Subgroups — C₃×C₅×#3555 #14276589

Order 1920.

1820 conjugacy classes of subgroups.

The subgroup lattice has 828 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×Q₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#557	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#557	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#556	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#556	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#552	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#544	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#542	C₂	1	2	yes	maximal
12	C₃×C₅×#541	C₂	1	2	yes	maximal, complemented
13	C₃×C₅×#541	C₂	1	2	yes	maximal, complemented
14	C₃×C₅×#541	C₂	1	4	yes	maximal, complemented
15	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
18	C₅×#3555	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
25	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
28	C₃×C₅×#126	C₂²	1	2	yes	—
29	C₃×C₅×#126	C₂²	1	4	yes	—
30	C₃×C₅×#126	C₂²	1	4	yes	—
31	C₃×C₅×#126	C₂²	1	4	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	2	yes	—
37	C₃×C₅×#125	C₂²	1	2	yes	—
38	C₃×C₅×#125	C₂²	1	4	yes	—
39	C₃×C₅×#125	C₂²	1	4	yes	—
40	C₃×C₅×#125	C₂²	1	4	yes	—
41	C₃×C₅×#125	C₂²	1	2	yes	—
42	C₃×C₅×#125	C₂²	1	4	yes	—
43	C₃×C₅×#125	C₂²	1	4	yes	—
44	C₃×C₅×#125	C₂²	1	2	yes	—
45	C₃×C₅×#124	C₂²	1	1	yes	characteristic
46	C₃×C₅×#124	C₂²	1	2	yes	—
47	C₃×C₅×#124	C₂²	1	4	yes	—
48	C₃×C₅×#123	C₂²	1	2	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	2	yes	—
52	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
53	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
54	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
55	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
56	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
57	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
58	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
59	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
60	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
61	C₃×C₅×#121	C₂²	1	1	yes	characteristic
62	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
63	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
64	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
65	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
66	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
67	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
68	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
69	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	—
70	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
71	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
72	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
73	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
74	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
75	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
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	C₃×C₅×#117	C₂²	1	4	yes	—
81	C₃×C₅×#117	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×#3555	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
85	C₅×#563	C₂×C₃	1	4	yes	complemented
86	C₅×Q₈²	C₂×C₃	1	1	yes	characteristic, complemented
87	C₅×#557	C₂×C₃	1	1	yes	characteristic, complemented
88	C₅×#557	C₂×C₃	1	2	yes	complemented
89	C₅×#556	C₂×C₃	1	2	yes	complemented
90	C₅×#556	C₂×C₃	1	2	yes	complemented
91	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
92	C₅×#554	C₂×C₃	1	1	yes	characteristic, complemented
93	C₅×#552	C₂×C₃	1	2	yes	complemented
94	C₅×#544	C₂×C₃	1	2	yes	complemented
95	C₅×#542	C₂×C₃	1	2	yes	—
96	C₅×#541	C₂×C₃	1	2	yes	complemented
97	C₅×#541	C₂×C₃	1	2	yes	complemented
98	C₅×#541	C₂×C₃	1	4	yes	complemented
99	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
100	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
101	C₅×#529	C₂×C₃	1	1	yes	characteristic
102	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
106	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
107	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
108	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
109	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
110	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
111	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
112	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
113	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
114	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
115	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
116	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
118	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
119	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
120	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
121	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
123	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
124	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
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	1	yes	characteristic
128	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
129	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
130	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
133	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
134	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
135	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
136	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
