Subgroups — C₃×C₅×#3559 #14276593

Order 1920.

2048 conjugacy classes of subgroups.

The subgroup lattice has 804 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	2	yes	maximal, complemented
2	C₃×C₅×#562	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#554	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#547	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#547	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#544	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#540	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#539	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#539	C₂	1	4	yes	maximal, complemented
12	C₃×C₅×#537	C₂	1	2	yes	maximal, complemented
13	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3559	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
18	C₂×C₃×C₅×#41	C₂²	1	4	yes	—
19	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
22	C₃×C₅×#127	C₂²	1	1	yes	characteristic
23	C₃×C₅×#126	C₂²	1	2	yes	—
24	C₃×C₅×#126	C₂²	1	4	yes	—
25	C₃×C₅×#126	C₂²	1	4	yes	—
26	C₃×C₅×#125	C₂²	1	2	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	1	yes	characteristic
31	C₃×C₅×#125	C₂²	1	4	yes	—
32	C₃×C₅×#125	C₂²	1	2	yes	—
33	C₃×C₅×#124	C₂²	1	1	yes	characteristic
34	C₃×C₅×#124	C₂²	1	2	yes	—
35	C₃×C₅×#123	C₂²	1	2	yes	—
36	C₃×C₅×#123	C₂²	1	4	yes	—
37	C₃×C₅×#123	C₂²	1	4	yes	—
38	C₃×C₅×#123	C₂²	1	4	yes	—
39	C₃×C₅×#123	C₂²	1	4	yes	—
40	C₃×C₅×#123	C₂²	1	4	yes	—
41	C₃×C₅×#123	C₂²	1	4	yes	—
42	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
44	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
45	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
46	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
47	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
48	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
49	C₃×C₅×#121	C₂²	1	1	yes	characteristic
50	C₃×C₅×#121	C₂²	1	2	yes	—
51	C₃×C₅×#121	C₂²	1	2	yes	—
52	C₃×C₅×#121	C₂²	1	4	yes	—
53	C₃×C₅×#121	C₂²	1	4	yes	—
54	C₃×C₅×#121	C₂²	1	4	yes	—
55	C₃×C₅×#121	C₂²	1	2	yes	—
56	C₃×C₅×#121	C₂²	1	4	yes	—
57	C₃×C₅×#121	C₂²	1	2	yes	—
58	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
59	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
60	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
61	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
62	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
63	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
64	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
65	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
66	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
67	C₃×C₅×#117	C₂²	1	2	yes	—
68	C₃×C₅×#117	C₂²	1	2	yes	—
69	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
70	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
72	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
74	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
75	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
76	C₃×#3559	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
77	C₅×#563	C₂×C₃	1	2	yes	complemented
78	C₅×#562	C₂×C₃	1	2	yes	complemented
79	C₅×#554	C₂×C₃	1	2	yes	complemented
80	C₅×#553	C₂×C₃	1	2	yes	complemented
81	C₅×#553	C₂×C₃	1	2	yes	complemented
82	C₅×#547	C₂×C₃	1	4	yes	complemented
83	C₅×#547	C₂×C₃	1	2	yes	complemented
84	C₅×#544	C₂×C₃	1	2	yes	complemented
85	C₅×#540	C₂×C₃	1	2	yes	complemented
86	C₅×#539	C₂×C₃	1	2	yes	complemented
87	C₅×#539	C₂×C₃	1	4	yes	complemented
88	C₅×#537	C₂×C₃	1	2	yes	complemented
89	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
90	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
92	C₃×C₅×#41	—	4	4	no	—
93	C₃×C₅×#41	—	4	8	no	—
94	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
96	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
97	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
98	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
99	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
100	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
101	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
103	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
104	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
105	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
106	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
107	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
108	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
109	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
110	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
111	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
112	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
113	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
114	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
115	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
116	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
117	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
118	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
119	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
