Subgroups — C₃×C₅×#3310 #14276344

Order 1920.

900 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₄²	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#490	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#482	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#478	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#468	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#450	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×#418	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3310	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×D₄	—	2	1	no	—
18	C₂²×C₃×C₅×D₄	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
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#127	C₂²	1	1	yes	characteristic
26	C₃×C₅×#126	—	2	1	no	—
27	C₃×C₅×#125	—	2	1	no	—
28	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#123	—	2	1	no	—
30	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
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×#120	—	2	1	no	—
36	C₃×C₅×#120	—	2	1	no	—
37	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₃×C₅×#117	—	2	1	no	—
41	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#107	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×#102	C₂²	1	1	yes	characteristic
49	C₃×C₅×#102	C₂²	1	1	yes	characteristic
50	C₃×C₅×#102	C₂²	1	1	yes	characteristic
51	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
56	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3310	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#552	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×D₄²	C₂×C₃	1	1	yes	characteristic
63	C₅×#490	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#482	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#480	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#478	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#468	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#465	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#450	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#450	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×#418	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	C₂⁴×C₃×C₅	—	2	1	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	—	2	2	no	—
80	C₂×C₃×C₅×D₄	—	2	2	no	—
81	C₂×C₃×C₅×D₄	—	2	1	no	—
82	C₂×C₃×C₅×D₄	—	2	1	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	—	4	1	no	—
88	C₂×C₃×C₅×D₄	—	4	1	no	—
89	C₂×C₃×C₅×D₄	—	4	4	no	—
90	C₂×C₃×C₅×D₄	D₄	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	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₄×C₅	—	2	1	no	—
95	C₂²×C₃×C₄×C₅	—	2	1	no	—
96	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₃×C₅×SD₁₆	—	2	2	no	—
99	C₃×C₅×SD₁₆	—	4	1	no	—
100	C₃×C₅×SD₁₆	—	4	1	no	—
101	C₃×C₅×M₁₆	—	4	1	no	—
102	C₂×C₃×C₅×C₈	—	4	1	no	—
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
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	C₃×C₅×C₄⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
125	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
126	C₃×C₄²×C₅	—	2	1	no	—
127	C₃×C₄²×C₅	—	2	1	no	—
128	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
129	C₃×#552	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×D₄²	C₂×C₅	1	1	yes	characteristic
131	C₃×#490	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#482	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#480	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#478	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#468	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#465	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#450	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×#418	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
144	C₂²×C₅×D₄	—	2	1	no	—
145	C₂²×C₅×D₄	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
148	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
149	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
151	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₅×#127	C₂²×C₃	1	1	yes	characteristic
153	C₅×#126	—	2	1	no	—
154	C₅×#125	—	2	1	no	—
155	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
156	C₅×#123	—	2	1	no	—
157	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
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×#120	—	2	1	no	—
163	C₅×#120	—	2	1	no	—
