Subgroups — C₃×C₅×#3308 #14276342

Order 1920.

840 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×#548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#477	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#468	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#448	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3308	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	—	2	1	no	—
18	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#124	—	2	1	no	—
27	C₃×C₅×#124	C₂²	1	1	yes	characteristic
28	C₃×C₅×#123	—	2	1	no	—
29	C₃×C₅×#123	—	2	1	no	—
30	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
31	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
32	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×#121	—	2	1	no	—
34	C₃×C₅×#121	C₂²	1	1	yes	characteristic
35	C₃×C₅×#121	C₂²	1	1	yes	characteristic
36	C₃×C₅×#121	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₅×D₄	—	2	1	no	—
39	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×C₅×#107	C₂²	1	1	yes	characteristic
44	C₃×C₅×#107	C₂²	1	1	yes	characteristic
45	C₃×C₅×#107	C₂²	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₃×C₅×#103	C₂²	1	1	yes	characteristic
48	C₃×C₅×#103	C₂²	1	1	yes	characteristic
49	C₃×C₅×#103	C₂²	1	1	yes	characteristic
50	C₃×C₅×#103	C₂²	1	1	yes	characteristic
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic
52	C₃×C₅×#103	C₂²	1	1	yes	characteristic
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic
54	C₃×C₅×#102	C₂²	1	1	yes	characteristic
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic
56	C₃×C₅×#102	C₂²	1	1	yes	characteristic
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
59	C₃×C₅×#97	C₂²	1	1	yes	characteristic
60	C₃×#3308	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#548	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#489	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#484	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#480	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#477	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#468	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#466	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#463	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#448	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#440	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#435	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#417	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic, complemented
76	C₃×C₅×#41	—	2	2	no	—
77	C₃×C₅×#41	—	4	1	no	—
78	C₃×C₅×#41	—	4	4	no	—
79	C₂×C₃×C₅×Q₈	—	2	1	no	—
80	C₂×C₃×C₅×Q₈	—	2	1	no	—
81	C₂×C₃×C₅×Q₈	—	2	2	no	—
82	C₂×C₃×C₅×Q₈	—	4	1	no	—
83	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×D₄	—	2	1	no	—
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	—	2	1	no	—
88	C₂×C₃×C₅×D₄	—	2	1	no	—
89	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
90	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	—	2	1	no	—
93	C₂²×C₃×C₄×C₅	—	2	1	no	—
94	C₂²×C₃×C₄×C₅	—	2	1	no	—
95	C₂²×C₃×C₄×C₅	—	2	1	no	—
96	C₂²×C₃×C₄×C₅	—	2	1	no	—
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₃×C₅×SD₁₆	—	2	2	no	—
100	C₃×C₅×SD₁₆	—	4	1	no	—
101	C₃×C₅×D₈	—	4	1	no	—
102	C₃×C₅×M₁₆	—	4	1	no	—