120	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
121	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
122	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
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	4	yes	—
126	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
127	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
131	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
133	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
148	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
149	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
150	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
151	C₃×C₄²×C₅	C₂³	1	2	yes	—
152	C₃×C₄²×C₅	C₂³	1	4	yes	—
153	C₃×#563	C₂×C₅	1	2	yes	complemented
154	C₃×#562	C₂×C₅	1	2	yes	complemented
155	C₃×#554	C₂×C₅	1	2	yes	complemented
156	C₃×#553	C₂×C₅	1	2	yes	complemented
157	C₃×#553	C₂×C₅	1	2	yes	complemented
158	C₃×#547	C₂×C₅	1	4	yes	complemented
159	C₃×#547	C₂×C₅	1	2	yes	complemented
160	C₃×#544	C₂×C₅	1	2	yes	complemented
161	C₃×#540	C₂×C₅	1	2	yes	complemented
162	C₃×#539	C₂×C₅	1	2	yes	complemented
163	C₃×#539	C₂×C₅	1	4	yes	complemented
164	C₃×#537	C₂×C₅	1	2	yes	complemented
165	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
166	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
167	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
168	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
169	C₂×C₅×#41	C₂²×C₃	1	4	yes	—
170	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
171	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
172	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
173	C₅×#127	C₂²×C₃	1	1	yes	characteristic
174	C₅×#126	C₂²×C₃	1	2	yes	—
175	C₅×#126	C₂²×C₃	1	4	yes	—
176	C₅×#126	C₂²×C₃	1	4	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	2	yes	—
181	C₅×#125	C₂²×C₃	1	1	yes	characteristic
182	C₅×#125	C₂²×C₃	1	4	yes	—
183	C₅×#125	C₂²×C₃	1	2	yes	—
184	C₅×#124	C₂²×C₃	1	1	yes	characteristic
185	C₅×#124	C₂²×C₃	1	2	yes	—
186	C₅×#123	C₂²×C₃	1	2	yes	—
187	C₅×#123	C₂²×C₃	1	4	yes	—
188	C₅×#123	C₂²×C₃	1	4	yes	—
189	C₅×#123	C₂²×C₃	1	4	yes	—
190	C₅×#123	C₂²×C₃	1	4	yes	—
191	C₅×#123	C₂²×C₃	1	4	yes	—
192	C₅×#123	C₂²×C₃	1	4	yes	—
193	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
194	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
195	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
196	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
197	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
198	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
199	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
200	C₅×#121	C₂²×C₃	1	1	yes	characteristic
201	C₅×#121	C₂²×C₃	1	2	yes	—
202	C₅×#121	C₂²×C₃	1	2	yes	—
203	C₅×#121	C₂²×C₃	1	4	yes	—
204	C₅×#121	C₂²×C₃	1	4	yes	—
205	C₅×#121	C₂²×C₃	1	4	yes	—
206	C₅×#121	C₂²×C₃	1	2	yes	—
207	C₅×#121	C₂²×C₃	1	4	yes	—
208	C₅×#121	C₂²×C₃	1	2	yes	—
209	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
210	C₄×C₅×D₄	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	2	yes	—
214	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
215	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
216	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
217	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
218	C₅×#117	C₂²×C₃	1	2	yes	—
219	C₅×#117	C₂²×C₃	1	2	yes	—
220	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
221	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
222	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
223	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
224	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
225	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
226	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
227	#3559	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
228	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
229	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
230	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
231	C₃×C₅×Q₈	—	4	1	no	—
232	C₃×C₅×Q₈	—	4	4	no	—
233	C₃×C₅×Q₈	—	4	2	no	—
234	C₃×C₅×D₄	—	2	4	no	—
235	C₃×C₅×D₄	—	2	8	no	—
236	C₃×C₅×D₄	—	2	4	no	—
237	C₃×C₅×D₄	—	4	4	no	—
238	C₃×C₅×D₄	—	4	2	no	—
239	C₃×C₅×D₄	—	4	1	no	—
240	C₃×C₅×D₄	—	4	4	no	—
241	C₃×C₅×D₄	—	4	2	no	—
242	C₂×C₃×C₄×C₅	—	2	2	no	—
243	C₂×C₃×C₄×C₅	—	2	4	no	—
244	C₂×C₃×C₄×C₅	—	2	2	no	—
245	C₂×C₃×C₄×C₅	—	2	4	no	—
246	C₂×C₃×C₄×C₅	—	4	2	no	—
247	C₂×C₃×C₄×C₅	—	4	4	no	—
248	C₂×C₃×C₄×C₅	—	4	1	no	—
249	C₂×C₃×C₄×C₅	—	4	4	no	—
250	C₂×C₃×C₄×C₅	—	4	4	no	—
251	C₂×C₃×C₄×C₅	—	4	4	no	—
252	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
253	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
254	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
255	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
256	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
257	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
258	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
259	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
260	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
261	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