164	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
165	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
166	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
167	C₅×#117	—	2	1	no	—
168	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₅×#107	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×#102	C₂²×C₃	1	1	yes	characteristic
176	C₅×#102	C₂²×C₃	1	1	yes	characteristic
177	C₅×#102	C₂²×C₃	1	1	yes	characteristic
178	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
180	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
186	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
187	#3310	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	—	4	2	no	—
194	C₂³×C₃×C₅	—	4	2	no	—
195	C₂³×C₃×C₅	—	8	1	no	—
196	C₂³×C₃×C₅	—	8	1	no	—
197	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
198	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
199	C₃×C₅×Q₈	—	2	1	no	—
200	C₃×C₅×Q₈	—	2	1	no	—
201	C₃×C₅×D₄	—	2	2	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	—	2	1	no	—
206	C₃×C₅×D₄	—	2	1	no	—
207	C₃×C₅×D₄	—	4	2	no	—
208	C₃×C₅×D₄	—	4	2	no	—
209	C₃×C₅×D₄	—	4	2	no	—
210	C₃×C₅×D₄	—	4	2	no	—
211	C₃×C₅×D₄	—	4	2	no	—
212	C₃×C₅×D₄	—	8	1	no	—
213	C₃×C₅×D₄	#41	1	2	yes	—
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	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	4	2	no	—
224	C₂×C₃×C₄×C₅	—	4	2	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	C₂²×C₃×D₄	—	2	1	no	—
235	C₂²×C₃×D₄	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
238	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
239	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
240	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
241	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
242	C₃×#127	C₂²×C₅	1	1	yes	characteristic
243	C₃×#126	—	2	1	no	—
244	C₃×#125	—	2	1	no	—
245	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
246	C₃×#123	—	2	1	no	—
247	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
248	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
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×#120	—	2	1	no	—
253	C₃×#120	—	2	1	no	—
254	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
256	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
257	C₃×#117	—	2	1	no	—
258	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
259	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₃×#107	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×#102	C₂²×C₅	1	1	yes	characteristic
266	C₃×#102	C₂²×C₅	1	1	yes	characteristic
267	C₃×#102	C₂²×C₅	1	1	yes	characteristic
268	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
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	C₂⁴×C₅	—	2	1	no	—
279	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
280	C₂×C₅×D₄	—	2	2	no	—
281	C₂×C₅×D₄	—	2	2	no	—
282	C₂×C₅×D₄	—	2	1	no	—
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	—	2	1	no	—
288	C₂×C₅×D₄	—	4	1	no	—
289	C₂×C₅×D₄	—	4	1	no	—
290	C₂×C₅×D₄	—	4	4	no	—
291	C₂×C₅×D₄	C₃×D₄	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	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
295	C₂²×C₄×C₅	—	2	1	no	—
296	C₂²×C₄×C₅	—	2	1	no	—
297	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
299	C₅×SD₁₆	—	2	2	no	—
300	C₅×SD₁₆	—	4	1	no	—
301	C₅×SD₁₆	—	4	1	no	—
302	C₅×M₁₆	—	4	1	no	—
303	C₂×C₅×C₈	—	4	1	no	—
304	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
305	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
306	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
307	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
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	—	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	C₃×D₄	1	1	yes	characteristic
326	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
327	C₄²×C₅	—	2	1	no	—
328	C₄²×C₅	—	2	1	no	—
329	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
330	#552	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	D₄²	C₂×C₃×C₅	1	1	yes	characteristic
332	#490	C₂×C₃×C₅	1	1	yes	characteristic, complemented
333	#482	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	#480	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#478	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	#468	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	#465	C₂×C₃×C₅	1	1	yes	characteristic, complemented
