Subgroups — C₃×C₅×#3563 #14276597

Order 1920.

1824 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#564	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#563	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#557	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#554	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#552	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#552	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#552	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#544	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#544	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#541	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#541	C₂	1	4	yes	maximal, complemented
12	C₃×C₅×#539	C₂	1	2	yes	maximal
13	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
15	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3563	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
20	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
22	C₃×C₅×#126	C₂²	1	2	yes	—
23	C₃×C₅×#126	C₂²	1	4	yes	—
24	C₃×C₅×#126	C₂²	1	4	yes	—
25	C₃×C₅×#126	C₂²	1	4	yes	—
26	C₃×C₅×#126	C₂²	1	4	yes	—
27	C₃×C₅×#125	C₂²	1	2	yes	—
28	C₃×C₅×#125	C₂²	1	2	yes	—
29	C₃×C₅×#125	C₂²	1	2	yes	—
30	C₃×C₅×#125	C₂²	1	2	yes	—
31	C₃×C₅×#125	C₂²	1	1	yes	characteristic
32	C₃×C₅×#125	C₂²	1	2	yes	—
33	C₃×C₅×#125	C₂²	1	4	yes	—
34	C₃×C₅×#125	C₂²	1	4	yes	—
35	C₃×C₅×#125	C₂²	1	4	yes	—
36	C₃×C₅×#125	C₂²	1	4	yes	—
37	C₃×C₅×#125	C₂²	1	4	yes	—
38	C₃×C₅×#125	C₂²	1	4	yes	—
39	C₃×C₅×#125	C₂²	1	2	yes	—
40	C₃×C₅×#125	C₂²	1	4	yes	—
41	C₃×C₅×#125	C₂²	1	4	yes	—
42	C₃×C₅×#124	C₂²	1	1	yes	characteristic
43	C₃×C₅×#123	C₂²	1	2	yes	—
44	C₃×C₅×#123	C₂²	1	4	yes	—
45	C₃×C₅×#123	C₂²	1	4	yes	—
46	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
48	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
49	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
50	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
52	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
53	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
54	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
55	C₃×C₅×#121	C₂²	1	1	yes	characteristic
56	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
57	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
58	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
59	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	—
60	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
61	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
62	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
63	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
64	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
65	C₃×C₅×#117	C₂²	1	2	yes	—
66	C₃×C₅×#117	C₂²	1	2	yes	—
67	C₃×C₅×#117	C₂²	1	4	yes	—
68	C₃×C₅×#117	C₂²	1	2	yes	—
69	C₃×C₅×#117	C₂²	1	4	yes	—
70	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
71	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
73	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
74	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
75	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
76	C₃×#3563	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
77	C₅×#564	C₂×C₃	1	2	yes	complemented
78	C₅×#563	C₂×C₃	1	2	yes	complemented
79	C₅×#557	C₂×C₃	1	2	yes	complemented
80	C₅×#554	C₂×C₃	1	2	yes	complemented
81	C₅×#552	C₂×C₃	1	4	yes	complemented
82	C₅×#552	C₂×C₃	1	2	yes	complemented
83	C₅×#552	C₂×C₃	1	2	yes	complemented
84	C₅×#544	C₂×C₃	1	2	yes	complemented
85	C₅×#544	C₂×C₃	1	2	yes	complemented
86	C₅×#541	C₂×C₃	1	2	yes	complemented
87	C₅×#541	C₂×C₃	1	4	yes	complemented
88	C₅×#539	C₂×C₃	1	2	yes	—
89	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
90	C₅×#529	C₂×C₃	1	1	yes	characteristic
91	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
93	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
94	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
95	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
97	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	2	yes	—
104	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
105	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
106	C₃×C₅×C₄⋊C₄	C₂³	1	2	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	4	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	2	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	2	yes	—
121	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
122	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
124	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
125	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
126	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
128	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
