Subgroups — C₃×C₅×#3539 #14276573

Order 1920.

2100 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#560	C₂	1	4	yes	maximal, complemented
2	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#553	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#552	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#550	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#547	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#540	C₂	1	4	yes	maximal, complemented
10	C₃×C₅×#539	C₂	1	4	yes	maximal, complemented
11	C₃×C₅×#537	C₂	1	2	yes	maximal, complemented
12	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#525	C₂	1	2	yes	maximal, complemented
14	C₅×#3539	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
17	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#127	C₂²	1	4	yes	—
21	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×#126	C₂²	1	4	yes	—
23	C₃×C₅×#126	C₂²	1	4	yes	—
24	C₃×C₅×#126	C₂²	1	4	yes	complemented
25	C₃×C₅×#125	C₂²	1	4	yes	complemented
26	C₃×C₅×#125	C₂²	1	4	yes	complemented
27	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#123	C₂²	1	4	yes	—
30	C₃×C₅×#123	C₂²	1	2	yes	—
31	C₃×C₅×#123	C₂²	1	4	yes	—
32	C₃×C₅×#123	C₂²	1	4	yes	—
33	C₃×C₅×#123	C₂²	1	4	yes	—
34	C₃×C₅×#123	C₂²	1	4	yes	complemented
35	C₃×C₅×#123	C₂²	1	4	yes	complemented
36	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
39	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
40	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
41	C₃×C₅×#121	C₂²	1	2	yes	—
42	C₃×C₅×#121	C₂²	1	2	yes	—
43	C₃×C₅×#121	C₂²	1	2	yes	—
44	C₃×C₅×#121	C₂²	1	4	yes	—
45	C₃×C₅×#121	C₂²	1	4	yes	—
46	C₃×C₅×#121	C₂²	1	4	yes	—
47	C₃×C₅×#121	C₂²	1	4	yes	—
48	C₃×C₅×#121	C₂²	1	4	yes	—
49	C₃×C₅×#121	C₂²	1	4	yes	—
50	C₃×C₅×#121	C₂²	1	4	yes	complemented
51	C₃×C₅×#121	C₂²	1	2	yes	complemented
52	C₃×C₅×#121	C₂²	1	4	yes	complemented
53	C₃×C₅×#120	C₂²	1	2	yes	—
54	C₃×C₅×#120	C₂²	1	4	yes	—
55	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
56	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
57	C₃×C₄×C₅×D₄	C₂²	1	2	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	4	yes	complemented
61	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
62	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
63	C₃×C₅×#117	C₂²	1	1	yes	characteristic
64	C₃×C₅×#117	C₂²	1	2	yes	—
65	C₃×C₅×#117	C₂²	1	4	yes	complemented
66	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
67	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
68	C₃×#3539	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#560	C₂×C₃	1	4	yes	complemented
70	C₅×#553	C₂×C₃	1	2	yes	complemented
71	C₅×#553	C₂×C₃	1	4	yes	complemented
72	C₅×#552	C₂×C₃	1	2	yes	complemented
73	C₅×#550	C₂×C₃	1	2	yes	complemented
74	C₅×#547	C₂×C₃	1	2	yes	complemented
75	C₅×#541	C₂×C₃	1	1	yes	characteristic, complemented
76	C₅×#540	C₂×C₃	1	1	yes	characteristic, complemented
77	C₅×#540	C₂×C₃	1	4	yes	complemented
78	C₅×#539	C₂×C₃	1	4	yes	complemented
79	C₅×#537	C₂×C₃	1	2	yes	complemented
80	C₅×#525	C₂×C₃	1	1	yes	characteristic, complemented
81	C₅×#525	C₂×C₃	1	2	yes	complemented
82	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
83	C₃×C₅×#41	—	4	2	no	—
84	C₃×C₅×#41	—	4	4	no	—
85	C₃×C₅×#41	—	4	4	no	—
86	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
87	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
89	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
90	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
91	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
92	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
93	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
94	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
95	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
96	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
97	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
99	C₂²×C₃×C₄×C₅	—	4	2	no	—
100	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
101	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
102	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
103	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
104	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
105	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
106	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
107	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
108	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
109	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