103	C₂×C₃×C₅×C₈	—	4	1	no	—
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₃×C₅×C₄⋊C₄	—	2	1	no	—
109	C₃×C₅×C₄⋊C₄	—	2	1	no	—
110	C₃×C₅×C₄⋊C₄	—	2	1	no	—
111	C₃×C₅×C₄⋊C₄	—	2	1	no	—
112	C₃×C₅×C₄⋊C₄	—	2	1	no	—
113	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
114	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
120	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
121	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
122	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
123	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
124	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
125	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
126	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
127	C₃×C₄²×C₅	—	2	1	no	—
128	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
129	C₃×#548	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#489	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#484	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#480	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#477	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#468	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#463	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#448	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#440	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#435	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#417	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
144	C₂×C₅×#41	—	2	1	no	—
145	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
146	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
151	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
152	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
153	C₅×#124	—	2	1	no	—
154	C₅×#124	C₂²×C₃	1	1	yes	characteristic
155	C₅×#123	—	2	1	no	—
156	C₅×#123	—	2	1	no	—
157	C₅×C₂²⋊Q₈	—	2	1	no	—
158	C₅×C₂²⋊Q₈	—	2	1	no	—
159	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
160	C₅×#121	—	2	1	no	—
161	C₅×#121	C₂²×C₃	1	1	yes	characteristic
162	C₅×#121	C₂²×C₃	1	1	yes	characteristic
163	C₅×#121	C₂²×C₃	1	1	yes	characteristic
164	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
165	C₄×C₅×D₄	—	2	1	no	—
166	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
167	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	C₅×#107	C₂²×C₃	1	1	yes	characteristic
171	C₅×#107	C₂²×C₃	1	1	yes	characteristic
172	C₅×#107	C₂²×C₃	1	1	yes	characteristic
173	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
174	C₅×#103	C₂²×C₃	1	1	yes	characteristic
175	C₅×#103	C₂²×C₃	1	1	yes	characteristic
176	C₅×#103	C₂²×C₃	1	1	yes	characteristic
177	C₅×#103	C₂²×C₃	1	1	yes	characteristic
178	C₅×#103	C₂²×C₃	1	1	yes	characteristic
179	C₅×#103	C₂²×C₃	1	1	yes	characteristic
180	C₅×#102	C₂²×C₃	1	1	yes	characteristic
181	C₅×#102	C₂²×C₃	1	1	yes	characteristic
182	C₅×#102	C₂²×C₃	1	1	yes	characteristic
183	C₅×#102	C₂²×C₃	1	1	yes	characteristic
184	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
185	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
186	C₅×#97	C₂²×C₃	1	1	yes	characteristic
187	#3308	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
188	C₂³×C₃×C₅	—	2	1	no	—
189	C₂³×C₃×C₅	—	2	1	no	—
