Subgroups — C₃×C₅×#3314 #14276348

Order 1920.

820 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×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic
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×#474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#468	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#452	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×#417	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3314	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#125	—	2	1	no	—
26	C₃×C₅×#124	C₂²	1	1	yes	characteristic
27	C₃×C₅×#123	—	2	1	no	—
28	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
29	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
30	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#121	—	2	1	no	—
34	C₃×C₅×#121	C₂²	1	1	yes	characteristic
35	C₃×C₅×#120	—	2	1	no	—
36	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×C₅×D₄	—	2	1	no	—
38	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
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×#107	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#107	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×#103	C₂²	1	1	yes	characteristic, complemented
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
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×#3314	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#554	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#546	C₂×C₃	1	1	yes	characteristic
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×#474	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#468	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#467	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#464	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#452	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×#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	C₂×C₃×C₅×Q₈	—	2	1	no	—
80	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
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	—	4	1	no	—
87	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
88	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	—	2	1	no	—
91	C₂²×C₃×C₄×C₅	—	2	1	no	—
92	C₂²×C₃×C₄×C₅	—	2	1	no	—
93	C₂²×C₃×C₄×C₅	—	2	1	no	—
94	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₃×C₅×Q₁₆	—	4	1	no	—
97	C₃×C₅×SD₁₆	—	2	2	no	—
98	C₃×C₅×SD₁₆	—	4	1	no	—
99	C₃×C₅×M₁₆	—	4	1	no	—
100	C₂×C₃×C₅×C₈	—	4	1	no	—
101	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₃×C₅×C₄⋊C₄	—	2	1	no	—
106	C₃×C₅×C₄⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
113	C₃×C₅×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
128	C₃×#554	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#546	C₂×C₅	1	1	yes	characteristic
130	C₃×#489	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#484	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#480	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#474	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#468	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#467	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#464	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#440	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#435	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#417	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
144	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
146	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
149	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
150	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
151	C₅×#125	—	2	1	no	—
152	C₅×#124	C₂²×C₃	1	1	yes	characteristic
153	C₅×#123	—	2	1	no	—
154	C₅×C₂²⋊Q₈	—	2	1	no	—
155	C₅×C₂²⋊Q₈	—	2	1	no	—
156	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
157	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
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×#120	—	2	1	no	—
162	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₄×C₅×D₄	—	2	1	no	—
