Subgroups — C₃×C₅×#3306 #14276340

Order 1920.

884 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#483	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#469	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#465	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×#447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#442	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×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3306	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×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₅×D₈	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, complemented
24	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×#124	C₂²	1	1	yes	characteristic
27	C₃×C₅×#123	—	2	1	no	—
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	C₂²	1	1	yes	characteristic
32	C₃×C₅×#121	—	2	1	no	—
33	C₃×C₅×#121	C₂²	1	1	yes	characteristic
34	C₃×C₅×#121	C₂²	1	1	yes	characteristic
35	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#120	—	2	1	no	—
37	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
43	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₅×#102	C₂²	1	1	yes	characteristic
51	C₃×C₅×#102	C₂²	1	1	yes	characteristic
52	C₃×C₅×#102	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, complemented
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3306	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#546	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#489	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#483	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#481	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#469	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#465	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×#447	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#442	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×#102	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂⁴×C₃×C₅	—	2	1	no	—
77	C₃×C₅×#41	—	2	2	no	—
78	C₃×C₅×#41	—	4	1	no	—
79	C₃×C₅×#41	—	4	4	no	—
80	C₂×C₃×C₅×Q₈	—	2	1	no	—
81	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	—	2	2	no	—
83	C₂×C₃×C₅×D₄	—	2	1	no	—
84	C₂×C₃×C₅×D₄	—	2	1	no	—
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	—	4	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	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
100	C₃×C₅×SD₁₆	—	4	1	no	—
101	C₃×C₅×D₈	—	2	2	no	—
102	C₃×C₅×D₈	—	4	1	no	—
103	C₃×C₅×M₁₆	—	4	1	no	—
104	C₂×C₃×C₅×C₈	—	4	1	no	—
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	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
126	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
127	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
128	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
129	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#546	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#489	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#483	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#481	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#469	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#465	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×#447	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#442	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×#102	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×D₄	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
148	C₂×C₅×D₈	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, complemented
151	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
152	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
153	C₅×#124	C₂²×C₃	1	1	yes	characteristic
154	C₅×#123	—	2	1	no	—
155	C₅×#123	—	2	1	no	—
156	C₅×#123	—	2	1	no	—
157	C₅×C₂²⋊Q₈	—	2	1	no	—
158	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₅×#121	—	2	1	no	—
160	C₅×#121	C₂²×C₃	1	1	yes	characteristic