190	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
191	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
192	C₃×C₅×Q₈	—	2	1	no	—
193	C₃×C₅×Q₈	—	2	1	no	—
194	C₃×C₅×Q₈	—	2	1	no	—
195	C₃×C₅×Q₈	—	4	2	no	—
196	C₃×C₅×Q₈	—	4	2	no	—
197	C₃×C₅×Q₈	#41	1	2	yes	complemented
198	C₃×C₅×D₄	—	2	2	no	—
199	C₃×C₅×D₄	—	2	1	no	—
200	C₃×C₅×D₄	—	2	1	no	—
201	C₃×C₅×D₄	—	2	1	no	—
202	C₃×C₅×D₄	—	2	1	no	—
203	C₃×C₅×D₄	—	4	2	no	—
204	C₃×C₅×D₄	—	4	2	no	—
205	C₃×C₅×D₄	—	4	2	no	—
206	C₃×C₅×D₄	—	4	2	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	4	2	no	—
218	C₂×C₃×C₄×C₅	—	4	2	no	—
219	C₂×C₃×C₄×C₅	—	4	2	no	—
220	C₂×C₃×C₄×C₅	—	4	2	no	—
221	C₂×C₃×C₄×C₅	—	4	2	no	—
222	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
223	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
224	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
225	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
226	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
227	C₃×C₅×C₈	—	2	1	no	—
228	C₃×C₅×C₈	—	2	1	no	—
229	C₃×C₅×C₈	—	2	1	no	—
230	C₃×C₅×C₈	—	2	1	no	—
231	C₂×C₃×#41	—	2	1	no	—
232	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
233	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
238	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
239	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
240	C₃×#124	—	2	1	no	—
241	C₃×#124	C₂²×C₅	1	1	yes	characteristic
242	C₃×#123	—	2	1	no	—
243	C₃×#123	—	2	1	no	—
244	C₃×C₂²⋊Q₈	—	2	1	no	—
245	C₃×C₂²⋊Q₈	—	2	1	no	—
246	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
247	C₃×#121	—	2	1	no	—
248	C₃×#121	C₂²×C₅	1	1	yes	characteristic
249	C₃×#121	C₂²×C₅	1	1	yes	characteristic
250	C₃×#121	C₂²×C₅	1	1	yes	characteristic
251	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
252	C₃×C₄×D₄	—	2	1	no	—
253	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
254	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
257	C₃×#107	C₂²×C₅	1	1	yes	characteristic
258	C₃×#107	C₂²×C₅	1	1	yes	characteristic
259	C₃×#107	C₂²×C₅	1	1	yes	characteristic
260	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
261	C₃×#103	C₂²×C₅	1	1	yes	characteristic
262	C₃×#103	C₂²×C₅	1	1	yes	characteristic
263	C₃×#103	C₂²×C₅	1	1	yes	characteristic
264	C₃×#103	C₂²×C₅	1	1	yes	characteristic
265	C₃×#103	C₂²×C₅	1	1	yes	characteristic
266	C₃×#103	C₂²×C₅	1	1	yes	characteristic
267	C₃×#102	C₂²×C₅	1	1	yes	characteristic
268	C₃×#102	C₂²×C₅	1	1	yes	characteristic
269	C₃×#102	C₂²×C₅	1	1	yes	characteristic
270	C₃×#102	C₂²×C₅	1	1	yes	characteristic
271	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
272	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	C₃×#97	C₂²×C₅	1	1	yes	characteristic
274	C₅×#41	—	2	2	no	—
275	C₅×#41	—	4	1	no	—
276	C₅×#41	—	4	4	no	—
277	C₂×C₅×Q₈	—	2	1	no	—
278	C₂×C₅×Q₈	—	2	1	no	—
279	C₂×C₅×Q₈	—	2	2	no	—
280	C₂×C₅×Q₈	—	4	1	no	—
281	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₅×D₄	—	2	1	no	—
284	C₂×C₅×D₄	—	2	1	no	—
285	C₂×C₅×D₄	—	2	1	no	—
286	C₂×C₅×D₄	—	2	1	no	—
287	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
288	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
290	C₂²×C₄×C₅	—	2	1	no	—
291	C₂²×C₄×C₅	—	2	1	no	—
292	C₂²×C₄×C₅	—	2	1	no	—
293	C₂²×C₄×C₅	—	2	1	no	—
294	C₂²×C₄×C₅	—	2	1	no	—
