Subgroups — C₃×C₅×#3270 #14276304

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 792 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	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#548	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#470	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×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#451	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×#3270	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×#137	—	2	4	no	—
22	C₂×C₃×C₅×Q₁₆	—	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×Q₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×Q₁₆	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×SD₁₆	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	—	2	1	no	—
35	C₃×C₅×C₄⋊Q₈	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	—	2	1	no	—
40	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
41	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
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×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×#103	C₂²	1	1	yes	characteristic
57	C₃×C₅×#103	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×#3270	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂²×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#548	C₂×C₃	1	1	yes	characteristic
67	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#470	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×#462	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#451	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#451	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	—	4	1	no	—
80	C₂×C₃×C₅×Q₈	—	2	1	no	—
81	C₂×C₃×C₅×Q₈	—	2	1	no	—
82	C₂×C₃×C₅×Q₈	—	2	1	no	—
83	C₂×C₃×C₅×Q₈	—	2	2	no	—
84	C₂×C₃×C₅×Q₈	—	2	2	no	—
85	C₂×C₃×C₅×Q₈	—	2	2	no	—
86	C₂×C₃×C₅×Q₈	—	4	1	no	—
87	C₂×C₃×C₅×Q₈	—	4	1	no	—
88	C₂×C₃×C₅×Q₈	—	4	1	no	—
89	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₅×D₄	—	2	1	no	—
95	C₂×C₃×C₅×D₄	—	2	1	no	—
96	C₂×C₃×C₅×D₄	D₄	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	C₂³	1	1	yes	characteristic
103	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
104	C₃×C₅×Q₁₆	—	2	2	no	—
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×Q₁₆	D₄	1	4	yes	complemented
110	C₃×C₅×SD₁₆	—	2	2	no	—
111	C₃×C₅×SD₁₆	—	2	2	no	—
112	C₃×C₅×SD₁₆	—	4	1	no	—
113	C₃×C₅×M₁₆	—	2	2	no	—
114	C₂×C₃×C₅×C₈	—	2	2	no	—
115	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
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	C₃×C₅×C₄⋊C₄	—	2	1	no	—
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	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	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
143	C₃×#548	C₂×C₅	1	1	yes	characteristic
144	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#470	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×#462	C₂×C₅	1	1	yes	characteristic, complemented
149	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
150	C₃×#451	C₂×C₅	1	1	yes	characteristic, complemented
151	C₃×#451	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	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
157	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₅×#137	—	2	4	no	—
160	C₂×C₅×Q₁₆	—	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×Q₁₆	C₂²×C₃	1	1	yes	characteristic
166	C₂×C₅×Q₁₆	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×SD₁₆	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	—	2	1	no	—
173	C₅×C₄⋊Q₈	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	—	2	1	no	—
178	C₅×C₂²⋊Q₈	—	2	1	no	—
179	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
180	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
181	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
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×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×#103	C₂²×C₃	1	1	yes	characteristic