110	C₃×C₅×C₄⋊C₄	C₂³	1	2	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×C₄⋊C₄	C₂³	1	4	yes	—
115	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
116	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
117	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
118	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
119	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
120	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
121	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
122	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₃×C₄²×C₅	C₂³	1	4	yes	—
136	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
137	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
138	C₃×C₄²×C₅	C₂³	1	4	yes	—
139	C₃×#560	C₂×C₅	1	4	yes	complemented
140	C₃×#553	C₂×C₅	1	2	yes	complemented
141	C₃×#553	C₂×C₅	1	4	yes	complemented
142	C₃×#552	C₂×C₅	1	2	yes	complemented
143	C₃×#550	C₂×C₅	1	2	yes	complemented
144	C₃×#547	C₂×C₅	1	2	yes	complemented
145	C₃×#541	C₂×C₅	1	1	yes	characteristic, complemented
146	C₃×#540	C₂×C₅	1	1	yes	characteristic, complemented
147	C₃×#540	C₂×C₅	1	4	yes	complemented
148	C₃×#539	C₂×C₅	1	4	yes	complemented
149	C₃×#537	C₂×C₅	1	2	yes	complemented
150	C₃×#525	C₂×C₅	1	1	yes	characteristic, complemented
151	C₃×#525	C₂×C₅	1	2	yes	complemented
152	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
154	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
155	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
156	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
157	C₅×#127	C₂²×C₃	1	4	yes	—
158	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
159	C₅×#126	C₂²×C₃	1	4	yes	—
160	C₅×#126	C₂²×C₃	1	4	yes	—
161	C₅×#126	C₂²×C₃	1	4	yes	complemented
162	C₅×#125	C₂²×C₃	1	4	yes	complemented
163	C₅×#125	C₂²×C₃	1	4	yes	complemented
164	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
165	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₅×#123	C₂²×C₃	1	4	yes	—
167	C₅×#123	C₂²×C₃	1	2	yes	—
168	C₅×#123	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	complemented
172	C₅×#123	C₂²×C₃	1	4	yes	complemented
173	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	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	4	yes	complemented
177	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
178	C₅×#121	C₂²×C₃	1	2	yes	—
179	C₅×#121	C₂²×C₃	1	2	yes	—
180	C₅×#121	C₂²×C₃	1	2	yes	—
181	C₅×#121	C₂²×C₃	1	4	yes	—
182	C₅×#121	C₂²×C₃	1	4	yes	—
183	C₅×#121	C₂²×C₃	1	4	yes	—
184	C₅×#121	C₂²×C₃	1	4	yes	—
185	C₅×#121	C₂²×C₃	1	4	yes	—
186	C₅×#121	C₂²×C₃	1	4	yes	—
187	C₅×#121	C₂²×C₃	1	4	yes	complemented
188	C₅×#121	C₂²×C₃	1	2	yes	complemented
189	C₅×#121	C₂²×C₃	1	4	yes	complemented
190	C₅×#120	C₂²×C₃	1	2	yes	—
191	C₅×#120	C₂²×C₃	1	4	yes	—
192	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
193	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
194	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
195	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
196	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
197	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
198	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
199	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
200	C₅×#117	C₂²×C₃	1	1	yes	characteristic
201	C₅×#117	C₂²×C₃	1	2	yes	—
202	C₅×#117	C₂²×C₃	1	4	yes	complemented
203	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
204	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
205	#3539	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
206	C₂³×C₃×C₅	—	4	1	no	—
207	C₂³×C₃×C₅	—	4	2	no	—
208	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
209	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
210	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
211	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
212	C₃×C₅×Q₈	—	2	4	no	—
213	C₃×C₅×Q₈	—	4	1	no	—
214	C₃×C₅×D₄	—	2	4	no	—
215	C₃×C₅×D₄	—	4	2	no	—
216	C₃×C₅×D₄	—	4	4	no	—
217	C₃×C₅×D₄	—	4	4	no	—
218	C₃×C₅×D₄	—	4	4	no	—
219	C₃×C₅×D₄	—	4	2	no	—
220	C₃×C₅×D₄	—	4	4	no	—
221	C₃×C₅×D₄	—	4	2	no	—
222	C₃×C₅×D₄	—	4	1	no	—
223	C₃×C₅×D₄	—	4	4	no	—
224	C₃×C₅×D₄	—	4	4	no	—
225	C₂×C₃×C₄×C₅	—	2	4	no	—
226	C₂×C₃×C₄×C₅	—	2	2	no	—
227	C₂×C₃×C₄×C₅	—	2	4	no	—
228	C₂×C₃×C₄×C₅	—	4	1	no	—
229	C₂×C₃×C₄×C₅	—	4	2	no	—
230	C₂×C₃×C₄×C₅	—	4	4	no	—
231	C₂×C₃×C₄×C₅	—	4	4	no	—
232	C₂×C₃×C₄×C₅	—	4	4	no	—
233	C₂×C₃×C₄×C₅	—	4	4	no	—
234	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
235	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
236	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