295	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
297	C₅×SD₁₆	—	2	2	no	—
298	C₅×SD₁₆	—	4	1	no	—
299	C₅×D₈	—	4	1	no	—
300	C₅×M₁₆	—	4	1	no	—
301	C₂×C₅×C₈	—	4	1	no	—
302	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
303	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
304	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
305	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
306	C₅×C₄⋊C₄	—	2	1	no	—
307	C₅×C₄⋊C₄	—	2	1	no	—
308	C₅×C₄⋊C₄	—	2	1	no	—
309	C₅×C₄⋊C₄	—	2	1	no	—
310	C₅×C₄⋊C₄	—	2	1	no	—
311	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
312	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
313	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
314	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
315	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
316	C₅×C₂²⋊C₄	—	2	1	no	—
317	C₅×C₂²⋊C₄	—	2	1	no	—
318	C₅×C₂²⋊C₄	—	2	1	no	—
319	C₅×C₂²⋊C₄	—	2	1	no	—
320	C₅×C₂²⋊C₄	—	2	1	no	—
321	C₅×C₂²⋊C₄	—	2	1	no	—
322	C₅×C₂²⋊C₄	—	2	1	no	—
323	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
324	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
325	C₄²×C₅	—	2	1	no	—
326	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
327	#548	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
329	#489	C₂×C₃×C₅	1	1	yes	characteristic, complemented
330	#484	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	#480	C₂×C₃×C₅	1	1	yes	characteristic, complemented
332	#477	C₂×C₃×C₅	1	1	yes	characteristic, complemented
333	#468	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	#466	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#463	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	#448	C₂×C₃×C₅	1	1	yes	characteristic, complemented
338	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
339	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
340	#417	C₂×C₃×C₅	1	1	yes	characteristic, complemented
341	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic, complemented
342	C₂²×C₃×C₅	—	2	1	no	—
343	C₂²×C₃×C₅	—	2	1	no	—
344	C₂²×C₃×C₅	—	2	1	no	—
345	C₂²×C₃×C₅	—	2	1	no	—
346	C₂²×C₃×C₅	—	2	1	no	—
347	C₂²×C₃×C₅	—	4	1	no	—
348	C₂²×C₃×C₅	—	4	1	no	—
349	C₂²×C₃×C₅	—	4	1	no	—
350	C₂²×C₃×C₅	—	4	1	no	—
351	C₂²×C₃×C₅	—	4	1	no	—
352	C₂²×C₃×C₅	—	4	1	no	—
353	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
354	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
355	C₃×C₄×C₅	—	2	1	no	—
356	C₃×C₄×C₅	—	2	1	no	—
357	C₃×C₄×C₅	—	2	2	no	—
358	C₃×C₄×C₅	—	2	1	no	—
359	C₃×C₄×C₅	—	2	1	no	—
360	C₃×C₄×C₅	—	4	1	no	—
361	C₃×C₄×C₅	—	4	1	no	—
362	C₃×C₄×C₅	—	4	1	no	—
363	C₃×C₄×C₅	—	4	1	no	—
364	C₃×C₄×C₅	—	4	1	no	—
365	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
366	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
367	C₃×#41	—	2	2	no	—
368	C₃×#41	—	4	1	no	—
369	C₃×#41	—	4	4	no	—
370	C₂×C₃×Q₈	—	2	1	no	—
371	C₂×C₃×Q₈	—	2	1	no	—
372	C₂×C₃×Q₈	—	2	2	no	—
373	C₂×C₃×Q₈	—	4	1	no	—
374	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₃×D₄	—	2	1	no	—
377	C₂×C₃×D₄	—	2	1	no	—
378	C₂×C₃×D₄	—	2	1	no	—
379	C₂×C₃×D₄	—	2	1	no	—
380	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
381	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
382	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