195	C₅×#103	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	#3270	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
201	C₂³×C₃×C₅	—	2	1	no	—
202	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
204	C₃×C₅×Q₈	—	2	1	no	—
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	—	4	2	no	—
214	C₃×C₅×Q₈	—	4	2	no	—
215	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
216	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
217	C₃×C₅×D₄	—	2	2	no	—
218	C₃×C₅×D₄	—	2	1	no	—
219	C₃×C₅×D₄	—	2	1	no	—
220	C₃×C₅×D₄	—	4	2	no	—
221	C₃×C₅×D₄	—	4	2	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
242	C₃×C₅×C₈	—	2	1	no	—
243	C₃×C₅×C₈	—	2	1	no	—
244	C₃×C₅×C₈	—	2	1	no	—
245	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
246	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
247	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
248	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
249	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
250	C₃×#137	—	2	4	no	—
251	C₂×C₃×Q₁₆	—	2	4	no	—
252	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
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×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×M₁₆	C₂²×C₅	1	1	yes	characteristic
262	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
263	C₃×C₄⋊Q₈	—	2	1	no	—
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×C₂²⋊Q₈	—	2	1	no	—
268	C₃×C₂²⋊Q₈	—	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	C₂²×C₅	1	1	yes	characteristic
275	C₃×C₄×Q₈	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	—	2	1	no	—
279	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
280	C₃×#106	C₂²×C₅	1	1	yes	characteristic
281	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
282	C₃×#103	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×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
289	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
290	C₃×#97	C₂²×C₅	1	1	yes	characteristic
291	C₅×#41	—	2	2	no	—
292	C₅×#41	—	4	1	no	—
293	C₂×C₅×Q₈	—	2	1	no	—
294	C₂×C₅×Q₈	—	2	1	no	—
295	C₂×C₅×Q₈	—	2	1	no	—
296	C₂×C₅×Q₈	—	2	2	no	—
297	C₂×C₅×Q₈	—	2	2	no	—
298	C₂×C₅×Q₈	—	2	2	no	—
299	C₂×C₅×Q₈	—	4	1	no	—
300	C₂×C₅×Q₈	—	4	1	no	—
301	C₂×C₅×Q₈	—	4	1	no	—
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×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	C₃×D₄	1	1	yes	characteristic
310	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
311	C₂²×C₄×C₅	—	2	1	no	—
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	C₂³×C₃	1	1	yes	characteristic
316	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
317	C₅×Q₁₆	—	2	2	no	—
318	C₅×Q₁₆	—	2	2	no	—
319	C₅×Q₁₆	—	2	2	no	—
320	C₅×Q₁₆	—	2	2	no	—
321	C₅×Q₁₆	—	4	1	no	—
322	C₅×Q₁₆	C₃×D₄	1	4	yes	complemented
323	C₅×SD₁₆	—	2	2	no	—
324	C₅×SD₁₆	—	2	2	no	—
325	C₅×SD₁₆	—	4	1	no	—
326	C₅×M₁₆	—	2	2	no	—
327	C₂×C₅×C₈	—	2	2	no	—
328	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
329	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
330	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
331	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
332	C₅×C₄⋊C₄	—	2	1	no	—
333	C₅×C₄⋊C₄	—	2	1	no	—
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	C₃×D₄	1	1	yes	characteristic
340	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
341	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
342	C₅×C₂²⋊C₄	—	2	1	no	—
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	C₃×D₄	1	1	yes	characteristic
349	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
350	C₄²×C₅	—	2	1	no	—
351	C₄²×C₅	—	2	1	no	—
352	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
353	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
354	C₂²×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
355	D₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