262	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
263	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
264	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
265	C₂×C₃×#41	C₂²×C₅	1	4	yes	—
266	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
267	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
268	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
269	C₃×#127	C₂²×C₅	1	1	yes	characteristic
270	C₃×#126	C₂²×C₅	1	4	yes	—
271	C₃×#126	C₂²×C₅	1	4	yes	—
272	C₃×#126	C₂²×C₅	1	2	yes	—
273	C₃×#125	C₂²×C₅	1	2	yes	—
274	C₃×#125	C₂²×C₅	1	1	yes	characteristic
275	C₃×#125	C₂²×C₅	1	2	yes	—
276	C₃×#125	C₂²×C₅	1	2	yes	—
277	C₃×#125	C₂²×C₅	1	2	yes	—
278	C₃×#125	C₂²×C₅	1	4	yes	—
279	C₃×#125	C₂²×C₅	1	2	yes	—
280	C₃×#124	C₂²×C₅	1	1	yes	characteristic
281	C₃×#124	C₂²×C₅	1	2	yes	—
282	C₃×#123	C₂²×C₅	1	4	yes	—
283	C₃×#123	C₂²×C₅	1	4	yes	—
284	C₃×#123	C₂²×C₅	1	4	yes	—
285	C₃×#123	C₂²×C₅	1	2	yes	—
286	C₃×#123	C₂²×C₅	1	4	yes	—
287	C₃×#123	C₂²×C₅	1	4	yes	—
288	C₃×#123	C₂²×C₅	1	4	yes	—
289	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
290	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
291	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
292	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
293	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
294	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
295	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
296	C₃×#121	C₂²×C₅	1	4	yes	—
297	C₃×#121	C₂²×C₅	1	4	yes	—
298	C₃×#121	C₂²×C₅	1	1	yes	characteristic
299	C₃×#121	C₂²×C₅	1	2	yes	—
300	C₃×#121	C₂²×C₅	1	2	yes	—
301	C₃×#121	C₂²×C₅	1	4	yes	—
302	C₃×#121	C₂²×C₅	1	4	yes	—
303	C₃×#121	C₂²×C₅	1	2	yes	—
304	C₃×#121	C₂²×C₅	1	2	yes	—
305	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
306	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
307	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
308	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
309	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
310	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
311	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
312	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
313	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
314	C₃×#117	C₂²×C₅	1	2	yes	—
315	C₃×#117	C₂²×C₅	1	2	yes	—
316	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
317	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
318	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
319	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
320	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
321	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
322	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
323	C₅×#41	—	4	4	no	—
324	C₅×#41	—	4	8	no	—
325	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
326	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
327	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
328	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
329	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
330	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
331	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
332	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
333	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
334	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
335	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
336	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
337	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
338	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
339	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
340	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
341	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
342	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
343	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
344	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
345	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
346	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
347	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
348	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
349	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
350	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
351	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
352	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
353	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
354	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
355	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
356	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
357	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
358	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
359	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
360	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
365	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
366	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
367	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