383	C₂²×C₃×C₄	—	2	1	no	—
384	C₂²×C₃×C₄	—	2	1	no	—
385	C₂²×C₃×C₄	—	2	1	no	—
386	C₂²×C₃×C₄	—	2	1	no	—
387	C₂²×C₃×C₄	—	2	1	no	—
388	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
390	C₃×SD₁₆	—	2	2	no	—
391	C₃×SD₁₆	—	4	1	no	—
392	C₃×D₈	—	4	1	no	—
393	C₃×M₁₆	—	4	1	no	—
394	C₂×C₃×C₈	—	4	1	no	—
395	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
396	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
397	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
398	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
399	C₃×C₄⋊C₄	—	2	1	no	—
400	C₃×C₄⋊C₄	—	2	1	no	—
401	C₃×C₄⋊C₄	—	2	1	no	—
402	C₃×C₄⋊C₄	—	2	1	no	—
403	C₃×C₄⋊C₄	—	2	1	no	—
404	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
405	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
406	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
407	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
408	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
409	C₃×C₂²⋊C₄	—	2	1	no	—
410	C₃×C₂²⋊C₄	—	2	1	no	—
411	C₃×C₂²⋊C₄	—	2	1	no	—
412	C₃×C₂²⋊C₄	—	2	1	no	—
413	C₃×C₂²⋊C₄	—	2	1	no	—
414	C₃×C₂²⋊C₄	—	2	1	no	—
415	C₃×C₂²⋊C₄	—	2	1	no	—
416	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
417	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
418	C₃×C₄²	—	2	1	no	—
419	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
420	C₂³×C₅	—	2	1	no	—
421	C₂³×C₅	—	2	1	no	—
422	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
423	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
424	C₅×Q₈	—	2	1	no	—
425	C₅×Q₈	—	2	1	no	—
426	C₅×Q₈	—	2	1	no	—
427	C₅×Q₈	—	4	2	no	—
428	C₅×Q₈	—	4	2	no	—
429	C₅×Q₈	C₃×#41	1	2	yes	complemented
430	C₅×D₄	—	2	2	no	—
431	C₅×D₄	—	2	1	no	—
432	C₅×D₄	—	2	1	no	—
433	C₅×D₄	—	2	1	no	—
434	C₅×D₄	—	2	1	no	—
435	C₅×D₄	—	4	2	no	—
436	C₅×D₄	—	4	2	no	—
437	C₅×D₄	—	4	2	no	—
438	C₅×D₄	—	4	2	no	—
439	C₂×C₄×C₅	—	2	1	no	—
440	C₂×C₄×C₅	—	2	1	no	—
441	C₂×C₄×C₅	—	2	1	no	—
442	C₂×C₄×C₅	—	2	1	no	—
443	C₂×C₄×C₅	—	2	1	no	—
444	C₂×C₄×C₅	—	2	1	no	—
445	C₂×C₄×C₅	—	2	1	no	—
446	C₂×C₄×C₅	—	2	1	no	—
447	C₂×C₄×C₅	—	2	1	no	—
448	C₂×C₄×C₅	—	2	1	no	—
449	C₂×C₄×C₅	—	4	2	no	—
450	C₂×C₄×C₅	—	4	2	no	—
451	C₂×C₄×C₅	—	4	2	no	—
452	C₂×C₄×C₅	—	4	2	no	—
453	C₂×C₄×C₅	—	4	2	no	—
454	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
455	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
456	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
457	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
458	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
459	C₅×C₈	—	2	1	no	—
460	C₅×C₈	—	2	1	no	—
461	C₅×C₈	—	2	1	no	—
462	C₅×C₈	—	2	1	no	—
463	C₂×#41	—	2	1	no	—
464	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
465	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
466	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
467	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
468	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
469	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
470	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
471	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
472	#124	—	2	1	no	—
473	#124	C₂²×C₃×C₅	1	1	yes	characteristic
474	#123	—	2	1	no	—
475	#123	—	2	1	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