356	#548	C₂×C₃×C₅	1	1	yes	characteristic
357	#497	C₂×C₃×C₅	1	1	yes	characteristic, complemented
358	#470	C₂×C₃×C₅	1	1	yes	characteristic, complemented
359	#465	C₂×C₃×C₅	1	1	yes	characteristic, complemented
360	#464	C₂×C₃×C₅	1	1	yes	characteristic, complemented
361	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
362	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
363	#451	C₂×C₃×C₅	1	1	yes	characteristic, complemented
364	#451	C₂×C₃×C₅	1	1	yes	characteristic, complemented
365	#448	C₂×C₃×C₅	1	1	yes	characteristic, complemented
366	#441	C₂×C₃×C₅	1	1	yes	characteristic, complemented
367	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
368	C₂²×C₃×C₅	—	2	1	no	—
369	C₂²×C₃×C₅	—	2	1	no	—
370	C₂²×C₃×C₅	—	2	1	no	—
371	C₂²×C₃×C₅	—	2	1	no	—
372	C₂²×C₃×C₅	—	2	1	no	—
373	C₂²×C₃×C₅	—	4	1	no	—
374	C₂²×C₃×C₅	—	4	1	no	—
375	C₂²×C₃×C₅	—	4	1	no	—
376	C₂²×C₃×C₅	#137	1	2	yes	complemented
377	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
378	C₃×C₄×C₅	—	2	1	no	—
379	C₃×C₄×C₅	—	2	1	no	—
380	C₃×C₄×C₅	—	2	2	no	—
381	C₃×C₄×C₅	—	2	2	no	—
382	C₃×C₄×C₅	—	2	1	no	—
383	C₃×C₄×C₅	—	2	1	no	—
384	C₃×C₄×C₅	—	4	1	no	—
385	C₃×C₄×C₅	—	4	1	no	—
386	C₃×C₄×C₅	—	4	1	no	—
387	C₃×C₄×C₅	—	4	1	no	—
388	C₃×C₄×C₅	—	4	1	no	—
389	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
390	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
391	C₃×#41	—	2	2	no	—
392	C₃×#41	—	4	1	no	—
393	C₂×C₃×Q₈	—	2	1	no	—
394	C₂×C₃×Q₈	—	2	1	no	—
395	C₂×C₃×Q₈	—	2	1	no	—
396	C₂×C₃×Q₈	—	2	2	no	—
397	C₂×C₃×Q₈	—	2	2	no	—
398	C₂×C₃×Q₈	—	2	2	no	—
399	C₂×C₃×Q₈	—	4	1	no	—
400	C₂×C₃×Q₈	—	4	1	no	—
401	C₂×C₃×Q₈	—	4	1	no	—
402	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
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	C₅×D₄	1	1	yes	characteristic
410	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
411	C₂²×C₃×C₄	—	2	1	no	—
412	C₂²×C₃×C₄	—	2	1	no	—
413	C₂²×C₃×C₄	—	2	1	no	—
414	C₂²×C₃×C₄	—	2	1	no	—
415	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
416	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
417	C₃×Q₁₆	—	2	2	no	—
418	C₃×Q₁₆	—	2	2	no	—
419	C₃×Q₁₆	—	2	2	no	—
420	C₃×Q₁₆	—	2	2	no	—
421	C₃×Q₁₆	—	4	1	no	—
422	C₃×Q₁₆	C₅×D₄	1	4	yes	complemented
423	C₃×SD₁₆	—	2	2	no	—
424	C₃×SD₁₆	—	2	2	no	—
425	C₃×SD₁₆	—	4	1	no	—
426	C₃×M₁₆	—	2	2	no	—
427	C₂×C₃×C₈	—	2	2	no	—
428	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
429	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
430	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
431	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
432	C₃×C₄⋊C₄	—	2	1	no	—
433	C₃×C₄⋊C₄	—	2	1	no	—
434	C₃×C₄⋊C₄	—	2	1	no	—
435	C₃×C₄⋊C₄	—	2	1	no	—
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	C₅×D₄	1	1	yes	characteristic
440	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
441	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
442	C₃×C₂²⋊C₄	—	2	1	no	—
443	C₃×C₂²⋊C₄	—	2	1	no	—
444	C₃×C₂²⋊C₄	—	2	1	no	—
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	C₅×D₄	1	1	yes	characteristic
449	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
450	C₃×C₄²	—	2	1	no	—
451	C₃×C₄²	—	2	1	no	—
452	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
453	C₂³×C₅	—	2	1	no	—
454	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
455	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
456	C₅×Q₈	—	2	1	no	—
457	C₅×Q₈	—	2	1	no	—
458	C₅×Q₈	—	2	1	no	—
459	C₅×Q₈	—	2	1	no	—
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	—	4	2	no	—
465	C₅×Q₈	—	4	2	no	—
466	C₅×Q₈	—	4	2	no	—
467	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
468	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
469	C₅×D₄	—	2	2	no	—
470	C₅×D₄	—	2	1	no	—
471	C₅×D₄	—	2	1	no	—
472	C₅×D₄	—	4	2	no	—
473	C₅×D₄	—	4	2	no	—
474	C₂×C₄×C₅	—	2	1	no	—
475	C₂×C₄×C₅	—	2	1	no	—
476	C₂×C₄×C₅	—	2	1	no	—
477	C₂×C₄×C₅	—	2	1	no	—