368	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
369	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
370	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
371	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
372	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
373	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
374	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
375	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
376	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
377	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
378	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
379	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
380	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
381	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
382	C₄²×C₅	C₂³×C₃	1	2	yes	—
383	C₄²×C₅	C₂³×C₃	1	4	yes	—
384	#563	C₂×C₃×C₅	1	2	yes	complemented
385	#562	C₂×C₃×C₅	1	2	yes	complemented
386	#554	C₂×C₃×C₅	1	2	yes	complemented
387	#553	C₂×C₃×C₅	1	2	yes	complemented
388	#553	C₂×C₃×C₅	1	2	yes	complemented
389	#547	C₂×C₃×C₅	1	4	yes	complemented
390	#547	C₂×C₃×C₅	1	2	yes	complemented
391	#544	C₂×C₃×C₅	1	2	yes	complemented
392	#540	C₂×C₃×C₅	1	2	yes	complemented
393	#539	C₂×C₃×C₅	1	2	yes	complemented
394	#539	C₂×C₃×C₅	1	4	yes	complemented
395	#537	C₂×C₃×C₅	1	2	yes	complemented
396	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
397	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
398	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic, complemented
399	C₂²×C₃×C₅	—	2	1	no	—
400	C₂²×C₃×C₅	—	2	1	no	—
401	C₂²×C₃×C₅	—	2	2	no	—
402	C₂²×C₃×C₅	—	2	4	no	—
403	C₂²×C₃×C₅	—	2	2	no	—
404	C₂²×C₃×C₅	—	2	4	no	—
405	C₂²×C₃×C₅	—	2	4	no	—
406	C₂²×C₃×C₅	—	2	2	no	—
407	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
408	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
409	C₃×C₄×C₅	—	2	1	no	—
410	C₃×C₄×C₅	—	2	4	no	—
411	C₃×C₄×C₅	—	2	1	no	—
412	C₃×C₄×C₅	—	2	4	no	—
413	C₃×C₄×C₅	—	2	2	no	—
414	C₃×C₄×C₅	—	2	1	no	—
415	C₃×C₄×C₅	—	2	2	no	—
416	C₃×C₄×C₅	—	2	4	no	—
417	C₃×C₄×C₅	—	2	2	no	—
418	C₃×C₄×C₅	—	2	1	no	—
419	C₃×C₄×C₅	—	2	1	no	—
420	C₃×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
421	C₃×#41	—	4	4	no	—
422	C₃×#41	—	4	8	no	—
423	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
425	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
426	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
427	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
428	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
429	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
430	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
431	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
432	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
433	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
434	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
435	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
436	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
437	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
438	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
439	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
440	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
441	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
442	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
443	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
444	C₃×C₄⋊C₄	C₂³×C₅	1	2	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	2	yes	—
448	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
449	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
450	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
451	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
452	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
453	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
454	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
455	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
456	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
457	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
458	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
459	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
460	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
461	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
462	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
463	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
464	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
465	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
466	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
467	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
468	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
469	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
470	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
471	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
472	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
473	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
474	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
