD₁₆	—	2	2	no	—
81	C₃×C₅×SD₁₆	—	2	2	no	—
82	C₃×C₅×SD₁₆	—	2	2	no	—
83	C₃×C₅×SD₁₆	—	2	2	no	—
84	C₃×C₅×SD₁₆	—	2	2	no	—
85	C₃×C₅×SD₁₆	D₄	1	1	yes	characteristic
86	C₃×C₅×SD₁₆	D₄	1	1	yes	characteristic
87	C₃×C₅×SD₁₆	D₄	1	2	yes	—
88	C₃×C₅×D₈	—	2	2	no	—
89	C₃×C₅×D₈	—	2	2	no	—
90	C₃×C₅×D₈	—	2	1	no	—
91	C₃×C₅×D₈	—	2	1	no	—
92	C₃×C₅×D₈	D₄	1	1	yes	characteristic
93	C₃×C₅×D₈	D₄	1	1	yes	characteristic
94	C₃×C₅×M₁₆	—	2	1	no	—
95	C₃×C₅×M₁₆	—	2	2	no	—
96	C₃×C₅×M₁₆	—	2	1	no	—
97	C₃×C₅×M₁₆	C₂³	1	1	yes	characteristic
98	C₃×C₅×M₁₆	C₂³	1	2	yes	—
99	C₃×C₅×M₁₆	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₅×C₈	—	2	1	no	—
101	C₂×C₃×C₅×C₈	—	2	2	no	—
102	C₂×C₃×C₅×C₈	—	2	1	no	—
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
106	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
107	C₃×#578	C₂×C₅	1	1	yes	characteristic, complemented
108	C₃×#577	C₂×C₅	1	2	yes	complemented
109	C₃×#576	C₂×C₅	1	1	yes	characteristic, complemented
110	C₃×#495	C₂×C₅	1	1	yes	characteristic, complemented
111	C₃×#473	C₂×C₅	1	1	yes	characteristic, complemented
112	C₃×#472	C₂×C₅	1	1	yes	characteristic, complemented
113	C₃×#471	C₂×C₅	1	2	yes	complemented
114	C₃×#455	C₂×C₅	1	2	yes	complemented
115	C₃×#454	C₂×C₅	1	2	yes	complemented
116	C₃×#443	C₂×C₅	1	1	yes	characteristic, complemented
117	C₃×#443	C₂×C₅	1	1	yes	characteristic, complemented
118	C₅×2₋¹⁺⁴	C₂²×C₃	1	2	yes	complemented
119	C₅×H(5,𝔽₂)	C₂²×C₃	1	2	yes	—
120	C₅×#137	—	2	2	no	—
121	C₅×#137	—	2	2	no	—
122	C₅×#137	C₂²×C₃	1	2	yes	—
123	C₅×#137	C₂²×C₃	1	2	yes	complemented
124	C₅×AGL(1,ℤ/8)	—	2	2	no	—
125	C₅×AGL(1,ℤ/8)	—	2	2	no	—
126	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	—
127	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	complemented
128	C₅×#135	—	2	1	no	—
129	C₅×#135	—	2	2	no	—
130	C₅×#135	—	2	1	no	—
131	C₅×#135	C₂²×C₃	1	1	yes	characteristic
132	C₅×#135	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₅×Q₁₆	—	2	1	no	—
134	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
135	C₂×C₅×SD₁₆	—	2	2	no	—
136	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
137	C₂×C₅×D₈	—	2	1	no	—
138	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
139	C₅×#131	C₂²×C₃	1	1	yes	characteristic
140	C₅×#131	C₂²×C₃	1	2	yes	complemented
141	C₅×#131	C₂²×C₃	1	1	yes	characteristic, complemented
142	C₅×#124	C₂²×C₃	1	2	yes	complemented
143	C₅×#108	C₂²×C₃	1	1	yes	characteristic, complemented
144	C₅×#108	C₂²×C₃	1	1	yes	characteristic, complemented
145	C₅×#104	C₂²×C₃	1	1	yes	characteristic
146	C₅×#104	C₂²×C₃	1	1	yes	characteristic, complemented
147	C₅×#104	C₂²×C₃	1	2	yes	complemented
148	C₅×#101	C₂²×C₃	1	2	yes	complemented