161	C₅×#121	C₂²×C₃	1	1	yes	characteristic
162	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₅×#120	—	2	1	no	—
164	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
165	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
166	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
170	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
176	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₅×#102	C₂²×C₃	1	1	yes	characteristic
178	C₅×#102	C₂²×C₃	1	1	yes	characteristic
179	C₅×#102	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, complemented
184	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
185	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
186	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
187	#3306	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	—	2	1	no	—
191	C₂³×C₃×C₅	—	4	2	no	—
192	C₂³×C₃×C₅	—	4	2	no	—
193	C₂³×C₃×C₅	—	8	1	no	—
194	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
195	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
196	C₃×C₅×Q₈	—	2	1	no	—
197	C₃×C₅×Q₈	—	2	1	no	—
198	C₃×C₅×Q₈	—	4	2	no	—
199	C₃×C₅×D₄	—	2	2	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	—	2	1	no	—
204	C₃×C₅×D₄	—	2	1	no	—
205	C₃×C₅×D₄	—	4	2	no	—
206	C₃×C₅×D₄	—	4	2	no	—
207	C₃×C₅×D₄	—	4	2	no	—
208	C₃×C₅×D₄	—	4	2	no	—
209	C₃×C₅×D₄	—	8	1	no	—
210	C₃×C₅×D₄	#41	1	2	yes	complemented
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	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	4	2	no	—
221	C₂×C₃×C₄×C₅	—	4	2	no	—
222	C₂×C₃×C₄×C₅	—	4	2	no	—
223	C₂×C₃×C₄×C₅	—	4	2	no	—
224	C₂×C₃×C₄×C₅	—	8	1	no	—
225	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
226	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
227	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
228	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
230	C₃×C₅×C₈	—	2	1	no	—
231	C₃×C₅×C₈	—	2	1	no	—
232	C₃×C₅×C₈	—	2	1	no	—
233	C₃×C₅×C₈	—	2	1	no	—
234	C₂×C₃×#41	—	2	1	no	—
235	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
236	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
238	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
241	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
242	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
243	C₃×#124	C₂²×C₅	1	1	yes	characteristic
244	C₃×#123	—	2	1	no	—
245	C₃×#123	—	2	1	no	—
246	C₃×#123	—	2	1	no	—
247	C₃×C₂²⋊Q₈	—	2	1	no	—
248	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
249	C₃×#121	—	2	1	no	—
250	C₃×#121	C₂²×C₅	1	1	yes	characteristic
251	C₃×#121	C₂²×C₅	1	1	yes	characteristic
252	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₃×#120	—	2	1	no	—
254	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
255	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
256	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
259	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
260	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
265	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
266	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
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×#102	C₂²×C₅	1	1	yes	characteristic
272	C₃×#102	C₂²×C₅	1	1	yes	characteristic
273	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
275	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
276	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
277	C₂⁴×C₅	—	2	1	no	—
278	C₅×#41	—	2	2	no	—
279	C₅×#41	—	4	1	no	—
280	C₅×#41	—	4	4	no	—
281	C₂×C₅×Q₈	—	2	1	no	—
282	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₅×D₄	—	2	2	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	—	2	1	no	—
288	C₂×C₅×D₄	—	2	1	no	—
289	C₂×C₅×D₄	—	4	1	no	—
290	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
291	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
294	C₂²×C₄×C₅	—	2	1	no	—
295	C₂²×C₄×C₅	—	2	1	no	—
296	C₂²×C₄×C₅	—	2	1	no	—