475	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
476	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
477	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
478	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
479	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
480	C₃×C₄²	C₂³×C₅	1	2	yes	—
481	C₃×C₄²	C₂³×C₅	1	4	yes	—
482	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
483	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
484	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
485	C₅×Q₈	—	4	1	no	—
486	C₅×Q₈	—	4	4	no	—
487	C₅×Q₈	—	4	2	no	—
488	C₅×D₄	—	2	4	no	—
489	C₅×D₄	—	2	8	no	—
490	C₅×D₄	—	2	4	no	—
491	C₅×D₄	—	4	4	no	—
492	C₅×D₄	—	4	2	no	—
493	C₅×D₄	—	4	1	no	—
494	C₅×D₄	—	4	4	no	—
495	C₅×D₄	—	4	2	no	—
496	C₂×C₄×C₅	—	2	2	no	—
497	C₂×C₄×C₅	—	2	4	no	—
498	C₂×C₄×C₅	—	2	2	no	—
499	C₂×C₄×C₅	—	2	4	no	—
500	C₂×C₄×C₅	—	4	2	no	—
501	C₂×C₄×C₅	—	4	4	no	—
502	C₂×C₄×C₅	—	4	1	no	—
503	C₂×C₄×C₅	—	4	4	no	—
504	C₂×C₄×C₅	—	4	4	no	—
505	C₂×C₄×C₅	—	4	4	no	—
506	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
507	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
508	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
509	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
510	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
511	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
512	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
513	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
514	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
515	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
516	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
517	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
518	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
519	C₂×#41	C₂²×C₃×C₅	1	4	yes	—
520	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
521	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
522	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
523	#127	C₂²×C₃×C₅	1	1	yes	characteristic
524	#126	C₂²×C₃×C₅	1	2	yes	—
525	#126	C₂²×C₃×C₅	1	4	yes	—
526	#126	C₂²×C₃×C₅	1	4	yes	—
527	#125	C₂²×C₃×C₅	1	2	yes	—
528	#125	C₂²×C₃×C₅	1	2	yes	—
529	#125	C₂²×C₃×C₅	1	2	yes	—
530	#125	C₂²×C₃×C₅	1	2	yes	—
531	#125	C₂²×C₃×C₅	1	1	yes	characteristic
532	#125	C₂²×C₃×C₅	1	4	yes	—
533	#125	C₂²×C₃×C₅	1	2	yes	—
534	#124	C₂²×C₃×C₅	1	1	yes	characteristic
535	#124	C₂²×C₃×C₅	1	2	yes	—
536	#123	C₂²×C₃×C₅	1	2	yes	—
537	#123	C₂²×C₃×C₅	1	4	yes	—
538	#123	C₂²×C₃×C₅	1	4	yes	—
539	#123	C₂²×C₃×C₅	1	4	yes	—
540	#123	C₂²×C₃×C₅	1	4	yes	—
541	#123	C₂²×C₃×C₅	1	4	yes	—
542	#123	C₂²×C₃×C₅	1	4	yes	—
543	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
544	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
545	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
546	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
547	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
548	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
549	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
550	#121	C₂²×C₃×C₅	1	1	yes	characteristic
551	#121	C₂²×C₃×C₅	1	2	yes	—
552	#121	C₂²×C₃×C₅	1	2	yes	—
553	#121	C₂²×C₃×C₅	1	4	yes	—
554	#121	C₂²×C₃×C₅	1	4	yes	—
555	#121	C₂²×C₃×C₅	1	4	yes	—
556	#121	C₂²×C₃×C₅	1	2	yes	—
557	#121	C₂²×C₃×C₅	1	4	yes	—
558	#121	C₂²×C₃×C₅	1	2	yes	—
559	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
560	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
561	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
562	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
563	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
564	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
565	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
566	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
567	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
568	#117	C₂²×C₃×C₅	1	2	yes	—
569	#117	C₂²×C₃×C₅	1	2	yes	—
570	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
571	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
573	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
575	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
576	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
577	C₂×C₃×C₅	—	2	2	no	—
578	C₂×C₃×C₅	—	4	2	no	—
579	C₂×C₃×C₅	—	4	4	no	—
580	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
582	C₂×C₃×C₅	#585	1	1	yes	characteristic
583	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
584	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
585	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
586	C₃×Q₈	—	4	1	no	—
587	C₃×Q₈	—	4	4	no	—
588	C₃×Q₈	—	4	2	no	—
589	C₃×D₄	—	2	4	no	—
590	C₃×D₄	—	2	8	no	—
591	C₃×D₄	—	2	4	no	—
592	C₃×D₄	—	4	4	no	—
593	C₃×D₄	—	4	2	no	—
594	C₃×D₄	—	4	1	no	—
595	C₃×D₄	—	4	4	no	—
596	C₃×D₄	—	4	2	no	—
597	C₂×C₃×C₄	—	2	2	no	—
598	C₂×C₃×C₄	—	2	4	no	—
599	C₂×C₃×C₄	—	2	2	no	—
600	C₂×C₃×C₄	—	2	4	no	—
601	C₂×C₃×C₄	—	4	2	no	—
602	C₂×C₃×C₄	—	4	4	no	—
603	C₂×C₃×C₄	—	4	1	no	—
604	C₂×C₃×C₄	—	4	4	no	—
605	C₂×C₃×C₄	—	4	4	no	—
606	C₂×C₃×C₄	—	4	4	no	—
607	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
