Subgroups — C₃×C₅×#3271 #14276305

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#448	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3271	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×#137	—	2	4	no	—
22	C₃×C₅×#135	—	2	4	no	—
23	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×#127	—	2	1	no	—
35	C₃×C₅×#127	C₂²	1	1	yes	characteristic
36	C₃×C₅×#124	—	2	1	no	—
37	C₃×C₅×#124	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
39	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₃×C₅×#121	—	2	1	no	—
41	C₃×C₅×#121	—	2	1	no	—
42	C₃×C₅×#121	—	2	1	no	—
43	C₃×C₅×#121	C₂²	1	1	yes	characteristic
44	C₃×C₅×#121	C₂²	1	1	yes	characteristic
45	C₃×C₅×#121	C₂²	1	1	yes	characteristic
46	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
47	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
48	C₃×C₄×C₅×D₄	—	2	1	no	—
49	C₃×C₄×C₅×D₄	—	2	1	no	—
50	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
51	C₃×C₅×#106	C₂²	1	1	yes	characteristic
52	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₃×C₅×#103	C₂²	1	1	yes	characteristic
54	C₃×C₅×#103	C₂²	1	1	yes	characteristic
55	C₃×C₅×#103	C₂²	1	1	yes	characteristic
56	C₃×C₅×#102	C₂²	1	1	yes	characteristic
57	C₃×C₅×#102	C₂²	1	1	yes	characteristic
58	C₃×C₅×#102	C₂²	1	1	yes	characteristic
59	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
61	C₃×C₅×#97	C₂²	1	1	yes	characteristic
62	C₃×#3271	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#550	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#548	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#496	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#469	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#465	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#464	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#448	C₂×C₃	1	1	yes	characteristic, complemented
76	C₅×#441	C₂×C₃	1	1	yes	characteristic, complemented
77	C₅×#435	C₂×C₃	1	1	yes	characteristic, complemented
78	C₃×C₅×#41	—	2	2	no	—
79	C₃×C₅×#41	—	2	2	no	—
80	C₃×C₅×#41	—	2	2	no	—
81	C₃×C₅×#41	—	4	1	no	—
82	C₃×C₅×#41	—	4	1	no	—
83	C₃×C₅×#41	—	4	1	no	—
84	C₂×C₃×C₅×Q₈	—	2	1	no	—
85	C₂×C₃×C₅×Q₈	—	2	2	no	—
86	C₂×C₃×C₅×Q₈	—	4	1	no	—
87	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₅×D₄	—	2	1	no	—
91	C₂×C₃×C₅×D₄	—	2	1	no	—
92	C₂×C₃×C₅×D₄	—	2	1	no	—
93	C₂×C₃×C₅×D₄	—	2	1	no	—
94	C₂×C₃×C₅×D₄	—	2	1	no	—
95	C₂×C₃×C₅×D₄	—	2	1	no	—
96	C₂×C₃×C₅×D₄	—	2	1	no	—
97	C₂×C₃×C₅×D₄	—	2	1	no	—
98	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
99	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
102	C₂²×C₃×C₄×C₅	—	2	1	no	—
103	C₂²×C₃×C₄×C₅	—	2	1	no	—
104	C₂²×C₃×C₄×C₅	—	2	1	no	—
105	C₂²×C₃×C₄×C₅	—	2	1	no	—
106	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
107	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
108	C₃×C₅×Q₁₆	—	2	2	no	—
109	C₃×C₅×Q₁₆	D₄	1	4	yes	complemented
110	C₃×C₅×SD₁₆	—	2	2	no	—
111	C₃×C₅×SD₁₆	—	2	2	no	—
112	C₃×C₅×SD₁₆	—	2	2	no	—
113	C₃×C₅×SD₁₆	—	2	2	no	—
114	C₃×C₅×SD₁₆	—	4	1	no	—
115	C₃×C₅×D₈	—	2	2	no	—
116	C₃×C₅×D₈	—	4	1	no	—
117	C₃×C₅×M₁₆	—	2	2	no	—
118	C₂×C₃×C₅×C₈	—	2	2	no	—
119	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
120	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
121	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
123	C₃×C₅×C₄⋊C₄	—	2	1	no	—
124	C₃×C₅×C₄⋊C₄	—	2	1	no	—
125	C₃×C₅×C₄⋊C₄	—	2	1	no	—
126	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
127	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