129	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
130	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
131	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
133	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
143	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
144	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
145	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
146	C₃×C₄²×C₅	C₂³	1	4	yes	—
147	C₃×C₄²×C₅	C₂³	1	4	yes	—
148	C₃×C₄²×C₅	C₂³	1	2	yes	—
149	C₃×C₄²×C₅	C₂³	1	4	yes	—
150	C₃×C₄²×C₅	C₂³	1	4	yes	—
151	C₃×#564	C₂×C₅	1	2	yes	complemented
152	C₃×#563	C₂×C₅	1	2	yes	complemented
153	C₃×#557	C₂×C₅	1	2	yes	complemented
154	C₃×#554	C₂×C₅	1	2	yes	complemented
155	C₃×#552	C₂×C₅	1	4	yes	complemented
156	C₃×#552	C₂×C₅	1	2	yes	complemented
157	C₃×#552	C₂×C₅	1	2	yes	complemented
158	C₃×#544	C₂×C₅	1	2	yes	complemented
159	C₃×#544	C₂×C₅	1	2	yes	complemented
160	C₃×#541	C₂×C₅	1	2	yes	complemented
161	C₃×#541	C₂×C₅	1	4	yes	complemented
162	C₃×#539	C₂×C₅	1	2	yes	—
163	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
164	C₃×#529	C₂×C₅	1	1	yes	characteristic
165	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
166	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
167	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
168	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
169	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
170	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
171	C₅×#126	C₂²×C₃	1	2	yes	—
172	C₅×#126	C₂²×C₃	1	4	yes	—
173	C₅×#126	C₂²×C₃	1	4	yes	—
174	C₅×#126	C₂²×C₃	1	4	yes	—
175	C₅×#126	C₂²×C₃	1	4	yes	—
176	C₅×#125	C₂²×C₃	1	2	yes	—
177	C₅×#125	C₂²×C₃	1	2	yes	—
178	C₅×#125	C₂²×C₃	1	2	yes	—
179	C₅×#125	C₂²×C₃	1	2	yes	—
180	C₅×#125	C₂²×C₃	1	1	yes	characteristic
181	C₅×#125	C₂²×C₃	1	2	yes	—
182	C₅×#125	C₂²×C₃	1	4	yes	—
183	C₅×#125	C₂²×C₃	1	4	yes	—
184	C₅×#125	C₂²×C₃	1	4	yes	—
185	C₅×#125	C₂²×C₃	1	4	yes	—
186	C₅×#125	C₂²×C₃	1	4	yes	—
187	C₅×#125	C₂²×C₃	1	4	yes	—
188	C₅×#125	C₂²×C₃	1	2	yes	—
189	C₅×#125	C₂²×C₃	1	4	yes	—
190	C₅×#125	C₂²×C₃	1	4	yes	—
191	C₅×#124	C₂²×C₃	1	1	yes	characteristic
192	C₅×#123	C₂²×C₃	1	2	yes	—
193	C₅×#123	C₂²×C₃	1	4	yes	—
194	C₅×#123	C₂²×C₃	1	4	yes	—
195	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
196	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
197	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
198	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
199	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
200	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
201	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
202	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
203	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
204	C₅×#121	C₂²×C₃	1	1	yes	characteristic
205	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
206	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
207	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
208	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	—
209	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
210	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
211	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
212	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
213	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
214	C₅×#117	C₂²×C₃	1	2	yes	—
215	C₅×#117	C₂²×C₃	1	2	yes	—
216	C₅×#117	C₂²×C₃	1	4	yes	—
217	C₅×#117	C₂²×C₃	1	2	yes	—
218	C₅×#117	C₂²×C₃	1	4	yes	—
219	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
220	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
221	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
222	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
223	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
224	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
225	#3563	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
226	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
227	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
228	C₃×C₅×Q₈	—	2	4	no	—
229	C₃×C₅×Q₈	—	4	4	no	—
230	C₃×C₅×Q₈	—	4	1	no	—
231	C₃×C₅×Q₈	—	4	2	no	—
232	C₃×C₅×D₄	—	2	4	no	—
233	C₃×C₅×D₄	—	4	1	no	—
234	C₂×C₃×C₄×C₅	—	2	2	no	—
235	C₂×C₃×C₄×C₅	—	2	4	no	—
236	C₂×C₃×C₄×C₅	—	2	2	no	—
237	C₂×C₃×C₄×C₅	—	2	4	no	—
238	C₂×C₃×C₄×C₅	—	4	2	no	—
239	C₂×C₃×C₄×C₅	—	4	4	no	—
240	C₂×C₃×C₄×C₅	—	4	1	no	—
241	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
242	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
243	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
244	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
245	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
246	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
247	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