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	—	4	2	no	—
486	C₂×C₄×C₅	—	4	2	no	—
487	C₂×C₄×C₅	—	4	2	no	—
488	C₂×C₄×C₅	—	4	2	no	—
489	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
490	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
491	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
492	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
493	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
494	C₅×C₈	—	2	1	no	—
495	C₅×C₈	—	2	1	no	—
496	C₅×C₈	—	2	1	no	—
497	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
498	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
499	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
500	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
501	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
502	#137	—	2	4	no	—
503	C₂×Q₁₆	—	2	4	no	—
504	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
505	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
506	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
507	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
508	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
509	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
510	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
511	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
512	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
513	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
514	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
515	C₄⋊Q₈	—	2	1	no	—
516	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
517	#124	—	2	1	no	—
518	#124	C₂²×C₃×C₅	1	1	yes	characteristic
519	C₂²⋊Q₈	—	2	1	no	—
520	C₂²⋊Q₈	—	2	1	no	—
521	C₂²⋊Q₈	—	2	1	no	—
522	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
523	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
524	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
525	#121	—	2	1	no	—
526	#121	C₂²×C₃×C₅	1	1	yes	characteristic
527	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
528	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
532	#106	C₂²×C₃×C₅	1	1	yes	characteristic
533	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
534	#103	C₂²×C₃×C₅	1	1	yes	characteristic
535	#103	C₂²×C₃×C₅	1	1	yes	characteristic
536	#103	C₂²×C₃×C₅	1	1	yes	characteristic
537	#103	C₂²×C₃×C₅	1	1	yes	characteristic
538	#103	C₂²×C₃×C₅	1	1	yes	characteristic
539	#102	C₂²×C₃×C₅	1	1	yes	characteristic
540	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
541	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
542	#97	C₂²×C₃×C₅	1	1	yes	characteristic
543	C₂×C₃×C₅	—	2	2	no	—
544	C₂×C₃×C₅	—	4	1	no	—
545	C₂×C₃×C₅	—	8	1	no	—
546	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
547	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
548	C₂×C₃×C₅	#578	1	1	yes	characteristic
549	C₂³×C₃	—	2	1	no	—
550	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
551	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
552	C₃×Q₈	—	2	1	no	—
553	C₃×Q₈	—	2	1	no	—
554	C₃×Q₈	—	2	1	no	—
555	C₃×Q₈	—	2	1	no	—
556	C₃×Q₈	—	2	1	no	—
557	C₃×Q₈	—	2	1	no	—
558	C₃×Q₈	—	2	1	no	—
559	C₃×Q₈	—	2	1	no	—
560	C₃×Q₈	—	4	2	no	—
561	C₃×Q₈	—	4	2	no	—
562	C₃×Q₈	—	4	2	no	—
563	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
564	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
565	C₃×D₄	—	2	2	no	—
566	C₃×D₄	—	2	1	no	—
567	C₃×D₄	—	2	1	no	—
568	C₃×D₄	—	4	2	no	—
569	C₃×D₄	—	4	2	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	1	no	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	2	1	no	—
575	C₂×C₃×C₄	—	2	1	no	—
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	—	4	2	no	—
582	C₂×C₃×C₄	—	4	2	no	—
583	C₂×C₃×C₄	—	4	2	no	—
584	C₂×C₃×C₄	—	4	2	no	—
585	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
586	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
587	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
