Subgroups — C₃×C₅×#3552 #14276586

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 872 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×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#554	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×D₄×Q₈	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#548	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#544	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
12	C₃×C₅×#541	C₂	1	2	yes	maximal, complemented
13	C₃×C₅×#539	C₂	1	4	yes	maximal, complemented
14	C₃×C₅×#536	C₂	1	2	yes	maximal, complemented
15	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#3552	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
20	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
21	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
22	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
28	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
29	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
30	C₃×C₅×#126	C₂²	1	2	yes	—
31	C₃×C₅×#126	C₂²	1	2	yes	—
32	C₃×C₅×#126	C₂²	1	4	yes	—
33	C₃×C₅×#126	C₂²	1	4	yes	—
34	C₃×C₅×#126	C₂²	1	4	yes	—
35	C₃×C₅×#125	C₂²	1	1	yes	characteristic
36	C₃×C₅×#125	C₂²	1	1	yes	characteristic
37	C₃×C₅×#125	C₂²	1	4	yes	—
38	C₃×C₅×#125	C₂²	1	4	yes	—
39	C₃×C₅×#125	C₂²	1	4	yes	—
40	C₃×C₅×#125	C₂²	1	2	yes	—
41	C₃×C₅×#124	C₂²	1	1	yes	characteristic
42	C₃×C₅×#124	C₂²	1	1	yes	characteristic
43	C₃×C₅×#124	C₂²	1	2	yes	—
44	C₃×C₅×#124	C₂²	1	4	yes	—
45	C₃×C₅×#123	C₂²	1	2	yes	—
46	C₃×C₅×#123	C₂²	1	2	yes	—
47	C₃×C₅×#123	C₂²	1	4	yes	—
48	C₃×C₅×#123	C₂²	1	4	yes	—
49	C₃×C₅×#123	C₂²	1	4	yes	—
50	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
51	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
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×C₂²⋊Q₈	C₂²	1	4	yes	—
56	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
57	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
58	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
59	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
60	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
61	C₃×C₅×#121	C₂²	1	1	yes	characteristic
62	C₃×C₅×#121	C₂²	1	1	yes	characteristic
63	C₃×C₅×#121	C₂²	1	4	yes	—
64	C₃×C₅×#121	C₂²	1	2	yes	—
65	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
66	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
67	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
68	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
69	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
70	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
71	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
72	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
73	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
74	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
75	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
76	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
77	C₃×C₅×#117	C₂²	1	2	yes	—
78	C₃×C₅×#117	C₂²	1	2	yes	—
79	C₃×C₅×#117	C₂²	1	2	yes	—
80	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
81	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
82	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
83	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
84	C₃×#3552	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
85	C₅×#563	C₂×C₃	1	4	yes	complemented
86	C₅×#557	C₂×C₃	1	1	yes	characteristic, complemented
87	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
88	C₅×#554	C₂×C₃	1	2	yes	complemented
89	C₅×#553	C₂×C₃	1	2	yes	complemented
90	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
91	C₅×D₄×Q₈	C₂×C₃	1	2	yes	complemented
92	C₅×#548	C₂×C₃	1	2	yes	complemented
93	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
94	C₅×#544	C₂×C₃	1	2	yes	complemented
95	C₅×#542	C₂×C₃	1	2	yes	complemented
96	C₅×#541	C₂×C₃	1	2	yes	complemented
97	C₅×#539	C₂×C₃	1	4	yes	complemented
98	C₅×#536	C₂×C₃	1	2	yes	complemented
99	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
100	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
101	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
102	C₃×C₅×#41	—	4	4	no	—
103	C₂×C₃×C₅×Q₈	—	4	4	no	—
104	C₂×C₃×C₅×Q₈	—	4	4	no	—
105	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
108	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
109	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
110	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
111	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
112	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
113	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
114	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
115	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
116	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
117	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
118	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
119	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
120	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
121	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
122	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
123	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
124	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
125	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
126	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
127	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
128	C₃×C₅×C₄⋊C₄	C₂³	1	2	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	1	yes	characteristic
133	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
134	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
135	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
136	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
137	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