149	C₅×#100	C₂²×C₃	1	2	yes	complemented
150	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
151	#3290	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
152	C₂³×C₃×C₅	—	2	2	no	—
153	C₂³×C₃×C₅	—	4	2	no	—
154	C₃×C₅×Q₈	—	2	2	no	—
155	C₃×C₅×Q₈	—	2	2	no	—
156	C₃×C₅×Q₈	—	4	2	no	—
157	C₃×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
158	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
159	C₃×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
160	C₃×C₅×D₄	—	2	1	no	—
161	C₃×C₅×D₄	—	2	2	no	—
162	C₃×C₅×D₄	—	2	1	no	—
163	C₃×C₅×D₄	—	2	2	no	—
164	C₃×C₅×D₄	—	2	2	no	—
165	C₃×C₅×D₄	—	4	2	no	—
166	C₃×C₅×D₄	—	4	2	no	—
167	C₃×C₅×D₄	—	4	2	no	—
168	C₃×C₅×D₄	C₂×D₄	1	1	yes	characteristic
169	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
170	C₃×C₅×D₄	C₂×D₄	1	1	yes	characteristic
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	2	no	—
173	C₂×C₃×C₄×C₅	—	2	1	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	2	no	—
176	C₂×C₃×C₄×C₅	—	4	2	no	—
177	C₂×C₃×C₄×C₅	—	4	2	no	—
178	C₂×C₃×C₄×C₅	—	4	2	no	—
179	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
180	C₃×C₅×C₈	—	2	1	no	—
181	C₃×C₅×C₈	—	2	2	no	—
182	C₃×C₅×C₈	—	2	1	no	—
183	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
184	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
185	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
186	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
187	C₃×2₋¹⁺⁴	C₂²×C₅	1	2	yes	complemented
188	C₃×H(5,𝔽₂)	C₂²×C₅	1	2	yes	—
189	C₃×#137	—	2	2	no	—
190	C₃×#137	—	2	2	no	—
191	C₃×#137	C₂²×C₅	1	2	yes	—
192	C₃×#137	C₂²×C₅	1	2	yes	complemented
193	C₃×AGL(1,ℤ/8)	—	2	2	no	—
194	C₃×AGL(1,ℤ/8)	—	2	2	no	—
195	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	—
196	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	complemented
197	C₃×#135	—	2	1	no	—
198	C₃×#135	—	2	2	no	—
199	C₃×#135	—	2	1	no	—
200	C₃×#135	C₂²×C₅	1	1	yes	characteristic
201	C₃×#135	C₂²×C₅	1	1	yes	characteristic
202	C₂×C₃×Q₁₆	—	2	1	no	—
203	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
204	C₂×C₃×SD₁₆	—	2	2	no	—
205	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
206	C₂×C₃×D₈	—	2	1	no	—
207	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
208	C₃×#131	C₂²×C₅	1	1	yes	characteristic
209	C₃×#131	C₂²×C₅	1	2	yes	complemented
210	C₃×#131	C₂²×C₅	1	1	yes	characteristic, complemented
211	C₃×#124	C₂²×C₅	1	2	yes	complemented
212	C₃×#108	C₂²×C₅	1	1	yes	characteristic, complemented
213	C₃×#108	C₂²×C₅	1	1	yes	characteristic, complemented
214	C₃×#104	C₂²×C₅	1	1	yes	characteristic
215	C₃×#104	C₂²×C₅	1	1	yes	characteristic, complemented
216	C₃×#104	C₂²×C₅	1	2	yes	complemented