297	C₂²×C₄×C₅	—	2	1	no	—
298	C₂²×C₄×C₅	—	2	1	no	—
299	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
300	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
301	C₅×SD₁₆	—	4	1	no	—
302	C₅×D₈	—	2	2	no	—
303	C₅×D₈	—	4	1	no	—
304	C₅×M₁₆	—	4	1	no	—
305	C₂×C₅×C₈	—	4	1	no	—
306	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
307	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
308	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
309	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
310	C₅×C₄⋊C₄	—	2	1	no	—
311	C₅×C₄⋊C₄	—	2	1	no	—
312	C₅×C₄⋊C₄	—	2	1	no	—
313	C₅×C₄⋊C₄	—	2	1	no	—
314	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
315	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
316	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
317	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
318	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
324	C₅×C₂²⋊C₄	—	2	1	no	—
325	C₅×C₂²⋊C₄	—	2	1	no	—
326	C₅×C₂²⋊C₄	—	2	1	no	—
327	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
328	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
329	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
330	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	#546	C₂×C₃×C₅	1	1	yes	characteristic, complemented
332	#489	C₂×C₃×C₅	1	1	yes	characteristic, complemented
333	#483	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	#481	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#476	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	#469	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	#465	C₂×C₃×C₅	1	1	yes	characteristic, complemented
338	#463	C₂×C₃×C₅	1	1	yes	characteristic, complemented
339	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
340	#447	C₂×C₃×C₅	1	1	yes	characteristic, complemented
341	#442	C₂×C₃×C₅	1	1	yes	characteristic, complemented
342	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
343	#417	C₂×C₃×C₅	1	1	yes	characteristic, complemented
344	C₂×#102	C₂×C₃×C₅	1	1	yes	characteristic, complemented
345	C₂²×C₃×C₅	—	2	1	no	—
346	C₂²×C₃×C₅	—	2	1	no	—
347	C₂²×C₃×C₅	—	2	1	no	—
348	C₂²×C₃×C₅	—	2	2	no	—
349	C₂²×C₃×C₅	—	2	1	no	—
350	C₂²×C₃×C₅	—	2	1	no	—
351	C₂²×C₃×C₅	—	4	1	no	—
352	C₂²×C₃×C₅	—	4	1	no	—
353	C₂²×C₃×C₅	—	4	1	no	—
354	C₂²×C₃×C₅	—	4	1	no	—
355	C₂²×C₃×C₅	—	4	1	no	—
356	C₂²×C₃×C₅	—	4	1	no	—
357	C₂²×C₃×C₅	—	4	1	no	—
358	C₂²×C₃×C₅	—	4	1	no	—
359	C₂²×C₃×C₅	—	8	4	no	—
360	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
361	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
362	C₃×C₄×C₅	—	2	1	no	—
363	C₃×C₄×C₅	—	2	1	no	—
364	C₃×C₄×C₅	—	2	1	no	—
365	C₃×C₄×C₅	—	2	1	no	—
366	C₃×C₄×C₅	—	4	1	no	—
367	C₃×C₄×C₅	—	4	1	no	—
368	C₃×C₄×C₅	—	4	1	no	—
369	C₃×C₄×C₅	—	4	1	no	—
370	C₃×C₄×C₅	—	4	1	no	—
371	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
372	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
373	C₂⁴×C₃	—	2	1	no	—
374	C₃×#41	—	2	2	no	—
375	C₃×#41	—	4	1	no	—
376	C₃×#41	—	4	4	no	—
377	C₂×C₃×Q₈	—	2	1	no	—
378	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₃×D₄	—	2	2	no	—
380	C₂×C₃×D₄	—	2	1	no	—
381	C₂×C₃×D₄	—	2	1	no	—
382	C₂×C₃×D₄	—	2	1	no	—
383	C₂×C₃×D₄	—	2	1	no	—
384	C₂×C₃×D₄	—	2	1	no	—
385	C₂×C₃×D₄	—	4	1	no	—
386	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
387	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
390	C₂²×C₃×C₄	—	2	1	no	—
391	C₂²×C₃×C₄	—	2	1	no	—
392	C₂²×C₃×C₄	—	2	1	no	—
393	C₂²×C₃×C₄	—	2	1	no	—
394	C₂²×C₃×C₄	—	2	1	no	—
395	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
396	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
397	C₃×SD₁₆	—	4	1	no	—
398	C₃×D₈	—	2	2	no	—
399	C₃×D₈	—	4	1	no	—
400	C₃×M₁₆	—	4	1	no	—
401	C₂×C₃×C₈	—	4	1	no	—
402	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
406	C₃×C₄⋊C₄	—	2	1	no	—
407	C₃×C₄⋊C₄	—	2	1	no	—
408	C₃×C₄⋊C₄	—	2	1	no	—
409	C₃×C₄⋊C₄	—	2	1	no	—