139	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
140	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
141	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
142	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
144	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
145	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
146	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
147	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
148	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
163	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
164	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
165	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
166	C₃×C₄²×C₅	C₂³	1	2	yes	—
167	C₃×C₄²×C₅	C₂³	1	2	yes	—
168	C₃×C₄²×C₅	C₂³	1	4	yes	—
169	C₃×C₄²×C₅	C₂³	1	4	yes	—
170	C₃×#563	C₂×C₅	1	4	yes	complemented
171	C₃×#557	C₂×C₅	1	1	yes	characteristic, complemented
172	C₃×#556	C₂×C₅	1	1	yes	characteristic, complemented
173	C₃×#554	C₂×C₅	1	2	yes	complemented
174	C₃×#553	C₂×C₅	1	2	yes	complemented
175	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
176	C₃×D₄×Q₈	C₂×C₅	1	2	yes	complemented
177	C₃×#548	C₂×C₅	1	2	yes	complemented
178	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
179	C₃×#544	C₂×C₅	1	2	yes	complemented
180	C₃×#542	C₂×C₅	1	2	yes	complemented
181	C₃×#541	C₂×C₅	1	2	yes	complemented
182	C₃×#539	C₂×C₅	1	4	yes	complemented
183	C₃×#536	C₂×C₅	1	2	yes	complemented
184	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
185	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
186	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
187	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
188	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
189	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
190	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
191	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
192	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
193	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
194	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
195	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
196	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
197	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
198	C₅×#126	C₂²×C₃	1	2	yes	—
199	C₅×#126	C₂²×C₃	1	2	yes	—
200	C₅×#126	C₂²×C₃	1	4	yes	—
201	C₅×#126	C₂²×C₃	1	4	yes	—
202	C₅×#126	C₂²×C₃	1	4	yes	—
203	C₅×#125	C₂²×C₃	1	1	yes	characteristic
204	C₅×#125	C₂²×C₃	1	1	yes	characteristic
205	C₅×#125	C₂²×C₃	1	4	yes	—
206	C₅×#125	C₂²×C₃	1	4	yes	—
207	C₅×#125	C₂²×C₃	1	4	yes	—
208	C₅×#125	C₂²×C₃	1	2	yes	—
209	C₅×#124	C₂²×C₃	1	1	yes	characteristic
210	C₅×#124	C₂²×C₃	1	1	yes	characteristic
211	C₅×#124	C₂²×C₃	1	2	yes	—
212	C₅×#124	C₂²×C₃	1	4	yes	—
213	C₅×#123	C₂²×C₃	1	2	yes	—
214	C₅×#123	C₂²×C₃	1	2	yes	—
215	C₅×#123	C₂²×C₃	1	4	yes	—
216	C₅×#123	C₂²×C₃	1	4	yes	—
217	C₅×#123	C₂²×C₃	1	4	yes	—
218	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
219	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
220	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
221	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
222	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
223	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
224	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
225	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
226	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
227	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
228	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
229	C₅×#121	C₂²×C₃	1	1	yes	characteristic
230	C₅×#121	C₂²×C₃	1	1	yes	characteristic
231	C₅×#121	C₂²×C₃	1	4	yes	—
232	C₅×#121	C₂²×C₃	1	2	yes	—
233	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
234	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
235	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
236	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
237	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
238	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
239	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
240	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
241	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
242	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
243	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
244	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
245	C₅×#117	C₂²×C₃	1	2	yes	—
246	C₅×#117	C₂²×C₃	1	2	yes	—
247	C₅×#117	C₂²×C₃	1	2	yes	—
248	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
249	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
250	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
251	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
252	#3552	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
253	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
254	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
255	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
256	C₃×C₅×Q₈	—	2	4	no	—
257	C₃×C₅×Q₈	—	2	2	no	—
258	C₃×C₅×Q₈	—	2	4	no	—
259	C₃×C₅×Q₈	—	2	2	no	—
260	C₃×C₅×Q₈	—	4	4	no	—
261	C₃×C₅×Q₈	—	4	4	no	—
262	C₃×C₅×D₄	—	2	4	no	—
263	C₃×C₅×D₄	—	2	4	no	—
264	C₃×C₅×D₄	—	2	2	no	—
265	C₃×C₅×D₄	—	2	2	no	—
266	C₃×C₅×D₄	—	4	4	no	—
267	C₂×C₃×C₄×C₅	—	2	2	no	—
268	C₂×C₃×C₄×C₅	—	2	2	no	—
269	C₂×C₃×C₄×C₅	—	2	4	no	—
270	C₂×C₃×C₄×C₅	—	2	2	no	—
271	C₂×C₃×C₄×C₅	—	2	4	no	—
272	C₂×C₃×C₄×C₅	—	4	4	no	—
273	C₂×C₃×C₄×C₅	—	4	4	no	—
274	C₂×C₃×C₄×C₅	—	4	4	no	—
275	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
276	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
277	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
278	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
282	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
