Subgroups — C₃×C₅×#2692 #14275726

Order 1920.

1072 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#396	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
11	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic
13	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic
14	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2692	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
23	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
44	C₃×C₅×#95	C₂²	1	1	yes	characteristic
45	C₃×C₅×#95	C₂²	1	1	yes	characteristic
46	C₃×C₅×#95	C₂²	1	1	yes	characteristic
47	C₃×C₅×#95	C₂²	1	1	yes	characteristic
48	C₃×C₅×#95	C₂²	1	1	yes	characteristic
49	C₃×C₅×#95	C₂²	1	1	yes	characteristic
50	C₃×C₅×#95	C₂²	1	1	yes	characteristic
51	C₃×C₅×#95	C₂²	1	1	yes	characteristic
52	C₃×C₅×#95	C₂²	1	1	yes	characteristic
53	C₃×C₅×#95	C₂²	1	1	yes	characteristic
54	C₃×#2692	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
55	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#399	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#398	C₂×C₃	1	1	yes	characteristic, complemented
59	C₅×#396	C₂×C₃	1	1	yes	characteristic, complemented
60	C₅×#395	C₂×C₃	1	1	yes	characteristic, complemented
61	C₅×#393	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#393	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#390	C₂×C₃	1	1	yes	characteristic
65	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#386	C₂×C₃	1	1	yes	characteristic
67	C₅×#386	C₂×C₃	1	1	yes	characteristic
68	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
71	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×Q₈	—	2	2	no	—
73	C₂×C₃×C₅×Q₈	—	2	2	no	—
74	C₂×C₃×C₅×Q₈	—	2	2	no	—
75	C₂×C₃×C₅×Q₈	—	4	1	no	—
76	C₂×C₃×C₅×Q₈	—	4	1	no	—
77	C₂×C₃×C₅×Q₈	—	4	1	no	—
78	C₂×C₃×C₅×D₄	—	4	1	no	—
79	C₂×C₃×C₅×D₄	—	4	1	no	—
80	C₂×C₃×C₅×D₄	Q₈	1	4	yes	complemented
81	C₂²×C₃×C₄×C₅	—	2	2	no	—
82	C₂²×C₃×C₄×C₅	—	2	2	no	—
83	C₂²×C₃×C₄×C₅	—	2	2	no	—
84	C₂²×C₃×C₄×C₅	—	4	1	no	—
85	C₂²×C₃×C₄×C₅	—	4	1	no	—
86	C₂²×C₃×C₄×C₅	—	4	1	no	—
87	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
100	C₃×C₅×C₄⋊C₄	—	2	2	no	—
101	C₃×C₅×C₄⋊C₄	—	2	2	no	—
102	C₃×C₅×C₄⋊C₄	—	2	2	no	—
103	C₃×C₅×C₄⋊C₄	—	2	2	no	—
104	C₃×C₅×C₄⋊C₄	—	4	1	no	—
105	C₃×C₅×C₄⋊C₄	—	4	1	no	—
106	C₃×C₅×C₄⋊C₄	—	4	1	no	—
107	C₃×C₅×C₄⋊C₄	—	4	1	no	—
108	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
109	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
110	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
111	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
112	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
113	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
114	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
115	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
116	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
117	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
119	C₃×C₄²×C₅	—	4	1	no	—
120	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
122	C₃×#399	C₂×C₅	1	1	yes	characteristic, complemented
123	C₃×#398	C₂×C₅	1	1	yes	characteristic, complemented
124	C₃×#396	C₂×C₅	1	1	yes	characteristic, complemented
125	C₃×#395	C₂×C₅	1	1	yes	characteristic, complemented
126	C₃×#393	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#393	C₂×C₅	1	1	yes	characteristic, complemented