608	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
609	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
610	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
611	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
612	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
613	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
614	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
615	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
616	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
617	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
618	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
619	C₂²×C₅	—	2	1	no	—
620	C₂²×C₅	—	2	1	no	—
621	C₂²×C₅	—	2	2	no	—
622	C₂²×C₅	—	2	4	no	—
623	C₂²×C₅	—	2	2	no	—
624	C₂²×C₅	—	2	4	no	—
625	C₂²×C₅	—	2	4	no	—
626	C₂²×C₅	—	2	2	no	—
627	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
628	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
629	C₄×C₅	—	2	1	no	—
630	C₄×C₅	—	2	4	no	—
631	C₄×C₅	—	2	1	no	—
632	C₄×C₅	—	2	4	no	—
633	C₄×C₅	—	2	2	no	—
634	C₄×C₅	—	2	1	no	—
635	C₄×C₅	—	2	2	no	—
636	C₄×C₅	—	2	4	no	—
637	C₄×C₅	—	2	2	no	—
638	C₄×C₅	—	2	1	no	—
639	C₄×C₅	—	2	1	no	—
640	C₄×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
641	#41	—	4	4	no	—
642	#41	—	4	8	no	—
643	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
644	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
645	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
646	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
647	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
648	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
649	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
650	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
651	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
652	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
653	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
654	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
655	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
656	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
657	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
658	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
659	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
660	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
661	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
662	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
663	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
664	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
665	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
666	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
667	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
668	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
669	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
670	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
671	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
672	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
673	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
674	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
675	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
676	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
677	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
678	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
679	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
680	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
681	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
682	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
683	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
684	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
685	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
686	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
687	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
688	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
689	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
690	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
691	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
692	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
693	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
694	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
695	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
696	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
697	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
698	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
699	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
700	C₄²	C₂³×C₃×C₅	1	2	yes	—
701	C₄²	C₂³×C₃×C₅	1	4	yes	—
702	C₃×C₅	#3559	1	1	yes	characteristic, direct product factor, Hall
703	C₂²×C₃	—	2	1	no	—
704	C₂²×C₃	—	2	1	no	—
705	C₂²×C₃	—	2	2	no	—
706	C₂²×C₃	—	2	4	no	—
707	C₂²×C₃	—	2	2	no	—
708	C₂²×C₃	—	2	4	no	—
709	C₂²×C₃	—	2	4	no	—
710	C₂²×C₃	—	2	2	no	—
711	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
712	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
713	C₃×C₄	—	2	1	no	—