338	#460	C₂×C₃×C₅	1	1	yes	characteristic, complemented
339	#450	C₂×C₃×C₅	1	1	yes	characteristic, complemented
340	#450	C₂×C₃×C₅	1	1	yes	characteristic, complemented
341	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
342	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
343	#418	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	—	8	4	no	—
361	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
362	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
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	—	2	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	—	4	1	no	—
372	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
373	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
374	C₂⁴×C₃	—	2	1	no	—
375	C₂⁴×C₃	—	2	1	no	—
376	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₃×D₄	—	2	2	no	—
378	C₂×C₃×D₄	—	2	2	no	—
379	C₂×C₃×D₄	—	2	1	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	—	4	1	no	—
387	C₂×C₃×D₄	—	4	4	no	—
388	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
389	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
391	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
392	C₂²×C₃×C₄	—	2	1	no	—
393	C₂²×C₃×C₄	—	2	1	no	—
394	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
395	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
396	C₃×SD₁₆	—	2	2	no	—
397	C₃×SD₁₆	—	4	1	no	—
398	C₃×SD₁₆	—	4	1	no	—
399	C₃×M₁₆	—	4	1	no	—
400	C₂×C₃×C₈	—	4	1	no	—
401	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
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	C₃×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
411	C₃×C₄⋊C₄	C₅×D₄	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×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	C₅×D₄	1	1	yes	characteristic
423	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
424	C₃×C₄²	—	2	1	no	—
425	C₃×C₄²	—	2	1	no	—
426	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
427	C₂³×C₅	—	2	1	no	—
428	C₂³×C₅	—	2	1	no	—
429	C₂³×C₅	—	2	1	no	—
430	C₂³×C₅	—	4	2	no	—
431	C₂³×C₅	—	4	2	no	—
432	C₂³×C₅	—	4	2	no	—
433	C₂³×C₅	—	4	2	no	—
434	C₂³×C₅	—	8	1	no	—
435	C₂³×C₅	—	8	1	no	—
436	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
437	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
438	C₅×Q₈	—	2	1	no	—
439	C₅×Q₈	—	2	1	no	—
440	C₅×D₄	—	2	2	no	—
441	C₅×D₄	—	2	1	no	—
442	C₅×D₄	—	2	1	no	—
443	C₅×D₄	—	2	1	no	—
444	C₅×D₄	—	2	1	no	—
445	C₅×D₄	—	2	1	no	—
446	C₅×D₄	—	4	2	no	—
447	C₅×D₄	—	4	2	no	—
448	C₅×D₄	—	4	2	no	—
449	C₅×D₄	—	4	2	no	—
450	C₅×D₄	—	4	2	no	—
451	C₅×D₄	—	8	1	no	—
452	C₅×D₄	C₃×#41	1	2	yes	—
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	—	2	1	no	—
459	C₂×C₄×C₅	—	2	1	no	—
460	C₂×C₄×C₅	—	2	1	no	—
461	C₂×C₄×C₅	—	2	1	no	—
462	C₂×C₄×C₅	—	4	2	no	—
463	C₂×C₄×C₅	—	4	2	no	—
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	C₂×C₃×D₄	1	1	yes	characteristic
468	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
469	C₅×C₈	—	2	1	no	—
470	C₅×C₈	—	2	1	no	—
471	C₅×C₈	—	2	1	no	—
472	C₅×C₈	—	2	1	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
475	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
476	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
477	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
478	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
479	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
480	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
481	#127	C₂²×C₃×C₅	1	1	yes	characteristic
482	#126	—	2	1	no	—
483	#125	—	2	1	no	—
484	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
485	#123	—	2	1	no	—
486	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
487	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
488	#121	—	2	1	no	—
489	#121	C₂²×C₃×C₅	1	1	yes	characteristic
490	#121	C₂²×C₃×C₅	1	1	yes	characteristic
491	#120	—	2	1	no	—
492	#120	—	2	1	no	—
493	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
494	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
495	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
496	#117	—	2	1	no	—
497	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
498	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
499	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
500	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