237	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
238	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
239	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
240	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
241	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
242	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
243	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
245	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
246	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
247	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
248	C₃×#127	C₂²×C₅	1	4	yes	—
249	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
250	C₃×#126	C₂²×C₅	1	4	yes	—
251	C₃×#126	C₂²×C₅	1	4	yes	—
252	C₃×#126	C₂²×C₅	1	4	yes	complemented
253	C₃×#125	C₂²×C₅	1	4	yes	complemented
254	C₃×#125	C₂²×C₅	1	4	yes	complemented
255	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
256	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₃×#123	C₂²×C₅	1	4	yes	—
258	C₃×#123	C₂²×C₅	1	4	yes	—
259	C₃×#123	C₂²×C₅	1	4	yes	—
260	C₃×#123	C₂²×C₅	1	4	yes	—
261	C₃×#123	C₂²×C₅	1	2	yes	—
262	C₃×#123	C₂²×C₅	1	4	yes	complemented
263	C₃×#123	C₂²×C₅	1	4	yes	complemented
264	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
265	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
266	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
267	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
268	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
269	C₃×#121	C₂²×C₅	1	4	yes	—
270	C₃×#121	C₂²×C₅	1	4	yes	—
271	C₃×#121	C₂²×C₅	1	4	yes	—
272	C₃×#121	C₂²×C₅	1	4	yes	—
273	C₃×#121	C₂²×C₅	1	4	yes	—
274	C₃×#121	C₂²×C₅	1	4	yes	—
275	C₃×#121	C₂²×C₅	1	2	yes	—
276	C₃×#121	C₂²×C₅	1	2	yes	—
277	C₃×#121	C₂²×C₅	1	2	yes	—
278	C₃×#121	C₂²×C₅	1	4	yes	complemented
279	C₃×#121	C₂²×C₅	1	2	yes	complemented
280	C₃×#121	C₂²×C₅	1	4	yes	complemented
281	C₃×#120	C₂²×C₅	1	2	yes	—
282	C₃×#120	C₂²×C₅	1	4	yes	—
283	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
284	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
285	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
286	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
287	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
288	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
289	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
290	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
291	C₃×#117	C₂²×C₅	1	1	yes	characteristic
292	C₃×#117	C₂²×C₅	1	2	yes	—
293	C₃×#117	C₂²×C₅	1	4	yes	complemented
294	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
295	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
296	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
297	C₅×#41	—	4	2	no	—
298	C₅×#41	—	4	4	no	—
299	C₅×#41	—	4	4	no	—
300	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
301	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
302	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
303	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
304	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
305	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
306	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
307	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
308	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
309	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
310	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
311	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
312	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
313	C₂²×C₄×C₅	—	4	2	no	—
314	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
315	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
316	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
317	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
318	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
319	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
320	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
321	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
322	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
323	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
324	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
325	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
326	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
327	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
328	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
329	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