410	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
411	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
412	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
413	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
414	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
415	C₃×C₂²⋊C₄	—	2	1	no	—
416	C₃×C₂²⋊C₄	—	2	1	no	—
417	C₃×C₂²⋊C₄	—	2	1	no	—
418	C₃×C₂²⋊C₄	—	2	1	no	—
419	C₃×C₂²⋊C₄	—	2	1	no	—
420	C₃×C₂²⋊C₄	—	2	1	no	—
421	C₃×C₂²⋊C₄	—	2	1	no	—
422	C₃×C₂²⋊C₄	—	2	1	no	—
423	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
424	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
425	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
426	C₂³×C₅	—	2	1	no	—
427	C₂³×C₅	—	2	1	no	—
428	C₂³×C₅	—	2	1	no	—
429	C₂³×C₅	—	4	2	no	—
430	C₂³×C₅	—	4	2	no	—
431	C₂³×C₅	—	8	1	no	—
432	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
433	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
434	C₅×Q₈	—	2	1	no	—
435	C₅×Q₈	—	2	1	no	—
436	C₅×Q₈	—	4	2	no	—
437	C₅×D₄	—	2	2	no	—
438	C₅×D₄	—	2	1	no	—
439	C₅×D₄	—	2	1	no	—
440	C₅×D₄	—	2	1	no	—
441	C₅×D₄	—	2	1	no	—
442	C₅×D₄	—	2	1	no	—
443	C₅×D₄	—	4	2	no	—
444	C₅×D₄	—	4	2	no	—
445	C₅×D₄	—	4	2	no	—
446	C₅×D₄	—	4	2	no	—
447	C₅×D₄	—	8	1	no	—
448	C₅×D₄	C₃×#41	1	2	yes	complemented
449	C₂×C₄×C₅	—	2	1	no	—
450	C₂×C₄×C₅	—	2	1	no	—
451	C₂×C₄×C₅	—	2	1	no	—
452	C₂×C₄×C₅	—	2	1	no	—
453	C₂×C₄×C₅	—	2	1	no	—
454	C₂×C₄×C₅	—	2	1	no	—
455	C₂×C₄×C₅	—	2	1	no	—
456	C₂×C₄×C₅	—	2	1	no	—
457	C₂×C₄×C₅	—	2	1	no	—
458	C₂×C₄×C₅	—	4	2	no	—
459	C₂×C₄×C₅	—	4	2	no	—
460	C₂×C₄×C₅	—	4	2	no	—
461	C₂×C₄×C₅	—	4	2	no	—
462	C₂×C₄×C₅	—	8	1	no	—
463	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
464	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
465	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
466	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
467	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
468	C₅×C₈	—	2	1	no	—
469	C₅×C₈	—	2	1	no	—
470	C₅×C₈	—	2	1	no	—
471	C₅×C₈	—	2	1	no	—
472	C₂×#41	—	2	1	no	—
473	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
474	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
475	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
476	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
477	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
478	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
479	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
480	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
481	#124	C₂²×C₃×C₅	1	1	yes	characteristic
482	#123	—	2	1	no	—
483	#123	—	2	1	no	—
484	#123	—	2	1	no	—
485	C₂²⋊Q₈	—	2	1	no	—
486	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
487	#121	—	2	1	no	—
488	#121	C₂²×C₃×C₅	1	1	yes	characteristic
489	#121	C₂²×C₃×C₅	1	1	yes	characteristic
490	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
491	#120	—	2	1	no	—
492	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
493	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
494	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
495	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
499	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
500	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
501	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
502	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
503	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
504	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
505	#102	C₂²×C₃×C₅	1	1	yes	characteristic
506	#102	C₂²×C₃×C₅	1	1	yes	characteristic
507	#102	C₂²×C₃×C₅	1	1	yes	characteristic
508	#102	C₂²×C₃×C₅	1	1	yes	characteristic
509	#102	C₂²×C₃×C₅	1	1	yes	characteristic
510	#102	C₂²×C₃×C₅	1	1	yes	characteristic
511	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
512	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
513	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
