Subgroups — C₃×C₅×#3269 #14276303

Order 1920.

956 conjugacy classes of subgroups.

The subgroup lattice has 808 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×#548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#468	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3269	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×Q₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×Q₁₆	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×SD₁₆	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×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₃×C₅×#124	—	2	1	no	—
36	C₃×C₅×#124	C₂²	1	1	yes	characteristic
37	C₃×C₅×#123	—	2	1	no	—
38	C₃×C₅×#123	—	2	1	no	—
39	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
40	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃×C₅×#121	—	2	1	no	—
44	C₃×C₅×#121	—	2	1	no	—
45	C₃×C₅×#121	C₂²	1	1	yes	characteristic
46	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
47	C₃×C₄×C₅×D₄	—	2	1	no	—
48	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
49	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×#107	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×#103	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×#3269	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×#548	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#468	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#467	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#463	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#462	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#451	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
76	C₅×#440	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×Q₈	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
96	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₅	—	2	1	no	—
99	C₂²×C₃×C₄×C₅	—	2	1	no	—
100	C₂²×C₃×C₄×C₅	—	2	1	no	—
101	C₂²×C₃×C₄×C₅	—	2	1	no	—
102	C₂²×C₃×C₄×C₅	—	2	1	no	—
103	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
104	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
105	C₃×C₅×Q₁₆	—	2	2	no	—
106	C₃×C₅×Q₁₆	—	2	2	no	—
107	C₃×C₅×Q₁₆	—	2	2	no	—
108	C₃×C₅×Q₁₆	—	4	1	no	—
109	C₃×C₅×SD₁₆	—	2	2	no	—
110	C₃×C₅×SD₁₆	—	2	2	no	—
111	C₃×C₅×SD₁₆	—	4	1	no	—
112	C₃×C₅×SD₁₆	D₄	1	4	yes	complemented
113	C₃×C₅×D₈	—	2	2	no	—
114	C₃×C₅×M₁₆	—	2	2	no	—
115	C₂×C₃×C₅×C₈	—	2	2	no	—
116	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
117	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
118	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
119	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
120	C₃×C₅×C₄⋊C₄	—	2	1	no	—
121	C₃×C₅×C₄⋊C₄	—	2	1	no	—
122	C₃×C₅×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
136	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
137	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
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×#548	C₂×C₅	1	1	yes	characteristic, complemented
143	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#468	C₂×C₅	1	1	yes	characteristic, complemented
146	C₃×#467	C₂×C₅	1	1	yes	characteristic, complemented
147	C₃×#463	C₂×C₅	1	1	yes	characteristic, complemented
148	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
149	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
150	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
151	C₃×#451	C₂×C₅	1	1	yes	characteristic, complemented
152	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
153	C₃×#440	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×Q₁₆	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₅×Q₁₆	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×SD₁₆	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×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