164	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
165	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
166	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
169	C₅×#107	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×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₅×#103	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×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
184	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
186	#3314	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
187	C₂³×C₃×C₅	—	2	1	no	—
188	C₂³×C₃×C₅	—	2	1	no	—
189	C₂³×C₃×C₅	—	4	2	no	—
190	C₂³×C₃×C₅	—	4	2	no	—
191	C₂³×C₃×C₅	—	8	1	no	—
192	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
193	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
194	C₃×C₅×Q₈	—	2	1	no	—
195	C₃×C₅×Q₈	—	2	1	no	—
196	C₃×C₅×Q₈	—	2	1	no	—
197	C₃×C₅×Q₈	—	2	1	no	—
198	C₃×C₅×Q₈	—	8	1	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	—	4	2	no	—
204	C₃×C₅×D₄	—	4	2	no	—
205	C₃×C₅×D₄	—	8	1	no	—
206	C₃×C₅×D₄	#41	1	2	yes	—
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	—	8	1	no	—
219	C₂×C₃×C₄×C₅	—	8	1	no	—
220	C₂×C₃×C₄×C₅	—	8	1	no	—
221	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
226	C₃×C₅×C₈	—	2	1	no	—
227	C₃×C₅×C₈	—	2	1	no	—
228	C₃×C₅×C₈	—	2	1	no	—
229	C₃×C₅×C₈	—	2	1	no	—
230	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
231	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
233	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
236	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
237	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
238	C₃×#125	—	2	1	no	—
239	C₃×#124	C₂²×C₅	1	1	yes	characteristic
240	C₃×#123	—	2	1	no	—
241	C₃×C₂²⋊Q₈	—	2	1	no	—
242	C₃×C₂²⋊Q₈	—	2	1	no	—
243	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
244	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
245	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
246	C₃×#121	—	2	1	no	—
247	C₃×#121	C₂²×C₅	1	1	yes	characteristic
248	C₃×#120	—	2	1	no	—
249	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
250	C₃×C₄×D₄	—	2	1	no	—
251	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
252	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
256	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
258	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
259	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₃×#102	C₂²×C₅	1	1	yes	characteristic
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
269	C₃×#102	C₂²×C₅	1	1	yes	characteristic
270	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
271	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₂⁴×C₅	—	2	1	no	—
274	C₅×#41	—	2	2	no	—
275	C₅×#41	—	4	1	no	—
276	C₂×C₅×Q₈	—	2	1	no	—
277	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
279	C₂×C₅×D₄	—	2	2	no	—
280	C₂×C₅×D₄	—	2	1	no	—
281	C₂×C₅×D₄	—	2	1	no	—
282	C₂×C₅×D₄	—	2	1	no	—
283	C₂×C₅×D₄	—	4	1	no	—
284	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
285	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
287	C₂²×C₄×C₅	—	2	1	no	—
288	C₂²×C₄×C₅	—	2	1	no	—
289	C₂²×C₄×C₅	—	2	1	no	—
290	C₂²×C₄×C₅	—	2	1	no	—
291	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
292	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
293	C₅×Q₁₆	—	4	1	no	—
294	C₅×SD₁₆	—	2	2	no	—
295	C₅×SD₁₆	—	4	1	no	—
296	C₅×M₁₆	—	4	1	no	—
297	C₂×C₅×C₈	—	4	1	no	—
298	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
299	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
300	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
301	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
302	C₅×C₄⋊C₄	—	2	1	no	—
303	C₅×C₄⋊C₄	—	2	1	no	—
304	C₅×C₄⋊C₄	—	2	1	no	—
305	C₅×C₄⋊C₄	—	2	1	no	—
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	C₃×D₄	1	1	yes	characteristic
310	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
311	C₅×C₄⋊C₄	C₂³×C₃	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×C₂²⋊C₄	—	2	1	no	—
315	C₅×C₂²⋊C₄	—	2	1	no	—