217	C₃×#101	C₂²×C₅	1	2	yes	complemented
218	C₃×#100	C₂²×C₅	1	2	yes	complemented
219	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
220	C₅×#41	—	2	2	no	—
221	C₅×#41	—	2	2	no	—
222	C₅×#41	—	2	2	no	—
223	C₅×#41	—	2	2	no	—
224	C₅×#41	—	4	2	no	—
225	C₅×#41	C₂³×C₃	1	1	yes	characteristic
226	C₅×#41	C₂³×C₃	1	2	yes	—
227	C₅×#41	C₂³×C₃	1	1	yes	characteristic
228	C₂×C₅×Q₈	—	2	2	no	—
229	C₂×C₅×Q₈	—	2	2	no	—
230	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
231	C₂×C₅×D₄	—	2	2	no	—
232	C₂×C₅×D₄	—	2	2	no	—
233	C₂×C₅×D₄	—	4	2	no	—
234	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
235	C₅×Q₁₆	—	2	2	no	—
236	C₅×Q₁₆	—	2	2	no	—
237	C₅×Q₁₆	—	2	1	no	—
238	C₅×Q₁₆	—	2	1	no	—
239	C₅×Q₁₆	C₃×D₄	1	1	yes	characteristic
240	C₅×Q₁₆	C₃×D₄	1	1	yes	characteristic
241	C₅×SD₁₆	—	2	2	no	—
242	C₅×SD₁₆	—	2	2	no	—
243	C₅×SD₁₆	—	2	2	no	—
244	C₅×SD₁₆	—	2	2	no	—
245	C₅×SD₁₆	—	2	2	no	—
246	C₅×SD₁₆	—	2	2	no	—
247	C₅×SD₁₆	C₃×D₄	1	1	yes	characteristic
248	C₅×SD₁₆	C₃×D₄	1	1	yes	characteristic
249	C₅×SD₁₆	C₃×D₄	1	2	yes	—
250	C₅×D₈	—	2	2	no	—
251	C₅×D₈	—	2	2	no	—
252	C₅×D₈	—	2	1	no	—
253	C₅×D₈	—	2	1	no	—
254	C₅×D₈	C₃×D₄	1	1	yes	characteristic
255	C₅×D₈	C₃×D₄	1	1	yes	characteristic
256	C₅×M₁₆	—	2	1	no	—
257	C₅×M₁₆	—	2	2	no	—
258	C₅×M₁₆	—	2	1	no	—
259	C₅×M₁₆	C₂³×C₃	1	1	yes	characteristic
260	C₅×M₁₆	C₂³×C₃	1	2	yes	—
261	C₅×M₁₆	C₂³×C₃	1	1	yes	characteristic
262	C₂×C₅×C₈	—	2	1	no	—
263	C₂×C₅×C₈	—	2	2	no	—
264	C₂×C₅×C₈	—	2	1	no	—
265	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
267	C₅×C₂²⋊C₄	—	4	2	no	—
268	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
269	#578	C₂×C₃×C₅	1	1	yes	characteristic, complemented
270	#577	C₂×C₃×C₅	1	2	yes	complemented
271	#576	C₂×C₃×C₅	1	1	yes	characteristic, complemented
272	#495	C₂×C₃×C₅	1	1	yes	characteristic, complemented
273	#473	C₂×C₃×C₅	1	1	yes	characteristic, complemented
274	#472	C₂×C₃×C₅	1	1	yes	characteristic, complemented
275	#471	C₂×C₃×C₅	1	2	yes	complemented
276	#455	C₂×C₃×C₅	1	2	yes	complemented
277	#454	C₂×C₃×C₅	1	2	yes	complemented
278	#443	C₂×C₃×C₅	1	1	yes	characteristic, complemented
279	#443	C₂×C₃×C₅	1	1	yes	characteristic, complemented
280	C₂²×C₃×C₅	—	2	1	no	—
281	C₂²×C₃×C₅	—	2	2	no	—
282	C₂²×C₃×C₅	—	2	1	no	—
283	C₂²×C₃×C₅	—	4	2	no	—
284	C₂²×C₃×C₅	—	8	2	no	—
285	C₂²×C₃×C₅	—	16	2	no	—
286	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
287	C₃×C₄×C₅	—	2	1	no	—
288	C₃×C₄×C₅	—	2	2	no	—
289	C₃×C₄×C₅	—	2	1	no	—
290	C₃×C₄×C₅	—	4	1	no	—
291	C₃×C₄×C₅	—	4	2	no	—
292	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
293	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
294	C₃×#41	—	2	2	no	—