173	C₅×#124	—	2	1	no	—
174	C₅×#124	C₂²×C₃	1	1	yes	characteristic
175	C₅×#123	—	2	1	no	—
176	C₅×#123	—	2	1	no	—
177	C₅×C₂²⋊Q₈	—	2	1	no	—
178	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
179	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
180	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
181	C₅×#121	—	2	1	no	—
182	C₅×#121	—	2	1	no	—
183	C₅×#121	C₂²×C₃	1	1	yes	characteristic
184	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
185	C₄×C₅×D₄	—	2	1	no	—
186	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
187	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
188	C₂×C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×#107	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×#103	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	#3269	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	C₂×D₄	1	1	yes	characteristic
204	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
205	C₃×C₅×Q₈	—	2	1	no	—
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	—	2	1	no	—
211	C₃×C₅×Q₈	—	2	1	no	—
212	C₃×C₅×Q₈	—	4	2	no	—
213	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
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	—	4	1	no	—
218	C₃×C₅×D₄	—	4	2	no	—
219	C₃×C₅×D₄	—	4	2	no	—
220	C₃×C₅×D₄	—	4	2	no	—
221	C₃×C₅×D₄	—	4	2	no	—
222	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	2	1	no	—
225	C₂×C₃×C₄×C₅	—	2	1	no	—
226	C₂×C₃×C₄×C₅	—	2	1	no	—
227	C₂×C₃×C₄×C₅	—	2	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	—	4	2	no	—
234	C₂×C₃×C₄×C₅	—	4	2	no	—
235	C₂×C₃×C₄×C₅	—	4	2	no	—
236	C₂×C₃×C₄×C₅	—	4	2	no	—
237	C₂×C₃×C₄×C₅	—	4	2	no	—
238	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
239	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
240	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
241	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
242	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
243	C₃×C₅×C₈	—	2	1	no	—
244	C₃×C₅×C₈	—	2	1	no	—
245	C₃×C₅×C₈	—	2	1	no	—
246	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
247	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
250	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
251	C₃×#137	—	2	4	no	—
252	C₃×#135	—	2	4	no	—
253	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₃×SD₁₆	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×D₈	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
263	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
264	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
265	C₃×#124	—	2	1	no	—
266	C₃×#124	C₂²×C₅	1	1	yes	characteristic
267	C₃×#123	—	2	1	no	—
268	C₃×#123	—	2	1	no	—
269	C₃×C₂²⋊Q₈	—	2	1	no	—
270	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
271	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
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	C₂²×C₅	1	1	yes	characteristic
276	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
277	C₃×C₄×D₄	—	2	1	no	—
278	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
279	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
280	C₂×C₃×C₄⋊C₄	—	2	1	no	—
281	C₃×#107	C₂²×C₅	1	1	yes	characteristic
282	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
283	C₃×#103	C₂²×C₅	1	1	yes	characteristic
284	C₃×#103	C₂²×C₅	1	1	yes	characteristic
285	C₃×#103	C₂²×C₅	1	1	yes	characteristic
286	C₃×#103	C₂²×C₅	1	1	yes	characteristic
287	C₃×#102	C₂²×C₅	1	1	yes	characteristic
288	C₃×#102	C₂²×C₅	1	1	yes	characteristic