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	C₃×D₄	1	1	yes	characteristic
322	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
323	C₄²×C₅	—	2	1	no	—
324	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
325	#554	C₂×C₃×C₅	1	1	yes	characteristic, complemented
326	#546	C₂×C₃×C₅	1	1	yes	characteristic
327	#489	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	#484	C₂×C₃×C₅	1	1	yes	characteristic, complemented
329	#480	C₂×C₃×C₅	1	1	yes	characteristic, complemented
330	#474	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	#468	C₂×C₃×C₅	1	1	yes	characteristic, complemented
332	#467	C₂×C₃×C₅	1	1	yes	characteristic, complemented
333	#464	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#450	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
338	#417	C₂×C₃×C₅	1	1	yes	characteristic, complemented
339	C₂×#102	C₂×C₃×C₅	1	1	yes	characteristic, complemented
340	C₂²×C₃×C₅	—	2	1	no	—
341	C₂²×C₃×C₅	—	2	1	no	—
342	C₂²×C₃×C₅	—	2	1	no	—
343	C₂²×C₃×C₅	—	2	2	no	—
344	C₂²×C₃×C₅	—	2	1	no	—
345	C₂²×C₃×C₅	—	2	1	no	—
346	C₂²×C₃×C₅	—	4	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	—	8	4	no	—
352	C₂²×C₃×C₅	#137	1	2	yes	—
353	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
354	C₃×C₄×C₅	—	2	1	no	—
355	C₃×C₄×C₅	—	2	1	no	—
356	C₃×C₄×C₅	—	2	1	no	—
357	C₃×C₄×C₅	—	2	1	no	—
358	C₃×C₄×C₅	—	4	1	no	—
359	C₃×C₄×C₅	—	4	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	C₂×#41	1	1	yes	characteristic
365	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
366	C₂⁴×C₃	—	2	1	no	—
367	C₃×#41	—	2	2	no	—
368	C₃×#41	—	4	1	no	—
369	C₂×C₃×Q₈	—	2	1	no	—
370	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
371	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
372	C₂×C₃×D₄	—	2	2	no	—
373	C₂×C₃×D₄	—	2	1	no	—
374	C₂×C₃×D₄	—	2	1	no	—
375	C₂×C₃×D₄	—	2	1	no	—
376	C₂×C₃×D₄	—	4	1	no	—
377	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
378	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
380	C₂²×C₃×C₄	—	2	1	no	—
381	C₂²×C₃×C₄	—	2	1	no	—
382	C₂²×C₃×C₄	—	2	1	no	—
383	C₂²×C₃×C₄	—	2	1	no	—
384	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
385	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
386	C₃×Q₁₆	—	4	1	no	—
387	C₃×SD₁₆	—	2	2	no	—
388	C₃×SD₁₆	—	4	1	no	—
389	C₃×M₁₆	—	4	1	no	—
390	C₂×C₃×C₈	—	4	1	no	—
391	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
392	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
393	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
394	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
395	C₃×C₄⋊C₄	—	2	1	no	—
396	C₃×C₄⋊C₄	—	2	1	no	—
397	C₃×C₄⋊C₄	—	2	1	no	—
398	C₃×C₄⋊C₄	—	2	1	no	—
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	C₅×D₄	1	1	yes	characteristic
403	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
404	C₃×C₄⋊C₄	C₂³×C₅	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×C₂²⋊C₄	—	2	1	no	—
408	C₃×C₂²⋊C₄	—	2	1	no	—
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	C₅×D₄	1	1	yes	characteristic
415	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
416	C₃×C₄²	—	2	1	no	—
417	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
418	C₂³×C₅	—	2	1	no	—
419	C₂³×C₅	—	2	1	no	—
420	C₂³×C₅	—	4	2	no	—
421	C₂³×C₅	—	4	2	no	—
422	C₂³×C₅	—	8	1	no	—
423	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
424	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
425	C₅×Q₈	—	2	1	no	—
426	C₅×Q₈	—	2	1	no	—
427	C₅×Q₈	—	2	1	no	—
428	C₅×Q₈	—	2	1	no	—
429	C₅×Q₈	—	8	1	no	—
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	—	4	2	no	—
435	C₅×D₄	—	4	2	no	—
436	C₅×D₄	—	8	1	no	—
437	C₅×D₄	C₃×#41	1	2	yes	—
438	C₂×C₄×C₅	—	2	1	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	—	4	2	no	—
449	C₂×C₄×C₅	—	8	1	no	—
450	C₂×C₄×C₅	—	8	1	no	—
451	C₂×C₄×C₅	—	8	1	no	—
452	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
453	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
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	C₂⁴×C₃	1	1	yes	characteristic
457	C₅×C₈	—	2	1	no	—