248	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
249	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
250	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
251	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
252	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
253	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
254	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
255	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
256	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
257	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
258	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
259	C₃×#126	C₂²×C₅	1	4	yes	—
260	C₃×#126	C₂²×C₅	1	4	yes	—
261	C₃×#126	C₂²×C₅	1	2	yes	—
262	C₃×#126	C₂²×C₅	1	4	yes	—
263	C₃×#126	C₂²×C₅	1	4	yes	—
264	C₃×#125	C₂²×C₅	1	2	yes	—
265	C₃×#125	C₂²×C₅	1	2	yes	—
266	C₃×#125	C₂²×C₅	1	1	yes	characteristic
267	C₃×#125	C₂²×C₅	1	4	yes	—
268	C₃×#125	C₂²×C₅	1	4	yes	—
269	C₃×#125	C₂²×C₅	1	4	yes	—
270	C₃×#125	C₂²×C₅	1	4	yes	—
271	C₃×#125	C₂²×C₅	1	4	yes	—
272	C₃×#125	C₂²×C₅	1	4	yes	—
273	C₃×#125	C₂²×C₅	1	2	yes	—
274	C₃×#125	C₂²×C₅	1	2	yes	—
275	C₃×#125	C₂²×C₅	1	2	yes	—
276	C₃×#125	C₂²×C₅	1	4	yes	—
277	C₃×#125	C₂²×C₅	1	4	yes	—
278	C₃×#125	C₂²×C₅	1	2	yes	—
279	C₃×#124	C₂²×C₅	1	1	yes	characteristic
280	C₃×#123	C₂²×C₅	1	4	yes	—
281	C₃×#123	C₂²×C₅	1	2	yes	—
282	C₃×#123	C₂²×C₅	1	4	yes	—
283	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
284	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
285	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
286	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
287	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
288	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
289	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
290	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
291	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
292	C₃×#121	C₂²×C₅	1	1	yes	characteristic
293	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
294	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
295	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
296	C₃×C₄×Q₈	C₂²×C₅	1	4	yes	—
297	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
298	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
299	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
300	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
301	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
302	C₃×#117	C₂²×C₅	1	2	yes	—
303	C₃×#117	C₂²×C₅	1	2	yes	—
304	C₃×#117	C₂²×C₅	1	4	yes	—
305	C₃×#117	C₂²×C₅	1	2	yes	—
306	C₃×#117	C₂²×C₅	1	4	yes	—
307	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
308	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
309	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
310	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
311	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
312	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
313	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
314	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
315	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
316	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
317	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
318	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
319	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
320	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
321	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
322	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
323	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
324	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
325	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
326	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
327	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
328	C₅×C₄⋊C₄	C₂³×C₃	1	2	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	4	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	2	yes	—
336	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
337	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
338	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
339	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
340	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
341	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
342	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
343	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
344	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
345	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
346	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
347	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
348	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