479	#121	—	2	1	no	—
480	#121	C₂²×C₃×C₅	1	1	yes	characteristic
481	#121	C₂²×C₃×C₅	1	1	yes	characteristic
482	#121	C₂²×C₃×C₅	1	1	yes	characteristic
483	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
484	C₄×D₄	—	2	1	no	—
485	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
486	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
489	#107	C₂²×C₃×C₅	1	1	yes	characteristic
490	#107	C₂²×C₃×C₅	1	1	yes	characteristic
491	#107	C₂²×C₃×C₅	1	1	yes	characteristic
492	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
493	#103	C₂²×C₃×C₅	1	1	yes	characteristic
494	#103	C₂²×C₃×C₅	1	1	yes	characteristic
495	#103	C₂²×C₃×C₅	1	1	yes	characteristic
496	#103	C₂²×C₃×C₅	1	1	yes	characteristic
497	#103	C₂²×C₃×C₅	1	1	yes	characteristic
498	#103	C₂²×C₃×C₅	1	1	yes	characteristic
499	#102	C₂²×C₃×C₅	1	1	yes	characteristic
500	#102	C₂²×C₃×C₅	1	1	yes	characteristic
501	#102	C₂²×C₃×C₅	1	1	yes	characteristic
502	#102	C₂²×C₃×C₅	1	1	yes	characteristic
503	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
504	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
505	#97	C₂²×C₃×C₅	1	1	yes	characteristic
506	C₂×C₃×C₅	—	2	2	no	—
507	C₂×C₃×C₅	—	4	1	no	—
508	C₂×C₃×C₅	—	8	1	no	—
509	C₂×C₃×C₅	—	8	1	no	—
510	C₂×C₃×C₅	#546	1	1	yes	characteristic
511	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
512	C₂×C₃×C₅	#578	1	1	yes	characteristic
513	C₂³×C₃	—	2	1	no	—
514	C₂³×C₃	—	2	1	no	—
515	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
516	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
517	C₃×Q₈	—	2	1	no	—
518	C₃×Q₈	—	2	1	no	—
519	C₃×Q₈	—	2	1	no	—
520	C₃×Q₈	—	4	2	no	—
521	C₃×Q₈	—	4	2	no	—
522	C₃×Q₈	C₅×#41	1	2	yes	complemented
523	C₃×D₄	—	2	2	no	—
524	C₃×D₄	—	2	1	no	—
525	C₃×D₄	—	2	1	no	—
526	C₃×D₄	—	2	1	no	—
527	C₃×D₄	—	2	1	no	—
528	C₃×D₄	—	4	2	no	—
529	C₃×D₄	—	4	2	no	—
530	C₃×D₄	—	4	2	no	—
531	C₃×D₄	—	4	2	no	—
532	C₂×C₃×C₄	—	2	1	no	—
533	C₂×C₃×C₄	—	2	1	no	—
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	2	1	no	—
537	C₂×C₃×C₄	—	2	1	no	—
538	C₂×C₃×C₄	—	2	1	no	—
539	C₂×C₃×C₄	—	2	1	no	—
540	C₂×C₃×C₄	—	2	1	no	—
541	C₂×C₃×C₄	—	2	1	no	—
542	C₂×C₃×C₄	—	4	2	no	—
543	C₂×C₃×C₄	—	4	2	no	—
544	C₂×C₃×C₄	—	4	2	no	—
545	C₂×C₃×C₄	—	4	2	no	—
546	C₂×C₃×C₄	—	4	2	no	—
547	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
548	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
549	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
550	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
551	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
552	C₃×C₈	—	2	1	no	—
553	C₃×C₈	—	2	1	no	—
554	C₃×C₈	—	2	1	no	—
555	C₃×C₈	—	2	1	no	—
556	C₂²×C₅	—	2	1	no	—
557	C₂²×C₅	—	2	1	no	—
558	C₂²×C₅	—	2	1	no	—
559	C₂²×C₅	—	2	1	no	—
560	C₂²×C₅	—	2	1	no	—
561	C₂²×C₅	—	4	1	no	—
562	C₂²×C₅	—	4	1	no	—
563	C₂²×C₅	—	4	1	no	—
564	C₂²×C₅	—	4	1	no	—
565	C₂²×C₅	—	4	1	no	—
566	C₂²×C₅	—	4	1	no	—
567	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
568	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
569	C₄×C₅	—	2	1	no	—
570	C₄×C₅	—	2	1	no	—
571	C₄×C₅	—	2	1	no	—
572	C₄×C₅	—	2	1	no	—
573	C₄×C₅	—	2	2	no	—
574	C₄×C₅	—	4	1	no	—
575	C₄×C₅	—	4	1	no	—
576	C₄×C₅	—	4	1	no	—
577	C₄×C₅	—	4	1	no	—
578	C₄×C₅	—	4	1	no	—
579	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
