Subgroups — C₃×C₅×#3557 #14276591

Order 1920.

1860 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#563	C₂	1	4	yes	maximal, complemented
2	C₃×C₅×#559	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#557	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#556	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#554	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#552	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#542	C₂	1	4	yes	maximal, complemented
9	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic
11	C₃×C₅×#539	C₂	1	4	yes	maximal, complemented
12	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#529	C₂	1	2	yes	maximal, complemented
14	C₅×#3557	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic
20	C₃×C₅×#126	C₂²	1	4	yes	—
21	C₃×C₅×#126	C₂²	1	4	yes	—
22	C₃×C₅×#126	C₂²	1	4	yes	—
23	C₃×C₅×#126	C₂²	1	4	yes	—
24	C₃×C₅×#126	C₂²	1	4	yes	—
25	C₃×C₅×#125	C₂²	1	2	yes	—
26	C₃×C₅×#125	C₂²	1	2	yes	—
27	C₃×C₅×#125	C₂²	1	4	yes	—
28	C₃×C₅×#125	C₂²	1	4	yes	—
29	C₃×C₅×#125	C₂²	1	1	yes	characteristic
30	C₃×C₅×#125	C₂²	1	4	yes	—
31	C₃×C₅×#125	C₂²	1	1	yes	characteristic
32	C₃×C₅×#124	C₂²	1	2	yes	—
33	C₃×C₅×#124	C₂²	1	4	yes	—
34	C₃×C₅×#124	C₂²	1	2	yes	—
35	C₃×C₅×#124	C₂²	1	4	yes	—
36	C₃×C₅×#123	C₂²	1	4	yes	—
37	C₃×C₅×#123	C₂²	1	4	yes	—
38	C₃×C₅×#123	C₂²	1	4	yes	—
39	C₃×C₅×#123	C₂²	1	4	yes	—
40	C₃×C₅×#123	C₂²	1	4	yes	—
41	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
42	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
45	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
46	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
47	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
48	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
49	C₃×C₅×#121	C₂²	1	2	yes	—
50	C₃×C₅×#121	C₂²	1	4	yes	—
51	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
52	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
53	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
54	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
55	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	—
56	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
57	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
58	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
59	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
60	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
61	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
62	C₃×C₅×#117	C₂²	1	4	yes	—
63	C₃×C₅×#117	C₂²	1	1	yes	characteristic
64	C₃×C₅×#117	C₂²	1	1	yes	characteristic
65	C₃×C₅×#117	C₂²	1	4	yes	—
66	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
67	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
68	C₃×#3557	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#563	C₂×C₃	1	4	yes	complemented
70	C₅×#559	C₂×C₃	1	2	yes	complemented
71	C₅×#557	C₂×C₃	1	2	yes	complemented
72	C₅×#556	C₂×C₃	1	2	yes	complemented
73	C₅×#554	C₂×C₃	1	2	yes	complemented
74	C₅×#552	C₂×C₃	1	4	yes	complemented
75	C₅×#542	C₂×C₃	1	2	yes	complemented
76	C₅×#542	C₂×C₃	1	4	yes	complemented
77	C₅×#541	C₂×C₃	1	1	yes	characteristic, complemented
78	C₅×#540	C₂×C₃	1	1	yes	characteristic
79	C₅×#539	C₂×C₃	1	4	yes	complemented
80	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
81	C₅×#529	C₂×C₃	1	2	yes	complemented
82	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
83	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
84	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
85	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
86	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
87	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
88	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
91	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
92	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
93	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
94	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
95	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
96	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
97	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
98	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
99	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
100	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
101	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
102	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
103	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
104	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
105	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
106	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
107	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
108	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
109	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
110	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
111	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
112	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
113	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
114	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
118	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