588	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
589	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
590	C₃×C₈	—	2	1	no	—
591	C₃×C₈	—	2	1	no	—
592	C₃×C₈	—	2	1	no	—
593	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
594	C₂²×C₅	—	2	1	no	—
595	C₂²×C₅	—	2	1	no	—
596	C₂²×C₅	—	2	1	no	—
597	C₂²×C₅	—	2	1	no	—
598	C₂²×C₅	—	2	1	no	—
599	C₂²×C₅	—	4	1	no	—
600	C₂²×C₅	—	4	1	no	—
601	C₂²×C₅	—	4	1	no	—
602	C₂²×C₅	C₃×#137	1	2	yes	complemented
603	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
604	C₄×C₅	—	2	1	no	—
605	C₄×C₅	—	2	1	no	—
606	C₄×C₅	—	2	1	no	—
607	C₄×C₅	—	2	1	no	—
608	C₄×C₅	—	2	2	no	—
609	C₄×C₅	—	2	2	no	—
610	C₄×C₅	—	4	1	no	—
611	C₄×C₅	—	4	1	no	—
612	C₄×C₅	—	4	1	no	—
613	C₄×C₅	—	4	1	no	—
614	C₄×C₅	—	4	1	no	—
615	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
616	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
617	#41	—	2	2	no	—
618	#41	—	4	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	4	1	no	—
626	C₂×Q₈	—	4	1	no	—
627	C₂×Q₈	—	4	1	no	—
628	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
629	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
630	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
631	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
632	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
636	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
642	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
643	Q₁₆	—	2	2	no	—
644	Q₁₆	—	2	2	no	—
645	Q₁₆	—	2	2	no	—
646	Q₁₆	—	2	2	no	—
647	Q₁₆	—	4	1	no	—
648	Q₁₆	C₃×C₅×D₄	1	4	yes	complemented
649	SD₁₆	—	2	2	no	—
650	SD₁₆	—	2	2	no	—
651	SD₁₆	—	4	1	no	—
652	M₁₆	—	2	2	no	—
653	C₂×C₈	—	2	2	no	—
654	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
655	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
656	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
657	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
666	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
667	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	2	1	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
675	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
676	C₄²	—	2	1	no	—
677	C₄²	—	2	1	no	—
678	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
679	C₃×C₅	#3270	1	1	yes	characteristic, direct product factor, Hall
680	C₂²×C₃	—	2	1	no	—
681	C₂²×C₃	—	2	1	no	—
682	C₂²×C₃	—	2	1	no	—
683	C₂²×C₃	—	2	1	no	—
684	C₂²×C₃	—	2	1	no	—
685	C₂²×C₃	—	4	1	no	—
686	C₂²×C₃	—	4	1	no	—
687	C₂²×C₃	—	4	1	no	—
688	C₂²×C₃	C₅×#137	1	2	yes	complemented
689	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
690	C₃×C₄	—	2	1	no	—
691	C₃×C₄	—	2	1	no	—
692	C₃×C₄	—	2	2	no	—
693	C₃×C₄	—	2	2	no	—
694	C₃×C₄	—	2	1	no	—
695	C₃×C₄	—	2	1	no	—
696	C₃×C₄	—	4	1	no	—
697	C₃×C₄	—	4	1	no	—
698	C₃×C₄	—	4	1	no	—
699	C₃×C₄	—	4	1	no	—
700	C₃×C₄	—	4	1	no	—
701	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
702	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
703	C₂×C₅	—	2	2	no	—
704	C₂×C₅	—	4	1	no	—
705	C₂×C₅	—	8	1	no	—
706	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
707	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
708	C₂×C₅	C₃×#578	1	1	yes	characteristic
709	C₂³	—	2	1	no	—
710	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
711	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
712	Q₈	—	2	1	no	—
713	Q₈	—	2	1	no	—
714	Q₈	—	2	1	no	—
715	Q₈	—	2	1	no	—
716	Q₈	—	2	1	no	—
717	Q₈	—	2	1	no	—
718	Q₈	—	2	1	no	—
719	Q₈	—	2	1	no	—
720	Q₈	—	4	2	no	—
721	Q₈	—	4	2	no	—
722	Q₈	—	4	2	no	—
723	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
724	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
725	D₄	—	2	2	no	—
726	D₄	—	2	1	no	—
727	D₄	—	2	1	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
746	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
747	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