137	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
138	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
139	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
140	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
141	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
142	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
143	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
144	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
145	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
157	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
158	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
159	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
160	C₃×C₄²×C₅	C₂³	1	4	yes	—
161	C₃×C₄²×C₅	C₂³	1	2	yes	—
162	C₃×C₄²×C₅	C₂³	1	2	yes	—
163	C₃×C₄²×C₅	C₂³	1	2	yes	—
164	C₃×C₄²×C₅	C₂³	1	4	yes	—
165	C₃×C₄²×C₅	C₂³	1	4	yes	—
166	C₃×C₄²×C₅	C₂³	1	4	yes	—
167	C₃×#563	C₂×C₅	1	4	yes	complemented
168	C₃×Q₈²	C₂×C₅	1	1	yes	characteristic, complemented
169	C₃×#557	C₂×C₅	1	1	yes	characteristic, complemented
170	C₃×#557	C₂×C₅	1	2	yes	complemented
171	C₃×#556	C₂×C₅	1	2	yes	complemented
172	C₃×#556	C₂×C₅	1	2	yes	complemented
173	C₃×#556	C₂×C₅	1	1	yes	characteristic, complemented
174	C₃×#554	C₂×C₅	1	1	yes	characteristic, complemented
175	C₃×#552	C₂×C₅	1	2	yes	complemented
176	C₃×#544	C₂×C₅	1	2	yes	complemented
177	C₃×#542	C₂×C₅	1	2	yes	—
178	C₃×#541	C₂×C₅	1	2	yes	complemented
179	C₃×#541	C₂×C₅	1	2	yes	complemented
180	C₃×#541	C₂×C₅	1	4	yes	complemented
181	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
182	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
183	C₃×#529	C₂×C₅	1	1	yes	characteristic
184	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
185	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
186	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
187	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
188	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
189	C₅×C₄⋊Q₈	C₂²×C₃	1	4	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	4	yes	—
193	C₅×#126	C₂²×C₃	1	2	yes	—
194	C₅×#126	C₂²×C₃	1	4	yes	—
195	C₅×#126	C₂²×C₃	1	4	yes	—
196	C₅×#126	C₂²×C₃	1	4	yes	—
197	C₅×#126	C₂²×C₃	1	4	yes	—
198	C₅×#126	C₂²×C₃	1	4	yes	—
199	C₅×#126	C₂²×C₃	1	4	yes	—
200	C₅×#125	C₂²×C₃	1	1	yes	characteristic
201	C₅×#125	C₂²×C₃	1	2	yes	—
202	C₅×#125	C₂²×C₃	1	2	yes	—
203	C₅×#125	C₂²×C₃	1	4	yes	—
204	C₅×#125	C₂²×C₃	1	4	yes	—
205	C₅×#125	C₂²×C₃	1	4	yes	—
206	C₅×#125	C₂²×C₃	1	2	yes	—
207	C₅×#125	C₂²×C₃	1	4	yes	—
208	C₅×#125	C₂²×C₃	1	4	yes	—
209	C₅×#125	C₂²×C₃	1	2	yes	—
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	4	yes	—
215	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
216	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
217	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
218	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
219	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
220	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
221	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
222	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
223	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
224	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
225	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
226	C₅×#121	C₂²×C₃	1	1	yes	characteristic
227	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
228	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
229	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
230	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
231	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
232	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
233	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
234	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	—
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×Q₈	C₂²×C₃	1	2	yes	—
239	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
240	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
241	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
242	C₅×#117	C₂²×C₃	1	2	yes	—
243	C₅×#117	C₂²×C₃	1	2	yes	—
244	C₅×#117	C₂²×C₃	1	2	yes	—
245	C₅×#117	C₂²×C₃	1	4	yes	—
246	C₅×#117	C₂²×C₃	1	2	yes	—
247	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
248	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
249	#3555	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
250	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
251	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
252	C₃×C₅×Q₈	—	2	2	no	—
253	C₃×C₅×Q₈	—	2	2	no	—
254	C₃×C₅×Q₈	—	2	2	no	—
255	C₃×C₅×Q₈	—	2	4	no	—
256	C₃×C₅×Q₈	—	4	2	no	—
257	C₃×C₅×Q₈	—	4	2	no	—
258	C₃×C₅×Q₈	—	4	4	no	—
259	C₃×C₅×D₄	—	2	2	no	—
260	C₃×C₅×D₄	—	4	2	no	—
261	C₂×C₃×C₄×C₅	—	2	2	no	—
262	C₂×C₃×C₄×C₅	—	2	4	no	—
263	C₂×C₃×C₄×C₅	—	2	2	no	—
264	C₂×C₃×C₄×C₅	—	4	4	no	—
265	C₂×C₃×C₄×C₅	—	4	1	no	—
266	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
267	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
268	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
269	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
270	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
271	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
272	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
273	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
275	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
276	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