349	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
350	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
351	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
352	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
353	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
354	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
355	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
356	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
357	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
358	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
359	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
360	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
361	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
362	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
363	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
364	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
365	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
366	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
367	C₄²×C₅	C₂³×C₃	1	4	yes	—
368	C₄²×C₅	C₂³×C₃	1	4	yes	—
369	C₄²×C₅	C₂³×C₃	1	2	yes	—
370	C₄²×C₅	C₂³×C₃	1	4	yes	—
371	C₄²×C₅	C₂³×C₃	1	4	yes	—
372	#564	C₂×C₃×C₅	1	2	yes	complemented
373	#563	C₂×C₃×C₅	1	2	yes	complemented
374	#557	C₂×C₃×C₅	1	2	yes	complemented
375	#554	C₂×C₃×C₅	1	2	yes	complemented
376	#552	C₂×C₃×C₅	1	4	yes	complemented
377	#552	C₂×C₃×C₅	1	2	yes	complemented
378	#552	C₂×C₃×C₅	1	2	yes	complemented
379	#544	C₂×C₃×C₅	1	2	yes	complemented
380	#544	C₂×C₃×C₅	1	2	yes	complemented
381	#541	C₂×C₃×C₅	1	2	yes	complemented
382	#541	C₂×C₃×C₅	1	4	yes	complemented
383	#539	C₂×C₃×C₅	1	2	yes	—
384	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
385	#529	C₂×C₃×C₅	1	1	yes	characteristic
386	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic, complemented
387	C₂²×C₃×C₅	—	2	1	no	—
388	C₂²×C₃×C₅	—	2	1	no	—
389	C₂²×C₃×C₅	—	2	2	no	—
390	C₂²×C₃×C₅	—	2	2	no	—
391	C₂²×C₃×C₅	—	2	2	no	—
392	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
393	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
394	C₃×C₄×C₅	—	2	1	no	—
395	C₃×C₄×C₅	—	2	1	no	—
396	C₃×C₄×C₅	—	2	4	no	—
397	C₃×C₄×C₅	—	2	1	no	—
398	C₃×C₄×C₅	—	2	2	no	—
399	C₃×C₄×C₅	—	2	2	no	—
400	C₃×C₄×C₅	—	2	4	no	—
401	C₃×C₄×C₅	—	2	4	no	—
402	C₃×C₄×C₅	—	2	1	no	—
403	C₃×C₄×C₅	—	2	4	no	—
404	C₃×C₄×C₅	—	2	1	no	—
405	C₃×C₄×C₅	—	2	2	no	—
406	C₃×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
407	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
408	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
409	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
410	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
411	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
412	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
413	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
415	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
416	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
417	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
419	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
420	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
421	C₃×C₄⋊C₄	C₂³×C₅	1	2	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×C₄⋊C₄	C₂³×C₅	1	4	yes	—
429	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
430	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
431	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
432	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
433	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
434	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
435	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
436	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
437	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
438	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
439	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
440	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
441	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
442	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
443	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
444	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
445	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
446	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
447	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
448	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
449	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
450	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
451	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
452	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
453	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