130	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
131	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
132	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
133	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
134	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
135	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
136	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
137	C₃×C₄²×C₅	—	2	1	no	—
138	C₃×C₄²×C₅	—	2	1	no	—
139	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
140	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#550	C₂×C₅	1	1	yes	characteristic, complemented
143	C₃×#548	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×#496	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#469	C₂×C₅	1	1	yes	characteristic, complemented
146	C₃×#465	C₂×C₅	1	1	yes	characteristic, complemented
147	C₃×#464	C₂×C₅	1	1	yes	characteristic, complemented
148	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
149	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
150	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
151	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
152	C₃×#448	C₂×C₅	1	1	yes	characteristic, complemented
153	C₃×#441	C₂×C₅	1	1	yes	characteristic, complemented
154	C₃×#435	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
158	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₅×#137	—	2	4	no	—
160	C₅×#135	—	2	4	no	—
161	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
162	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
166	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
169	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
170	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
171	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
172	C₅×#127	—	2	1	no	—
173	C₅×#127	C₂²×C₃	1	1	yes	characteristic
174	C₅×#124	—	2	1	no	—
175	C₅×#124	C₂²×C₃	1	1	yes	characteristic
176	C₅×C₂²⋊Q₈	—	2	1	no	—
177	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
178	C₅×#121	—	2	1	no	—
179	C₅×#121	—	2	1	no	—
180	C₅×#121	—	2	1	no	—
181	C₅×#121	C₂²×C₃	1	1	yes	characteristic
182	C₅×#121	C₂²×C₃	1	1	yes	characteristic
183	C₅×#121	C₂²×C₃	1	1	yes	characteristic
184	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
185	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
186	C₄×C₅×D₄	—	2	1	no	—
187	C₄×C₅×D₄	—	2	1	no	—
188	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
189	C₅×#106	C₂²×C₃	1	1	yes	characteristic
190	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
191	C₅×#103	C₂²×C₃	1	1	yes	characteristic
192	C₅×#103	C₂²×C₃	1	1	yes	characteristic
193	C₅×#103	C₂²×C₃	1	1	yes	characteristic
194	C₅×#102	C₂²×C₃	1	1	yes	characteristic
195	C₅×#102	C₂²×C₃	1	1	yes	characteristic
196	C₅×#102	C₂²×C₃	1	1	yes	characteristic
197	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
198	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
199	C₅×#97	C₂²×C₃	1	1	yes	characteristic
200	#3271	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
201	C₂³×C₃×C₅	—	2	1	no	—
202	C₂³×C₃×C₅	—	2	1	no	—
203	C₂³×C₃×C₅	—	2	1	no	—
204	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
205	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
206	C₃×C₅×Q₈	—	2	1	no	—
207	C₃×C₅×Q₈	—	2	1	no	—
208	C₃×C₅×Q₈	—	2	1	no	—
209	C₃×C₅×Q₈	—	2	1	no	—
210	C₃×C₅×Q₈	—	4	2	no	—
211	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
212	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