514	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
515	C₂×C₃×C₅	—	2	2	no	—
516	C₂×C₃×C₅	—	4	1	no	—
517	C₂×C₃×C₅	—	4	2	no	—
518	C₂×C₃×C₅	—	8	1	no	—
519	C₂×C₃×C₅	—	8	1	no	—
520	C₂×C₃×C₅	#546	1	1	yes	characteristic
521	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
522	C₂×C₃×C₅	#577	1	1	yes	characteristic
523	C₂³×C₃	—	2	1	no	—
524	C₂³×C₃	—	2	1	no	—
525	C₂³×C₃	—	2	1	no	—
526	C₂³×C₃	—	4	2	no	—
527	C₂³×C₃	—	4	2	no	—
528	C₂³×C₃	—	8	1	no	—
529	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
530	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
531	C₃×Q₈	—	2	1	no	—
532	C₃×Q₈	—	2	1	no	—
533	C₃×Q₈	—	4	2	no	—
534	C₃×D₄	—	2	2	no	—
535	C₃×D₄	—	2	1	no	—
536	C₃×D₄	—	2	1	no	—
537	C₃×D₄	—	2	1	no	—
538	C₃×D₄	—	2	1	no	—
539	C₃×D₄	—	2	1	no	—
540	C₃×D₄	—	4	2	no	—
541	C₃×D₄	—	4	2	no	—
542	C₃×D₄	—	4	2	no	—
543	C₃×D₄	—	4	2	no	—
544	C₃×D₄	—	8	1	no	—
545	C₃×D₄	C₅×#41	1	2	yes	complemented
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	1	no	—
549	C₂×C₃×C₄	—	2	1	no	—
550	C₂×C₃×C₄	—	2	1	no	—
551	C₂×C₃×C₄	—	2	1	no	—
552	C₂×C₃×C₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	—	2	1	no	—
555	C₂×C₃×C₄	—	4	2	no	—
556	C₂×C₃×C₄	—	4	2	no	—
557	C₂×C₃×C₄	—	4	2	no	—
558	C₂×C₃×C₄	—	4	2	no	—
559	C₂×C₃×C₄	—	8	1	no	—
560	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
561	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
562	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
563	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
564	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
565	C₃×C₈	—	2	1	no	—
566	C₃×C₈	—	2	1	no	—
567	C₃×C₈	—	2	1	no	—
568	C₃×C₈	—	2	1	no	—
569	C₂²×C₅	—	2	1	no	—
570	C₂²×C₅	—	2	1	no	—
571	C₂²×C₅	—	2	1	no	—
572	C₂²×C₅	—	2	1	no	—
573	C₂²×C₅	—	2	1	no	—
574	C₂²×C₅	—	2	2	no	—
575	C₂²×C₅	—	4	1	no	—
576	C₂²×C₅	—	4	1	no	—
577	C₂²×C₅	—	4	1	no	—
578	C₂²×C₅	—	4	1	no	—
579	C₂²×C₅	—	4	1	no	—
580	C₂²×C₅	—	4	1	no	—
581	C₂²×C₅	—	4	1	no	—
582	C₂²×C₅	—	4	1	no	—
583	C₂²×C₅	—	8	4	no	—
584	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
585	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
586	C₄×C₅	—	2	1	no	—
587	C₄×C₅	—	2	1	no	—
588	C₄×C₅	—	2	1	no	—
589	C₄×C₅	—	2	1	no	—
590	C₄×C₅	—	4	1	no	—
591	C₄×C₅	—	4	1	no	—
592	C₄×C₅	—	4	1	no	—
593	C₄×C₅	—	4	1	no	—
594	C₄×C₅	—	4	1	no	—
595	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
596	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
597	C₂⁴	—	2	1	no	—
598	#41	—	2	2	no	—
599	#41	—	4	1	no	—
600	#41	—	4	4	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	4	1	no	—
610	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
611	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
612	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
613	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
620	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
621	SD₁₆	—	4	1	no	—
622	D₈	—	2	2	no	—
623	D₈	—	4	1	no	—
624	M₁₆	—	4	1	no	—
625	C₂×C₈	—	4	1	no	—
626	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
627	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
628	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
629	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
635	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
636	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
637	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
638	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
648	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
649	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
650	C₃×C₅	#3306	1	1	yes	characteristic, direct product factor, Hall
651	C₂²×C₃	—	2	1	no	—
652	C₂²×C₃	—	2	1	no	—
653	C₂²×C₃	—	2	1	no	—
654	C₂²×C₃	—	2	2	no	—
655	C₂²×C₃	—	2	1	no	—
656	C₂²×C₃	—	2	1	no	—
657	C₂²×C₃	—	4	1	no	—
658	C₂²×C₃	—	4	1	no	—
659	C₂²×C₃	—	4	1	no	—
660	C₂²×C₃	—	4	1	no	—
661	C₂²×C₃	—	4	1	no	—
662	C₂²×C₃	—	4	1	no	—
663	C₂²×C₃	—	4	1	no	—