295	C₃×#41	—	2	2	no	—
296	C₃×#41	—	2	2	no	—
297	C₃×#41	—	2	2	no	—
298	C₃×#41	—	4	2	no	—
299	C₃×#41	C₂³×C₅	1	1	yes	characteristic
300	C₃×#41	C₂³×C₅	1	2	yes	—
301	C₃×#41	C₂³×C₅	1	1	yes	characteristic
302	C₂×C₃×Q₈	—	2	2	no	—
303	C₂×C₃×Q₈	—	2	2	no	—
304	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
305	C₂×C₃×D₄	—	2	2	no	—
306	C₂×C₃×D₄	—	2	2	no	—
307	C₂×C₃×D₄	—	4	2	no	—
308	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
309	C₃×Q₁₆	—	2	2	no	—
310	C₃×Q₁₆	—	2	2	no	—
311	C₃×Q₁₆	—	2	1	no	—
312	C₃×Q₁₆	—	2	1	no	—
313	C₃×Q₁₆	C₅×D₄	1	1	yes	characteristic
314	C₃×Q₁₆	C₅×D₄	1	1	yes	characteristic
315	C₃×SD₁₆	—	2	2	no	—
316	C₃×SD₁₆	—	2	2	no	—
317	C₃×SD₁₆	—	2	2	no	—
318	C₃×SD₁₆	—	2	2	no	—
319	C₃×SD₁₆	—	2	2	no	—
320	C₃×SD₁₆	—	2	2	no	—
321	C₃×SD₁₆	C₅×D₄	1	1	yes	characteristic
322	C₃×SD₁₆	C₅×D₄	1	1	yes	characteristic
323	C₃×SD₁₆	C₅×D₄	1	2	yes	—
324	C₃×D₈	—	2	2	no	—
325	C₃×D₈	—	2	2	no	—
326	C₃×D₈	—	2	1	no	—
327	C₃×D₈	—	2	1	no	—
328	C₃×D₈	C₅×D₄	1	1	yes	characteristic
329	C₃×D₈	C₅×D₄	1	1	yes	characteristic
330	C₃×M₁₆	—	2	1	no	—
331	C₃×M₁₆	—	2	2	no	—
332	C₃×M₁₆	—	2	1	no	—
333	C₃×M₁₆	C₂³×C₅	1	1	yes	characteristic
334	C₃×M₁₆	C₂³×C₅	1	2	yes	—
335	C₃×M₁₆	C₂³×C₅	1	1	yes	characteristic
336	C₂×C₃×C₈	—	2	1	no	—
337	C₂×C₃×C₈	—	2	2	no	—
338	C₂×C₃×C₈	—	2	1	no	—
339	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
340	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
341	C₃×C₂²⋊C₄	—	4	2	no	—
342	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
343	C₂³×C₅	—	2	2	no	—
344	C₂³×C₅	—	4	2	no	—
345	C₅×Q₈	—	2	2	no	—
346	C₅×Q₈	—	2	2	no	—
347	C₅×Q₈	—	4	2	no	—
348	C₅×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
349	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
350	C₅×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
351	C₅×D₄	—	2	1	no	—
352	C₅×D₄	—	2	2	no	—
353	C₅×D₄	—	2	1	no	—
354	C₅×D₄	—	2	2	no	—
355	C₅×D₄	—	2	2	no	—
356	C₅×D₄	—	4	2	no	—
357	C₅×D₄	—	4	2	no	—
358	C₅×D₄	—	4	2	no	—
359	C₅×D₄	C₂×C₃×D₄	1	1	yes	characteristic
360	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
361	C₅×D₄	C₂×C₃×D₄	1	1	yes	characteristic
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	2	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	1	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	4	2	no	—
368	C₂×C₄×C₅	—	4	2	no	—
369	C₂×C₄×C₅	—	4	2	no	—
370	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
371	C₅×C₈	—	2	1	no	—
372	C₅×C₈	—	2	2	no	—
373	C₅×C₈	—	2	1	no	—
374	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
375	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
376	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