283	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
284	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
285	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
286	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
287	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
288	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
289	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
290	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
291	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
292	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
293	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
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	1	yes	characteristic
297	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
298	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
299	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
300	C₃×#126	C₂²×C₅	1	2	yes	—
301	C₃×#126	C₂²×C₅	1	2	yes	—
302	C₃×#126	C₂²×C₅	1	4	yes	—
303	C₃×#126	C₂²×C₅	1	4	yes	—
304	C₃×#126	C₂²×C₅	1	4	yes	—
305	C₃×#125	C₂²×C₅	1	4	yes	—
306	C₃×#125	C₂²×C₅	1	4	yes	—
307	C₃×#125	C₂²×C₅	1	1	yes	characteristic
308	C₃×#125	C₂²×C₅	1	1	yes	characteristic
309	C₃×#125	C₂²×C₅	1	4	yes	—
310	C₃×#125	C₂²×C₅	1	2	yes	—
311	C₃×#124	C₂²×C₅	1	4	yes	—
312	C₃×#124	C₂²×C₅	1	1	yes	characteristic
313	C₃×#124	C₂²×C₅	1	1	yes	characteristic
314	C₃×#124	C₂²×C₅	1	2	yes	—
315	C₃×#123	C₂²×C₅	1	4	yes	—
316	C₃×#123	C₂²×C₅	1	4	yes	—
317	C₃×#123	C₂²×C₅	1	2	yes	—
318	C₃×#123	C₂²×C₅	1	2	yes	—
319	C₃×#123	C₂²×C₅	1	4	yes	—
320	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
321	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
322	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
323	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
324	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
325	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
326	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
327	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
328	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
329	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
330	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
331	C₃×#121	C₂²×C₅	1	1	yes	characteristic
332	C₃×#121	C₂²×C₅	1	1	yes	characteristic
333	C₃×#121	C₂²×C₅	1	4	yes	—
334	C₃×#121	C₂²×C₅	1	2	yes	—
335	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
336	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
337	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
338	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
339	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
340	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
341	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
342	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
343	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
344	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
345	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
346	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
347	C₃×#117	C₂²×C₅	1	2	yes	—
348	C₃×#117	C₂²×C₅	1	2	yes	—
349	C₃×#117	C₂²×C₅	1	2	yes	—
350	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
351	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
352	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
353	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
354	C₅×#41	—	4	4	no	—
355	C₂×C₅×Q₈	—	4	4	no	—
356	C₂×C₅×Q₈	—	4	4	no	—
357	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
358	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
359	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
360	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
361	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
362	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
363	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
364	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
365	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
366	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
367	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
368	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
369	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
370	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
371	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
372	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
373	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
374	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
375	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
376	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
377	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
378	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
379	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
380	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
381	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
382	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
383	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
384	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
385	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
386	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
387	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
388	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
389	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
390	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
391	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
392	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
393	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
394	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
395	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
396	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