289	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
290	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
291	C₃×#97	C₂²×C₅	1	1	yes	characteristic
292	C₅×#41	—	2	2	no	—
293	C₅×#41	—	2	2	no	—
294	C₅×#41	—	2	2	no	—
295	C₅×#41	—	4	1	no	—
296	C₅×#41	—	4	1	no	—
297	C₅×#41	—	4	1	no	—
298	C₂×C₅×Q₈	—	2	1	no	—
299	C₂×C₅×Q₈	—	2	2	no	—
300	C₂×C₅×Q₈	—	4	1	no	—
301	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
302	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
303	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
304	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
305	C₂×C₅×D₄	—	2	1	no	—
306	C₂×C₅×D₄	—	2	1	no	—
307	C₂×C₅×D₄	—	2	1	no	—
308	C₂×C₅×D₄	—	2	1	no	—
309	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
310	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
311	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
312	C₂²×C₄×C₅	—	2	1	no	—
313	C₂²×C₄×C₅	—	2	1	no	—
314	C₂²×C₄×C₅	—	2	1	no	—
315	C₂²×C₄×C₅	—	2	1	no	—
316	C₂²×C₄×C₅	—	2	1	no	—
317	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
319	C₅×Q₁₆	—	2	2	no	—
320	C₅×Q₁₆	—	2	2	no	—
321	C₅×Q₁₆	—	2	2	no	—
322	C₅×Q₁₆	—	4	1	no	—
323	C₅×SD₁₆	—	2	2	no	—
324	C₅×SD₁₆	—	2	2	no	—
325	C₅×SD₁₆	—	4	1	no	—
326	C₅×SD₁₆	C₃×D₄	1	4	yes	complemented
327	C₅×D₈	—	2	2	no	—
328	C₅×M₁₆	—	2	2	no	—
329	C₂×C₅×C₈	—	2	2	no	—
330	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
331	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
332	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
333	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
334	C₅×C₄⋊C₄	—	2	1	no	—
335	C₅×C₄⋊C₄	—	2	1	no	—
336	C₅×C₄⋊C₄	—	2	1	no	—
337	C₅×C₄⋊C₄	—	2	1	no	—
338	C₅×C₄⋊C₄	—	2	1	no	—
339	C₅×C₄⋊C₄	—	2	1	no	—
340	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
341	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
342	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
343	C₅×C₂²⋊C₄	—	2	1	no	—
344	C₅×C₂²⋊C₄	—	2	1	no	—
345	C₅×C₂²⋊C₄	—	2	1	no	—
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	C₃×D₄	1	1	yes	characteristic
351	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
352	C₄²×C₅	—	2	1	no	—
353	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
354	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
355	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
356	#548	C₂×C₃×C₅	1	1	yes	characteristic, complemented
357	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
358	#497	C₂×C₃×C₅	1	1	yes	characteristic, complemented
359	#468	C₂×C₃×C₅	1	1	yes	characteristic, complemented
360	#467	C₂×C₃×C₅	1	1	yes	characteristic, complemented
361	#463	C₂×C₃×C₅	1	1	yes	characteristic, complemented
362	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
363	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
364	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
365	#451	C₂×C₃×C₅	1	1	yes	characteristic, complemented
366	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
367	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
368	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
369	C₂²×C₃×C₅	—	2	1	no	—
370	C₂²×C₃×C₅	—	2	1	no	—
371	C₂²×C₃×C₅	—	2	2	no	—
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	—	4	1	no	—
377	C₂²×C₃×C₅	—	4	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	C₂²×D₄	1	1	yes	characteristic
382	C₃×C₄×C₅	—	2	1	no	—
383	C₃×C₄×C₅	—	2	1	no	—
384	C₃×C₄×C₅	—	2	2	no	—
385	C₃×C₄×C₅	—	2	1	no	—
386	C₃×C₄×C₅	—	2	1	no	—
387	C₃×C₄×C₅	—	4	1	no	—
388	C₃×C₄×C₅	—	4	1	no	—
389	C₃×C₄×C₅	—	4	1	no	—
390	C₃×C₄×C₅	—	4	1	no	—
391	C₃×C₄×C₅	—	4	1	no	—
392	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