277	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
278	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
279	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
282	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
283	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
284	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
285	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
286	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
287	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
288	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
289	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
290	C₃×#126	C₂²×C₅	1	4	yes	—
291	C₃×#126	C₂²×C₅	1	4	yes	—
292	C₃×#126	C₂²×C₅	1	4	yes	—
293	C₃×#126	C₂²×C₅	1	4	yes	—
294	C₃×#126	C₂²×C₅	1	2	yes	—
295	C₃×#126	C₂²×C₅	1	4	yes	—
296	C₃×#126	C₂²×C₅	1	4	yes	—
297	C₃×#125	C₂²×C₅	1	4	yes	—
298	C₃×#125	C₂²×C₅	1	4	yes	—
299	C₃×#125	C₂²×C₅	1	1	yes	characteristic
300	C₃×#125	C₂²×C₅	1	2	yes	—
301	C₃×#125	C₂²×C₅	1	2	yes	—
302	C₃×#125	C₂²×C₅	1	4	yes	—
303	C₃×#125	C₂²×C₅	1	4	yes	—
304	C₃×#125	C₂²×C₅	1	4	yes	—
305	C₃×#125	C₂²×C₅	1	2	yes	—
306	C₃×#125	C₂²×C₅	1	2	yes	—
307	C₃×#124	C₂²×C₅	1	4	yes	—
308	C₃×#124	C₂²×C₅	1	1	yes	characteristic
309	C₃×#124	C₂²×C₅	1	2	yes	—
310	C₃×#123	C₂²×C₅	1	2	yes	—
311	C₃×#123	C₂²×C₅	1	4	yes	—
312	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
313	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
314	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
315	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
316	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
317	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
318	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
319	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
320	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
321	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
322	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
323	C₃×#121	C₂²×C₅	1	1	yes	characteristic
324	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
325	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
326	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
327	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
328	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
329	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
330	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
331	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
332	C₃×C₄×Q₈	C₂²×C₅	1	4	yes	—
333	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
334	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
335	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
336	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
337	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
338	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
339	C₃×#117	C₂²×C₅	1	2	yes	—
340	C₃×#117	C₂²×C₅	1	2	yes	—
341	C₃×#117	C₂²×C₅	1	2	yes	—
342	C₃×#117	C₂²×C₅	1	4	yes	—
343	C₃×#117	C₂²×C₅	1	2	yes	—
344	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
345	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
346	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
347	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
348	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
349	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
350	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
351	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
352	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
353	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
354	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
355	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
356	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
357	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
358	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
359	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
360	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
361	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
362	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
363	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
364	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
365	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
366	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
367	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
368	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
369	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
370	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
371	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
372	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
373	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
374	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
375	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
376	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
377	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
378	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
379	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
380	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
381	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
382	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
383	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