458	C₅×C₈	—	2	1	no	—
459	C₅×C₈	—	2	1	no	—
460	C₅×C₈	—	2	1	no	—
461	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
462	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
464	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
465	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
466	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
467	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
468	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
469	#125	—	2	1	no	—
470	#124	C₂²×C₃×C₅	1	1	yes	characteristic
471	#123	—	2	1	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
475	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
476	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
477	#121	—	2	1	no	—
478	#121	C₂²×C₃×C₅	1	1	yes	characteristic
479	#120	—	2	1	no	—
480	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
481	C₄×D₄	—	2	1	no	—
482	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
483	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
488	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
489	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
490	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
491	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
492	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
493	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
494	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
495	#102	C₂²×C₃×C₅	1	1	yes	characteristic
496	#102	C₂²×C₃×C₅	1	1	yes	characteristic
497	#102	C₂²×C₃×C₅	1	1	yes	characteristic
498	#102	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	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
502	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
503	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
504	C₂×C₃×C₅	—	2	2	no	—
505	C₂×C₃×C₅	—	4	1	no	—
506	C₂×C₃×C₅	—	4	2	no	—
507	C₂×C₃×C₅	—	8	1	no	—
508	C₂×C₃×C₅	#546	1	1	yes	characteristic
509	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
510	C₂×C₃×C₅	#576	1	1	yes	characteristic
511	C₂³×C₃	—	2	1	no	—
512	C₂³×C₃	—	2	1	no	—
513	C₂³×C₃	—	4	2	no	—
514	C₂³×C₃	—	4	2	no	—
515	C₂³×C₃	—	8	1	no	—
516	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
517	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
518	C₃×Q₈	—	2	1	no	—
519	C₃×Q₈	—	2	1	no	—
520	C₃×Q₈	—	2	1	no	—
521	C₃×Q₈	—	2	1	no	—
522	C₃×Q₈	—	8	1	no	—
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	—	4	2	no	—
528	C₃×D₄	—	4	2	no	—
529	C₃×D₄	—	8	1	no	—
530	C₃×D₄	C₅×#41	1	2	yes	—
531	C₂×C₃×C₄	—	2	1	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	—	4	2	no	—
542	C₂×C₃×C₄	—	8	1	no	—
543	C₂×C₃×C₄	—	8	1	no	—
544	C₂×C₃×C₄	—	8	1	no	—
545	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
546	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
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	C₂⁴×C₅	1	1	yes	characteristic
550	C₃×C₈	—	2	1	no	—
551	C₃×C₈	—	2	1	no	—
552	C₃×C₈	—	2	1	no	—
553	C₃×C₈	—	2	1	no	—
554	C₂²×C₅	—	2	1	no	—
555	C₂²×C₅	—	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	2	no	—
560	C₂²×C₅	—	4	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	—	8	4	no	—
566	C₂²×C₅	C₃×#137	1	2	yes	—
567	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
568	C₄×C₅	—	2	1	no	—
569	C₄×C₅	—	2	1	no	—
570	C₄×C₅	—	2	1	no	—
571	C₄×C₅	—	2	1	no	—
572	C₄×C₅	—	4	1	no	—
573	C₄×C₅	—	4	1	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	C₂×C₃×#41	1	1	yes	characteristic
579	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂⁴	—	2	1	no	—
581	#41	—	2	2	no	—
582	#41	—	4	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
585	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	4	1	no	—
591	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
592	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
593	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
599	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
600	Q₁₆	—	4	1	no	—
601	SD₁₆	—	2	2	no	—
602	SD₁₆	—	4	1	no	—
603	M₁₆	—	4	1	no	—
604	C₂×C₈	—	4	1	no	—