748	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
749	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
750	C₈	—	2	1	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
754	C₂×C₃	—	2	2	no	—
755	C₂×C₃	—	4	1	no	—
756	C₂×C₃	—	8	1	no	—
757	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
758	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
759	C₂×C₃	C₅×#578	1	1	yes	characteristic
760	C₅	C₃×#3270	1	1	yes	characteristic, direct product factor, Sylow
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	C₃×C₅×#137	1	2	yes	complemented
770	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
771	C₄	—	2	1	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	2	no	—
774	C₄	—	2	2	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	1	no	—
777	C₄	—	4	1	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	1	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	1	no	—
782	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
783	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
784	C₃	C₅×#3270	1	1	yes	characteristic, direct product factor, Sylow
785	C₂	—	2	2	no	—
786	C₂	—	4	1	no	—
787	C₂	—	8	1	no	—
788	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
789	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
790	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
prime radical	C₃×C₅×#548	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. C₂×C₃×C₅×#137	C₂	semidirect
2. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
3. C₃×C₅×D₄×Q₈	C₂	semidirect
5. C₃×C₅×#497	C₂	semidirect
6. C₃×C₅×#470	C₂	semidirect
7. C₃×C₅×#465	C₂	semidirect
8. C₃×C₅×#464	C₂	semidirect
9. C₃×C₅×#462	C₂	semidirect
10. C₃×C₅×#452	C₂	semidirect
11. C₃×C₅×#451	C₂	semidirect
12. C₃×C₅×#451	C₂	semidirect
13. C₃×C₅×#448	C₂	semidirect
14. C₃×C₅×#441	C₂	semidirect
15. C₃×C₅×#435	C₂	semidirect
16. C₅×#3270	C₃	direct (N × H)
62. C₃×#3270	C₅	direct (N × H)
63. C₂×C₅×#137	C₂×C₃	semidirect
64. C₂²×C₅×Q₁₆	C₂×C₃	semidirect
65. C₅×D₄×Q₈	C₂×C₃	semidirect
67. C₅×#497	C₂×C₃	semidirect
68. C₅×#470	C₂×C₃	semidirect
69. C₅×#465	C₂×C₃	semidirect
70. C₅×#464	C₂×C₃	semidirect
71. C₅×#462	C₂×C₃	semidirect
72. C₅×#452	C₂×C₃	semidirect
73. C₅×#451	C₂×C₃	semidirect
74. C₅×#451	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. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
142. C₃×D₄×Q₈	C₂×C₅	semidirect
144. C₃×#497	C₂×C₅	semidirect
145. C₃×#470	C₂×C₅	semidirect
146. C₃×#465	C₂×C₅	semidirect
147. C₃×#464	C₂×C₅	semidirect
148. C₃×#462	C₂×C₅	semidirect
149. C₃×#452	C₂×C₅	semidirect
150. C₃×#451	C₂×C₅	semidirect
151. C₃×#451	C₂×C₅	semidirect
152. C₃×#448	C₂×C₅	semidirect
153. C₃×#441	C₂×C₅	semidirect
154. C₃×#435	C₂×C₅	semidirect
200. #3270	C₃×C₅	direct (N × H)
322. C₅×Q₁₆	C₃×D₄	semidirect
353. C₂×#137	C₂×C₃×C₅	semidirect
354. C₂²×Q₁₆	C₂×C₃×C₅	semidirect
355. D₄×Q₈	C₂×C₃×C₅	semidirect
357. #497	C₂×C₃×C₅	semidirect
358. #470	C₂×C₃×C₅	semidirect
359. #465	C₂×C₃×C₅	semidirect
360. #464	C₂×C₃×C₅	semidirect
361. #462	C₂×C₃×C₅	semidirect
362. #452	C₂×C₃×C₅	semidirect
363. #451	C₂×C₃×C₅	semidirect
364. #451	C₂×C₃×C₅	semidirect
365. #448	C₂×C₃×C₅	semidirect
366. #441	C₂×C₃×C₅	semidirect
367. #435	C₂×C₃×C₅	semidirect
376. C₂²×C₃×C₅	#137	semidirect
422. C₃×Q₁₆	C₅×D₄	semidirect
602. C₂²×C₅	C₃×#137	semidirect
648. Q₁₆	C₃×C₅×D₄	semidirect
679. C₃×C₅	#3270	direct (N × H)
688. C₂²×C₃	C₅×#137	semidirect
760. C₅	C₃×#3270	direct (N × H)
769. C₂²	C₃×C₅×#137	semidirect
784. C₃	C₅×#3270	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
C₂²×C₃×C₅×Q₁₆	2
C₃×C₅×D₄×Q₈	2
C₃×C₅×#548	2
C₃×C₅×#497	2
C₃×C₅×#470	2
C₃×C₅×#465	2
C₃×C₅×#464	2
C₃×C₅×#462	2
C₃×C₅×#452	2
C₃×C₅×#451	2
C₃×C₅×#448	2
C₃×C₅×#441	2
C₃×C₅×#435	2
C₅×#3270	3
C₃×#3270	5

Subgroups — C3×C5×#3270 #14276304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3270 #14276304