119	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
127	C₃×C₄²×C₅	C₂³	1	2	yes	—
128	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
129	C₃×C₄²×C₅	C₂³	1	4	yes	—
130	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
131	C₃×C₄²×C₅	C₂³	1	2	yes	—
132	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
133	C₃×C₄²×C₅	C₂³	1	4	yes	—
134	C₃×C₄²×C₅	C₂³	1	4	yes	—
135	C₃×#563	C₂×C₅	1	4	yes	complemented
136	C₃×#559	C₂×C₅	1	2	yes	complemented
137	C₃×#557	C₂×C₅	1	2	yes	complemented
138	C₃×#556	C₂×C₅	1	2	yes	complemented
139	C₃×#554	C₂×C₅	1	2	yes	complemented
140	C₃×#552	C₂×C₅	1	4	yes	complemented
141	C₃×#542	C₂×C₅	1	2	yes	complemented
142	C₃×#542	C₂×C₅	1	4	yes	complemented
143	C₃×#541	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×#540	C₂×C₅	1	1	yes	characteristic
145	C₃×#539	C₂×C₅	1	4	yes	complemented
146	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
147	C₃×#529	C₂×C₅	1	2	yes	complemented
148	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
149	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
150	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
151	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
152	C₅×#127	C₂²×C₃	1	1	yes	characteristic
153	C₅×#126	C₂²×C₃	1	4	yes	—
154	C₅×#126	C₂²×C₃	1	4	yes	—
155	C₅×#126	C₂²×C₃	1	4	yes	—
156	C₅×#126	C₂²×C₃	1	4	yes	—
157	C₅×#126	C₂²×C₃	1	4	yes	—
158	C₅×#125	C₂²×C₃	1	2	yes	—
159	C₅×#125	C₂²×C₃	1	2	yes	—
160	C₅×#125	C₂²×C₃	1	4	yes	—
161	C₅×#125	C₂²×C₃	1	4	yes	—
162	C₅×#125	C₂²×C₃	1	1	yes	characteristic
163	C₅×#125	C₂²×C₃	1	4	yes	—
164	C₅×#125	C₂²×C₃	1	1	yes	characteristic
165	C₅×#124	C₂²×C₃	1	2	yes	—
166	C₅×#124	C₂²×C₃	1	4	yes	—
167	C₅×#124	C₂²×C₃	1	2	yes	—
168	C₅×#124	C₂²×C₃	1	4	yes	—
169	C₅×#123	C₂²×C₃	1	4	yes	—
170	C₅×#123	C₂²×C₃	1	4	yes	—
171	C₅×#123	C₂²×C₃	1	4	yes	—
172	C₅×#123	C₂²×C₃	1	4	yes	—
173	C₅×#123	C₂²×C₃	1	4	yes	—
174	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
175	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
176	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
177	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
178	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
179	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
180	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
181	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
182	C₅×#121	C₂²×C₃	1	2	yes	—
183	C₅×#121	C₂²×C₃	1	4	yes	—
184	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
185	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
186	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
187	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
188	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	—
189	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
190	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
191	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
192	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
193	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
194	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
195	C₅×#117	C₂²×C₃	1	4	yes	—
196	C₅×#117	C₂²×C₃	1	1	yes	characteristic
197	C₅×#117	C₂²×C₃	1	1	yes	characteristic
198	C₅×#117	C₂²×C₃	1	4	yes	—
199	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
200	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
201	#3557	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
202	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
203	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
204	C₃×C₅×Q₈	—	2	4	no	—
205	C₃×C₅×Q₈	—	4	2	no	—
206	C₃×C₅×Q₈	—	4	4	no	—
207	C₃×C₅×Q₈	—	4	2	no	—
208	C₃×C₅×D₄	—	2	4	no	—
209	C₃×C₅×D₄	—	4	4	no	—
210	C₃×C₅×D₄	—	4	4	no	—
211	C₂×C₃×C₄×C₅	—	2	2	no	—
212	C₂×C₃×C₄×C₅	—	4	4	no	—
213	C₂×C₃×C₄×C₅	—	4	2	no	—
214	C₂×C₃×C₄×C₅	—	4	4	no	—
215	C₂×C₃×C₄×C₅	—	4	4	no	—
216	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
217	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
218	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
219	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
220	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
221	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
222	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
223	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
224	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
225	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
226	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
227	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
228	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
229	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
230	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
231	C₃×#127	C₂²×C₅	1	1	yes	characteristic
232	C₃×#126	C₂²×C₅	1	4	yes	—
233	C₃×#126	C₂²×C₅	1	4	yes	—
234	C₃×#126	C₂²×C₅	1	4	yes	—
235	C₃×#126	C₂²×C₅	1	4	yes	—
236	C₃×#126	C₂²×C₅	1	4	yes	—
237	C₃×#125	C₂²×C₅	1	4	yes	—
238	C₃×#125	C₂²×C₅	1	4	yes	—
239	C₃×#125	C₂²×C₅	1	2	yes	—
240	C₃×#125	C₂²×C₅	1	2	yes	—
241	C₃×#125	C₂²×C₅	1	4	yes	—
242	C₃×#125	C₂²×C₅	1	1	yes	characteristic
243	C₃×#125	C₂²×C₅	1	1	yes	characteristic
244	C₃×#124	C₂²×C₅	1	4	yes	—
245	C₃×#124	C₂²×C₅	1	2	yes	—
246	C₃×#124	C₂²×C₅	1	2	yes	—