377	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
378	2₋¹⁺⁴	C₂²×C₃×C₅	1	2	yes	complemented
379	H(5,𝔽₂)	C₂²×C₃×C₅	1	2	yes	—
380	#137	—	2	2	no	—
381	#137	—	2	2	no	—
382	#137	C₂²×C₃×C₅	1	2	yes	—
383	#137	C₂²×C₃×C₅	1	2	yes	complemented
384	AGL(1,ℤ/8)	—	2	2	no	—
385	AGL(1,ℤ/8)	—	2	2	no	—
386	AGL(1,ℤ/8)	C₂²×C₃×C₅	1	2	yes	—
387	AGL(1,ℤ/8)	C₂²×C₃×C₅	1	2	yes	complemented
388	#135	—	2	1	no	—
389	#135	—	2	2	no	—
390	#135	—	2	1	no	—
391	#135	C₂²×C₃×C₅	1	1	yes	characteristic
392	#135	C₂²×C₃×C₅	1	1	yes	characteristic
393	C₂×Q₁₆	—	2	1	no	—
394	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
395	C₂×SD₁₆	—	2	2	no	—
396	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
397	C₂×D₈	—	2	1	no	—
398	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
399	#131	C₂²×C₃×C₅	1	1	yes	characteristic
400	#131	C₂²×C₃×C₅	1	2	yes	complemented
401	#131	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
402	#124	C₂²×C₃×C₅	1	2	yes	complemented
403	#108	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
404	#108	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
405	#104	C₂²×C₃×C₅	1	1	yes	characteristic
406	#104	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
407	#104	C₂²×C₃×C₅	1	2	yes	complemented
408	#101	C₂²×C₃×C₅	1	2	yes	complemented
409	#100	C₂²×C₃×C₅	1	2	yes	complemented
410	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
411	C₂×C₃×C₅	—	2	1	no	—
412	C₂×C₃×C₅	—	4	1	no	—
413	C₂×C₃×C₅	—	4	2	no	—
414	C₂×C₃×C₅	—	4	1	no	—
415	C₂×C₃×C₅	—	8	2	no	—
416	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
417	C₂³×C₃	—	2	2	no	—
418	C₂³×C₃	—	4	2	no	—
419	C₃×Q₈	—	2	2	no	—
420	C₃×Q₈	—	2	2	no	—
421	C₃×Q₈	—	4	2	no	—
422	C₃×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
423	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
424	C₃×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
425	C₃×D₄	—	2	1	no	—
426	C₃×D₄	—	2	2	no	—
427	C₃×D₄	—	2	1	no	—
428	C₃×D₄	—	2	2	no	—
429	C₃×D₄	—	2	2	no	—
430	C₃×D₄	—	4	2	no	—
431	C₃×D₄	—	4	2	no	—
432	C₃×D₄	—	4	2	no	—
433	C₃×D₄	C₂×C₅×D₄	1	1	yes	characteristic
434	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
435	C₃×D₄	C₂×C₅×D₄	1	1	yes	characteristic
436	C₂×C₃×C₄	—	2	1	no	—
437	C₂×C₃×C₄	—	2	2	no	—
438	C₂×C₃×C₄	—	2	1	no	—
439	C₂×C₃×C₄	—	2	1	no	—
440	C₂×C₃×C₄	—	2	2	no	—
441	C₂×C₃×C₄	—	4	2	no	—
442	C₂×C₃×C₄	—	4	2	no	—
443	C₂×C₃×C₄	—	4	2	no	—
444	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
445	C₃×C₈	—	2	1	no	—
446	C₃×C₈	—	2	2	no	—
447	C₃×C₈	—	2	1	no	—
448	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
449	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
450	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