213	C₃×C₅×D₄	—	2	1	no	—
214	C₃×C₅×D₄	—	2	1	no	—
215	C₃×C₅×D₄	—	2	1	no	—
216	C₃×C₅×D₄	—	2	1	no	—
217	C₃×C₅×D₄	—	2	1	no	—
218	C₃×C₅×D₄	—	2	1	no	—
219	C₃×C₅×D₄	—	4	1	no	—
220	C₃×C₅×D₄	—	4	2	no	—
221	C₃×C₅×D₄	—	4	2	no	—
222	C₃×C₅×D₄	—	4	2	no	—
223	C₃×C₅×D₄	—	4	2	no	—
224	C₃×C₅×D₄	—	4	2	no	—
225	C₃×C₅×D₄	—	8	1	no	—
226	C₃×C₅×D₄	—	8	1	no	—
227	C₃×C₅×D₄	—	8	1	no	—
228	C₂×C₃×C₄×C₅	—	2	1	no	—
229	C₂×C₃×C₄×C₅	—	2	1	no	—
230	C₂×C₃×C₄×C₅	—	2	1	no	—
231	C₂×C₃×C₄×C₅	—	2	1	no	—
232	C₂×C₃×C₄×C₅	—	2	1	no	—
233	C₂×C₃×C₄×C₅	—	2	1	no	—
234	C₂×C₃×C₄×C₅	—	2	1	no	—
235	C₂×C₃×C₄×C₅	—	2	1	no	—
236	C₂×C₃×C₄×C₅	—	2	1	no	—
237	C₂×C₃×C₄×C₅	—	4	2	no	—
238	C₂×C₃×C₄×C₅	—	4	2	no	—
239	C₂×C₃×C₄×C₅	—	4	2	no	—
240	C₂×C₃×C₄×C₅	—	4	2	no	—
241	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
242	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
243	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
245	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
246	C₃×C₅×C₈	—	2	1	no	—
247	C₃×C₅×C₈	—	2	1	no	—
248	C₃×C₅×C₈	—	2	1	no	—
249	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
250	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
253	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
254	C₃×#137	—	2	4	no	—
255	C₃×#135	—	2	4	no	—
256	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
266	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
267	C₃×#127	—	2	1	no	—
268	C₃×#127	C₂²×C₅	1	1	yes	characteristic
269	C₃×#124	—	2	1	no	—
270	C₃×#124	C₂²×C₅	1	1	yes	characteristic
271	C₃×C₂²⋊Q₈	—	2	1	no	—
272	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
273	C₃×#121	—	2	1	no	—
274	C₃×#121	—	2	1	no	—
275	C₃×#121	—	2	1	no	—
276	C₃×#121	C₂²×C₅	1	1	yes	characteristic
277	C₃×#121	C₂²×C₅	1	1	yes	characteristic
278	C₃×#121	C₂²×C₅	1	1	yes	characteristic
279	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
280	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
281	C₃×C₄×D₄	—	2	1	no	—
282	C₃×C₄×D₄	—	2	1	no	—
283	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
284	C₃×#106	C₂²×C₅	1	1	yes	characteristic
285	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
286	C₃×#103	C₂²×C₅	1	1	yes	characteristic
287	C₃×#103	C₂²×C₅	1	1	yes	characteristic
288	C₃×#103	C₂²×C₅	1	1	yes	characteristic
289	C₃×#102	C₂²×C₅	1	1	yes	characteristic
290	C₃×#102	C₂²×C₅	1	1	yes	characteristic
291	C₃×#102	C₂²×C₅	1	1	yes	characteristic
292	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
293	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
294	C₃×#97	C₂²×C₅	1	1	yes	characteristic
295	C₅×#41	—	2	2	no	—
296	C₅×#41	—	2	2	no	—
297	C₅×#41	—	2	2	no	—
298	C₅×#41	—	4	1	no	—
299	C₅×#41	—	4	1	no	—
300	C₅×#41	—	4	1	no	—
301	C₂×C₅×Q₈	—	2	1	no	—
302	C₂×C₅×Q₈	—	2	2	no	—
303	C₂×C₅×Q₈	—	4	1	no	—
304	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
305	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
306	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
307	C₂×C₅×D₄	—	2	1	no	—
308	C₂×C₅×D₄	—	2	1	no	—
309	C₂×C₅×D₄	—	2	1	no	—
310	C₂×C₅×D₄	—	2	1	no	—
311	C₂×C₅×D₄	—	2	1	no	—
312	C₂×C₅×D₄	—	2	1	no	—
313	C₂×C₅×D₄	—	2	1	no	—
314	C₂×C₅×D₄	—	2	1	no	—
315	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
316	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
317	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
318	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
319	C₂²×C₄×C₅	—	2	1	no	—
320	C₂²×C₄×C₅	—	2	1	no	—
321	C₂²×C₄×C₅	—	2	1	no	—
322	C₂²×C₄×C₅	—	2	1	no	—