501	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
502	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
503	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
504	#102	C₂²×C₃×C₅	1	1	yes	characteristic
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, complemented
508	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
509	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
510	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
511	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
512	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
513	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
514	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
515	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
516	C₂×C₃×C₅	—	2	2	no	—
517	C₂×C₃×C₅	—	4	1	no	—
518	C₂×C₃×C₅	—	4	2	no	—
519	C₂×C₃×C₅	—	8	1	no	—
520	C₂×C₃×C₅	—	8	1	no	—
521	C₂×C₃×C₅	#546	1	1	yes	characteristic
522	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
523	C₂×C₃×C₅	#577	1	1	yes	characteristic
524	C₂³×C₃	—	2	1	no	—
525	C₂³×C₃	—	2	1	no	—
526	C₂³×C₃	—	2	1	no	—
527	C₂³×C₃	—	4	2	no	—
528	C₂³×C₃	—	4	2	no	—
529	C₂³×C₃	—	4	2	no	—
530	C₂³×C₃	—	4	2	no	—
531	C₂³×C₃	—	8	1	no	—
532	C₂³×C₃	—	8	1	no	—
533	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
534	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
535	C₃×Q₈	—	2	1	no	—
536	C₃×Q₈	—	2	1	no	—
537	C₃×D₄	—	2	2	no	—
538	C₃×D₄	—	2	1	no	—
539	C₃×D₄	—	2	1	no	—
540	C₃×D₄	—	2	1	no	—
541	C₃×D₄	—	2	1	no	—
542	C₃×D₄	—	2	1	no	—
543	C₃×D₄	—	4	2	no	—
544	C₃×D₄	—	4	2	no	—
545	C₃×D₄	—	4	2	no	—
546	C₃×D₄	—	4	2	no	—
547	C₃×D₄	—	4	2	no	—
548	C₃×D₄	—	8	1	no	—
549	C₃×D₄	C₅×#41	1	2	yes	—
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	—	2	1	no	—
556	C₂×C₃×C₄	—	2	1	no	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	1	no	—
559	C₂×C₃×C₄	—	4	2	no	—
560	C₂×C₃×C₄	—	4	2	no	—
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	C₂×C₅×D₄	1	1	yes	characteristic
565	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
566	C₃×C₈	—	2	1	no	—
567	C₃×C₈	—	2	1	no	—
568	C₃×C₈	—	2	1	no	—
569	C₃×C₈	—	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	1	no	—
575	C₂²×C₅	—	2	2	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	—	4	1	no	—
584	C₂²×C₅	—	8	4	no	—
585	C₂²×C₅	—	8	4	no	—
586	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
587	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
588	C₄×C₅	—	2	1	no	—
589	C₄×C₅	—	2	1	no	—
590	C₄×C₅	—	2	1	no	—
591	C₄×C₅	—	2	1	no	—
592	C₄×C₅	—	4	1	no	—
593	C₄×C₅	—	4	1	no	—
594	C₄×C₅	—	4	1	no	—
595	C₄×C₅	—	4	1	no	—
596	C₄×C₅	—	4	1	no	—
597	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
598	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
599	C₂⁴	—	2	1	no	—
600	C₂⁴	—	2	1	no	—
601	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
602	C₂×D₄	—	2	2	no	—
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	—	2	1	no	—
610	C₂×D₄	—	4	1	no	—
611	C₂×D₄	—	4	1	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
614	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
615	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
616	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
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	—	2	2	no	—
622	SD₁₆	—	4	1	no	—
623	SD₁₆	—	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	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	C₃×C₅×D₄	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	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
640	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
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	—	2	1	no	—
650	C₄²	—	2	1	no	—
651	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
652	C₃×C₅	#3310	1	1	yes	characteristic, direct product factor, Hall
653	C₂²×C₃	—	2	1	no	—
654	C₂²×C₃	—	2	1	no	—
655	C₂²×C₃	—	2	1	no	—
656	C₂²×C₃	—	2	2	no	—
657	C₂²×C₃	—	2	1	no	—
658	C₂²×C₃	—	2	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	—	4	1	no	—
666	C₂²×C₃	—	4	1	no	—
667	C₂²×C₃	—	8	4	no	—
668	C₂²×C₃	—	8	4	no	—
669	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
670	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
671	C₃×C₄	—	2	1	no	—
672	C₃×C₄	—	2	1	no	—
673	C₃×C₄	—	2	1	no	—
674	C₃×C₄	—	2	1	no	—
675	C₃×C₄	—	4	1	no	—
676	C₃×C₄	—	4	1	no	—
677	C₃×C₄	—	4	1	no	—
678	C₃×C₄	—	4	1	no	—