605	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
606	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
607	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
608	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
617	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
618	C₄⋊C₄	C₂³×C₃×C₅	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	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
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	C₃×C₅×D₄	1	1	yes	characteristic
629	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
630	C₄²	—	2	1	no	—
631	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
632	C₃×C₅	#3314	1	1	yes	characteristic, direct product factor, Hall
633	C₂²×C₃	—	2	1	no	—
634	C₂²×C₃	—	2	1	no	—
635	C₂²×C₃	—	2	1	no	—
636	C₂²×C₃	—	2	2	no	—
637	C₂²×C₃	—	2	1	no	—
638	C₂²×C₃	—	2	1	no	—
639	C₂²×C₃	—	4	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	—	8	4	no	—
645	C₂²×C₃	C₅×#137	1	2	yes	—
646	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
647	C₃×C₄	—	2	1	no	—
648	C₃×C₄	—	2	1	no	—
649	C₃×C₄	—	2	1	no	—
650	C₃×C₄	—	2	1	no	—
651	C₃×C₄	—	4	1	no	—
652	C₃×C₄	—	4	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	C₂×C₅×#41	1	1	yes	characteristic
658	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
659	C₂×C₅	—	2	2	no	—
660	C₂×C₅	—	4	1	no	—
661	C₂×C₅	—	4	2	no	—
662	C₂×C₅	—	8	1	no	—
663	C₂×C₅	C₃×#546	1	1	yes	characteristic
664	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
665	C₂×C₅	C₃×#576	1	1	yes	characteristic
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	4	2	no	—
669	C₂³	—	4	2	no	—
670	C₂³	—	8	1	no	—
671	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
672	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
673	Q₈	—	2	1	no	—
674	Q₈	—	2	1	no	—
675	Q₈	—	2	1	no	—
676	Q₈	—	2	1	no	—
677	Q₈	—	8	1	no	—
678	D₄	—	2	2	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	—	8	1	no	—
685	D₄	C₃×C₅×#41	1	2	yes	—
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	—	8	1	no	—
698	C₂×C₄	—	8	1	no	—
699	C₂×C₄	—	8	1	no	—
700	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
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	C₂⁴×C₃×C₅	1	1	yes	characteristic
705	C₈	—	2	1	no	—
706	C₈	—	2	1	no	—
707	C₈	—	2	1	no	—
708	C₈	—	2	1	no	—
709	C₂×C₃	—	2	2	no	—
710	C₂×C₃	—	4	1	no	—
711	C₂×C₃	—	4	2	no	—
712	C₂×C₃	—	8	1	no	—
713	C₂×C₃	C₅×#546	1	1	yes	characteristic
714	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
715	C₂×C₃	C₅×#576	1	1	yes	characteristic
716	C₅	C₃×#3314	1	1	yes	characteristic, direct product factor, Sylow
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	2	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	—	8	4	no	—
729	C₂²	C₃×C₅×#137	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	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	4	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×#3314	1	1	yes	characteristic, direct product factor, Sylow
744	C₂	—	2	2	no	—
745	C₂	—	4	1	no	—
746	C₂	—	4	2	no	—
747	C₂	—	8	1	no	—
748	C₂	C₃×C₅×#546	1	1	yes	characteristic
749	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
750	C₂	C₃×C₅×#576	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×#546	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×#554	C₂	semidirect
3. C₃×C₅×#489	C₂	semidirect
4. C₃×C₅×#484	C₂	semidirect
5. C₃×C₅×#480	C₂	semidirect
6. C₃×C₅×#474	C₂	semidirect
7. C₃×C₅×#468	C₂	semidirect
8. C₃×C₅×#467	C₂	semidirect
9. C₃×C₅×#464	C₂	semidirect
10. C₃×C₅×#452	C₂	semidirect
11. C₃×C₅×#450	C₂	semidirect
12. C₃×C₅×#440	C₂	semidirect
13. C₃×C₅×#435	C₂	semidirect
14. C₃×C₅×#417	C₂	semidirect
15. C₂×C₃×C₅×#102	C₂	semidirect
16. C₅×#3314	C₃	direct (N × H)
19. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
22. C₂×C₃×C₅×M₁₆	C₂²	semidirect
24. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
32. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₄×C₅×Q₈	C₂²	semidirect
41. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