323	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
324	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
325	C₅×Q₁₆	—	2	2	no	—
326	C₅×Q₁₆	C₃×D₄	1	4	yes	complemented
327	C₅×SD₁₆	—	2	2	no	—
328	C₅×SD₁₆	—	2	2	no	—
329	C₅×SD₁₆	—	2	2	no	—
330	C₅×SD₁₆	—	2	2	no	—
331	C₅×SD₁₆	—	4	1	no	—
332	C₅×D₈	—	2	2	no	—
333	C₅×D₈	—	4	1	no	—
334	C₅×M₁₆	—	2	2	no	—
335	C₂×C₅×C₈	—	2	2	no	—
336	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
337	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
338	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
339	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
340	C₅×C₄⋊C₄	—	2	1	no	—
341	C₅×C₄⋊C₄	—	2	1	no	—
342	C₅×C₄⋊C₄	—	2	1	no	—
343	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
344	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
345	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
346	C₅×C₂²⋊C₄	—	2	1	no	—
347	C₅×C₂²⋊C₄	—	2	1	no	—
348	C₅×C₂²⋊C₄	—	2	1	no	—
349	C₅×C₂²⋊C₄	—	2	1	no	—
350	C₅×C₂²⋊C₄	—	2	1	no	—
351	C₅×C₂²⋊C₄	—	2	1	no	—
352	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
353	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
354	C₄²×C₅	—	2	1	no	—
355	C₄²×C₅	—	2	1	no	—
356	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
357	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
358	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
359	#550	C₂×C₃×C₅	1	1	yes	characteristic, complemented
360	#548	C₂×C₃×C₅	1	1	yes	characteristic, complemented
361	#496	C₂×C₃×C₅	1	1	yes	characteristic, complemented
362	#469	C₂×C₃×C₅	1	1	yes	characteristic, complemented
363	#465	C₂×C₃×C₅	1	1	yes	characteristic, complemented
364	#464	C₂×C₃×C₅	1	1	yes	characteristic, complemented
365	#460	C₂×C₃×C₅	1	1	yes	characteristic, complemented
366	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
367	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
368	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
369	#448	C₂×C₃×C₅	1	1	yes	characteristic, complemented
370	#441	C₂×C₃×C₅	1	1	yes	characteristic, complemented
371	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
372	C₂²×C₃×C₅	—	2	1	no	—
373	C₂²×C₃×C₅	—	2	1	no	—
374	C₂²×C₃×C₅	—	2	1	no	—
375	C₂²×C₃×C₅	—	2	1	no	—
376	C₂²×C₃×C₅	—	2	1	no	—
377	C₂²×C₃×C₅	—	2	1	no	—
378	C₂²×C₃×C₅	—	4	1	no	—
379	C₂²×C₃×C₅	—	4	1	no	—
380	C₂²×C₃×C₅	—	4	1	no	—
381	C₂²×C₃×C₅	—	4	1	no	—
382	C₂²×C₃×C₅	—	4	1	no	—
383	C₂²×C₃×C₅	—	4	1	no	—
384	C₂²×C₃×C₅	—	4	1	no	—
385	C₂²×C₃×C₅	—	4	1	no	—
386	C₂²×C₃×C₅	—	4	1	no	—
387	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
388	C₃×C₄×C₅	—	2	1	no	—
389	C₃×C₄×C₅	—	2	1	no	—
390	C₃×C₄×C₅	—	2	2	no	—
391	C₃×C₄×C₅	—	2	2	no	—
392	C₃×C₄×C₅	—	2	1	no	—
393	C₃×C₄×C₅	—	2	1	no	—
394	C₃×C₄×C₅	—	4	1	no	—
395	C₃×C₄×C₅	—	4	1	no	—
396	C₃×C₄×C₅	—	4	1	no	—
397	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
398	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
399	C₃×#41	—	2	2	no	—
400	C₃×#41	—	2	2	no	—
401	C₃×#41	—	2	2	no	—
402	C₃×#41	—	4	1	no	—
403	C₃×#41	—	4	1	no	—
404	C₃×#41	—	4	1	no	—
405	C₂×C₃×Q₈	—	2	1	no	—
406	C₂×C₃×Q₈	—	2	2	no	—
407	C₂×C₃×Q₈	—	4	1	no	—
408	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
409	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
411	C₂×C₃×D₄	—	2	1	no	—
412	C₂×C₃×D₄	—	2	1	no	—
413	C₂×C₃×D₄	—	2	1	no	—
414	C₂×C₃×D₄	—	2	1	no	—
415	C₂×C₃×D₄	—	2	1	no	—
416	C₂×C₃×D₄	—	2	1	no	—
417	C₂×C₃×D₄	—	2	1	no	—
418	C₂×C₃×D₄	—	2	1	no	—
419	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