454	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
455	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
456	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
457	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
458	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
459	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
460	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
461	C₃×C₄²	C₂³×C₅	1	4	yes	—
462	C₃×C₄²	C₂³×C₅	1	4	yes	—
463	C₃×C₄²	C₂³×C₅	1	2	yes	—
464	C₃×C₄²	C₂³×C₅	1	4	yes	—
465	C₃×C₄²	C₂³×C₅	1	4	yes	—
466	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
467	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
468	C₅×Q₈	—	2	4	no	—
469	C₅×Q₈	—	4	4	no	—
470	C₅×Q₈	—	4	1	no	—
471	C₅×Q₈	—	4	2	no	—
472	C₅×D₄	—	2	4	no	—
473	C₅×D₄	—	4	1	no	—
474	C₂×C₄×C₅	—	2	2	no	—
475	C₂×C₄×C₅	—	2	4	no	—
476	C₂×C₄×C₅	—	2	2	no	—
477	C₂×C₄×C₅	—	2	4	no	—
478	C₂×C₄×C₅	—	4	2	no	—
479	C₂×C₄×C₅	—	4	4	no	—
480	C₂×C₄×C₅	—	4	1	no	—
481	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
482	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
483	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
484	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
485	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
486	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
487	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
488	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
489	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
490	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
491	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
492	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
493	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
494	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
495	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
496	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
497	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
498	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
499	#126	C₂²×C₃×C₅	1	2	yes	—
500	#126	C₂²×C₃×C₅	1	4	yes	—
501	#126	C₂²×C₃×C₅	1	4	yes	—
502	#126	C₂²×C₃×C₅	1	4	yes	—
503	#126	C₂²×C₃×C₅	1	4	yes	—
504	#125	C₂²×C₃×C₅	1	2	yes	—
505	#125	C₂²×C₃×C₅	1	2	yes	—
506	#125	C₂²×C₃×C₅	1	2	yes	—
507	#125	C₂²×C₃×C₅	1	2	yes	—
508	#125	C₂²×C₃×C₅	1	1	yes	characteristic
509	#125	C₂²×C₃×C₅	1	2	yes	—
510	#125	C₂²×C₃×C₅	1	4	yes	—
511	#125	C₂²×C₃×C₅	1	4	yes	—
512	#125	C₂²×C₃×C₅	1	4	yes	—
513	#125	C₂²×C₃×C₅	1	4	yes	—
514	#125	C₂²×C₃×C₅	1	4	yes	—
515	#125	C₂²×C₃×C₅	1	4	yes	—
516	#125	C₂²×C₃×C₅	1	2	yes	—
517	#125	C₂²×C₃×C₅	1	4	yes	—
518	#125	C₂²×C₃×C₅	1	4	yes	—
519	#124	C₂²×C₃×C₅	1	1	yes	characteristic
520	#123	C₂²×C₃×C₅	1	2	yes	—
521	#123	C₂²×C₃×C₅	1	4	yes	—
522	#123	C₂²×C₃×C₅	1	4	yes	—
523	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
524	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
525	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
526	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
527	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
528	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
529	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
530	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
531	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
532	#121	C₂²×C₃×C₅	1	1	yes	characteristic
533	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
534	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
535	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
536	C₄×Q₈	C₂²×C₃×C₅	1	4	yes	—
537	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
538	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
539	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
540	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
541	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
542	#117	C₂²×C₃×C₅	1	2	yes	—
543	#117	C₂²×C₃×C₅	1	2	yes	—
544	#117	C₂²×C₃×C₅	1	4	yes	—
545	#117	C₂²×C₃×C₅	1	2	yes	—
546	#117	C₂²×C₃×C₅	1	4	yes	—
547	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
548	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
550	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
552	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
553	C₂×C₃×C₅	—	2	2	no	—
554	C₂×C₃×C₅	—	4	2	no	—
555	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
556	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
557	C₂×C₃×C₅	#585	1	1	yes	characteristic
558	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
559	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
560	C₃×Q₈	—	2	4	no	—
561	C₃×Q₈	—	4	4	no	—
562	C₃×Q₈	—	4	1	no	—
563	C₃×Q₈	—	4	2	no	—
564	C₃×D₄	—	2	4	no	—
565	C₃×D₄	—	4	1	no	—
566	C₂×C₃×C₄	—	2	2	no	—
567	C₂×C₃×C₄	—	2	4	no	—