451	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
452	C₂²×C₅	—	2	1	no	—
453	C₂²×C₅	—	2	2	no	—
454	C₂²×C₅	—	2	1	no	—
455	C₂²×C₅	—	4	2	no	—
456	C₂²×C₅	—	8	2	no	—
457	C₂²×C₅	—	16	2	no	—
458	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
459	C₄×C₅	—	2	1	no	—
460	C₄×C₅	—	2	2	no	—
461	C₄×C₅	—	2	1	no	—
462	C₄×C₅	—	4	1	no	—
463	C₄×C₅	—	4	2	no	—
464	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
465	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
466	#41	—	2	2	no	—
467	#41	—	2	2	no	—
468	#41	—	2	2	no	—
469	#41	—	2	2	no	—
470	#41	—	4	2	no	—
471	#41	C₂³×C₃×C₅	1	1	yes	characteristic
472	#41	C₂³×C₃×C₅	1	2	yes	—
473	#41	C₂³×C₃×C₅	1	1	yes	characteristic
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	4	2	no	—
480	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
481	Q₁₆	—	2	2	no	—
482	Q₁₆	—	2	2	no	—
483	Q₁₆	—	2	1	no	—
484	Q₁₆	—	2	1	no	—
485	Q₁₆	C₃×C₅×D₄	1	1	yes	characteristic
486	Q₁₆	C₃×C₅×D₄	1	1	yes	characteristic
487	SD₁₆	—	2	2	no	—
488	SD₁₆	—	2	2	no	—
489	SD₁₆	—	2	2	no	—
490	SD₁₆	—	2	2	no	—
491	SD₁₆	—	2	2	no	—
492	SD₁₆	—	2	2	no	—
493	SD₁₆	C₃×C₅×D₄	1	1	yes	characteristic
494	SD₁₆	C₃×C₅×D₄	1	1	yes	characteristic
495	SD₁₆	C₃×C₅×D₄	1	2	yes	—
496	D₈	—	2	2	no	—
497	D₈	—	2	2	no	—
498	D₈	—	2	1	no	—
499	D₈	—	2	1	no	—
500	D₈	C₃×C₅×D₄	1	1	yes	characteristic
501	D₈	C₃×C₅×D₄	1	1	yes	characteristic
502	M₁₆	—	2	1	no	—
503	M₁₆	—	2	2	no	—
504	M₁₆	—	2	1	no	—
505	M₁₆	C₂³×C₃×C₅	1	1	yes	characteristic
506	M₁₆	C₂³×C₃×C₅	1	2	yes	—
507	M₁₆	C₂³×C₃×C₅	1	1	yes	characteristic
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
512	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
513	C₂²⋊C₄	—	4	2	no	—
514	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
515	C₃×C₅	#3290	1	1	yes	characteristic, direct product factor, Hall
516	C₂²×C₃	—	2	1	no	—
517	C₂²×C₃	—	2	2	no	—
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	—	4	2	no	—
520	C₂²×C₃	—	8	2	no	—
521	C₂²×C₃	—	16	2	no	—
522	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	2	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	4	1	no	—
527	C₃×C₄	—	4	2	no	—
528	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
529	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
530	C₂×C₅	—	2	1	no	—
531	C₂×C₅	—	4	1	no	—
532	C₂×C₅	—	4	2	no	—
533	C₂×C₅	—	4	1	no	—
534	C₂×C₅	—	8	2	no	—
535	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
536	C₂³	—	2	2	no	—
537	C₂³	—	4	2	no	—
538	Q₈	—	2	2	no	—
539	Q₈	—	2	2	no	—
540	Q₈	—	4	2	no	—
541	Q₈	C₂×C₃×C₅×D₄	1	1	yes	characteristic
542	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
543	Q₈	C₂×C₃×C₅×D₄	1	1	yes	characteristic