43. C₃×C₅×#107	C₂²	semidirect
44. C₃×C₅×#107	C₂²	semidirect
45. C₃×C₅×#107	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
50. C₃×C₅×#103	C₂²	semidirect
58. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
59. C₃×C₅×#97	C₂²	semidirect
60. C₃×#3314	C₅	direct (N × H)
61. C₅×#554	C₂×C₃	semidirect
63. C₅×#489	C₂×C₃	semidirect
64. C₅×#484	C₂×C₃	semidirect
65. C₅×#480	C₂×C₃	semidirect
66. C₅×#474	C₂×C₃	semidirect
67. C₅×#468	C₂×C₃	semidirect
68. C₅×#467	C₂×C₃	semidirect
69. C₅×#464	C₂×C₃	semidirect
70. C₅×#452	C₂×C₃	semidirect
71. C₅×#450	C₂×C₃	semidirect
72. C₅×#440	C₂×C₃	semidirect
73. C₅×#435	C₂×C₃	semidirect
74. C₅×#417	C₂×C₃	semidirect
75. C₂×C₅×#102	C₂×C₃	semidirect
128. C₃×#554	C₂×C₅	semidirect
130. C₃×#489	C₂×C₅	semidirect
131. C₃×#484	C₂×C₅	semidirect
132. C₃×#480	C₂×C₅	semidirect
133. C₃×#474	C₂×C₅	semidirect
134. C₃×#468	C₂×C₅	semidirect
135. C₃×#467	C₂×C₅	semidirect
136. C₃×#464	C₂×C₅	semidirect
137. C₃×#452	C₂×C₅	semidirect
138. C₃×#450	C₂×C₅	semidirect
139. C₃×#440	C₂×C₅	semidirect
140. C₃×#435	C₂×C₅	semidirect
141. C₃×#417	C₂×C₅	semidirect
142. C₂×C₃×#102	C₂×C₅	semidirect
145. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
148. C₂×C₅×M₁₆	C₂²×C₃	semidirect
150. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
158. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
162. C₄×C₅×Q₈	C₂²×C₃	semidirect
167. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
169. C₅×#107	C₂²×C₃	semidirect
170. C₅×#107	C₂²×C₃	semidirect
171. C₅×#107	C₂²×C₃	semidirect
172. C₅×C₄⋊C₈	C₂²×C₃	semidirect
173. C₅×#103	C₂²×C₃	semidirect
174. C₅×#103	C₂²×C₃	semidirect
175. C₅×#103	C₂²×C₃	semidirect
176. C₅×#103	C₂²×C₃	semidirect
184. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
185. C₅×#97	C₂²×C₃	semidirect
186. #3314	C₃×C₅	direct (N × H)
232. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
235. C₂×C₃×M₁₆	C₂²×C₅	semidirect
237. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
245. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
249. C₃×C₄×Q₈	C₂²×C₅	semidirect
254. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
256. C₃×#107	C₂²×C₅	semidirect
257. C₃×#107	C₂²×C₅	semidirect
258. C₃×#107	C₂²×C₅	semidirect
259. C₃×C₄⋊C₈	C₂²×C₅	semidirect
260. C₃×#103	C₂²×C₅	semidirect
261. C₃×#103	C₂²×C₅	semidirect
262. C₃×#103	C₂²×C₅	semidirect
263. C₃×#103	C₂²×C₅	semidirect
271. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
272. C₃×#97	C₂²×C₅	semidirect
325. #554	C₂×C₃×C₅	semidirect
327. #489	C₂×C₃×C₅	semidirect
328. #484	C₂×C₃×C₅	semidirect
329. #480	C₂×C₃×C₅	semidirect
330. #474	C₂×C₃×C₅	semidirect
331. #468	C₂×C₃×C₅	semidirect
332. #467	C₂×C₃×C₅	semidirect
333. #464	C₂×C₃×C₅	semidirect
334. #452	C₂×C₃×C₅	semidirect
335. #450	C₂×C₃×C₅	semidirect
336. #440	C₂×C₃×C₅	semidirect
337. #435	C₂×C₃×C₅	semidirect
338. #417	C₂×C₃×C₅	semidirect
339. C₂×#102	C₂×C₃×C₅	semidirect
463. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
466. C₂×M₁₆	C₂²×C₃×C₅	semidirect
468. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
476. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
480. C₄×Q₈	C₂²×C₃×C₅	semidirect
485. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
487. #107	C₂²×C₃×C₅	semidirect
488. #107	C₂²×C₃×C₅	semidirect
489. #107	C₂²×C₃×C₅	semidirect
490. C₄⋊C₈	C₂²×C₃×C₅	semidirect
491. #103	C₂²×C₃×C₅	semidirect
492. #103	C₂²×C₃×C₅	semidirect
493. #103	C₂²×C₃×C₅	semidirect
494. #103	C₂²×C₃×C₅	semidirect
502. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
503. #97	C₂²×C₃×C₅	semidirect
632. C₃×C₅	#3314	direct (N × H)
716. C₅	C₃×#3314	direct (N × H)
743. C₃	C₅×#3314	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×#554	2
C₃×C₅×#546	2
C₃×C₅×#489	2
C₃×C₅×#484	2
C₃×C₅×#480	2
C₃×C₅×#474	2
C₃×C₅×#468	2
C₃×C₅×#467	2
C₃×C₅×#464	2
C₃×C₅×#452	2
C₃×C₅×#450	2
C₃×C₅×#440	2
C₃×C₅×#435	2
C₃×C₅×#417	2
C₂×C₃×C₅×#102	2
C₅×#3314	3
C₃×#3314	5

Subgroups — C3×C5×#3314 #14276348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3314 #14276348