679	C₃×C₄	—	4	1	no	—
680	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
681	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
682	C₂×C₅	—	2	2	no	—
683	C₂×C₅	—	4	1	no	—
684	C₂×C₅	—	4	2	no	—
685	C₂×C₅	—	8	1	no	—
686	C₂×C₅	—	8	1	no	—
687	C₂×C₅	C₃×#546	1	1	yes	characteristic
688	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
689	C₂×C₅	C₃×#577	1	1	yes	characteristic
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	4	2	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	2	no	—
697	C₂³	—	8	1	no	—
698	C₂³	—	8	1	no	—
699	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
700	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
701	Q₈	—	2	1	no	—
702	Q₈	—	2	1	no	—
703	D₄	—	2	2	no	—
704	D₄	—	2	1	no	—
705	D₄	—	2	1	no	—
706	D₄	—	2	1	no	—
707	D₄	—	2	1	no	—
708	D₄	—	2	1	no	—
709	D₄	—	4	2	no	—
710	D₄	—	4	2	no	—
711	D₄	—	4	2	no	—
712	D₄	—	4	2	no	—
713	D₄	—	4	2	no	—
714	D₄	—	8	1	no	—
715	D₄	C₃×C₅×#41	1	2	yes	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
728	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
729	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
730	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
731	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
732	C₈	—	2	1	no	—
733	C₈	—	2	1	no	—
734	C₈	—	2	1	no	—
735	C₈	—	2	1	no	—
736	C₂×C₃	—	2	2	no	—
737	C₂×C₃	—	4	1	no	—
738	C₂×C₃	—	4	2	no	—
739	C₂×C₃	—	8	1	no	—
740	C₂×C₃	—	8	1	no	—
741	C₂×C₃	C₅×#546	1	1	yes	characteristic
742	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
743	C₂×C₃	C₅×#577	1	1	yes	characteristic
744	C₅	C₃×#3310	1	1	yes	characteristic, direct product factor, Sylow
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	2	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	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	8	4	no	—
760	C₂²	—	8	4	no	—
761	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
762	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
763	C₄	—	2	1	no	—
764	C₄	—	2	1	no	—
765	C₄	—	2	1	no	—
766	C₄	—	2	1	no	—
767	C₄	—	4	1	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	1	no	—
772	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
773	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
774	C₃	C₅×#3310	1	1	yes	characteristic, direct product factor, Sylow
775	C₂	—	2	2	no	—
776	C₂	—	4	1	no	—
777	C₂	—	4	2	no	—
778	C₂	—	8	1	no	—
779	C₂	—	8	1	no	—
780	C₂	C₃×C₅×#546	1	1	yes	characteristic
781	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
782	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
prime radical	C₃×C₅×D₄²	C₂
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×#552	C₂	semidirect
3. C₃×C₅×#490	C₂	semidirect
4. C₃×C₅×#482	C₂	semidirect
5. C₃×C₅×#480	C₂	semidirect
6. C₃×C₅×#478	C₂	semidirect
7. C₃×C₅×#468	C₂	semidirect
8. C₃×C₅×#465	C₂	semidirect
9. C₃×C₅×#460	C₂	semidirect
10. C₃×C₅×#450	C₂	semidirect
11. C₃×C₅×#450	C₂	semidirect
12. C₃×C₅×#440	C₂	semidirect
13. C₃×C₅×#435	C₂	semidirect
14. C₃×C₅×#418	C₂	semidirect
15. C₂×C₃×C₅×#102	C₂	semidirect
16. C₅×#3310	C₃	direct (N × H)
21. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
22. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
23. C₂×C₃×C₅×M₁₆	C₂²	semidirect
24. C₂²×C₃×C₅×C₈	C₂²	semidirect
28. C₃×C₅×#125	C₂²	semidirect
30. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
31. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
37. C₃×C₄×C₅×Q₈	C₂²	semidirect
41. C₃×C₅×#117	C₂²	semidirect
42. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
43. C₃×C₅×#107	C₂²	semidirect
44. C₃×C₅×#107	C₂²	semidirect
45. C₃×C₅×#106	C₂²	semidirect
46. C₃×C₅×C₄⋊C₈	C₂²	semidirect
47. C₃×C₅×#103	C₂²	semidirect
51. C₃×C₅×#102	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₃×C₅×#102	C₂²	semidirect
55. C₃×C₅×#102	C₂²	semidirect
56. C₃×C₅×#102	C₂²	semidirect
57. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
58. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
59. C₃×C₅×#97	C₂²	semidirect
60. C₃×#3310	C₅	direct (N × H)
61. C₅×#552	C₂×C₃	semidirect
63. C₅×#490	C₂×C₃	semidirect
64. C₅×#482	C₂×C₃	semidirect
65. C₅×#480	C₂×C₃	semidirect
66. C₅×#478	C₂×C₃	semidirect
67. C₅×#468	C₂×C₃	semidirect
68. C₅×#465	C₂×C₃	semidirect
69. C₅×#460	C₂×C₃	semidirect
70. C₅×#450	C₂×C₃	semidirect
71. C₅×#450	C₂×C₃	semidirect
72. C₅×#440	C₂×C₃	semidirect