420	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
421	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
422	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
423	C₂²×C₃×C₄	—	2	1	no	—
424	C₂²×C₃×C₄	—	2	1	no	—
425	C₂²×C₃×C₄	—	2	1	no	—
426	C₂²×C₃×C₄	—	2	1	no	—
427	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
429	C₃×Q₁₆	—	2	2	no	—
430	C₃×Q₁₆	C₅×D₄	1	4	yes	complemented
431	C₃×SD₁₆	—	2	2	no	—
432	C₃×SD₁₆	—	2	2	no	—
433	C₃×SD₁₆	—	2	2	no	—
434	C₃×SD₁₆	—	2	2	no	—
435	C₃×SD₁₆	—	4	1	no	—
436	C₃×D₈	—	2	2	no	—
437	C₃×D₈	—	4	1	no	—
438	C₃×M₁₆	—	2	2	no	—
439	C₂×C₃×C₈	—	2	2	no	—
440	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
441	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
442	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
443	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
444	C₃×C₄⋊C₄	—	2	1	no	—
445	C₃×C₄⋊C₄	—	2	1	no	—
446	C₃×C₄⋊C₄	—	2	1	no	—
447	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
448	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
449	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
450	C₃×C₂²⋊C₄	—	2	1	no	—
451	C₃×C₂²⋊C₄	—	2	1	no	—
452	C₃×C₂²⋊C₄	—	2	1	no	—
453	C₃×C₂²⋊C₄	—	2	1	no	—
454	C₃×C₂²⋊C₄	—	2	1	no	—
455	C₃×C₂²⋊C₄	—	2	1	no	—
456	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
457	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
458	C₃×C₄²	—	2	1	no	—
459	C₃×C₄²	—	2	1	no	—
460	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
461	C₂³×C₅	—	2	1	no	—
462	C₂³×C₅	—	2	1	no	—
463	C₂³×C₅	—	2	1	no	—
464	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
465	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
466	C₅×Q₈	—	2	1	no	—
467	C₅×Q₈	—	2	1	no	—
468	C₅×Q₈	—	2	1	no	—
469	C₅×Q₈	—	2	1	no	—
470	C₅×Q₈	—	4	2	no	—
471	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
472	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
473	C₅×D₄	—	2	1	no	—
474	C₅×D₄	—	2	1	no	—
475	C₅×D₄	—	2	1	no	—
476	C₅×D₄	—	2	1	no	—
477	C₅×D₄	—	2	1	no	—
478	C₅×D₄	—	2	1	no	—
479	C₅×D₄	—	4	1	no	—
480	C₅×D₄	—	4	2	no	—
481	C₅×D₄	—	4	2	no	—
482	C₅×D₄	—	4	2	no	—
483	C₅×D₄	—	4	2	no	—
484	C₅×D₄	—	4	2	no	—
485	C₅×D₄	—	8	1	no	—
486	C₅×D₄	—	8	1	no	—
487	C₅×D₄	—	8	1	no	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	1	no	—
494	C₂×C₄×C₅	—	2	1	no	—
495	C₂×C₄×C₅	—	2	1	no	—
496	C₂×C₄×C₅	—	2	1	no	—
497	C₂×C₄×C₅	—	4	2	no	—
498	C₂×C₄×C₅	—	4	2	no	—
499	C₂×C₄×C₅	—	4	2	no	—
500	C₂×C₄×C₅	—	4	2	no	—
501	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
502	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
503	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
504	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
505	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
506	C₅×C₈	—	2	1	no	—
507	C₅×C₈	—	2	1	no	—
508	C₅×C₈	—	2	1	no	—
509	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
510	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
511	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
512	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
513	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
514	#137	—	2	4	no	—
515	#135	—	2	4	no	—
516	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
517	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
518	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
519	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
520	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
521	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