664	C₂²×C₃	—	4	1	no	—
665	C₂²×C₃	—	8	4	no	—
666	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
667	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
668	C₃×C₄	—	2	1	no	—
669	C₃×C₄	—	2	1	no	—
670	C₃×C₄	—	2	1	no	—
671	C₃×C₄	—	2	1	no	—
672	C₃×C₄	—	4	1	no	—
673	C₃×C₄	—	4	1	no	—
674	C₃×C₄	—	4	1	no	—
675	C₃×C₄	—	4	1	no	—
676	C₃×C₄	—	4	1	no	—
677	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
678	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂×C₅	—	2	2	no	—
680	C₂×C₅	—	4	1	no	—
681	C₂×C₅	—	4	2	no	—
682	C₂×C₅	—	8	1	no	—
683	C₂×C₅	—	8	1	no	—
684	C₂×C₅	C₃×#546	1	1	yes	characteristic
685	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
686	C₂×C₅	C₃×#577	1	1	yes	characteristic
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	2	no	—
692	C₂³	—	8	1	no	—
693	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
694	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
695	Q₈	—	2	1	no	—
696	Q₈	—	2	1	no	—
697	Q₈	—	4	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	1	no	—
700	D₄	—	2	1	no	—
701	D₄	—	2	1	no	—
702	D₄	—	2	1	no	—
703	D₄	—	2	1	no	—
704	D₄	—	4	2	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	8	1	no	—
709	D₄	C₃×C₅×#41	1	2	yes	complemented
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	8	1	no	—
724	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
725	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
726	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
727	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
728	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
729	C₈	—	2	1	no	—
730	C₈	—	2	1	no	—
731	C₈	—	2	1	no	—
732	C₈	—	2	1	no	—
733	C₂×C₃	—	2	2	no	—
734	C₂×C₃	—	4	1	no	—
735	C₂×C₃	—	4	2	no	—
736	C₂×C₃	—	8	1	no	—
737	C₂×C₃	—	8	1	no	—
738	C₂×C₃	C₅×#546	1	1	yes	characteristic
739	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
740	C₂×C₃	C₅×#577	1	1	yes	characteristic
741	C₅	C₃×#3306	1	1	yes	characteristic, direct product factor, Sylow
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	1	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	8	4	no	—
757	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
758	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
759	C₄	—	2	1	no	—
760	C₄	—	2	1	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	1	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	1	no	—
768	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
769	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
770	C₃	C₅×#3306	1	1	yes	characteristic, direct product factor, Sylow
771	C₂	—	2	2	no	—
772	C₂	—	4	1	no	—
773	C₂	—	4	2	no	—
774	C₂	—	8	1	no	—
775	C₂	—	8	1	no	—
776	C₂	C₃×C₅×#546	1	1	yes	characteristic
777	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
778	C₂	C₃×C₅×#577	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×#547	C₂	semidirect
2. C₃×C₅×#546	C₂	semidirect
3. C₃×C₅×#489	C₂	semidirect
4. C₃×C₅×#483	C₂	semidirect
5. C₃×C₅×#481	C₂	semidirect
6. C₃×C₅×#476	C₂	semidirect
7. C₃×C₅×#469	C₂	semidirect
8. C₃×C₅×#465	C₂	semidirect
9. C₃×C₅×#463	C₂	semidirect
10. C₃×C₅×#449	C₂	semidirect
11. C₃×C₅×#447	C₂	semidirect
12. C₃×C₅×#442	C₂	semidirect
13. C₃×C₅×#435	C₂	semidirect
14. C₃×C₅×#417	C₂	semidirect
15. C₂×C₃×C₅×#102	C₂	semidirect
16. C₅×#3306	C₃	direct (N × H)
20. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
23. C₂×C₃×C₅×M₁₆	C₂²	semidirect
25. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
35. C₃×C₅×#121	C₂²	semidirect
39. C₃×C₄×C₅×D₄	C₂²	semidirect
41. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
43. C₃×C₅×#106	C₂²	semidirect
44. C₃×C₅×#106	C₂²	semidirect
45. C₃×C₅×#106	C₂²	semidirect
46. C₃×C₅×C₄⋊C₈	C₂²	semidirect
47. C₃×C₅×#103	C₂²	semidirect
48. C₃×C₅×#103	C₂²	semidirect
49. C₃×C₅×#103	C₂²	semidirect
56. C₃×C₅×#102	C₂²	semidirect
58. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
59. C₃×C₅×#97	C₂²	semidirect