384	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
385	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
386	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
387	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
388	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
389	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
390	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
391	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
392	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
393	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
394	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
395	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
396	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
397	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
398	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
399	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
400	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
401	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
402	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
403	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
404	C₄²×C₅	C₂³×C₃	1	4	yes	—
405	C₄²×C₅	C₂³×C₃	1	2	yes	—
406	C₄²×C₅	C₂³×C₃	1	2	yes	—
407	C₄²×C₅	C₂³×C₃	1	2	yes	—
408	C₄²×C₅	C₂³×C₃	1	4	yes	—
409	C₄²×C₅	C₂³×C₃	1	4	yes	—
410	C₄²×C₅	C₂³×C₃	1	4	yes	—
411	#563	C₂×C₃×C₅	1	4	yes	complemented
412	Q₈²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
413	#557	C₂×C₃×C₅	1	1	yes	characteristic, complemented
414	#557	C₂×C₃×C₅	1	2	yes	complemented
415	#556	C₂×C₃×C₅	1	2	yes	complemented
416	#556	C₂×C₃×C₅	1	2	yes	complemented
417	#556	C₂×C₃×C₅	1	1	yes	characteristic, complemented
418	#554	C₂×C₃×C₅	1	1	yes	characteristic, complemented
419	#552	C₂×C₃×C₅	1	2	yes	complemented
420	#544	C₂×C₃×C₅	1	2	yes	complemented
421	#542	C₂×C₃×C₅	1	2	yes	—
422	#541	C₂×C₃×C₅	1	2	yes	complemented
423	#541	C₂×C₃×C₅	1	2	yes	complemented
424	#541	C₂×C₃×C₅	1	4	yes	complemented
425	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
426	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
427	#529	C₂×C₃×C₅	1	1	yes	characteristic
428	C₂²×C₃×C₅	—	2	1	no	—
429	C₂²×C₃×C₅	—	2	1	no	—
430	C₂²×C₃×C₅	—	2	2	no	—
431	C₂²×C₃×C₅	—	2	2	no	—
432	C₂²×C₃×C₅	—	2	2	no	—
433	C₂²×C₃×C₅	—	2	1	no	—
434	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
435	C₃×C₄×C₅	—	2	1	no	—
436	C₃×C₄×C₅	—	2	2	no	—
437	C₃×C₄×C₅	—	2	1	no	—
438	C₃×C₄×C₅	—	2	2	no	—
439	C₃×C₄×C₅	—	2	2	no	—
440	C₃×C₄×C₅	—	2	4	no	—
441	C₃×C₄×C₅	—	2	2	no	—
442	C₃×C₄×C₅	—	2	2	no	—
443	C₃×C₄×C₅	—	2	4	no	—
444	C₃×C₄×C₅	—	2	1	no	—
445	C₃×C₄×C₅	—	2	1	no	—
446	C₃×C₄×C₅	—	2	2	no	—
447	C₃×C₄×C₅	—	2	2	no	—
448	C₃×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
449	C₃×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
450	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
451	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
452	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
453	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
454	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
455	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
456	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
457	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
458	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
459	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
460	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
461	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
462	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
463	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
464	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
465	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
466	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
467	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
468	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
469	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
470	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
471	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
472	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
473	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
474	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
475	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
476	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
477	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
478	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
479	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
480	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
481	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
482	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
483	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
484	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
485	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
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	2	yes	—
489	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
490	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
491	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
492	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
493	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
494	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
495	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
496	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