247	C₃×#124	C₂²×C₅	1	4	yes	—
248	C₃×#123	C₂²×C₅	1	4	yes	—
249	C₃×#123	C₂²×C₅	1	4	yes	—
250	C₃×#123	C₂²×C₅	1	4	yes	—
251	C₃×#123	C₂²×C₅	1	4	yes	—
252	C₃×#123	C₂²×C₅	1	4	yes	—
253	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
254	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
255	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
256	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
257	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
258	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
259	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
260	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
261	C₃×#121	C₂²×C₅	1	2	yes	—
262	C₃×#121	C₂²×C₅	1	4	yes	—
263	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
264	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
265	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
266	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
267	C₃×C₄×Q₈	C₂²×C₅	1	4	yes	—
268	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
269	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
270	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
271	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
272	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
273	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
274	C₃×#117	C₂²×C₅	1	4	yes	—
275	C₃×#117	C₂²×C₅	1	1	yes	characteristic
276	C₃×#117	C₂²×C₅	1	1	yes	characteristic
277	C₃×#117	C₂²×C₅	1	4	yes	—
278	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
279	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
280	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
281	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
282	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
283	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
284	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
285	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
286	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
287	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
289	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
290	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
291	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
292	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
293	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
294	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
295	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
296	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
297	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
298	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
299	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
300	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
301	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
302	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
303	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
304	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
305	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
306	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
307	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
308	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
309	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
310	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
311	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
312	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
313	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
314	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
315	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
316	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
317	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
318	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
319	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
320	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
321	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
322	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
323	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
324	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
325	C₄²×C₅	C₂³×C₃	1	2	yes	—
326	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
327	C₄²×C₅	C₂³×C₃	1	4	yes	—
328	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
329	C₄²×C₅	C₂³×C₃	1	2	yes	—
330	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
331	C₄²×C₅	C₂³×C₃	1	4	yes	—
332	C₄²×C₅	C₂³×C₃	1	4	yes	—
333	#563	C₂×C₃×C₅	1	4	yes	complemented
334	#559	C₂×C₃×C₅	1	2	yes	complemented
335	#557	C₂×C₃×C₅	1	2	yes	complemented
336	#556	C₂×C₃×C₅	1	2	yes	complemented
337	#554	C₂×C₃×C₅	1	2	yes	complemented
338	#552	C₂×C₃×C₅	1	4	yes	complemented
339	#542	C₂×C₃×C₅	1	2	yes	complemented
340	#542	C₂×C₃×C₅	1	4	yes	complemented
341	#541	C₂×C₃×C₅	1	1	yes	characteristic, complemented
342	#540	C₂×C₃×C₅	1	1	yes	characteristic
343	#539	C₂×C₃×C₅	1	4	yes	complemented
344	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
345	#529	C₂×C₃×C₅	1	2	yes	complemented
346	C₂²×C₃×C₅	—	2	1	no	—
347	C₂²×C₃×C₅	—	2	4	no	—
348	C₂²×C₃×C₅	—	2	4	no	—
349	C₂²×C₃×C₅	—	2	2	no	—
350	C₂²×C₃×C₅	—	2	4	no	—