580	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
581	#41	—	2	2	no	—
582	#41	—	4	1	no	—
583	#41	—	4	4	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	4	1	no	—
588	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
589	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
595	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
596	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
603	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
604	SD₁₆	—	2	2	no	—
605	SD₁₆	—	4	1	no	—
606	D₈	—	4	1	no	—
607	M₁₆	—	4	1	no	—
608	C₂×C₈	—	4	1	no	—
609	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
610	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
611	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
612	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
619	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
620	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
621	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
622	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
631	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
632	C₄²	—	2	1	no	—
633	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
634	C₃×C₅	#3308	1	1	yes	characteristic, direct product factor, Hall
635	C₂²×C₃	—	2	1	no	—
636	C₂²×C₃	—	2	1	no	—
637	C₂²×C₃	—	2	1	no	—
638	C₂²×C₃	—	2	1	no	—
639	C₂²×C₃	—	2	1	no	—
640	C₂²×C₃	—	4	1	no	—
641	C₂²×C₃	—	4	1	no	—
642	C₂²×C₃	—	4	1	no	—
643	C₂²×C₃	—	4	1	no	—
644	C₂²×C₃	—	4	1	no	—
645	C₂²×C₃	—	4	1	no	—
646	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
647	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
648	C₃×C₄	—	2	1	no	—
649	C₃×C₄	—	2	1	no	—
650	C₃×C₄	—	2	2	no	—
651	C₃×C₄	—	2	1	no	—
652	C₃×C₄	—	2	1	no	—
653	C₃×C₄	—	4	1	no	—
654	C₃×C₄	—	4	1	no	—
655	C₃×C₄	—	4	1	no	—
656	C₃×C₄	—	4	1	no	—
657	C₃×C₄	—	4	1	no	—
658	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
659	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
660	C₂×C₅	—	2	2	no	—
661	C₂×C₅	—	4	1	no	—
662	C₂×C₅	—	8	1	no	—
663	C₂×C₅	—	8	1	no	—
664	C₂×C₅	C₃×#546	1	1	yes	characteristic
665	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
666	C₂×C₅	C₃×#578	1	1	yes	characteristic
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
670	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
671	Q₈	—	2	1	no	—
672	Q₈	—	2	1	no	—
673	Q₈	—	2	1	no	—
674	Q₈	—	4	2	no	—
675	Q₈	—	4	2	no	—
676	Q₈	C₃×C₅×#41	1	2	yes	complemented
677	D₄	—	2	2	no	—
678	D₄	—	2	1	no	—
679	D₄	—	2	1	no	—
680	D₄	—	2	1	no	—
681	D₄	—	2	1	no	—
682	D₄	—	4	2	no	—
683	D₄	—	4	2	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	4	2	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	—	4	2	no	—
699	C₂×C₄	—	4	2	no	—
700	C₂×C₄	—	4	2	no	—
701	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
702	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
703	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
704	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
705	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
706	C₈	—	2	1	no	—
707	C₈	—	2	1	no	—
708	C₈	—	2	1	no	—
709	C₈	—	2	1	no	—
710	C₂×C₃	—	2	2	no	—
711	C₂×C₃	—	4	1	no	—
712	C₂×C₃	—	8	1	no	—
713	C₂×C₃	—	8	1	no	—
714	C₂×C₃	C₅×#546	1	1	yes	characteristic