497	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
498	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
499	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
500	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
501	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
502	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
503	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
504	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
505	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
506	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
507	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
508	C₃×C₄²	C₂³×C₅	1	4	yes	—
509	C₃×C₄²	C₂³×C₅	1	2	yes	—
510	C₃×C₄²	C₂³×C₅	1	2	yes	—
511	C₃×C₄²	C₂³×C₅	1	2	yes	—
512	C₃×C₄²	C₂³×C₅	1	4	yes	—
513	C₃×C₄²	C₂³×C₅	1	4	yes	—
514	C₃×C₄²	C₂³×C₅	1	4	yes	—
515	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
516	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
517	C₅×Q₈	—	2	2	no	—
518	C₅×Q₈	—	2	2	no	—
519	C₅×Q₈	—	2	2	no	—
520	C₅×Q₈	—	2	4	no	—
521	C₅×Q₈	—	4	2	no	—
522	C₅×Q₈	—	4	2	no	—
523	C₅×Q₈	—	4	4	no	—
524	C₅×D₄	—	2	2	no	—
525	C₅×D₄	—	4	2	no	—
526	C₂×C₄×C₅	—	2	2	no	—
527	C₂×C₄×C₅	—	2	4	no	—
528	C₂×C₄×C₅	—	2	2	no	—
529	C₂×C₄×C₅	—	4	4	no	—
530	C₂×C₄×C₅	—	4	1	no	—
531	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
532	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
533	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
534	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
535	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
536	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
537	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
538	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
539	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
540	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
541	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
542	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
543	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
544	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
545	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
546	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
547	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
548	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
549	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
550	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
551	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
552	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
553	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
554	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
555	#126	C₂²×C₃×C₅	1	2	yes	—
556	#126	C₂²×C₃×C₅	1	4	yes	—
557	#126	C₂²×C₃×C₅	1	4	yes	—
558	#126	C₂²×C₃×C₅	1	4	yes	—
559	#126	C₂²×C₃×C₅	1	4	yes	—
560	#126	C₂²×C₃×C₅	1	4	yes	—
561	#126	C₂²×C₃×C₅	1	4	yes	—
562	#125	C₂²×C₃×C₅	1	1	yes	characteristic
563	#125	C₂²×C₃×C₅	1	2	yes	—
564	#125	C₂²×C₃×C₅	1	2	yes	—
565	#125	C₂²×C₃×C₅	1	4	yes	—
566	#125	C₂²×C₃×C₅	1	4	yes	—
567	#125	C₂²×C₃×C₅	1	4	yes	—
568	#125	C₂²×C₃×C₅	1	2	yes	—
569	#125	C₂²×C₃×C₅	1	4	yes	—
570	#125	C₂²×C₃×C₅	1	4	yes	—
571	#125	C₂²×C₃×C₅	1	2	yes	—
572	#124	C₂²×C₃×C₅	1	1	yes	characteristic
573	#124	C₂²×C₃×C₅	1	2	yes	—
574	#124	C₂²×C₃×C₅	1	4	yes	—
575	#123	C₂²×C₃×C₅	1	2	yes	—
576	#123	C₂²×C₃×C₅	1	4	yes	—
577	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
578	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
579	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
580	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
581	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
582	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
583	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
584	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
585	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
586	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
587	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
588	#121	C₂²×C₃×C₅	1	1	yes	characteristic
589	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
590	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
591	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
592	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
593	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
594	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
595	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
596	C₄×Q₈	C₂²×C₃×C₅	1	4	yes	—
597	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
598	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
599	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
600	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
601	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
602	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
603	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
604	#117	C₂²×C₃×C₅	1	2	yes	—
605	#117	C₂²×C₃×C₅	1	2	yes	—
606	#117	C₂²×C₃×C₅	1	2	yes	—
607	#117	C₂²×C₃×C₅	1	4	yes	—
608	#117	C₂²×C₃×C₅	1	2	yes	—
609	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
610	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
611	C₂×C₃×C₅	—	4	1	no	—
612	C₂×C₃×C₅	—	4	2	no	—
613	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
614	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
615	C₂×C₃×C₅	#585	1	1	yes	characteristic