522	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
523	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
524	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
525	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
526	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
527	#127	—	2	1	no	—
528	#127	C₂²×C₃×C₅	1	1	yes	characteristic
529	#124	—	2	1	no	—
530	#124	C₂²×C₃×C₅	1	1	yes	characteristic
531	C₂²⋊Q₈	—	2	1	no	—
532	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
533	#121	—	2	1	no	—
534	#121	—	2	1	no	—
535	#121	—	2	1	no	—
536	#121	C₂²×C₃×C₅	1	1	yes	characteristic
537	#121	C₂²×C₃×C₅	1	1	yes	characteristic
538	#121	C₂²×C₃×C₅	1	1	yes	characteristic
539	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
540	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
544	#106	C₂²×C₃×C₅	1	1	yes	characteristic
545	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
546	#103	C₂²×C₃×C₅	1	1	yes	characteristic
547	#103	C₂²×C₃×C₅	1	1	yes	characteristic
548	#103	C₂²×C₃×C₅	1	1	yes	characteristic
549	#102	C₂²×C₃×C₅	1	1	yes	characteristic
550	#102	C₂²×C₃×C₅	1	1	yes	characteristic
551	#102	C₂²×C₃×C₅	1	1	yes	characteristic
552	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
553	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
554	#97	C₂²×C₃×C₅	1	1	yes	characteristic
555	C₂×C₃×C₅	—	4	1	no	—
556	C₂×C₃×C₅	—	4	1	no	—
557	C₂×C₃×C₅	—	8	1	no	—
558	C₂×C₃×C₅	—	8	1	no	—
559	C₂×C₃×C₅	—	8	1	no	—
560	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
561	C₂×C₃×C₅	#575	1	1	yes	characteristic
562	C₂×C₃×C₅	#577	1	1	yes	characteristic
563	C₂³×C₃	—	2	1	no	—
564	C₂³×C₃	—	2	1	no	—
565	C₂³×C₃	—	2	1	no	—
566	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
567	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
568	C₃×Q₈	—	2	1	no	—
569	C₃×Q₈	—	2	1	no	—
570	C₃×Q₈	—	2	1	no	—
571	C₃×Q₈	—	2	1	no	—
572	C₃×Q₈	—	4	2	no	—
573	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
574	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
575	C₃×D₄	—	2	1	no	—
576	C₃×D₄	—	2	1	no	—
577	C₃×D₄	—	2	1	no	—
578	C₃×D₄	—	2	1	no	—
579	C₃×D₄	—	2	1	no	—
580	C₃×D₄	—	2	1	no	—
581	C₃×D₄	—	4	1	no	—
582	C₃×D₄	—	4	2	no	—
583	C₃×D₄	—	4	2	no	—
584	C₃×D₄	—	4	2	no	—
585	C₃×D₄	—	4	2	no	—
586	C₃×D₄	—	4	2	no	—
587	C₃×D₄	—	8	1	no	—
588	C₃×D₄	—	8	1	no	—
589	C₃×D₄	—	8	1	no	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	1	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	1	no	—
597	C₂×C₃×C₄	—	2	1	no	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	4	2	no	—
600	C₂×C₃×C₄	—	4	2	no	—
601	C₂×C₃×C₄	—	4	2	no	—
602	C₂×C₃×C₄	—	4	2	no	—
603	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
604	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
605	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
606	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
607	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
608	C₃×C₈	—	2	1	no	—
609	C₃×C₈	—	2	1	no	—
610	C₃×C₈	—	2	1	no	—
611	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
612	C₂²×C₅	—	2	1	no	—
613	C₂²×C₅	—	2	1	no	—
614	C₂²×C₅	—	2	1	no	—
615	C₂²×C₅	—	2	1	no	—
616	C₂²×C₅	—	2	1	no	—
617	C₂²×C₅	—	2	1	no	—
618	C₂²×C₅	—	4	1	no	—
619	C₂²×C₅	—	4	1	no	—
620	C₂²×C₅	—	4	1	no	—
621	C₂²×C₅	—	4	1	no	—
622	C₂²×C₅	—	4	1	no	—
623	C₂²×C₅	—	4	1	no	—
624	C₂²×C₅	—	4	1	no	—
625	C₂²×C₅	—	4	1	no	—
626	C₂²×C₅	—	4	1	no	—
627	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
628	C₄×C₅	—	2	1	no	—
629	C₄×C₅	—	2	1	no	—
630	C₄×C₅	—	2	1	no	—