393	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
394	C₃×#41	—	2	2	no	—
395	C₃×#41	—	2	2	no	—
396	C₃×#41	—	2	2	no	—
397	C₃×#41	—	4	1	no	—
398	C₃×#41	—	4	1	no	—
399	C₃×#41	—	4	1	no	—
400	C₂×C₃×Q₈	—	2	1	no	—
401	C₂×C₃×Q₈	—	2	2	no	—
402	C₂×C₃×Q₈	—	4	1	no	—
403	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
406	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
407	C₂×C₃×D₄	—	2	1	no	—
408	C₂×C₃×D₄	—	2	1	no	—
409	C₂×C₃×D₄	—	2	1	no	—
410	C₂×C₃×D₄	—	2	1	no	—
411	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
412	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
413	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
414	C₂²×C₃×C₄	—	2	1	no	—
415	C₂²×C₃×C₄	—	2	1	no	—
416	C₂²×C₃×C₄	—	2	1	no	—
417	C₂²×C₃×C₄	—	2	1	no	—
418	C₂²×C₃×C₄	—	2	1	no	—
419	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
421	C₃×Q₁₆	—	2	2	no	—
422	C₃×Q₁₆	—	2	2	no	—
423	C₃×Q₁₆	—	2	2	no	—
424	C₃×Q₁₆	—	4	1	no	—
425	C₃×SD₁₆	—	2	2	no	—
426	C₃×SD₁₆	—	2	2	no	—
427	C₃×SD₁₆	—	4	1	no	—
428	C₃×SD₁₆	C₅×D₄	1	4	yes	complemented
429	C₃×D₈	—	2	2	no	—
430	C₃×M₁₆	—	2	2	no	—
431	C₂×C₃×C₈	—	2	2	no	—
432	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
433	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
434	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
436	C₃×C₄⋊C₄	—	2	1	no	—
437	C₃×C₄⋊C₄	—	2	1	no	—
438	C₃×C₄⋊C₄	—	2	1	no	—
439	C₃×C₄⋊C₄	—	2	1	no	—
440	C₃×C₄⋊C₄	—	2	1	no	—
441	C₃×C₄⋊C₄	—	2	1	no	—
442	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
443	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
444	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
445	C₃×C₂²⋊C₄	—	2	1	no	—
446	C₃×C₂²⋊C₄	—	2	1	no	—
447	C₃×C₂²⋊C₄	—	2	1	no	—
448	C₃×C₂²⋊C₄	—	2	1	no	—
449	C₃×C₂²⋊C₄	—	2	1	no	—
450	C₃×C₂²⋊C₄	—	2	1	no	—
451	C₃×C₂²⋊C₄	—	2	1	no	—
452	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
453	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
454	C₃×C₄²	—	2	1	no	—
455	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
456	C₂³×C₅	—	2	1	no	—
457	C₂³×C₅	—	2	1	no	—
458	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
459	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
460	C₅×Q₈	—	2	1	no	—
461	C₅×Q₈	—	2	1	no	—
462	C₅×Q₈	—	2	1	no	—
463	C₅×Q₈	—	2	1	no	—
464	C₅×Q₈	—	2	1	no	—
465	C₅×Q₈	—	2	1	no	—
466	C₅×Q₈	—	2	1	no	—
467	C₅×Q₈	—	4	2	no	—
468	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
469	C₅×D₄	—	2	1	no	—
470	C₅×D₄	—	2	1	no	—
471	C₅×D₄	—	2	1	no	—
472	C₅×D₄	—	4	1	no	—
473	C₅×D₄	—	4	2	no	—
474	C₅×D₄	—	4	2	no	—
475	C₅×D₄	—	4	2	no	—
476	C₅×D₄	—	4	2	no	—
477	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
478	C₂×C₄×C₅	—	2	1	no	—
479	C₂×C₄×C₅	—	2	1	no	—
480	C₂×C₄×C₅	—	2	1	no	—
481	C₂×C₄×C₅	—	2	1	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	2	1	no	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	2	1	no	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	2	1	no	—
488	C₂×C₄×C₅	—	4	2	no	—
489	C₂×C₄×C₅	—	4	2	no	—
490	C₂×C₄×C₅	—	4	2	no	—
491	C₂×C₄×C₅	—	4	2	no	—
492	C₂×C₄×C₅	—	4	2	no	—
493	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
494	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
495	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
496	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
497	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
498	C₅×C₈	—	2	1	no	—
499	C₅×C₈	—	2	1	no	—
500	C₅×C₈	—	2	1	no	—
501	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
502	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
503	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
504	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