616	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
617	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
618	C₃×Q₈	—	2	2	no	—
619	C₃×Q₈	—	2	2	no	—
620	C₃×Q₈	—	2	2	no	—
621	C₃×Q₈	—	2	4	no	—
622	C₃×Q₈	—	4	2	no	—
623	C₃×Q₈	—	4	2	no	—
624	C₃×Q₈	—	4	4	no	—
625	C₃×D₄	—	2	2	no	—
626	C₃×D₄	—	4	2	no	—
627	C₂×C₃×C₄	—	2	2	no	—
628	C₂×C₃×C₄	—	2	4	no	—
629	C₂×C₃×C₄	—	2	2	no	—
630	C₂×C₃×C₄	—	4	4	no	—
631	C₂×C₃×C₄	—	4	1	no	—
632	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
633	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
634	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
635	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
636	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
637	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
638	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
639	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
640	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
641	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
642	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
643	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
644	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
645	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
646	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
647	C₂²×C₅	—	2	1	no	—
648	C₂²×C₅	—	2	1	no	—
649	C₂²×C₅	—	2	2	no	—
650	C₂²×C₅	—	2	2	no	—
651	C₂²×C₅	—	2	2	no	—
652	C₂²×C₅	—	2	1	no	—
653	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
654	C₄×C₅	—	2	1	no	—
655	C₄×C₅	—	2	2	no	—
656	C₄×C₅	—	2	1	no	—
657	C₄×C₅	—	2	2	no	—
658	C₄×C₅	—	2	2	no	—
659	C₄×C₅	—	2	4	no	—
660	C₄×C₅	—	2	2	no	—
661	C₄×C₅	—	2	2	no	—
662	C₄×C₅	—	2	4	no	—
663	C₄×C₅	—	2	1	no	—
664	C₄×C₅	—	2	1	no	—
665	C₄×C₅	—	2	2	no	—
666	C₄×C₅	—	2	2	no	—
667	C₄×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
668	C₄×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
669	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
670	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
671	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
672	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
673	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
674	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
675	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
676	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
677	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
678	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
679	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
680	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
681	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
682	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
683	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
684	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
685	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
686	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
687	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
688	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
689	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
690	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
691	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
692	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
693	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
694	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
695	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
696	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
697	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
698	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
699	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
700	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
701	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
702	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
703	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
704	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
705	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
706	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
707	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
708	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
709	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
710	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
711	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
712	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
713	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
714	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
715	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
716	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
717	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
718	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
719	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
720	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
721	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
722	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
723	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
724	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
725	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
726	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
727	C₄²	C₂³×C₃×C₅	1	4	yes	—
728	C₄²	C₂³×C₃×C₅	1	2	yes	—
729	C₄²	C₂³×C₃×C₅	1	2	yes	—