397	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
398	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
400	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
401	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
402	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
403	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
404	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
405	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
406	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
407	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
408	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
409	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
410	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
411	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
412	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
413	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
414	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
415	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
416	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
417	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
418	C₄²×C₅	C₂³×C₃	1	2	yes	—
419	C₄²×C₅	C₂³×C₃	1	2	yes	—
420	C₄²×C₅	C₂³×C₃	1	4	yes	—
421	C₄²×C₅	C₂³×C₃	1	4	yes	—
422	#563	C₂×C₃×C₅	1	4	yes	complemented
423	#557	C₂×C₃×C₅	1	1	yes	characteristic, complemented
424	#556	C₂×C₃×C₅	1	1	yes	characteristic, complemented
425	#554	C₂×C₃×C₅	1	2	yes	complemented
426	#553	C₂×C₃×C₅	1	2	yes	complemented
427	D₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
428	D₄×Q₈	C₂×C₃×C₅	1	2	yes	complemented
429	#548	C₂×C₃×C₅	1	2	yes	complemented
430	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
431	#544	C₂×C₃×C₅	1	2	yes	complemented
432	#542	C₂×C₃×C₅	1	2	yes	complemented
433	#541	C₂×C₃×C₅	1	2	yes	complemented
434	#539	C₂×C₃×C₅	1	4	yes	complemented
435	#536	C₂×C₃×C₅	1	2	yes	complemented
436	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
437	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
438	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
439	C₂²×C₃×C₅	—	2	1	no	—
440	C₂²×C₃×C₅	—	2	1	no	—
441	C₂²×C₃×C₅	—	2	2	no	—
442	C₂²×C₃×C₅	—	2	2	no	—
443	C₂²×C₃×C₅	—	2	2	no	—
444	C₂²×C₃×C₅	—	2	2	no	—
445	C₂²×C₃×C₅	—	2	2	no	—
446	C₂²×C₃×C₅	—	2	2	no	—
447	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
448	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
449	C₃×C₄×C₅	—	2	2	no	—
450	C₃×C₄×C₅	—	2	1	no	—
451	C₃×C₄×C₅	—	2	4	no	—
452	C₃×C₄×C₅	—	2	4	no	—
453	C₃×C₄×C₅	—	2	2	no	—
454	C₃×C₄×C₅	—	2	1	no	—
455	C₃×C₄×C₅	—	2	1	no	—
456	C₃×C₄×C₅	—	2	1	no	—
457	C₃×C₄×C₅	—	2	2	no	—
458	C₃×C₄×C₅	—	2	2	no	—
459	C₃×C₄×C₅	—	2	2	no	—
460	C₃×C₄×C₅	—	2	2	no	—
461	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
462	C₃×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
463	C₃×#41	—	4	4	no	—
464	C₂×C₃×Q₈	—	4	4	no	—
465	C₂×C₃×Q₈	—	4	4	no	—
466	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
467	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
468	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
469	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
470	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
471	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
472	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
473	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
474	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
475	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
476	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
477	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
478	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
479	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
480	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
481	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
482	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
483	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
484	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
485	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
486	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
487	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
488	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
489	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
490	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
491	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
492	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
493	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
494	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
495	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
496	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
497	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
498	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
499	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
500	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
501	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
502	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
503	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
504	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
505	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
506	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
507	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
508	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
509	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
510	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
511	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
512	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
513	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
514	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