330	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
331	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
332	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
333	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
334	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
335	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
336	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
337	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
338	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
339	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
340	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
341	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
342	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
343	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
344	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
345	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
346	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
347	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
348	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
349	C₄²×C₅	C₂³×C₃	1	4	yes	—
350	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
351	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
352	C₄²×C₅	C₂³×C₃	1	4	yes	—
353	#560	C₂×C₃×C₅	1	4	yes	complemented
354	#553	C₂×C₃×C₅	1	2	yes	complemented
355	#553	C₂×C₃×C₅	1	4	yes	complemented
356	#552	C₂×C₃×C₅	1	2	yes	complemented
357	#550	C₂×C₃×C₅	1	2	yes	complemented
358	#547	C₂×C₃×C₅	1	2	yes	complemented
359	#541	C₂×C₃×C₅	1	1	yes	characteristic, complemented
360	#540	C₂×C₃×C₅	1	1	yes	characteristic, complemented
361	#540	C₂×C₃×C₅	1	4	yes	complemented
362	#539	C₂×C₃×C₅	1	4	yes	complemented
363	#537	C₂×C₃×C₅	1	2	yes	complemented
364	#525	C₂×C₃×C₅	1	1	yes	characteristic, complemented
365	#525	C₂×C₃×C₅	1	2	yes	complemented
366	C₂²×C₃×C₅	—	2	2	no	—
367	C₂²×C₃×C₅	—	2	1	no	—
368	C₂²×C₃×C₅	—	2	2	no	—
369	C₂²×C₃×C₅	—	2	4	no	—
370	C₂²×C₃×C₅	—	2	2	no	—
371	C₂²×C₃×C₅	—	2	4	no	—
372	C₂²×C₃×C₅	—	2	2	no	—
373	C₂²×C₃×C₅	—	2	4	no	—
374	C₂²×C₃×C₅	—	2	2	no	—
375	C₂²×C₃×C₅	—	2	2	no	—
376	C₂²×C₃×C₅	—	2	2	no	—
377	C₂²×C₃×C₅	—	4	4	no	—
378	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
379	C₃×C₄×C₅	—	2	2	no	—
380	C₃×C₄×C₅	—	2	1	no	—
381	C₃×C₄×C₅	—	2	2	no	—
382	C₃×C₄×C₅	—	2	4	no	—
383	C₃×C₄×C₅	—	2	2	no	—
384	C₃×C₄×C₅	—	2	4	no	—
385	C₃×C₄×C₅	—	2	4	no	—
386	C₃×C₄×C₅	—	2	2	no	—
387	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
388	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
389	C₃×#41	—	4	2	no	—
390	C₃×#41	—	4	4	no	—
391	C₃×#41	—	4	4	no	—
392	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
393	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
394	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
395	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
396	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
397	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
398	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
399	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
400	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
401	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
402	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
403	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
405	C₂²×C₃×C₄	—	4	2	no	—
406	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
407	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
408	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
409	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
410	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
411	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
412	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
413	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
415	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
416	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
417	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
418	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
419	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
420	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
421	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
422	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
423	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
424	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
425	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
426	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