730	C₄²	C₂³×C₃×C₅	1	2	yes	—
731	C₄²	C₂³×C₃×C₅	1	4	yes	—
732	C₄²	C₂³×C₃×C₅	1	4	yes	—
733	C₄²	C₂³×C₃×C₅	1	4	yes	—
734	C₃×C₅	#3555	1	1	yes	characteristic, direct product factor, Hall
735	C₂²×C₃	—	2	1	no	—
736	C₂²×C₃	—	2	1	no	—
737	C₂²×C₃	—	2	2	no	—
738	C₂²×C₃	—	2	2	no	—
739	C₂²×C₃	—	2	2	no	—
740	C₂²×C₃	—	2	1	no	—
741	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
742	C₃×C₄	—	2	1	no	—
743	C₃×C₄	—	2	2	no	—
744	C₃×C₄	—	2	1	no	—
745	C₃×C₄	—	2	2	no	—
746	C₃×C₄	—	2	2	no	—
747	C₃×C₄	—	2	4	no	—
748	C₃×C₄	—	2	2	no	—
749	C₃×C₄	—	2	2	no	—
750	C₃×C₄	—	2	4	no	—
751	C₃×C₄	—	2	1	no	—
752	C₃×C₄	—	2	1	no	—
753	C₃×C₄	—	2	2	no	—
754	C₃×C₄	—	2	2	no	—
755	C₃×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
756	C₃×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
757	C₂×C₅	—	4	1	no	—
758	C₂×C₅	—	4	2	no	—
759	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
760	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
761	C₂×C₅	C₃×#585	1	1	yes	characteristic
762	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
763	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
764	Q₈	—	2	2	no	—
765	Q₈	—	2	2	no	—
766	Q₈	—	2	2	no	—
767	Q₈	—	2	4	no	—
768	Q₈	—	4	2	no	—
769	Q₈	—	4	2	no	—
770	Q₈	—	4	4	no	—
771	D₄	—	2	2	no	—
772	D₄	—	4	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
779	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
780	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
781	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
782	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
783	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
784	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
785	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
786	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
787	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
788	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
789	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
790	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
791	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
792	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
793	C₂×C₃	—	4	1	no	—
794	C₂×C₃	—	4	2	no	—
795	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
796	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
797	C₂×C₃	C₅×#585	1	1	yes	characteristic
798	C₅	C₃×#3555	1	1	yes	characteristic, direct product factor, Sylow
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	1	no	—
805	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
806	C₄	—	2	1	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	1	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	2	no	—
811	C₄	—	2	4	no	—
812	C₄	—	2	2	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	4	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
820	C₄	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
821	C₃	C₅×#3555	1	1	yes	characteristic, direct product factor, Sylow
822	C₂	—	4	1	no	—
823	C₂	—	4	2	no	—
824	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
825	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
826	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×#563	C₂	semidirect
2. C₃×C₅×Q₈²	C₂	semidirect
3. C₃×C₅×#557	C₂	semidirect
4. C₃×C₅×#557	C₂	semidirect
5. C₃×C₅×#556	C₂	semidirect
6. C₃×C₅×#556	C₂	semidirect
7. C₃×C₅×#556	C₂	semidirect
8. C₃×C₅×#554	C₂	semidirect
9. C₃×C₅×#552	C₂	semidirect
10. C₃×C₅×#544	C₂	semidirect
12. C₃×C₅×#541	C₂	semidirect
13. C₃×C₅×#541	C₂	semidirect
14. C₃×C₅×#541	C₂	semidirect
15. C₃×C₅×#533	C₂	semidirect
16. C₃×C₅×#533	C₂	semidirect
18. C₅×#3555	C₃	direct (N × H)
84. C₃×#3555	C₅	direct (N × H)
85. C₅×#563	C₂×C₃	semidirect
86. C₅×Q₈²	C₂×C₃	semidirect
87. C₅×#557	C₂×C₃	semidirect
88. C₅×#557	C₂×C₃	semidirect
89. C₅×#556	C₂×C₃	semidirect
90. C₅×#556	C₂×C₃	semidirect
91. C₅×#556	C₂×C₃	semidirect
92. C₅×#554	C₂×C₃	semidirect
93. C₅×#552	C₂×C₃	semidirect
94. C₅×#544	C₂×C₃	semidirect
96. C₅×#541	C₂×C₃	semidirect
97. C₅×#541	C₂×C₃	semidirect
98. C₅×#541	C₂×C₃	semidirect
99. C₅×#533	C₂×C₃	semidirect
100. C₅×#533	C₂×C₃	semidirect
167. C₃×#563	C₂×C₅	semidirect
168. C₃×Q₈²	C₂×C₅	semidirect
169. C₃×#557	C₂×C₅	semidirect
170. C₃×#557	C₂×C₅	semidirect
171. C₃×#556	C₂×C₅	semidirect
172. C₃×#556	C₂×C₅	semidirect
173. C₃×#556	C₂×C₅	semidirect
174. C₃×#554	C₂×C₅	semidirect
175. C₃×#552	C₂×C₅	semidirect
176. C₃×#544	C₂×C₅	semidirect
178. C₃×#541	C₂×C₅	semidirect
179. C₃×#541	C₂×C₅	semidirect
180. C₃×#541	C₂×C₅	semidirect
181. C₃×#533	C₂×C₅	semidirect
182. C₃×#533	C₂×C₅	semidirect
249. #3555	C₃×C₅	direct (N × H)
411. #563	C₂×C₃×C₅	semidirect
412. Q₈²	C₂×C₃×C₅	semidirect
413. #557	C₂×C₃×C₅	semidirect
414. #557	C₂×C₃×C₅	semidirect
415. #556	C₂×C₃×C₅	semidirect
416. #556	C₂×C₃×C₅	semidirect
417. #556	C₂×C₃×C₅	semidirect
418. #554	C₂×C₃×C₅	semidirect
419. #552	C₂×C₃×C₅	semidirect
420. #544	C₂×C₃×C₅	semidirect
422. #541	C₂×C₃×C₅	semidirect
423. #541	C₂×C₃×C₅	semidirect
424. #541	C₂×C₃×C₅	semidirect
425. #533	C₂×C₃×C₅	semidirect
426. #533	C₂×C₃×C₅	semidirect
734. C₃×C₅	#3555	direct (N × H)
798. C₅	C₃×#3555	direct (N × H)
821. C₃	C₅×#3555	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×Q₈²	2
C₃×C₅×#557	2
C₃×C₅×#556	2
C₃×C₅×#554	2
C₃×C₅×#552	2
C₃×C₅×#544	2
C₃×C₅×#542	2
C₃×C₅×#541	2
C₃×C₅×#533	2
C₃×C₅×#529	2
C₅×#3555	3
C₃×#3555	5

Subgroups — C3×C5×#3555 #14276589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3555 #14276589