544	D₄	—	2	1	no	—
545	D₄	—	2	2	no	—
546	D₄	—	2	1	no	—
547	D₄	—	2	2	no	—
548	D₄	—	2	2	no	—
549	D₄	—	4	2	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	D₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
553	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
554	D₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
564	C₈	—	2	1	no	—
565	C₈	—	2	2	no	—
566	C₈	—	2	1	no	—
567	C₈	C₂×C₃×C₅×D₄	1	1	yes	characteristic
568	C₈	C₂×C₃×C₅×D₄	1	1	yes	characteristic
569	C₈	C₂×C₃×C₅×D₄	1	1	yes	characteristic
570	C₈	C₂×C₃×C₅×D₄	1	1	yes	characteristic
571	C₂×C₃	—	2	1	no	—
572	C₂×C₃	—	4	1	no	—
573	C₂×C₃	—	4	2	no	—
574	C₂×C₃	—	4	1	no	—
575	C₂×C₃	—	8	2	no	—
576	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
577	C₅	C₃×#3290	1	1	yes	characteristic, direct product factor, Sylow
578	C₂²	—	2	1	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	8	2	no	—
583	C₂²	—	16	2	no	—
584	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	2	no	—
590	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
591	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
592	C₃	C₅×#3290	1	1	yes	characteristic, direct product factor, Sylow
593	C₂	—	2	1	no	—
594	C₂	—	4	1	no	—
595	C₂	—	4	2	no	—
596	C₂	—	4	1	no	—
597	C₂	—	8	2	no	—
598	C₂	C₃×C₅×D₄²	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#578	C₂	semidirect
2. C₃×C₅×#577	C₂	semidirect
3. C₃×C₅×#576	C₂	semidirect
4. C₃×C₅×#495	C₂	semidirect
5. C₃×C₅×#473	C₂	semidirect
6. C₃×C₅×#472	C₂	semidirect
7. C₃×C₅×#471	C₂	semidirect
8. C₃×C₅×#455	C₂	semidirect
9. C₃×C₅×#454	C₂	semidirect
10. C₃×C₅×#443	C₂	semidirect
11. C₃×C₅×#443	C₂	semidirect
12. C₅×#3290	C₃	direct (N × H)
13. C₃×C₅×2₋¹⁺⁴	C₂²	semidirect
18. C₃×C₅×#137	C₂²	semidirect
22. C₃×C₅×AGL(1,ℤ/8)	C₂²	semidirect
29. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
31. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
35. C₃×C₅×#131	C₂²	semidirect
36. C₃×C₅×#131	C₂²	semidirect
37. C₃×C₅×#124	C₂²	semidirect
38. C₃×C₅×#108	C₂²	semidirect
39. C₃×C₅×#108	C₂²	semidirect
41. C₃×C₅×#104	C₂²	semidirect
42. C₃×C₅×#104	C₂²	semidirect
43. C₃×C₅×#101	C₂²	semidirect
44. C₃×C₅×#100	C₂²	semidirect
45. C₃×C₄×C₅×C₈	C₂²	semidirect
46. C₃×#3290	C₅	direct (N × H)
47. C₅×#578	C₂×C₃	semidirect
48. C₅×#577	C₂×C₃	semidirect
49. C₅×#576	C₂×C₃	semidirect
50. C₅×#495	C₂×C₃	semidirect
51. C₅×#473	C₂×C₃	semidirect
52. C₅×#472	C₂×C₃	semidirect
53. C₅×#471	C₂×C₃	semidirect
54. C₅×#455	C₂×C₃	semidirect
55. C₅×#454	C₂×C₃	semidirect
56. C₅×#443	C₂×C₃	semidirect
57. C₅×#443	C₂×C₃	semidirect
107. C₃×#578	C₂×C₅	semidirect
108. C₃×#577	C₂×C₅	semidirect
109. C₃×#576	C₂×C₅	semidirect