427	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
428	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
429	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
430	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
431	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
432	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
433	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
434	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
435	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
436	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
437	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
438	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
439	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
440	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
441	C₃×C₄²	C₂³×C₅	1	4	yes	—
442	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
443	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
444	C₃×C₄²	C₂³×C₅	1	4	yes	—
445	C₂³×C₅	—	4	1	no	—
446	C₂³×C₅	—	4	2	no	—
447	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
448	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
449	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
450	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
451	C₅×Q₈	—	2	4	no	—
452	C₅×Q₈	—	4	1	no	—
453	C₅×D₄	—	2	4	no	—
454	C₅×D₄	—	4	2	no	—
455	C₅×D₄	—	4	4	no	—
456	C₅×D₄	—	4	4	no	—
457	C₅×D₄	—	4	4	no	—
458	C₅×D₄	—	4	2	no	—
459	C₅×D₄	—	4	4	no	—
460	C₅×D₄	—	4	2	no	—
461	C₅×D₄	—	4	1	no	—
462	C₅×D₄	—	4	4	no	—
463	C₅×D₄	—	4	4	no	—
464	C₂×C₄×C₅	—	2	4	no	—
465	C₂×C₄×C₅	—	2	2	no	—
466	C₂×C₄×C₅	—	2	4	no	—
467	C₂×C₄×C₅	—	4	1	no	—
468	C₂×C₄×C₅	—	4	2	no	—
469	C₂×C₄×C₅	—	4	4	no	—
470	C₂×C₄×C₅	—	4	4	no	—
471	C₂×C₄×C₅	—	4	4	no	—
472	C₂×C₄×C₅	—	4	4	no	—
473	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
474	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
475	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
476	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
477	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
478	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
479	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
480	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
481	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
482	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
483	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
484	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
485	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
486	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
487	#127	C₂²×C₃×C₅	1	4	yes	—
488	#127	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
489	#126	C₂²×C₃×C₅	1	4	yes	—
490	#126	C₂²×C₃×C₅	1	4	yes	—
491	#126	C₂²×C₃×C₅	1	4	yes	complemented
492	#125	C₂²×C₃×C₅	1	4	yes	complemented
493	#125	C₂²×C₃×C₅	1	4	yes	complemented
494	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
495	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
496	#123	C₂²×C₃×C₅	1	4	yes	—
497	#123	C₂²×C₃×C₅	1	2	yes	—
498	#123	C₂²×C₃×C₅	1	4	yes	—
499	#123	C₂²×C₃×C₅	1	4	yes	—
500	#123	C₂²×C₃×C₅	1	4	yes	—
501	#123	C₂²×C₃×C₅	1	4	yes	complemented
502	#123	C₂²×C₃×C₅	1	4	yes	complemented
503	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
504	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
505	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
506	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
507	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
508	#121	C₂²×C₃×C₅	1	2	yes	—
509	#121	C₂²×C₃×C₅	1	2	yes	—
510	#121	C₂²×C₃×C₅	1	2	yes	—
511	#121	C₂²×C₃×C₅	1	4	yes	—
512	#121	C₂²×C₃×C₅	1	4	yes	—
513	#121	C₂²×C₃×C₅	1	4	yes	—
514	#121	C₂²×C₃×C₅	1	4	yes	—
515	#121	C₂²×C₃×C₅	1	4	yes	—
516	#121	C₂²×C₃×C₅	1	4	yes	—
517	#121	C₂²×C₃×C₅	1	4	yes	complemented
518	#121	C₂²×C₃×C₅	1	2	yes	complemented
519	#121	C₂²×C₃×C₅	1	4	yes	complemented
520	#120	C₂²×C₃×C₅	1	2	yes	—
521	#120	C₂²×C₃×C₅	1	4	yes	—
522	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
523	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
524	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
525	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
526	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
527	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
528	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
529	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
530	#117	C₂²×C₃×C₅	1	1	yes	characteristic