505	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
506	#137	—	2	4	no	—
507	#135	—	2	4	no	—
508	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
509	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
510	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
511	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
512	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
513	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
514	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
515	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
516	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
517	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
518	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
519	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
520	#124	—	2	1	no	—
521	#124	C₂²×C₃×C₅	1	1	yes	characteristic
522	#123	—	2	1	no	—
523	#123	—	2	1	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
526	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
527	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
528	#121	—	2	1	no	—
529	#121	—	2	1	no	—
530	#121	C₂²×C₃×C₅	1	1	yes	characteristic
531	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
534	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
535	C₂×C₄⋊C₄	—	2	1	no	—
536	#107	C₂²×C₃×C₅	1	1	yes	characteristic
537	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
538	#103	C₂²×C₃×C₅	1	1	yes	characteristic
539	#103	C₂²×C₃×C₅	1	1	yes	characteristic
540	#103	C₂²×C₃×C₅	1	1	yes	characteristic
541	#103	C₂²×C₃×C₅	1	1	yes	characteristic
542	#102	C₂²×C₃×C₅	1	1	yes	characteristic
543	#102	C₂²×C₃×C₅	1	1	yes	characteristic
544	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
545	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
546	#97	C₂²×C₃×C₅	1	1	yes	characteristic
547	C₂×C₃×C₅	—	4	1	no	—
548	C₂×C₃×C₅	—	4	1	no	—
549	C₂×C₃×C₅	—	4	2	no	—
550	C₂×C₃×C₅	—	8	1	no	—
551	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
552	C₂×C₃×C₅	#575	1	1	yes	characteristic
553	C₂×C₃×C₅	#578	1	1	yes	characteristic
554	C₂³×C₃	—	2	1	no	—
555	C₂³×C₃	—	2	1	no	—
556	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
557	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
558	C₃×Q₈	—	2	1	no	—
559	C₃×Q₈	—	2	1	no	—
560	C₃×Q₈	—	2	1	no	—
561	C₃×Q₈	—	2	1	no	—
562	C₃×Q₈	—	2	1	no	—
563	C₃×Q₈	—	2	1	no	—
564	C₃×Q₈	—	2	1	no	—
565	C₃×Q₈	—	4	2	no	—
566	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
567	C₃×D₄	—	2	1	no	—
568	C₃×D₄	—	2	1	no	—
569	C₃×D₄	—	2	1	no	—
570	C₃×D₄	—	4	1	no	—
571	C₃×D₄	—	4	2	no	—
572	C₃×D₄	—	4	2	no	—
573	C₃×D₄	—	4	2	no	—
574	C₃×D₄	—	4	2	no	—
575	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	2	1	no	—
582	C₂×C₃×C₄	—	2	1	no	—
583	C₂×C₃×C₄	—	2	1	no	—
584	C₂×C₃×C₄	—	2	1	no	—
585	C₂×C₃×C₄	—	2	1	no	—
586	C₂×C₃×C₄	—	4	2	no	—
587	C₂×C₃×C₄	—	4	2	no	—
588	C₂×C₃×C₄	—	4	2	no	—
589	C₂×C₃×C₄	—	4	2	no	—
590	C₂×C₃×C₄	—	4	2	no	—
591	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
592	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
593	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
594	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
595	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
596	C₃×C₈	—	2	1	no	—
597	C₃×C₈	—	2	1	no	—
598	C₃×C₈	—	2	1	no	—
599	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
600	C₂²×C₅	—	2	1	no	—
601	C₂²×C₅	—	2	1	no	—
602	C₂²×C₅	—	2	1	no	—
603	C₂²×C₅	—	2	1	no	—
604	C₂²×C₅	—	2	1	no	—
605	C₂²×C₅	—	2	1	no	—
606	C₂²×C₅	—	2	2	no	—
607	C₂²×C₅	—	4	1	no	—
608	C₂²×C₅	—	4	1	no	—
609	C₂²×C₅	—	4	1	no	—
610	C₂²×C₅	—	4	1	no	—