351	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
352	C₃×C₄×C₅	—	2	1	no	—
353	C₃×C₄×C₅	—	2	4	no	—
354	C₃×C₄×C₅	—	2	2	no	—
355	C₃×C₄×C₅	—	2	4	no	—
356	C₃×C₄×C₅	—	2	2	no	—
357	C₃×C₄×C₅	—	2	2	no	—
358	C₃×C₄×C₅	—	2	4	no	—
359	C₃×C₄×C₅	—	2	2	no	—
360	C₃×C₄×C₅	—	2	2	no	—
361	C₃×C₄×C₅	—	2	2	no	—
362	C₃×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
363	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
364	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
365	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
366	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
367	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
368	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
369	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
370	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
371	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
372	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
373	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
374	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
375	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
376	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
377	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
378	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
379	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
380	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
381	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
382	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
383	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
384	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
385	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
386	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
387	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
388	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
389	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
390	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
391	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
392	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
393	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
394	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
395	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
396	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
397	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
398	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
399	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
400	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
401	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
402	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
403	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
404	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
405	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
406	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
407	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
408	C₃×C₄²	C₂³×C₅	1	2	yes	—
409	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
410	C₃×C₄²	C₂³×C₅	1	4	yes	—
411	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
412	C₃×C₄²	C₂³×C₅	1	2	yes	—
413	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
414	C₃×C₄²	C₂³×C₅	1	4	yes	—
415	C₃×C₄²	C₂³×C₅	1	4	yes	—
416	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
417	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
418	C₅×Q₈	—	2	4	no	—
419	C₅×Q₈	—	4	2	no	—
420	C₅×Q₈	—	4	4	no	—
421	C₅×Q₈	—	4	2	no	—
422	C₅×D₄	—	2	4	no	—
423	C₅×D₄	—	4	4	no	—
424	C₅×D₄	—	4	4	no	—
425	C₂×C₄×C₅	—	2	2	no	—
426	C₂×C₄×C₅	—	4	4	no	—
427	C₂×C₄×C₅	—	4	2	no	—
428	C₂×C₄×C₅	—	4	4	no	—
429	C₂×C₄×C₅	—	4	4	no	—
430	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
431	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
432	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
433	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
434	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
435	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
436	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
437	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
438	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
439	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
440	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
441	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
442	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
443	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
444	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
445	#127	C₂²×C₃×C₅	1	1	yes	characteristic
446	#126	C₂²×C₃×C₅	1	4	yes	—
447	#126	C₂²×C₃×C₅	1	4	yes	—
448	#126	C₂²×C₃×C₅	1	4	yes	—
449	#126	C₂²×C₃×C₅	1	4	yes	—
450	#126	C₂²×C₃×C₅	1	4	yes	—
451	#125	C₂²×C₃×C₅	1	2	yes	—
452	#125	C₂²×C₃×C₅	1	2	yes	—
453	#125	C₂²×C₃×C₅	1	4	yes	—
454	#125	C₂²×C₃×C₅	1	4	yes	—
455	#125	C₂²×C₃×C₅	1	1	yes	characteristic
456	#125	C₂²×C₃×C₅	1	4	yes	—
457	#125	C₂²×C₃×C₅	1	1	yes	characteristic
458	#124	C₂²×C₃×C₅	1	2	yes	—
459	#124	C₂²×C₃×C₅	1	4	yes	—
460	#124	C₂²×C₃×C₅	1	2	yes	—
461	#124	C₂²×C₃×C₅	1	4	yes	—
462	#123	C₂²×C₃×C₅	1	4	yes	—