110. C₃×#495	C₂×C₅	semidirect
111. C₃×#473	C₂×C₅	semidirect
112. C₃×#472	C₂×C₅	semidirect
113. C₃×#471	C₂×C₅	semidirect
114. C₃×#455	C₂×C₅	semidirect
115. C₃×#454	C₂×C₅	semidirect
116. C₃×#443	C₂×C₅	semidirect
117. C₃×#443	C₂×C₅	semidirect
118. C₅×2₋¹⁺⁴	C₂²×C₃	semidirect
123. C₅×#137	C₂²×C₃	semidirect
127. C₅×AGL(1,ℤ/8)	C₂²×C₃	semidirect
134. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
136. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
140. C₅×#131	C₂²×C₃	semidirect
141. C₅×#131	C₂²×C₃	semidirect
142. C₅×#124	C₂²×C₃	semidirect
143. C₅×#108	C₂²×C₃	semidirect
144. C₅×#108	C₂²×C₃	semidirect
146. C₅×#104	C₂²×C₃	semidirect
147. C₅×#104	C₂²×C₃	semidirect
148. C₅×#101	C₂²×C₃	semidirect
149. C₅×#100	C₂²×C₃	semidirect
150. C₄×C₅×C₈	C₂²×C₃	semidirect
151. #3290	C₃×C₅	direct (N × H)
187. C₃×2₋¹⁺⁴	C₂²×C₅	semidirect
192. C₃×#137	C₂²×C₅	semidirect
196. C₃×AGL(1,ℤ/8)	C₂²×C₅	semidirect
203. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
205. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
209. C₃×#131	C₂²×C₅	semidirect
210. C₃×#131	C₂²×C₅	semidirect
211. C₃×#124	C₂²×C₅	semidirect
212. C₃×#108	C₂²×C₅	semidirect
213. C₃×#108	C₂²×C₅	semidirect
215. C₃×#104	C₂²×C₅	semidirect
216. C₃×#104	C₂²×C₅	semidirect
217. C₃×#101	C₂²×C₅	semidirect
218. C₃×#100	C₂²×C₅	semidirect
219. C₃×C₄×C₈	C₂²×C₅	semidirect
269. #578	C₂×C₃×C₅	semidirect
270. #577	C₂×C₃×C₅	semidirect
271. #576	C₂×C₃×C₅	semidirect
272. #495	C₂×C₃×C₅	semidirect
273. #473	C₂×C₃×C₅	semidirect
274. #472	C₂×C₃×C₅	semidirect
275. #471	C₂×C₃×C₅	semidirect
276. #455	C₂×C₃×C₅	semidirect
277. #454	C₂×C₃×C₅	semidirect
278. #443	C₂×C₃×C₅	semidirect
279. #443	C₂×C₃×C₅	semidirect
378. 2₋¹⁺⁴	C₂²×C₃×C₅	semidirect
383. #137	C₂²×C₃×C₅	semidirect
387. AGL(1,ℤ/8)	C₂²×C₃×C₅	semidirect
394. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
396. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
400. #131	C₂²×C₃×C₅	semidirect
401. #131	C₂²×C₃×C₅	semidirect
402. #124	C₂²×C₃×C₅	semidirect
403. #108	C₂²×C₃×C₅	semidirect
404. #108	C₂²×C₃×C₅	semidirect
406. #104	C₂²×C₃×C₅	semidirect
407. #104	C₂²×C₃×C₅	semidirect
408. #101	C₂²×C₃×C₅	semidirect
409. #100	C₂²×C₃×C₅	semidirect
410. C₄×C₈	C₂²×C₃×C₅	semidirect
515. C₃×C₅	#3290	direct (N × H)
577. C₅	C₃×#3290	direct (N × H)
592. C₃	C₅×#3290	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×#578	2
C₃×C₅×#577	2
C₃×C₅×#576	2
C₃×C₅×#495	2
C₃×C₅×#473	2
C₃×C₅×#472	2
C₃×C₅×#471	2
C₃×C₅×#455	2
C₃×C₅×#454	2
C₃×C₅×#443	2
C₅×#3290	3
C₃×#3290	5

Subgroups — C3×C5×#3290 #14276324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3290 #14276324