531	#117	C₂²×C₃×C₅	1	2	yes	—
532	#117	C₂²×C₃×C₅	1	4	yes	complemented
533	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
534	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
535	C₂×C₃×C₅	—	4	2	no	—
536	C₂×C₃×C₅	—	4	4	no	—
537	C₂×C₃×C₅	—	4	2	no	—
538	C₂×C₃×C₅	—	4	1	no	—
539	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂×C₃×C₅	#585	1	2	yes	—
541	C₂³×C₃	—	4	1	no	—
542	C₂³×C₃	—	4	2	no	—
543	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
544	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
545	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
546	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
547	C₃×Q₈	—	2	4	no	—
548	C₃×Q₈	—	4	1	no	—
549	C₃×D₄	—	2	4	no	—
550	C₃×D₄	—	4	2	no	—
551	C₃×D₄	—	4	4	no	—
552	C₃×D₄	—	4	4	no	—
553	C₃×D₄	—	4	4	no	—
554	C₃×D₄	—	4	2	no	—
555	C₃×D₄	—	4	4	no	—
556	C₃×D₄	—	4	2	no	—
557	C₃×D₄	—	4	1	no	—
558	C₃×D₄	—	4	4	no	—
559	C₃×D₄	—	4	4	no	—
560	C₂×C₃×C₄	—	2	4	no	—
561	C₂×C₃×C₄	—	2	2	no	—
562	C₂×C₃×C₄	—	2	4	no	—
563	C₂×C₃×C₄	—	4	1	no	—
564	C₂×C₃×C₄	—	4	2	no	—
565	C₂×C₃×C₄	—	4	4	no	—
566	C₂×C₃×C₄	—	4	4	no	—
567	C₂×C₃×C₄	—	4	4	no	—
568	C₂×C₃×C₄	—	4	4	no	—
569	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
570	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
571	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
572	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
573	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
574	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
575	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
576	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
577	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
578	C₂²×C₅	—	2	2	no	—
579	C₂²×C₅	—	2	1	no	—
580	C₂²×C₅	—	2	2	no	—
581	C₂²×C₅	—	2	4	no	—
582	C₂²×C₅	—	2	2	no	—
583	C₂²×C₅	—	2	4	no	—
584	C₂²×C₅	—	2	2	no	—
585	C₂²×C₅	—	2	4	no	—
586	C₂²×C₅	—	2	2	no	—
587	C₂²×C₅	—	2	2	no	—
588	C₂²×C₅	—	2	2	no	—
589	C₂²×C₅	—	4	4	no	—
590	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
591	C₄×C₅	—	2	2	no	—
592	C₄×C₅	—	2	1	no	—
593	C₄×C₅	—	2	2	no	—
594	C₄×C₅	—	2	4	no	—
595	C₄×C₅	—	2	2	no	—
596	C₄×C₅	—	2	4	no	—
597	C₄×C₅	—	2	4	no	—
598	C₄×C₅	—	2	2	no	—
599	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
600	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
601	#41	—	4	2	no	—
602	#41	—	4	4	no	—
603	#41	—	4	4	no	—
604	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
605	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
606	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
607	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
608	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
609	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
610	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
611	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
612	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
613	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
614	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
615	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
616	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
617	C₂²×C₄	—	4	2	no	—
618	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
619	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
620	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
621	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
622	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
623	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
624	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
625	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
626	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
627	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
628	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
629	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
630	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
631	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
632	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
633	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
634	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
635	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
636	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
637	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
638	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
639	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
640	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