128	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#390	C₂×C₅	1	1	yes	characteristic
130	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#386	C₂×C₅	1	1	yes	characteristic
132	C₃×#386	C₂×C₅	1	1	yes	characteristic
133	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
135	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
136	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
137	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
138	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
139	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
140	C₅×C₂²⋊Q₈	—	2	4	no	—
141	C₅×C₂²⋊Q₈	—	2	4	no	—
142	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
162	C₅×#95	C₂²×C₃	1	1	yes	characteristic
163	C₅×#95	C₂²×C₃	1	1	yes	characteristic
164	C₅×#95	C₂²×C₃	1	1	yes	characteristic
165	C₅×#95	C₂²×C₃	1	1	yes	characteristic
166	C₅×#95	C₂²×C₃	1	1	yes	characteristic
167	C₅×#95	C₂²×C₃	1	1	yes	characteristic
168	C₅×#95	C₂²×C₃	1	1	yes	characteristic
169	C₅×#95	C₂²×C₃	1	1	yes	characteristic
170	C₅×#95	C₂²×C₃	1	1	yes	characteristic
171	C₅×#95	C₂²×C₃	1	1	yes	characteristic
172	#2692	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
173	C₂³×C₃×C₅	—	2	1	no	—
174	C₂³×C₃×C₅	—	2	1	no	—
175	C₂³×C₃×C₅	—	2	1	no	—
176	C₂³×C₃×C₅	—	2	1	no	—
177	C₂³×C₃×C₅	—	2	1	no	—
178	C₂³×C₃×C₅	—	2	1	no	—
179	C₂³×C₃×C₅	—	2	1	no	—
180	C₂³×C₃×C₅	—	2	1	no	—
181	C₂³×C₃×C₅	—	2	1	no	—
182	C₂³×C₃×C₅	—	2	1	no	—
183	C₂³×C₃×C₅	—	2	1	no	—
184	C₂³×C₃×C₅	—	2	1	no	—
185	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
186	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
187	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
188	C₃×C₅×Q₈	—	4	4	no	—
189	C₃×C₅×Q₈	—	4	4	no	—
190	C₃×C₅×D₄	—	4	4	no	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	2	1	no	—
194	C₂×C₃×C₄×C₅	—	2	1	no	—
195	C₂×C₃×C₄×C₅	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	2	1	no	—
200	C₂×C₃×C₄×C₅	—	2	1	no	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
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	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	2	1	no	—
225	C₂×C₃×C₄×C₅	—	4	4	no	—
226	C₂×C₃×C₄×C₅	—	4	4	no	—
227	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
228	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
229	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
230	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
231	C₂×C₃×C₄×C₅	#41	1	2	yes	—
232	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
233	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
234	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
235	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
236	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
237	C₃×C₂²⋊Q₈	—	2	4	no	—
238	C₃×C₂²⋊Q₈	—	2	4	no	—
239	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
259	C₃×#95	C₂²×C₅	1	1	yes	characteristic
260	C₃×#95	C₂²×C₅	1	1	yes	characteristic
261	C₃×#95	C₂²×C₅	1	1	yes	characteristic
262	C₃×#95	C₂²×C₅	1	1	yes	characteristic
263	C₃×#95	C₂²×C₅	1	1	yes	characteristic
264	C₃×#95	C₂²×C₅	1	1	yes	characteristic
265	C₃×#95	C₂²×C₅	1	1	yes	characteristic
266	C₃×#95	C₂²×C₅	1	1	yes	characteristic
267	C₃×#95	C₂²×C₅	1	1	yes	characteristic
268	C₃×#95	C₂²×C₅	1	1	yes	characteristic
269	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
270	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
271	C₂×C₅×Q₈	—	2	2	no	—