568	C₂×C₃×C₄	—	2	2	no	—
569	C₂×C₃×C₄	—	2	4	no	—
570	C₂×C₃×C₄	—	4	2	no	—
571	C₂×C₃×C₄	—	4	4	no	—
572	C₂×C₃×C₄	—	4	1	no	—
573	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
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	2	yes	—
577	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
578	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
579	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
580	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
581	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
582	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
583	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
584	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
585	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
586	C₂²×C₅	—	2	1	no	—
587	C₂²×C₅	—	2	1	no	—
588	C₂²×C₅	—	2	2	no	—
589	C₂²×C₅	—	2	2	no	—
590	C₂²×C₅	—	2	2	no	—
591	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
592	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
593	C₄×C₅	—	2	1	no	—
594	C₄×C₅	—	2	1	no	—
595	C₄×C₅	—	2	4	no	—
596	C₄×C₅	—	2	1	no	—
597	C₄×C₅	—	2	2	no	—
598	C₄×C₅	—	2	2	no	—
599	C₄×C₅	—	2	4	no	—
600	C₄×C₅	—	2	4	no	—
601	C₄×C₅	—	2	1	no	—
602	C₄×C₅	—	2	4	no	—
603	C₄×C₅	—	2	1	no	—
604	C₄×C₅	—	2	2	no	—
605	C₄×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
606	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
607	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
608	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
609	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
610	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
611	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
612	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
613	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
614	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
615	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
616	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
617	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
618	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
619	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
620	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
621	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
622	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
623	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
624	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
625	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
626	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
627	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
628	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
629	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
630	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
631	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
632	C₄⋊C₄	C₂³×C₃×C₅	1	2	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	2	yes	—
636	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
637	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
638	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
639	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
640	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
641	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
642	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
643	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
644	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
645	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
646	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
647	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
648	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
649	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
650	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
651	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
652	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
653	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
654	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
655	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
656	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
657	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
658	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
659	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
660	C₄²	C₂³×C₃×C₅	1	4	yes	—
661	C₄²	C₂³×C₃×C₅	1	4	yes	—
662	C₄²	C₂³×C₃×C₅	1	2	yes	—
663	C₄²	C₂³×C₃×C₅	1	4	yes	—
664	C₄²	C₂³×C₃×C₅	1	4	yes	—
665	C₃×C₅	#3563	1	1	yes	characteristic, direct product factor, Hall
666	C₂²×C₃	—	2	1	no	—
667	C₂²×C₃	—	2	1	no	—
668	C₂²×C₃	—	2	2	no	—
669	C₂²×C₃	—	2	2	no	—
670	C₂²×C₃	—	2	2	no	—
671	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