631	C₄×C₅	—	2	1	no	—
632	C₄×C₅	—	2	2	no	—
633	C₄×C₅	—	2	2	no	—
634	C₄×C₅	—	4	1	no	—
635	C₄×C₅	—	4	1	no	—
636	C₄×C₅	—	4	1	no	—
637	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
638	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
639	#41	—	2	2	no	—
640	#41	—	2	2	no	—
641	#41	—	2	2	no	—
642	#41	—	4	1	no	—
643	#41	—	4	1	no	—
644	#41	—	4	1	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	4	1	no	—
648	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
649	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
650	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
660	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
661	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
662	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
668	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
669	Q₁₆	—	2	2	no	—
670	Q₁₆	C₃×C₅×D₄	1	4	yes	complemented
671	SD₁₆	—	2	2	no	—
672	SD₁₆	—	2	2	no	—
673	SD₁₆	—	2	2	no	—
674	SD₁₆	—	2	2	no	—
675	SD₁₆	—	4	1	no	—
676	D₈	—	2	2	no	—
677	D₈	—	4	1	no	—
678	M₁₆	—	2	2	no	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
681	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
682	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
683	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
688	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
689	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	1	no	—
695	C₂²⋊C₄	—	2	1	no	—
696	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
697	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
701	C₃×C₅	#3271	1	1	yes	characteristic, direct product factor, Hall
702	C₂²×C₃	—	2	1	no	—
703	C₂²×C₃	—	2	1	no	—
704	C₂²×C₃	—	2	1	no	—
705	C₂²×C₃	—	2	1	no	—
706	C₂²×C₃	—	2	1	no	—
707	C₂²×C₃	—	2	1	no	—
708	C₂²×C₃	—	4	1	no	—
709	C₂²×C₃	—	4	1	no	—
710	C₂²×C₃	—	4	1	no	—
711	C₂²×C₃	—	4	1	no	—
712	C₂²×C₃	—	4	1	no	—
713	C₂²×C₃	—	4	1	no	—
714	C₂²×C₃	—	4	1	no	—
715	C₂²×C₃	—	4	1	no	—
716	C₂²×C₃	—	4	1	no	—
717	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
718	C₃×C₄	—	2	1	no	—
719	C₃×C₄	—	2	1	no	—
720	C₃×C₄	—	2	2	no	—
721	C₃×C₄	—	2	2	no	—
722	C₃×C₄	—	2	1	no	—
723	C₃×C₄	—	2	1	no	—
724	C₃×C₄	—	4	1	no	—
725	C₃×C₄	—	4	1	no	—
726	C₃×C₄	—	4	1	no	—
727	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
728	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
729	C₂×C₅	—	4	1	no	—
730	C₂×C₅	—	4	1	no	—
731	C₂×C₅	—	8	1	no	—
732	C₂×C₅	—	8	1	no	—
733	C₂×C₅	—	8	1	no	—
734	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
735	C₂×C₅	C₃×#575	1	1	yes	characteristic
736	C₂×C₅	C₃×#577	1	1	yes	characteristic
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
741	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
742	Q₈	—	2	1	no	—
743	Q₈	—	2	1	no	—
744	Q₈	—	2	1	no	—
745	Q₈	—	2	1	no	—
746	Q₈	—	4	2	no	—
747	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
748	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
749	D₄	—	2	1	no	—
750	D₄	—	2	1	no	—
751	D₄	—	2	1	no	—
752	D₄	—	2	1	no	—
753	D₄	—	2	1	no	—
754	D₄	—	2	1	no	—
755	D₄	—	4	1	no	—
756	D₄	—	4	2	no	—
757	D₄	—	4	2	no	—
758	D₄	—	4	2	no	—
759	D₄	—	4	2	no	—
760	D₄	—	4	2	no	—
761	D₄	—	8	1	no	—
762	D₄	—	8	1	no	—
763	D₄	—	8	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	2	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
778	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
779	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
780	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