60. C₃×#3306	C₅	direct (N × H)
61. C₅×#547	C₂×C₃	semidirect
62. C₅×#546	C₂×C₃	semidirect
63. C₅×#489	C₂×C₃	semidirect
64. C₅×#483	C₂×C₃	semidirect
65. C₅×#481	C₂×C₃	semidirect
66. C₅×#476	C₂×C₃	semidirect
67. C₅×#469	C₂×C₃	semidirect
68. C₅×#465	C₂×C₃	semidirect
69. C₅×#463	C₂×C₃	semidirect
70. C₅×#449	C₂×C₃	semidirect
71. C₅×#447	C₂×C₃	semidirect
72. C₅×#442	C₂×C₃	semidirect
73. C₅×#435	C₂×C₃	semidirect
74. C₅×#417	C₂×C₃	semidirect
75. C₂×C₅×#102	C₂×C₃	semidirect
129. C₃×#547	C₂×C₅	semidirect
130. C₃×#546	C₂×C₅	semidirect
131. C₃×#489	C₂×C₅	semidirect
132. C₃×#483	C₂×C₅	semidirect
133. C₃×#481	C₂×C₅	semidirect
134. C₃×#476	C₂×C₅	semidirect
135. C₃×#469	C₂×C₅	semidirect
136. C₃×#465	C₂×C₅	semidirect
137. C₃×#463	C₂×C₅	semidirect
138. C₃×#449	C₂×C₅	semidirect
139. C₃×#447	C₂×C₅	semidirect
140. C₃×#442	C₂×C₅	semidirect
141. C₃×#435	C₂×C₅	semidirect
142. C₃×#417	C₂×C₅	semidirect
143. C₂×C₃×#102	C₂×C₅	semidirect
147. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
150. C₂×C₅×M₁₆	C₂²×C₃	semidirect
152. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
162. C₅×#121	C₂²×C₃	semidirect
166. C₄×C₅×D₄	C₂²×C₃	semidirect
168. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
170. C₅×#106	C₂²×C₃	semidirect
171. C₅×#106	C₂²×C₃	semidirect
172. C₅×#106	C₂²×C₃	semidirect
173. C₅×C₄⋊C₈	C₂²×C₃	semidirect
174. C₅×#103	C₂²×C₃	semidirect
175. C₅×#103	C₂²×C₃	semidirect
176. C₅×#103	C₂²×C₃	semidirect
183. C₅×#102	C₂²×C₃	semidirect
185. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
186. C₅×#97	C₂²×C₃	semidirect
187. #3306	C₃×C₅	direct (N × H)
210. C₃×C₅×D₄	#41	semidirect
237. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
240. C₂×C₃×M₁₆	C₂²×C₅	semidirect
242. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
252. C₃×#121	C₂²×C₅	semidirect
256. C₃×C₄×D₄	C₂²×C₅	semidirect
258. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
260. C₃×#106	C₂²×C₅	semidirect
261. C₃×#106	C₂²×C₅	semidirect
262. C₃×#106	C₂²×C₅	semidirect
263. C₃×C₄⋊C₈	C₂²×C₅	semidirect
264. C₃×#103	C₂²×C₅	semidirect
265. C₃×#103	C₂²×C₅	semidirect
266. C₃×#103	C₂²×C₅	semidirect
273. C₃×#102	C₂²×C₅	semidirect
275. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
276. C₃×#97	C₂²×C₅	semidirect
330. #547	C₂×C₃×C₅	semidirect
331. #546	C₂×C₃×C₅	semidirect
332. #489	C₂×C₃×C₅	semidirect
333. #483	C₂×C₃×C₅	semidirect
334. #481	C₂×C₃×C₅	semidirect
335. #476	C₂×C₃×C₅	semidirect
336. #469	C₂×C₃×C₅	semidirect
337. #465	C₂×C₃×C₅	semidirect
338. #463	C₂×C₃×C₅	semidirect
339. #449	C₂×C₃×C₅	semidirect
340. #447	C₂×C₃×C₅	semidirect
341. #442	C₂×C₃×C₅	semidirect
342. #435	C₂×C₃×C₅	semidirect
343. #417	C₂×C₃×C₅	semidirect
344. C₂×#102	C₂×C₃×C₅	semidirect
448. C₅×D₄	C₃×#41	semidirect
475. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
478. C₂×M₁₆	C₂²×C₃×C₅	semidirect
480. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
490. #121	C₂²×C₃×C₅	semidirect
494. C₄×D₄	C₂²×C₃×C₅	semidirect
496. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
498. #106	C₂²×C₃×C₅	semidirect
499. #106	C₂²×C₃×C₅	semidirect
500. #106	C₂²×C₃×C₅	semidirect
501. C₄⋊C₈	C₂²×C₃×C₅	semidirect
502. #103	C₂²×C₃×C₅	semidirect
503. #103	C₂²×C₃×C₅	semidirect
504. #103	C₂²×C₃×C₅	semidirect
511. #102	C₂²×C₃×C₅	semidirect
513. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
514. #97	C₂²×C₃×C₅	semidirect
545. C₃×D₄	C₅×#41	semidirect
650. C₃×C₅	#3306	direct (N × H)
709. D₄	C₃×C₅×#41	semidirect
741. C₅	C₃×#3306	direct (N × H)
770. C₃	C₅×#3306	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×#547	2
C₃×C₅×#546	2
C₃×C₅×#489	2
C₃×C₅×#483	2
C₃×C₅×#481	2
C₃×C₅×#476	2
C₃×C₅×#469	2
C₃×C₅×#465	2
C₃×C₅×#463	2
C₃×C₅×#449	2
C₃×C₅×#447	2
C₃×C₅×#442	2
C₃×C₅×#435	2
C₃×C₅×#417	2
C₂×C₃×C₅×#102	2
C₅×#3306	3
C₃×#3306	5

Subgroups — C3×C5×#3306 #14276340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3306 #14276340