73. C₅×#435	C₂×C₃	semidirect
74. C₅×#418	C₂×C₃	semidirect
75. C₂×C₅×#102	C₂×C₃	semidirect
129. C₃×#552	C₂×C₅	semidirect
131. C₃×#490	C₂×C₅	semidirect
132. C₃×#482	C₂×C₅	semidirect
133. C₃×#480	C₂×C₅	semidirect
134. C₃×#478	C₂×C₅	semidirect
135. C₃×#468	C₂×C₅	semidirect
136. C₃×#465	C₂×C₅	semidirect
137. C₃×#460	C₂×C₅	semidirect
138. C₃×#450	C₂×C₅	semidirect
139. C₃×#450	C₂×C₅	semidirect
140. C₃×#440	C₂×C₅	semidirect
141. C₃×#435	C₂×C₅	semidirect
142. C₃×#418	C₂×C₅	semidirect
143. C₂×C₃×#102	C₂×C₅	semidirect
148. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
149. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
150. C₂×C₅×M₁₆	C₂²×C₃	semidirect
151. C₂²×C₅×C₈	C₂²×C₃	semidirect
155. C₅×#125	C₂²×C₃	semidirect
157. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
158. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
164. C₄×C₅×Q₈	C₂²×C₃	semidirect
168. C₅×#117	C₂²×C₃	semidirect
169. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
170. C₅×#107	C₂²×C₃	semidirect
171. C₅×#107	C₂²×C₃	semidirect
172. C₅×#106	C₂²×C₃	semidirect
173. C₅×C₄⋊C₈	C₂²×C₃	semidirect
174. C₅×#103	C₂²×C₃	semidirect
178. C₅×#102	C₂²×C₃	semidirect
179. C₅×#102	C₂²×C₃	semidirect
180. C₅×#102	C₂²×C₃	semidirect
181. C₅×#102	C₂²×C₃	semidirect
182. C₅×#102	C₂²×C₃	semidirect
183. C₅×#102	C₂²×C₃	semidirect
184. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
185. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
186. C₅×#97	C₂²×C₃	semidirect
187. #3310	C₃×C₅	direct (N × H)
238. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
239. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
240. C₂×C₃×M₁₆	C₂²×C₅	semidirect
241. C₂²×C₃×C₈	C₂²×C₅	semidirect
245. C₃×#125	C₂²×C₅	semidirect
247. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
248. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
254. C₃×C₄×Q₈	C₂²×C₅	semidirect
258. C₃×#117	C₂²×C₅	semidirect
259. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
260. C₃×#107	C₂²×C₅	semidirect
261. C₃×#107	C₂²×C₅	semidirect
262. C₃×#106	C₂²×C₅	semidirect
263. C₃×C₄⋊C₈	C₂²×C₅	semidirect
264. C₃×#103	C₂²×C₅	semidirect
268. C₃×#102	C₂²×C₅	semidirect
269. C₃×#102	C₂²×C₅	semidirect
270. C₃×#102	C₂²×C₅	semidirect
271. C₃×#102	C₂²×C₅	semidirect
272. C₃×#102	C₂²×C₅	semidirect
273. C₃×#102	C₂²×C₅	semidirect
274. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
275. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
276. C₃×#97	C₂²×C₅	semidirect
330. #552	C₂×C₃×C₅	semidirect
332. #490	C₂×C₃×C₅	semidirect
333. #482	C₂×C₃×C₅	semidirect
334. #480	C₂×C₃×C₅	semidirect
335. #478	C₂×C₃×C₅	semidirect
336. #468	C₂×C₃×C₅	semidirect
337. #465	C₂×C₃×C₅	semidirect
338. #460	C₂×C₃×C₅	semidirect
339. #450	C₂×C₃×C₅	semidirect
340. #450	C₂×C₃×C₅	semidirect
341. #440	C₂×C₃×C₅	semidirect
342. #435	C₂×C₃×C₅	semidirect
343. #418	C₂×C₃×C₅	semidirect
344. C₂×#102	C₂×C₃×C₅	semidirect
477. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
478. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
479. C₂×M₁₆	C₂²×C₃×C₅	semidirect
480. C₂²×C₈	C₂²×C₃×C₅	semidirect
484. #125	C₂²×C₃×C₅	semidirect
486. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
487. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
493. C₄×Q₈	C₂²×C₃×C₅	semidirect
497. #117	C₂²×C₃×C₅	semidirect
498. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
499. #107	C₂²×C₃×C₅	semidirect
500. #107	C₂²×C₃×C₅	semidirect
501. #106	C₂²×C₃×C₅	semidirect
502. C₄⋊C₈	C₂²×C₃×C₅	semidirect
503. #103	C₂²×C₃×C₅	semidirect
507. #102	C₂²×C₃×C₅	semidirect
508. #102	C₂²×C₃×C₅	semidirect
509. #102	C₂²×C₃×C₅	semidirect
510. #102	C₂²×C₃×C₅	semidirect
511. #102	C₂²×C₃×C₅	semidirect
512. #102	C₂²×C₃×C₅	semidirect
513. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
514. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
515. #97	C₂²×C₃×C₅	semidirect
652. C₃×C₅	#3310	direct (N × H)
744. C₅	C₃×#3310	direct (N × H)
774. C₃	C₅×#3310	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×#552	2
C₃×C₅×D₄²	2
C₃×C₅×#490	2
C₃×C₅×#482	2
C₃×C₅×#480	2
C₃×C₅×#478	2
C₃×C₅×#468	2
C₃×C₅×#465	2
C₃×C₅×#460	2
C₃×C₅×#450	2
C₃×C₅×#440	2
C₃×C₅×#435	2
C₃×C₅×#418	2
C₂×C₃×C₅×#102	2
C₅×#3310	3
C₃×#3310	5

Subgroups — C3×C5×#3310 #14276344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3310 #14276344