715	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
716	C₂×C₃	C₅×#578	1	1	yes	characteristic
717	C₅	C₃×#3308	1	1	yes	characteristic, direct product factor, Sylow
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
730	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	1	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	1	no	—
741	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
742	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
743	C₃	C₅×#3308	1	1	yes	characteristic, direct product factor, Sylow
744	C₂	—	2	2	no	—
745	C₂	—	4	1	no	—
746	C₂	—	8	1	no	—
747	C₂	—	8	1	no	—
748	C₂	C₃×C₅×#546	1	1	yes	characteristic
749	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
750	C₂	C₃×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₅×#548	C₂	semidirect
2. C₃×C₅×#547	C₂	semidirect
3. C₃×C₅×#489	C₂	semidirect
4. C₃×C₅×#484	C₂	semidirect
5. C₃×C₅×#480	C₂	semidirect
6. C₃×C₅×#477	C₂	semidirect
7. C₃×C₅×#468	C₂	semidirect
8. C₃×C₅×#466	C₂	semidirect
9. C₃×C₅×#463	C₂	semidirect
10. C₃×C₅×#449	C₂	semidirect
11. C₃×C₅×#448	C₂	semidirect
12. C₃×C₅×#440	C₂	semidirect
13. C₃×C₅×#435	C₂	semidirect
14. C₃×C₅×#417	C₂	semidirect
15. C₂×C₃×C₅×#103	C₂	semidirect
16. C₅×#3308	C₃	direct (N × H)
60. C₃×#3308	C₅	direct (N × H)
61. C₅×#548	C₂×C₃	semidirect
62. C₅×#547	C₂×C₃	semidirect
63. C₅×#489	C₂×C₃	semidirect
64. C₅×#484	C₂×C₃	semidirect
65. C₅×#480	C₂×C₃	semidirect
66. C₅×#477	C₂×C₃	semidirect
67. C₅×#468	C₂×C₃	semidirect
68. C₅×#466	C₂×C₃	semidirect
69. C₅×#463	C₂×C₃	semidirect
70. C₅×#449	C₂×C₃	semidirect
71. C₅×#448	C₂×C₃	semidirect
72. C₅×#440	C₂×C₃	semidirect
73. C₅×#435	C₂×C₃	semidirect
74. C₅×#417	C₂×C₃	semidirect
75. C₂×C₅×#103	C₂×C₃	semidirect
129. C₃×#548	C₂×C₅	semidirect
130. C₃×#547	C₂×C₅	semidirect
131. C₃×#489	C₂×C₅	semidirect
132. C₃×#484	C₂×C₅	semidirect
133. C₃×#480	C₂×C₅	semidirect
134. C₃×#477	C₂×C₅	semidirect
135. C₃×#468	C₂×C₅	semidirect
136. C₃×#466	C₂×C₅	semidirect
137. C₃×#463	C₂×C₅	semidirect
138. C₃×#449	C₂×C₅	semidirect
139. C₃×#448	C₂×C₅	semidirect
140. C₃×#440	C₂×C₅	semidirect
141. C₃×#435	C₂×C₅	semidirect
142. C₃×#417	C₂×C₅	semidirect
143. C₂×C₃×#103	C₂×C₅	semidirect
187. #3308	C₃×C₅	direct (N × H)
197. C₃×C₅×Q₈	#41	semidirect
327. #548	C₂×C₃×C₅	semidirect
328. #547	C₂×C₃×C₅	semidirect
329. #489	C₂×C₃×C₅	semidirect
330. #484	C₂×C₃×C₅	semidirect
331. #480	C₂×C₃×C₅	semidirect
332. #477	C₂×C₃×C₅	semidirect
333. #468	C₂×C₃×C₅	semidirect
334. #466	C₂×C₃×C₅	semidirect
335. #463	C₂×C₃×C₅	semidirect
336. #449	C₂×C₃×C₅	semidirect
337. #448	C₂×C₃×C₅	semidirect
338. #440	C₂×C₃×C₅	semidirect
339. #435	C₂×C₃×C₅	semidirect
340. #417	C₂×C₃×C₅	semidirect
341. C₂×#103	C₂×C₃×C₅	semidirect
429. C₅×Q₈	C₃×#41	semidirect
522. C₃×Q₈	C₅×#41	semidirect
634. C₃×C₅	#3308	direct (N × H)
676. Q₈	C₃×C₅×#41	semidirect
717. C₅	C₃×#3308	direct (N × H)
743. C₃	C₅×#3308	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×#548	2
C₃×C₅×#547	2
C₃×C₅×#489	2
C₃×C₅×#484	2
C₃×C₅×#480	2
C₃×C₅×#477	2
C₃×C₅×#468	2
C₃×C₅×#466	2
C₃×C₅×#463	2
C₃×C₅×#449	2
C₃×C₅×#448	2
C₃×C₅×#440	2
C₃×C₅×#435	2
C₃×C₅×#417	2
C₂×C₃×C₅×#103	2
C₅×#3308	3
C₃×#3308	5

Subgroups — C3×C5×#3308 #14276342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3308 #14276342