611	C₂²×C₅	—	4	1	no	—
612	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
613	C₄×C₅	—	2	1	no	—
614	C₄×C₅	—	2	1	no	—
615	C₄×C₅	—	2	1	no	—
616	C₄×C₅	—	2	1	no	—
617	C₄×C₅	—	2	2	no	—
618	C₄×C₅	—	4	1	no	—
619	C₄×C₅	—	4	1	no	—
620	C₄×C₅	—	4	1	no	—
621	C₄×C₅	—	4	1	no	—
622	C₄×C₅	—	4	1	no	—
623	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
624	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
625	#41	—	2	2	no	—
626	#41	—	2	2	no	—
627	#41	—	2	2	no	—
628	#41	—	4	1	no	—
629	#41	—	4	1	no	—
630	#41	—	4	1	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	2	no	—
633	C₂×Q₈	—	4	1	no	—
634	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
635	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
636	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
637	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
643	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
644	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
651	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
652	Q₁₆	—	2	2	no	—
653	Q₁₆	—	2	2	no	—
654	Q₁₆	—	2	2	no	—
655	Q₁₆	—	4	1	no	—
656	SD₁₆	—	2	2	no	—
657	SD₁₆	—	2	2	no	—
658	SD₁₆	—	4	1	no	—
659	SD₁₆	C₃×C₅×D₄	1	4	yes	complemented
660	D₈	—	2	2	no	—
661	M₁₆	—	2	2	no	—
662	C₂×C₈	—	2	2	no	—
663	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
664	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
665	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
666	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
674	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
675	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
676	C₂²⋊C₄	—	2	1	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	1	no	—
679	C₂²⋊C₄	—	2	1	no	—
680	C₂²⋊C₄	—	2	1	no	—
681	C₂²⋊C₄	—	2	1	no	—
682	C₂²⋊C₄	—	2	1	no	—
683	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
684	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
685	C₄²	—	2	1	no	—
686	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
687	C₃×C₅	#3269	1	1	yes	characteristic, direct product factor, Hall
688	C₂²×C₃	—	2	1	no	—
689	C₂²×C₃	—	2	1	no	—
690	C₂²×C₃	—	2	2	no	—
691	C₂²×C₃	—	2	1	no	—
692	C₂²×C₃	—	2	1	no	—
693	C₂²×C₃	—	2	1	no	—
694	C₂²×C₃	—	2	1	no	—
695	C₂²×C₃	—	4	1	no	—
696	C₂²×C₃	—	4	1	no	—
697	C₂²×C₃	—	4	1	no	—
698	C₂²×C₃	—	4	1	no	—
699	C₂²×C₃	—	4	1	no	—
700	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
701	C₃×C₄	—	2	1	no	—
702	C₃×C₄	—	2	1	no	—
703	C₃×C₄	—	2	2	no	—
704	C₃×C₄	—	2	1	no	—
705	C₃×C₄	—	2	1	no	—
706	C₃×C₄	—	4	1	no	—
707	C₃×C₄	—	4	1	no	—
708	C₃×C₄	—	4	1	no	—
709	C₃×C₄	—	4	1	no	—
710	C₃×C₄	—	4	1	no	—
711	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
712	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
713	C₂×C₅	—	4	1	no	—
714	C₂×C₅	—	4	1	no	—
715	C₂×C₅	—	4	2	no	—
716	C₂×C₅	—	8	1	no	—
717	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
718	C₂×C₅	C₃×#575	1	1	yes	characteristic
719	C₂×C₅	C₃×#578	1	1	yes	characteristic
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
723	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
724	Q₈	—	2	1	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	2	1	no	—
727	Q₈	—	2	1	no	—
728	Q₈	—	2	1	no	—
729	Q₈	—	2	1	no	—
730	Q₈	—	2	1	no	—
731	Q₈	—	4	2	no	—
732	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
733	D₄	—	2	1	no	—
734	D₄	—	2	1	no	—
735	D₄	—	2	1	no	—
736	D₄	—	4	1	no	—
737	D₄	—	4	2	no	—
738	D₄	—	4	2	no	—
739	D₄	—	4	2	no	—
740	D₄	—	4	2	no	—
741	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
758	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
759	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