781	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
782	C₈	—	2	1	no	—
783	C₈	—	2	1	no	—
784	C₈	—	2	1	no	—
785	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
786	C₂×C₃	—	4	1	no	—
787	C₂×C₃	—	4	1	no	—
788	C₂×C₃	—	8	1	no	—
789	C₂×C₃	—	8	1	no	—
790	C₂×C₃	—	8	1	no	—
791	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
792	C₂×C₃	C₅×#575	1	1	yes	characteristic
793	C₂×C₃	C₅×#577	1	1	yes	characteristic
794	C₅	C₃×#3271	1	1	yes	characteristic, direct product factor, Sylow
795	C₂²	—	2	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	1	no	—
820	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
821	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
822	C₃	C₅×#3271	1	1	yes	characteristic, direct product factor, Sylow
823	C₂	—	4	1	no	—
824	C₂	—	4	1	no	—
825	C₂	—	8	1	no	—
826	C₂	—	8	1	no	—
827	C₂	—	8	1	no	—
828	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
829	C₂	C₃×C₅×#575	1	1	yes	characteristic
830	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. C₂×C₃×C₅×#137	C₂	semidirect
2. C₂×C₃×C₅×#135	C₂	semidirect
3. C₃×C₅×#550	C₂	semidirect
4. C₃×C₅×#548	C₂	semidirect
5. C₃×C₅×#496	C₂	semidirect
6. C₃×C₅×#469	C₂	semidirect
7. C₃×C₅×#465	C₂	semidirect
8. C₃×C₅×#464	C₂	semidirect
9. C₃×C₅×#460	C₂	semidirect
10. C₃×C₅×#452	C₂	semidirect
11. C₃×C₅×#449	C₂	semidirect
12. C₃×C₅×#449	C₂	semidirect
13. C₃×C₅×#448	C₂	semidirect
14. C₃×C₅×#441	C₂	semidirect
15. C₃×C₅×#435	C₂	semidirect
16. C₅×#3271	C₃	direct (N × H)
62. C₃×#3271	C₅	direct (N × H)
63. C₂×C₅×#137	C₂×C₃	semidirect
64. C₂×C₅×#135	C₂×C₃	semidirect
65. C₅×#550	C₂×C₃	semidirect
66. C₅×#548	C₂×C₃	semidirect
67. C₅×#496	C₂×C₃	semidirect
68. C₅×#469	C₂×C₃	semidirect
69. C₅×#465	C₂×C₃	semidirect
70. C₅×#464	C₂×C₃	semidirect
71. C₅×#460	C₂×C₃	semidirect
72. C₅×#452	C₂×C₃	semidirect
73. C₅×#449	C₂×C₃	semidirect
74. C₅×#449	C₂×C₃	semidirect
75. C₅×#448	C₂×C₃	semidirect
76. C₅×#441	C₂×C₃	semidirect
77. C₅×#435	C₂×C₃	semidirect
109. C₃×C₅×Q₁₆	D₄	semidirect
140. C₂×C₃×#137	C₂×C₅	semidirect
141. C₂×C₃×#135	C₂×C₅	semidirect
142. C₃×#550	C₂×C₅	semidirect
143. C₃×#548	C₂×C₅	semidirect
144. C₃×#496	C₂×C₅	semidirect
145. C₃×#469	C₂×C₅	semidirect
146. C₃×#465	C₂×C₅	semidirect
147. C₃×#464	C₂×C₅	semidirect
148. C₃×#460	C₂×C₅	semidirect
149. C₃×#452	C₂×C₅	semidirect
150. C₃×#449	C₂×C₅	semidirect
151. C₃×#449	C₂×C₅	semidirect
152. C₃×#448	C₂×C₅	semidirect
153. C₃×#441	C₂×C₅	semidirect
154. C₃×#435	C₂×C₅	semidirect
200. #3271	C₃×C₅	direct (N × H)
326. C₅×Q₁₆	C₃×D₄	semidirect
357. C₂×#137	C₂×C₃×C₅	semidirect
358. C₂×#135	C₂×C₃×C₅	semidirect
359. #550	C₂×C₃×C₅	semidirect
360. #548	C₂×C₃×C₅	semidirect
361. #496	C₂×C₃×C₅	semidirect
362. #469	C₂×C₃×C₅	semidirect
363. #465	C₂×C₃×C₅	semidirect
364. #464	C₂×C₃×C₅	semidirect
365. #460	C₂×C₃×C₅	semidirect
366. #452	C₂×C₃×C₅	semidirect
367. #449	C₂×C₃×C₅	semidirect
368. #449	C₂×C₃×C₅	semidirect
369. #448	C₂×C₃×C₅	semidirect
370. #441	C₂×C₃×C₅	semidirect
371. #435	C₂×C₃×C₅	semidirect
430. C₃×Q₁₆	C₅×D₄	semidirect
670. Q₁₆	C₃×C₅×D₄	semidirect
701. C₃×C₅	#3271	direct (N × H)
794. C₅	C₃×#3271	direct (N × H)
822. C₃	C₅×#3271	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#137	2
C₂×C₃×C₅×#135	2
C₃×C₅×#550	2
C₃×C₅×#548	2
C₃×C₅×#496	2
C₃×C₅×#469	2
C₃×C₅×#465	2
C₃×C₅×#464	2
C₃×C₅×#460	2
C₃×C₅×#452	2
C₃×C₅×#449	2
C₃×C₅×#448	2
C₃×C₅×#441	2
C₃×C₅×#435	2
C₅×#3271	3
C₃×#3271	5

Subgroups — C3×C5×#3271 #14276305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3271 #14276305