515	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
516	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
517	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
518	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
519	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
520	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
521	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
522	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
523	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
524	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
525	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
526	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
527	C₃×C₄²	C₂³×C₅	1	2	yes	—
528	C₃×C₄²	C₂³×C₅	1	2	yes	—
529	C₃×C₄²	C₂³×C₅	1	4	yes	—
530	C₃×C₄²	C₂³×C₅	1	4	yes	—
531	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
532	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
533	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
534	C₅×Q₈	—	2	4	no	—
535	C₅×Q₈	—	2	2	no	—
536	C₅×Q₈	—	2	4	no	—
537	C₅×Q₈	—	2	2	no	—
538	C₅×Q₈	—	4	4	no	—
539	C₅×Q₈	—	4	4	no	—
540	C₅×D₄	—	2	4	no	—
541	C₅×D₄	—	2	4	no	—
542	C₅×D₄	—	2	2	no	—
543	C₅×D₄	—	2	2	no	—
544	C₅×D₄	—	4	4	no	—
545	C₂×C₄×C₅	—	2	2	no	—
546	C₂×C₄×C₅	—	2	2	no	—
547	C₂×C₄×C₅	—	2	4	no	—
548	C₂×C₄×C₅	—	2	2	no	—
549	C₂×C₄×C₅	—	2	4	no	—
550	C₂×C₄×C₅	—	4	4	no	—
551	C₂×C₄×C₅	—	4	4	no	—
552	C₂×C₄×C₅	—	4	4	no	—
553	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
554	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
555	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
556	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
557	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
558	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
559	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
560	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
561	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
562	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
563	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
564	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
565	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
566	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
567	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
568	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
569	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
570	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
571	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
572	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
573	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
574	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
575	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
576	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
577	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
578	#126	C₂²×C₃×C₅	1	2	yes	—
579	#126	C₂²×C₃×C₅	1	2	yes	—
580	#126	C₂²×C₃×C₅	1	4	yes	—
581	#126	C₂²×C₃×C₅	1	4	yes	—
582	#126	C₂²×C₃×C₅	1	4	yes	—
583	#125	C₂²×C₃×C₅	1	1	yes	characteristic
584	#125	C₂²×C₃×C₅	1	1	yes	characteristic
585	#125	C₂²×C₃×C₅	1	4	yes	—
586	#125	C₂²×C₃×C₅	1	4	yes	—
587	#125	C₂²×C₃×C₅	1	4	yes	—
588	#125	C₂²×C₃×C₅	1	2	yes	—
589	#124	C₂²×C₃×C₅	1	1	yes	characteristic
590	#124	C₂²×C₃×C₅	1	1	yes	characteristic
591	#124	C₂²×C₃×C₅	1	2	yes	—
592	#124	C₂²×C₃×C₅	1	4	yes	—
593	#123	C₂²×C₃×C₅	1	2	yes	—
594	#123	C₂²×C₃×C₅	1	2	yes	—
595	#123	C₂²×C₃×C₅	1	4	yes	—
596	#123	C₂²×C₃×C₅	1	4	yes	—
597	#123	C₂²×C₃×C₅	1	4	yes	—
598	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
599	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
600	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
601	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
602	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
603	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
604	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
605	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
606	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
607	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
608	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
609	#121	C₂²×C₃×C₅	1	1	yes	characteristic
610	#121	C₂²×C₃×C₅	1	1	yes	characteristic
611	#121	C₂²×C₃×C₅	1	4	yes	—
612	#121	C₂²×C₃×C₅	1	2	yes	—
613	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
614	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
615	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
616	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
617	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
618	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
619	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
620	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
621	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
622	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
623	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
624	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
625	#117	C₂²×C₃×C₅	1	2	yes	—
626	#117	C₂²×C₃×C₅	1	2	yes	—
627	#117	C₂²×C₃×C₅	1	2	yes	—
628	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
629	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
630	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
631	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
632	C₂×C₃×C₅	—	2	2	no	—
633	C₂×C₃×C₅	—	4	2	no	—
634	C₂×C₃×C₅	—	4	2	no	—
635	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
636	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
637	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
638	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
639	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
640	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