463	#123	C₂²×C₃×C₅	1	4	yes	—
464	#123	C₂²×C₃×C₅	1	4	yes	—
465	#123	C₂²×C₃×C₅	1	4	yes	—
466	#123	C₂²×C₃×C₅	1	4	yes	—
467	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
468	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
469	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
470	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
471	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
472	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
473	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
474	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
475	#121	C₂²×C₃×C₅	1	2	yes	—
476	#121	C₂²×C₃×C₅	1	4	yes	—
477	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
478	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
479	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
480	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
481	C₄×Q₈	C₂²×C₃×C₅	1	4	yes	—
482	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
483	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
484	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
485	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
486	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
487	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
488	#117	C₂²×C₃×C₅	1	4	yes	—
489	#117	C₂²×C₃×C₅	1	1	yes	characteristic
490	#117	C₂²×C₃×C₅	1	1	yes	characteristic
491	#117	C₂²×C₃×C₅	1	4	yes	—
492	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
493	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
494	C₂×C₃×C₅	—	4	1	no	—
495	C₂×C₃×C₅	—	4	4	no	—
496	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
497	C₂×C₃×C₅	#585	1	2	yes	—
498	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
499	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
500	C₃×Q₈	—	2	4	no	—
501	C₃×Q₈	—	4	2	no	—
502	C₃×Q₈	—	4	4	no	—
503	C₃×Q₈	—	4	2	no	—
504	C₃×D₄	—	2	4	no	—
505	C₃×D₄	—	4	4	no	—
506	C₃×D₄	—	4	4	no	—
507	C₂×C₃×C₄	—	2	2	no	—
508	C₂×C₃×C₄	—	4	4	no	—
509	C₂×C₃×C₄	—	4	2	no	—
510	C₂×C₃×C₄	—	4	4	no	—
511	C₂×C₃×C₄	—	4	4	no	—
512	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
513	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
514	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
515	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
516	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
517	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
518	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
519	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
520	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
521	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
522	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
523	C₂²×C₅	—	2	1	no	—
524	C₂²×C₅	—	2	4	no	—
525	C₂²×C₅	—	2	4	no	—
526	C₂²×C₅	—	2	2	no	—
527	C₂²×C₅	—	2	4	no	—
528	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
529	C₄×C₅	—	2	1	no	—
530	C₄×C₅	—	2	4	no	—
531	C₄×C₅	—	2	2	no	—
532	C₄×C₅	—	2	4	no	—
533	C₄×C₅	—	2	2	no	—
534	C₄×C₅	—	2	2	no	—
535	C₄×C₅	—	2	4	no	—
536	C₄×C₅	—	2	2	no	—
537	C₄×C₅	—	2	2	no	—
538	C₄×C₅	—	2	2	no	—
539	C₄×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
540	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
541	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
542	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
543	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
544	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
545	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
546	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
547	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
548	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
549	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
550	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
551	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
552	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
553	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
554	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
555	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
556	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
557	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
558	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
559	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
560	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
561	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
562	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
563	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
564	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
565	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
566	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
567	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
568	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
569	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
570	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
571	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
572	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
573	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