672	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
673	C₃×C₄	—	2	1	no	—
674	C₃×C₄	—	2	1	no	—
675	C₃×C₄	—	2	4	no	—
676	C₃×C₄	—	2	1	no	—
677	C₃×C₄	—	2	2	no	—
678	C₃×C₄	—	2	2	no	—
679	C₃×C₄	—	2	4	no	—
680	C₃×C₄	—	2	4	no	—
681	C₃×C₄	—	2	1	no	—
682	C₃×C₄	—	2	4	no	—
683	C₃×C₄	—	2	1	no	—
684	C₃×C₄	—	2	2	no	—
685	C₃×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
686	C₂×C₅	—	2	2	no	—
687	C₂×C₅	—	4	2	no	—
688	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
689	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
690	C₂×C₅	C₃×#585	1	1	yes	characteristic
691	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
692	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
693	Q₈	—	2	4	no	—
694	Q₈	—	4	4	no	—
695	Q₈	—	4	1	no	—
696	Q₈	—	4	2	no	—
697	D₄	—	2	4	no	—
698	D₄	—	4	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	4	2	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
707	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
708	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
709	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
710	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
711	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
712	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
713	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
714	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
715	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
716	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
717	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
718	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
719	C₂×C₃	—	2	2	no	—
720	C₂×C₃	—	4	2	no	—
721	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
722	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
723	C₂×C₃	C₅×#585	1	1	yes	characteristic
724	C₅	C₃×#3563	1	1	yes	characteristic, direct product factor, Sylow
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	2	no	—
730	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
731	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	2	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	4	no	—
739	C₄	—	2	4	no	—
740	C₄	—	2	1	no	—
741	C₄	—	2	4	no	—
742	C₄	—	2	1	no	—
743	C₄	—	2	2	no	—
744	C₄	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
745	C₃	C₅×#3563	1	1	yes	characteristic, direct product factor, Sylow
746	C₂	—	2	2	no	—
747	C₂	—	4	2	no	—
748	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
749	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
750	C₂	C₃×C₅×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
prime radical	C₃×C₅×#121	C₂²
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×#564	C₂	semidirect
2. C₃×C₅×#563	C₂	semidirect
3. C₃×C₅×#557	C₂	semidirect
4. C₃×C₅×#554	C₂	semidirect
5. C₃×C₅×#552	C₂	semidirect
6. C₃×C₅×#552	C₂	semidirect
7. C₃×C₅×#552	C₂	semidirect
8. C₃×C₅×#544	C₂	semidirect
9. C₃×C₅×#544	C₂	semidirect
10. C₃×C₅×#541	C₂	semidirect
11. C₃×C₅×#541	C₂	semidirect
13. C₃×C₅×#533	C₂	semidirect
15. C₂×C₃×C₅×#125	C₂	semidirect
16. C₅×#3563	C₃	direct (N × H)
76. C₃×#3563	C₅	direct (N × H)
77. C₅×#564	C₂×C₃	semidirect
78. C₅×#563	C₂×C₃	semidirect
79. C₅×#557	C₂×C₃	semidirect
80. C₅×#554	C₂×C₃	semidirect
81. C₅×#552	C₂×C₃	semidirect
82. C₅×#552	C₂×C₃	semidirect
83. C₅×#552	C₂×C₃	semidirect
84. C₅×#544	C₂×C₃	semidirect
85. C₅×#544	C₂×C₃	semidirect
86. C₅×#541	C₂×C₃	semidirect
87. C₅×#541	C₂×C₃	semidirect
89. C₅×#533	C₂×C₃	semidirect
91. C₂×C₅×#125	C₂×C₃	semidirect
151. C₃×#564	C₂×C₅	semidirect
152. C₃×#563	C₂×C₅	semidirect
153. C₃×#557	C₂×C₅	semidirect
154. C₃×#554	C₂×C₅	semidirect
155. C₃×#552	C₂×C₅	semidirect
156. C₃×#552	C₂×C₅	semidirect
157. C₃×#552	C₂×C₅	semidirect
158. C₃×#544	C₂×C₅	semidirect
159. C₃×#544	C₂×C₅	semidirect
160. C₃×#541	C₂×C₅	semidirect
161. C₃×#541	C₂×C₅	semidirect
163. C₃×#533	C₂×C₅	semidirect
165. C₂×C₃×#125	C₂×C₅	semidirect
225. #3563	C₃×C₅	direct (N × H)
372. #564	C₂×C₃×C₅	semidirect
373. #563	C₂×C₃×C₅	semidirect
374. #557	C₂×C₃×C₅	semidirect
375. #554	C₂×C₃×C₅	semidirect
376. #552	C₂×C₃×C₅	semidirect
377. #552	C₂×C₃×C₅	semidirect
378. #552	C₂×C₃×C₅	semidirect
379. #544	C₂×C₃×C₅	semidirect
380. #544	C₂×C₃×C₅	semidirect
381. #541	C₂×C₃×C₅	semidirect
382. #541	C₂×C₃×C₅	semidirect
384. #533	C₂×C₃×C₅	semidirect
386. C₂×#125	C₂×C₃×C₅	semidirect
665. C₃×C₅	#3563	direct (N × H)
724. C₅	C₃×#3563	direct (N × H)
745. C₃	C₅×#3563	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×#564	2
C₃×C₅×#563	2
C₃×C₅×#557	2
C₃×C₅×#554	2
C₃×C₅×#552	2
C₃×C₅×#544	2
C₃×C₅×#541	2
C₃×C₅×#539	2
C₃×C₅×#533	2
C₃×C₅×#529	2
C₂×C₃×C₅×#125	2
C₅×#3563	3
C₃×#3563	5

Subgroups — C3×C5×#3563 #14276597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3563 #14276597