641	C₃×Q₈	—	2	4	no	—
642	C₃×Q₈	—	2	2	no	—
643	C₃×Q₈	—	2	4	no	—
644	C₃×Q₈	—	2	2	no	—
645	C₃×Q₈	—	4	4	no	—
646	C₃×Q₈	—	4	4	no	—
647	C₃×D₄	—	2	4	no	—
648	C₃×D₄	—	2	4	no	—
649	C₃×D₄	—	2	2	no	—
650	C₃×D₄	—	2	2	no	—
651	C₃×D₄	—	4	4	no	—
652	C₂×C₃×C₄	—	2	2	no	—
653	C₂×C₃×C₄	—	2	2	no	—
654	C₂×C₃×C₄	—	2	4	no	—
655	C₂×C₃×C₄	—	2	2	no	—
656	C₂×C₃×C₄	—	2	4	no	—
657	C₂×C₃×C₄	—	4	4	no	—
658	C₂×C₃×C₄	—	4	4	no	—
659	C₂×C₃×C₄	—	4	4	no	—
660	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
661	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
662	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
663	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
664	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
665	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
666	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
667	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
668	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
669	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
670	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
671	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
672	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
673	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
674	C₂²×C₅	—	2	1	no	—
675	C₂²×C₅	—	2	1	no	—
676	C₂²×C₅	—	2	2	no	—
677	C₂²×C₅	—	2	2	no	—
678	C₂²×C₅	—	2	2	no	—
679	C₂²×C₅	—	2	2	no	—
680	C₂²×C₅	—	2	2	no	—
681	C₂²×C₅	—	2	2	no	—
682	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
683	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
684	C₄×C₅	—	2	2	no	—
685	C₄×C₅	—	2	1	no	—
686	C₄×C₅	—	2	4	no	—
687	C₄×C₅	—	2	4	no	—
688	C₄×C₅	—	2	2	no	—
689	C₄×C₅	—	2	1	no	—
690	C₄×C₅	—	2	1	no	—
691	C₄×C₅	—	2	1	no	—
692	C₄×C₅	—	2	2	no	—
693	C₄×C₅	—	2	2	no	—
694	C₄×C₅	—	2	2	no	—
695	C₄×C₅	—	2	2	no	—
696	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
697	C₄×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
698	#41	—	4	4	no	—
699	C₂×Q₈	—	4	4	no	—
700	C₂×Q₈	—	4	4	no	—
701	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
702	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
703	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
704	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
705	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
706	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
707	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
708	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
709	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
710	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
711	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
712	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
713	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
714	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
715	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
716	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
717	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
718	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
719	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
720	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
721	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
722	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
723	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
724	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
725	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
726	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
727	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
728	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
729	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
730	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
731	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
732	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
733	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
734	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
735	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
736	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
737	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
738	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
739	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
740	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
741	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
742	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
743	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
744	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
745	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
746	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
747	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
748	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
749	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
750	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
751	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
752	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
753	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
754	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
755	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
756	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
757	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
758	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
759	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
760	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
761	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
762	C₄²	C₂³×C₃×C₅	1	2	yes	—
763	C₄²	C₂³×C₃×C₅	1	2	yes	—
764	C₄²	C₂³×C₃×C₅	1	4	yes	—
765	C₄²	C₂³×C₃×C₅	1	4	yes	—
766	C₃×C₅	#3552	1	1	yes	characteristic, direct product factor, Hall
767	C₂²×C₃	—	2	1	no	—