760	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
761	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
762	C₈	—	2	1	no	—
763	C₈	—	2	1	no	—
764	C₈	—	2	1	no	—
765	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
766	C₂×C₃	—	4	1	no	—
767	C₂×C₃	—	4	1	no	—
768	C₂×C₃	—	4	2	no	—
769	C₂×C₃	—	8	1	no	—
770	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
771	C₂×C₃	C₅×#575	1	1	yes	characteristic
772	C₂×C₃	C₅×#578	1	1	yes	characteristic
773	C₅	C₃×#3269	1	1	yes	characteristic, direct product factor, Sylow
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	1	no	—
791	C₄	—	2	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	1	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	1	no	—
797	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
798	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
799	C₃	C₅×#3269	1	1	yes	characteristic, direct product factor, Sylow
800	C₂	—	4	1	no	—
801	C₂	—	4	1	no	—
802	C₂	—	4	2	no	—
803	C₂	—	8	1	no	—
804	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
805	C₂	C₃×C₅×#575	1	1	yes	characteristic
806	C₂	C₃×C₅×#578	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#137	C₂	semidirect
2. C₂×C₃×C₅×#135	C₂	semidirect
3. C₃×C₅×#548	C₂	semidirect
4. C₃×C₅×#547	C₂	semidirect
5. C₃×C₅×#497	C₂	semidirect
6. C₃×C₅×#468	C₂	semidirect
7. C₃×C₅×#467	C₂	semidirect
8. C₃×C₅×#463	C₂	semidirect
9. C₃×C₅×#462	C₂	semidirect
10. C₃×C₅×#452	C₂	semidirect
11. C₃×C₅×#452	C₂	semidirect
12. C₃×C₅×#451	C₂	semidirect
13. C₃×C₅×#449	C₂	semidirect
14. C₃×C₅×#440	C₂	semidirect
15. C₃×C₅×#435	C₂	semidirect
16. C₅×#3269	C₃	direct (N × H)
62. C₃×#3269	C₅	direct (N × H)
63. C₂×C₅×#137	C₂×C₃	semidirect
64. C₂×C₅×#135	C₂×C₃	semidirect
65. C₅×#548	C₂×C₃	semidirect
66. C₅×#547	C₂×C₃	semidirect
67. C₅×#497	C₂×C₃	semidirect
68. C₅×#468	C₂×C₃	semidirect
69. C₅×#467	C₂×C₃	semidirect
70. C₅×#463	C₂×C₃	semidirect
71. C₅×#462	C₂×C₃	semidirect
72. C₅×#452	C₂×C₃	semidirect
73. C₅×#452	C₂×C₃	semidirect
74. C₅×#451	C₂×C₃	semidirect
75. C₅×#449	C₂×C₃	semidirect
76. C₅×#440	C₂×C₃	semidirect
77. C₅×#435	C₂×C₃	semidirect
112. C₃×C₅×SD₁₆	D₄	semidirect
140. C₂×C₃×#137	C₂×C₅	semidirect
141. C₂×C₃×#135	C₂×C₅	semidirect
142. C₃×#548	C₂×C₅	semidirect
143. C₃×#547	C₂×C₅	semidirect
144. C₃×#497	C₂×C₅	semidirect
145. C₃×#468	C₂×C₅	semidirect
146. C₃×#467	C₂×C₅	semidirect
147. C₃×#463	C₂×C₅	semidirect
148. C₃×#462	C₂×C₅	semidirect
149. C₃×#452	C₂×C₅	semidirect
150. C₃×#452	C₂×C₅	semidirect
151. C₃×#451	C₂×C₅	semidirect
152. C₃×#449	C₂×C₅	semidirect
153. C₃×#440	C₂×C₅	semidirect
154. C₃×#435	C₂×C₅	semidirect
200. #3269	C₃×C₅	direct (N × H)
326. C₅×SD₁₆	C₃×D₄	semidirect
354. C₂×#137	C₂×C₃×C₅	semidirect
355. C₂×#135	C₂×C₃×C₅	semidirect
356. #548	C₂×C₃×C₅	semidirect
357. #547	C₂×C₃×C₅	semidirect
358. #497	C₂×C₃×C₅	semidirect
359. #468	C₂×C₃×C₅	semidirect
360. #467	C₂×C₃×C₅	semidirect
361. #463	C₂×C₃×C₅	semidirect
362. #462	C₂×C₃×C₅	semidirect
363. #452	C₂×C₃×C₅	semidirect
364. #452	C₂×C₃×C₅	semidirect
365. #451	C₂×C₃×C₅	semidirect
366. #449	C₂×C₃×C₅	semidirect
367. #440	C₂×C₃×C₅	semidirect
368. #435	C₂×C₃×C₅	semidirect
428. C₃×SD₁₆	C₅×D₄	semidirect
659. SD₁₆	C₃×C₅×D₄	semidirect
687. C₃×C₅	#3269	direct (N × H)
773. C₅	C₃×#3269	direct (N × H)
799. C₃	C₅×#3269	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×#548	2
C₃×C₅×#547	2
C₃×C₅×#497	2
C₃×C₅×#468	2
C₃×C₅×#467	2
C₃×C₅×#463	2
C₃×C₅×#462	2
C₃×C₅×#452	2
C₃×C₅×#451	2
C₃×C₅×#449	2
C₃×C₅×#440	2
C₃×C₅×#435	2
C₅×#3269	3
C₃×#3269	5

Subgroups — C3×C5×#3269 #14276303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3269 #14276303