641	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
642	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
643	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
644	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
645	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
646	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
647	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
648	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
649	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
650	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
651	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
652	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
653	C₄²	C₂³×C₃×C₅	1	4	yes	—
654	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
655	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
656	C₄²	C₂³×C₃×C₅	1	4	yes	—
657	C₃×C₅	#3539	1	1	yes	characteristic, direct product factor, Hall
658	C₂²×C₃	—	2	2	no	—
659	C₂²×C₃	—	2	1	no	—
660	C₂²×C₃	—	2	2	no	—
661	C₂²×C₃	—	2	4	no	—
662	C₂²×C₃	—	2	2	no	—
663	C₂²×C₃	—	2	4	no	—
664	C₂²×C₃	—	2	2	no	—
665	C₂²×C₃	—	2	4	no	—
666	C₂²×C₃	—	2	2	no	—
667	C₂²×C₃	—	2	2	no	—
668	C₂²×C₃	—	2	2	no	—
669	C₂²×C₃	—	4	4	no	—
670	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
671	C₃×C₄	—	2	2	no	—
672	C₃×C₄	—	2	1	no	—
673	C₃×C₄	—	2	2	no	—
674	C₃×C₄	—	2	4	no	—
675	C₃×C₄	—	2	2	no	—
676	C₃×C₄	—	2	4	no	—
677	C₃×C₄	—	2	4	no	—
678	C₃×C₄	—	2	2	no	—
679	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
680	C₂×C₅	—	4	2	no	—
681	C₂×C₅	—	4	1	no	—
682	C₂×C₅	—	4	2	no	—
683	C₂×C₅	—	4	4	no	—
684	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂×C₅	C₃×#585	1	2	yes	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	2	no	—
688	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
689	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
690	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
691	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
692	Q₈	—	2	4	no	—
693	Q₈	—	4	1	no	—
694	D₄	—	2	4	no	—
695	D₄	—	4	2	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	4	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	2	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	4	no	—
702	D₄	—	4	4	no	—
703	D₄	—	4	2	no	—
704	D₄	—	4	4	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
715	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
716	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
717	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
718	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
719	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
720	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
721	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
722	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
723	C₂×C₃	—	4	2	no	—
724	C₂×C₃	—	4	1	no	—
725	C₂×C₃	—	4	2	no	—
726	C₂×C₃	—	4	4	no	—
727	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
728	C₂×C₃	C₅×#585	1	2	yes	—
729	C₅	C₃×#3539	1	1	yes	characteristic, direct product factor, Sylow
730	C₂²	—	2	2	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	4	4	no	—
742	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
743	C₄	—	2	2	no	—
744	C₄	—	2	1	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	4	no	—
750	C₄	—	2	2	no	—
751	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
752	C₃	C₅×#3539	1	1	yes	characteristic, direct product factor, Sylow
753	C₂	—	4	2	no	—
754	C₂	—	4	1	no	—
755	C₂	—	4	2	no	—
756	C₂	—	4	4	no	—
757	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
758	C₂	C₃×C₅×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
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×#560	C₂	semidirect
2. C₃×C₅×#553	C₂	semidirect
3. C₃×C₅×#553	C₂	semidirect
4. C₃×C₅×#552	C₂	semidirect
5. C₃×C₅×#550	C₂	semidirect
6. C₃×C₅×#547	C₂	semidirect
7. C₃×C₅×#541	C₂	semidirect
8. C₃×C₅×#540	C₂	semidirect
9. C₃×C₅×#540	C₂	semidirect
10. C₃×C₅×#539	C₂	semidirect
11. C₃×C₅×#537	C₂	semidirect
12. C₃×C₅×#525	C₂	semidirect
13. C₃×C₅×#525	C₂	semidirect
14. C₅×#3539	C₃	direct (N × H)
17. C₂×C₃×C₅×#41	C₂²	semidirect
19. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₃×C₅×#127	C₂²	semidirect
24. C₃×C₅×#126	C₂²	semidirect
25. C₃×C₅×#125	C₂²	semidirect
26. C₃×C₅×#125	C₂²	semidirect
27. C₃×C₅×#125	C₂²	semidirect
28. C₃×C₅×#125	C₂²	semidirect
34. C₃×C₅×#123	C₂²	semidirect
35. C₃×C₅×#123	C₂²	semidirect
39. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
40. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