768	C₂²×C₃	—	2	1	no	—
769	C₂²×C₃	—	2	2	no	—
770	C₂²×C₃	—	2	2	no	—
771	C₂²×C₃	—	2	2	no	—
772	C₂²×C₃	—	2	2	no	—
773	C₂²×C₃	—	2	2	no	—
774	C₂²×C₃	—	2	2	no	—
775	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
776	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
777	C₃×C₄	—	2	2	no	—
778	C₃×C₄	—	2	1	no	—
779	C₃×C₄	—	2	4	no	—
780	C₃×C₄	—	2	4	no	—
781	C₃×C₄	—	2	2	no	—
782	C₃×C₄	—	2	1	no	—
783	C₃×C₄	—	2	1	no	—
784	C₃×C₄	—	2	1	no	—
785	C₃×C₄	—	2	2	no	—
786	C₃×C₄	—	2	2	no	—
787	C₃×C₄	—	2	2	no	—
788	C₃×C₄	—	2	2	no	—
789	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
790	C₃×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
791	C₂×C₅	—	2	2	no	—
792	C₂×C₅	—	4	2	no	—
793	C₂×C₅	—	4	2	no	—
794	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
795	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
796	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
797	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
798	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
799	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
800	Q₈	—	2	4	no	—
801	Q₈	—	2	2	no	—
802	Q₈	—	2	4	no	—
803	Q₈	—	2	2	no	—
804	Q₈	—	4	4	no	—
805	Q₈	—	4	4	no	—
806	D₄	—	2	4	no	—
807	D₄	—	2	4	no	—
808	D₄	—	2	2	no	—
809	D₄	—	2	2	no	—
810	D₄	—	4	4	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
820	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
821	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
822	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
823	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
824	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
825	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
826	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
827	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
828	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
829	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
830	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
831	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
832	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
833	C₂×C₃	—	2	2	no	—
834	C₂×C₃	—	4	2	no	—
835	C₂×C₃	—	4	2	no	—
836	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
837	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
838	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
839	C₅	C₃×#3552	1	1	yes	characteristic, direct product factor, Sylow
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
849	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
850	C₄	—	2	2	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	4	no	—
853	C₄	—	2	4	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
863	C₄	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
864	C₃	C₅×#3552	1	1	yes	characteristic, direct product factor, Sylow
865	C₂	—	2	2	no	—
866	C₂	—	4	2	no	—
867	C₂	—	4	2	no	—
868	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
869	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
870	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic

	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×#563	C₂	semidirect
2. C₃×C₅×#557	C₂	semidirect
3. C₃×C₅×#556	C₂	semidirect
4. C₃×C₅×#554	C₂	semidirect
5. C₃×C₅×#553	C₂	semidirect
6. C₃×C₅×D₄×Q₈	C₂	semidirect
7. C₃×C₅×D₄×Q₈	C₂	semidirect
8. C₃×C₅×#548	C₂	semidirect
9. C₃×C₅×#547	C₂	semidirect
10. C₃×C₅×#544	C₂	semidirect
11. C₃×C₅×#542	C₂	semidirect
12. C₃×C₅×#541	C₂	semidirect
13. C₃×C₅×#539	C₂	semidirect
14. C₃×C₅×#536	C₂	semidirect
15. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
16. C₃×C₅×#529	C₂	semidirect
17. C₃×C₅×#529	C₂	semidirect
18. C₅×#3552	C₃	direct (N × H)
84. C₃×#3552	C₅	direct (N × H)
85. C₅×#563	C₂×C₃	semidirect
86. C₅×#557	C₂×C₃	semidirect
87. C₅×#556	C₂×C₃	semidirect
88. C₅×#554	C₂×C₃	semidirect
89. C₅×#553	C₂×C₃	semidirect
90. C₅×D₄×Q₈	C₂×C₃	semidirect
91. C₅×D₄×Q₈	C₂×C₃	semidirect
92. C₅×#548	C₂×C₃	semidirect
93. C₅×#547	C₂×C₃	semidirect
94. C₅×#544	C₂×C₃	semidirect
95. C₅×#542	C₂×C₃	semidirect
96. C₅×#541	C₂×C₃	semidirect
97. C₅×#539	C₂×C₃	semidirect
98. C₅×#536	C₂×C₃	semidirect
99. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
100. C₅×#529	C₂×C₃	semidirect
101. C₅×#529	C₂×C₃	semidirect
170. C₃×#563	C₂×C₅	semidirect
171. C₃×#557	C₂×C₅	semidirect
172. C₃×#556	C₂×C₅	semidirect
173. C₃×#554	C₂×C₅	semidirect
174. C₃×#553	C₂×C₅	semidirect
175. C₃×D₄×Q₈	C₂×C₅	semidirect
176. C₃×D₄×Q₈	C₂×C₅	semidirect
177. C₃×#548	C₂×C₅	semidirect
178. C₃×#547	C₂×C₅	semidirect
179. C₃×#544	C₂×C₅	semidirect
180. C₃×#542	C₂×C₅	semidirect
181. C₃×#541	C₂×C₅	semidirect
182. C₃×#539	C₂×C₅	semidirect
183. C₃×#536	C₂×C₅	semidirect
184. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
185. C₃×#529	C₂×C₅	semidirect
186. C₃×#529	C₂×C₅	semidirect
252. #3552	C₃×C₅	direct (N × H)
422. #563	C₂×C₃×C₅	semidirect
423. #557	C₂×C₃×C₅	semidirect
424. #556	C₂×C₃×C₅	semidirect
425. #554	C₂×C₃×C₅	semidirect
426. #553	C₂×C₃×C₅	semidirect
427. D₄×Q₈	C₂×C₃×C₅	semidirect
428. D₄×Q₈	C₂×C₃×C₅	semidirect
429. #548	C₂×C₃×C₅	semidirect
430. #547	C₂×C₃×C₅	semidirect
431. #544	C₂×C₃×C₅	semidirect
432. #542	C₂×C₃×C₅	semidirect
433. #541	C₂×C₃×C₅	semidirect
434. #539	C₂×C₃×C₅	semidirect
435. #536	C₂×C₃×C₅	semidirect
436. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
437. #529	C₂×C₃×C₅	semidirect
438. #529	C₂×C₃×C₅	semidirect
766. C₃×C₅	#3552	direct (N × H)
839. C₅	C₃×#3552	direct (N × H)
864. C₃	C₅×#3552	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×#557	2
C₃×C₅×#556	2
C₃×C₅×#554	2
C₃×C₅×#553	2
C₃×C₅×D₄×Q₈	2
C₃×C₅×#548	2
C₃×C₅×#547	2
C₃×C₅×#544	2
C₃×C₅×#542	2
C₃×C₅×#541	2
C₃×C₅×#539	2
C₃×C₅×#536	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₃×C₅×#529	2
C₅×#3552	3
C₃×#3552	5

Subgroups — C3×C5×#3552 #14276586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3552 #14276586