574	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
575	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
576	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
577	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
578	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
579	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
580	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
581	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
582	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
583	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
584	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
585	C₄²	C₂³×C₃×C₅	1	2	yes	—
586	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
587	C₄²	C₂³×C₃×C₅	1	4	yes	—
588	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
589	C₄²	C₂³×C₃×C₅	1	2	yes	—
590	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
591	C₄²	C₂³×C₃×C₅	1	4	yes	—
592	C₄²	C₂³×C₃×C₅	1	4	yes	—
593	C₃×C₅	#3557	1	1	yes	characteristic, direct product factor, Hall
594	C₂²×C₃	—	2	1	no	—
595	C₂²×C₃	—	2	4	no	—
596	C₂²×C₃	—	2	4	no	—
597	C₂²×C₃	—	2	2	no	—
598	C₂²×C₃	—	2	4	no	—
599	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
600	C₃×C₄	—	2	1	no	—
601	C₃×C₄	—	2	4	no	—
602	C₃×C₄	—	2	2	no	—
603	C₃×C₄	—	2	4	no	—
604	C₃×C₄	—	2	2	no	—
605	C₃×C₄	—	2	2	no	—
606	C₃×C₄	—	2	4	no	—
607	C₃×C₄	—	2	2	no	—
608	C₃×C₄	—	2	2	no	—
609	C₃×C₄	—	2	2	no	—
610	C₃×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
611	C₂×C₅	—	4	1	no	—
612	C₂×C₅	—	4	4	no	—
613	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
614	C₂×C₅	C₃×#585	1	2	yes	—
615	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
616	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
617	Q₈	—	2	4	no	—
618	Q₈	—	4	2	no	—
619	Q₈	—	4	4	no	—
620	Q₈	—	4	2	no	—
621	D₄	—	2	4	no	—
622	D₄	—	4	4	no	—
623	D₄	—	4	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
630	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
631	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
632	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
633	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
634	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
635	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
636	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
637	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
638	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
639	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
640	C₂×C₃	—	4	1	no	—
641	C₂×C₃	—	4	4	no	—
642	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
643	C₂×C₃	C₅×#585	1	2	yes	—
644	C₅	C₃×#3557	1	1	yes	characteristic, direct product factor, Sylow
645	C₂²	—	2	1	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	4	no	—
650	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	4	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	4	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
662	C₃	C₅×#3557	1	1	yes	characteristic, direct product factor, Sylow
663	C₂	—	4	1	no	—
664	C₂	—	4	4	no	—
665	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
666	C₂	C₃×C₅×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
prime radical	C₃×C₅×#540	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#563	C₂	semidirect
2. C₃×C₅×#559	C₂	semidirect
3. C₃×C₅×#557	C₂	semidirect
4. C₃×C₅×#556	C₂	semidirect
5. C₃×C₅×#554	C₂	semidirect
6. C₃×C₅×#552	C₂	semidirect
7. C₃×C₅×#542	C₂	semidirect
8. C₃×C₅×#542	C₂	semidirect
9. C₃×C₅×#541	C₂	semidirect
11. C₃×C₅×#539	C₂	semidirect
12. C₃×C₅×#533	C₂	semidirect
13. C₃×C₅×#529	C₂	semidirect
14. C₅×#3557	C₃	direct (N × H)
68. C₃×#3557	C₅	direct (N × H)
69. C₅×#563	C₂×C₃	semidirect
70. C₅×#559	C₂×C₃	semidirect
71. C₅×#557	C₂×C₃	semidirect
72. C₅×#556	C₂×C₃	semidirect
73. C₅×#554	C₂×C₃	semidirect
74. C₅×#552	C₂×C₃	semidirect
75. C₅×#542	C₂×C₃	semidirect
76. C₅×#542	C₂×C₃	semidirect
77. C₅×#541	C₂×C₃	semidirect
79. C₅×#539	C₂×C₃	semidirect
80. C₅×#533	C₂×C₃	semidirect
81. C₅×#529	C₂×C₃	semidirect
135. C₃×#563	C₂×C₅	semidirect
136. C₃×#559	C₂×C₅	semidirect
137. C₃×#557	C₂×C₅	semidirect
138. C₃×#556	C₂×C₅	semidirect
139. C₃×#554	C₂×C₅	semidirect
140. C₃×#552	C₂×C₅	semidirect
141. C₃×#542	C₂×C₅	semidirect
142. C₃×#542	C₂×C₅	semidirect
143. C₃×#541	C₂×C₅	semidirect
145. C₃×#539	C₂×C₅	semidirect
146. C₃×#533	C₂×C₅	semidirect
147. C₃×#529	C₂×C₅	semidirect
201. #3557	C₃×C₅	direct (N × H)
333. #563	C₂×C₃×C₅	semidirect
334. #559	C₂×C₃×C₅	semidirect
335. #557	C₂×C₃×C₅	semidirect
336. #556	C₂×C₃×C₅	semidirect
337. #554	C₂×C₃×C₅	semidirect
338. #552	C₂×C₃×C₅	semidirect
339. #542	C₂×C₃×C₅	semidirect
340. #542	C₂×C₃×C₅	semidirect
341. #541	C₂×C₃×C₅	semidirect
343. #539	C₂×C₃×C₅	semidirect
344. #533	C₂×C₃×C₅	semidirect
345. #529	C₂×C₃×C₅	semidirect
593. C₃×C₅	#3557	direct (N × H)
644. C₅	C₃×#3557	direct (N × H)
662. C₃	C₅×#3557	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×#563	2
C₃×C₅×#559	2
C₃×C₅×#557	2
C₃×C₅×#556	2
C₃×C₅×#554	2
C₃×C₅×#552	2
C₃×C₅×#542	2
C₃×C₅×#541	2
C₃×C₅×#540	2
C₃×C₅×#539	2
C₃×C₅×#533	2
C₃×C₅×#529	2
C₅×#3557	3
C₃×#3557	5

Subgroups — C3×C5×#3557 #14276591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3557 #14276591