714	C₃×C₄	—	2	4	no	—
715	C₃×C₄	—	2	1	no	—
716	C₃×C₄	—	2	4	no	—
717	C₃×C₄	—	2	2	no	—
718	C₃×C₄	—	2	1	no	—
719	C₃×C₄	—	2	2	no	—
720	C₃×C₄	—	2	4	no	—
721	C₃×C₄	—	2	2	no	—
722	C₃×C₄	—	2	1	no	—
723	C₃×C₄	—	2	1	no	—
724	C₃×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
725	C₂×C₅	—	2	2	no	—
726	C₂×C₅	—	4	2	no	—
727	C₂×C₅	—	4	4	no	—
728	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
729	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
730	C₂×C₅	C₃×#585	1	1	yes	characteristic
731	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
732	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
733	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
734	Q₈	—	4	4	no	—
735	Q₈	—	4	2	no	—
736	Q₈	—	4	1	no	—
737	D₄	—	2	4	no	—
738	D₄	—	2	8	no	—
739	D₄	—	2	4	no	—
740	D₄	—	4	4	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	2	no	—
744	D₄	—	4	1	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	4	4	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	4	4	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
756	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
757	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
758	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
759	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
760	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
761	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
762	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
763	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
764	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
765	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
766	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
767	C₂×C₃	—	2	2	no	—
768	C₂×C₃	—	4	2	no	—
769	C₂×C₃	—	4	4	no	—
770	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
771	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
772	C₂×C₃	C₅×#585	1	1	yes	characteristic
773	C₅	C₃×#3559	1	1	yes	characteristic, direct product factor, Sylow
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	2	4	no	—
781	C₂²	—	2	2	no	—
782	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
783	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
784	C₄	—	2	1	no	—
785	C₄	—	2	4	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	4	no	—
788	C₄	—	2	2	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	4	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	1	no	—
794	C₄	—	2	1	no	—
795	C₄	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
796	C₃	C₅×#3559	1	1	yes	characteristic, direct product factor, Sylow
797	C₂	—	2	2	no	—
798	C₂	—	4	2	no	—
799	C₂	—	4	4	no	—
800	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
801	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
802	C₂	C₃×C₅×#585	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×#562	C₂	semidirect
3. C₃×C₅×#554	C₂	semidirect
4. C₃×C₅×#553	C₂	semidirect
5. C₃×C₅×#553	C₂	semidirect
6. C₃×C₅×#547	C₂	semidirect
7. C₃×C₅×#547	C₂	semidirect
8. C₃×C₅×#544	C₂	semidirect
9. C₃×C₅×#540	C₂	semidirect
10. C₃×C₅×#539	C₂	semidirect
11. C₃×C₅×#539	C₂	semidirect
12. C₃×C₅×#537	C₂	semidirect
13. C₃×C₅×#532	C₂	semidirect
14. C₃×C₅×#529	C₂	semidirect
15. C₂×C₃×C₅×#125	C₂	semidirect
16. C₅×#3559	C₃	direct (N × H)
76. C₃×#3559	C₅	direct (N × H)
77. C₅×#563	C₂×C₃	semidirect
78. C₅×#562	C₂×C₃	semidirect
79. C₅×#554	C₂×C₃	semidirect
80. C₅×#553	C₂×C₃	semidirect
81. C₅×#553	C₂×C₃	semidirect
82. C₅×#547	C₂×C₃	semidirect
83. C₅×#547	C₂×C₃	semidirect
84. C₅×#544	C₂×C₃	semidirect
85. C₅×#540	C₂×C₃	semidirect
86. C₅×#539	C₂×C₃	semidirect
87. C₅×#539	C₂×C₃	semidirect
88. C₅×#537	C₂×C₃	semidirect
89. C₅×#532	C₂×C₃	semidirect
90. C₅×#529	C₂×C₃	semidirect
91. C₂×C₅×#125	C₂×C₃	semidirect
153. C₃×#563	C₂×C₅	semidirect
154. C₃×#562	C₂×C₅	semidirect
155. C₃×#554	C₂×C₅	semidirect
156. C₃×#553	C₂×C₅	semidirect
157. C₃×#553	C₂×C₅	semidirect
158. C₃×#547	C₂×C₅	semidirect
159. C₃×#547	C₂×C₅	semidirect
160. C₃×#544	C₂×C₅	semidirect
161. C₃×#540	C₂×C₅	semidirect
162. C₃×#539	C₂×C₅	semidirect
163. C₃×#539	C₂×C₅	semidirect
164. C₃×#537	C₂×C₅	semidirect
165. C₃×#532	C₂×C₅	semidirect
166. C₃×#529	C₂×C₅	semidirect
167. C₂×C₃×#125	C₂×C₅	semidirect
227. #3559	C₃×C₅	direct (N × H)
384. #563	C₂×C₃×C₅	semidirect
385. #562	C₂×C₃×C₅	semidirect
386. #554	C₂×C₃×C₅	semidirect
387. #553	C₂×C₃×C₅	semidirect
388. #553	C₂×C₃×C₅	semidirect
389. #547	C₂×C₃×C₅	semidirect
390. #547	C₂×C₃×C₅	semidirect
391. #544	C₂×C₃×C₅	semidirect
392. #540	C₂×C₃×C₅	semidirect
393. #539	C₂×C₃×C₅	semidirect
394. #539	C₂×C₃×C₅	semidirect
395. #537	C₂×C₃×C₅	semidirect
396. #532	C₂×C₃×C₅	semidirect
397. #529	C₂×C₃×C₅	semidirect
398. C₂×#125	C₂×C₃×C₅	semidirect
702. C₃×C₅	#3559	direct (N × H)
773. C₅	C₃×#3559	direct (N × H)
796. C₃	C₅×#3559	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×#562	2
C₃×C₅×#554	2
C₃×C₅×#553	2
C₃×C₅×#547	2
C₃×C₅×#544	2
C₃×C₅×#540	2
C₃×C₅×#539	2
C₃×C₅×#537	2
C₃×C₅×#532	2
C₃×C₅×#529	2
C₂×C₃×C₅×#125	2
C₅×#3559	3
C₃×#3559	5

Subgroups — C3×C5×#3559 #14276593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3559 #14276593