50. C₃×C₅×#121	C₂²	semidirect
51. C₃×C₅×#121	C₂²	semidirect
52. C₃×C₅×#121	C₂²	semidirect
55. C₃×C₄×C₅×Q₈	C₂²	semidirect
60. C₃×C₄×C₅×D₄	C₂²	semidirect
61. C₃×C₄×C₅×D₄	C₂²	semidirect
62. C₃×C₄×C₅×D₄	C₂²	semidirect
65. C₃×C₅×#117	C₂²	semidirect
66. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
67. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
68. C₃×#3539	C₅	direct (N × H)
69. C₅×#560	C₂×C₃	semidirect
70. C₅×#553	C₂×C₃	semidirect
71. C₅×#553	C₂×C₃	semidirect
72. C₅×#552	C₂×C₃	semidirect
73. C₅×#550	C₂×C₃	semidirect
74. C₅×#547	C₂×C₃	semidirect
75. C₅×#541	C₂×C₃	semidirect
76. C₅×#540	C₂×C₃	semidirect
77. C₅×#540	C₂×C₃	semidirect
78. C₅×#539	C₂×C₃	semidirect
79. C₅×#537	C₂×C₃	semidirect
80. C₅×#525	C₂×C₃	semidirect
81. C₅×#525	C₂×C₃	semidirect
139. C₃×#560	C₂×C₅	semidirect
140. C₃×#553	C₂×C₅	semidirect
141. C₃×#553	C₂×C₅	semidirect
142. C₃×#552	C₂×C₅	semidirect
143. C₃×#550	C₂×C₅	semidirect
144. C₃×#547	C₂×C₅	semidirect
145. C₃×#541	C₂×C₅	semidirect
146. C₃×#540	C₂×C₅	semidirect
147. C₃×#540	C₂×C₅	semidirect
148. C₃×#539	C₂×C₅	semidirect
149. C₃×#537	C₂×C₅	semidirect
150. C₃×#525	C₂×C₅	semidirect
151. C₃×#525	C₂×C₅	semidirect
154. C₂×C₅×#41	C₂²×C₃	semidirect
156. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
158. C₅×#127	C₂²×C₃	semidirect
161. C₅×#126	C₂²×C₃	semidirect
162. C₅×#125	C₂²×C₃	semidirect
163. C₅×#125	C₂²×C₃	semidirect
164. C₅×#125	C₂²×C₃	semidirect
165. C₅×#125	C₂²×C₃	semidirect
171. C₅×#123	C₂²×C₃	semidirect
172. C₅×#123	C₂²×C₃	semidirect
176. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
177. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
187. C₅×#121	C₂²×C₃	semidirect
188. C₅×#121	C₂²×C₃	semidirect
189. C₅×#121	C₂²×C₃	semidirect
192. C₄×C₅×Q₈	C₂²×C₃	semidirect
197. C₄×C₅×D₄	C₂²×C₃	semidirect
198. C₄×C₅×D₄	C₂²×C₃	semidirect
199. C₄×C₅×D₄	C₂²×C₃	semidirect
202. C₅×#117	C₂²×C₃	semidirect
203. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
204. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
205. #3539	C₃×C₅	direct (N × H)
245. C₂×C₃×#41	C₂²×C₅	semidirect
247. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
249. C₃×#127	C₂²×C₅	semidirect
252. C₃×#126	C₂²×C₅	semidirect
253. C₃×#125	C₂²×C₅	semidirect
254. C₃×#125	C₂²×C₅	semidirect
255. C₃×#125	C₂²×C₅	semidirect
256. C₃×#125	C₂²×C₅	semidirect
262. C₃×#123	C₂²×C₅	semidirect
263. C₃×#123	C₂²×C₅	semidirect
267. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
268. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
278. C₃×#121	C₂²×C₅	semidirect
279. C₃×#121	C₂²×C₅	semidirect
280. C₃×#121	C₂²×C₅	semidirect
283. C₃×C₄×Q₈	C₂²×C₅	semidirect
288. C₃×C₄×D₄	C₂²×C₅	semidirect
289. C₃×C₄×D₄	C₂²×C₅	semidirect
290. C₃×C₄×D₄	C₂²×C₅	semidirect
293. C₃×#117	C₂²×C₅	semidirect
294. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
295. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
353. #560	C₂×C₃×C₅	semidirect
354. #553	C₂×C₃×C₅	semidirect
355. #553	C₂×C₃×C₅	semidirect
356. #552	C₂×C₃×C₅	semidirect
357. #550	C₂×C₃×C₅	semidirect
358. #547	C₂×C₃×C₅	semidirect
359. #541	C₂×C₃×C₅	semidirect
360. #540	C₂×C₃×C₅	semidirect
361. #540	C₂×C₃×C₅	semidirect
362. #539	C₂×C₃×C₅	semidirect
363. #537	C₂×C₃×C₅	semidirect
364. #525	C₂×C₃×C₅	semidirect
365. #525	C₂×C₃×C₅	semidirect
484. C₂×#41	C₂²×C₃×C₅	semidirect
486. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
488. #127	C₂²×C₃×C₅	semidirect
491. #126	C₂²×C₃×C₅	semidirect
492. #125	C₂²×C₃×C₅	semidirect
493. #125	C₂²×C₃×C₅	semidirect
494. #125	C₂²×C₃×C₅	semidirect
495. #125	C₂²×C₃×C₅	semidirect
501. #123	C₂²×C₃×C₅	semidirect
502. #123	C₂²×C₃×C₅	semidirect
506. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
507. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
517. #121	C₂²×C₃×C₅	semidirect
518. #121	C₂²×C₃×C₅	semidirect
519. #121	C₂²×C₃×C₅	semidirect
522. C₄×Q₈	C₂²×C₃×C₅	semidirect
527. C₄×D₄	C₂²×C₃×C₅	semidirect
528. C₄×D₄	C₂²×C₃×C₅	semidirect
529. C₄×D₄	C₂²×C₃×C₅	semidirect
532. #117	C₂²×C₃×C₅	semidirect
533. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
534. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
657. C₃×C₅	#3539	direct (N × H)
729. C₅	C₃×#3539	direct (N × H)
752. C₃	C₅×#3539	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×#560	2
C₃×C₅×#553	2
C₃×C₅×#552	2
C₃×C₅×#550	2
C₃×C₅×#547	2
C₃×C₅×#541	2
C₃×C₅×#540	2
C₃×C₅×#539	2
C₃×C₅×#537	2
C₃×C₅×#525	2
C₅×#3539	3
C₃×#3539	5

Subgroups — C3×C5×#3539 #14276573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3539 #14276573