272	C₂×C₅×Q₈	—	2	2	no	—
273	C₂×C₅×Q₈	—	2	2	no	—
274	C₂×C₅×Q₈	—	4	1	no	—
275	C₂×C₅×Q₈	—	4	1	no	—
276	C₂×C₅×Q₈	—	4	1	no	—
277	C₂×C₅×D₄	—	4	1	no	—
278	C₂×C₅×D₄	—	4	1	no	—
279	C₂×C₅×D₄	C₃×Q₈	1	4	yes	complemented
280	C₂²×C₄×C₅	—	2	2	no	—
281	C₂²×C₄×C₅	—	2	2	no	—
282	C₂²×C₄×C₅	—	2	2	no	—
283	C₂²×C₄×C₅	—	4	1	no	—
284	C₂²×C₄×C₅	—	4	1	no	—
285	C₂²×C₄×C₅	—	4	1	no	—
286	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
287	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
289	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
290	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
292	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
293	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
294	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
295	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
299	C₅×C₄⋊C₄	—	2	2	no	—
300	C₅×C₄⋊C₄	—	2	2	no	—
301	C₅×C₄⋊C₄	—	2	2	no	—
302	C₅×C₄⋊C₄	—	2	2	no	—
303	C₅×C₄⋊C₄	—	4	1	no	—
304	C₅×C₄⋊C₄	—	4	1	no	—
305	C₅×C₄⋊C₄	—	4	1	no	—
306	C₅×C₄⋊C₄	—	4	1	no	—
307	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	complemented
308	C₅×C₂²⋊C₄	—	2	2	no	—
309	C₅×C₂²⋊C₄	—	2	2	no	—
310	C₅×C₂²⋊C₄	—	2	2	no	—
311	C₅×C₂²⋊C₄	—	2	2	no	—
312	C₅×C₂²⋊C₄	—	2	2	no	—
313	C₅×C₂²⋊C₄	—	4	1	no	—
314	C₅×C₂²⋊C₄	—	4	1	no	—
315	C₅×C₂²⋊C₄	—	4	1	no	—
316	C₅×C₂²⋊C₄	—	4	1	no	—
317	C₅×C₂²⋊C₄	—	4	1	no	—
318	C₄²×C₅	—	4	1	no	—
319	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
320	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
321	#399	C₂×C₃×C₅	1	1	yes	characteristic, complemented
322	#398	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	#396	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	#395	C₂×C₃×C₅	1	1	yes	characteristic, complemented
325	#393	C₂×C₃×C₅	1	1	yes	characteristic, complemented
326	#393	C₂×C₃×C₅	1	1	yes	characteristic, complemented
327	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	#390	C₂×C₃×C₅	1	1	yes	characteristic
329	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
330	#386	C₂×C₃×C₅	1	1	yes	characteristic
331	#386	C₂×C₃×C₅	1	1	yes	characteristic
332	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
333	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	C₂²×C₃×C₅	—	2	2	no	—
335	C₂²×C₃×C₅	—	2	2	no	—
336	C₂²×C₃×C₅	—	2	2	no	—
337	C₂²×C₃×C₅	—	2	2	no	—
338	C₂²×C₃×C₅	—	2	2	no	—
339	C₂²×C₃×C₅	—	2	2	no	—
340	C₂²×C₃×C₅	—	4	1	no	—
341	C₂²×C₃×C₅	—	4	1	no	—
342	C₂²×C₃×C₅	—	4	1	no	—
343	C₂²×C₃×C₅	—	4	1	no	—
344	C₂²×C₃×C₅	—	4	1	no	—
345	C₂²×C₃×C₅	—	4	1	no	—
346	C₂²×C₃×C₅	—	4	1	no	—
347	C₂²×C₃×C₅	—	4	1	no	—
348	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
349	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
350	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
351	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
353	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
355	C₃×C₄×C₅	—	2	2	no	—
356	C₃×C₄×C₅	—	2	2	no	—
357	C₃×C₄×C₅	—	2	2	no	—
358	C₃×C₄×C₅	—	2	2	no	—
359	C₃×C₄×C₅	—	2	2	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	—	4	1	no	—
365	C₃×C₄×C₅	—	4	1	no	—
366	C₃×C₄×C₅	—	4	1	no	—
367	C₃×C₄×C₅	—	4	1	no	—
368	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
369	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
370	C₂×C₃×Q₈	—	2	2	no	—
371	C₂×C₃×Q₈	—	2	2	no	—
372	C₂×C₃×Q₈	—	2	2	no	—
373	C₂×C₃×Q₈	—	4	1	no	—
374	C₂×C₃×Q₈	—	4	1	no	—
375	C₂×C₃×Q₈	—	4	1	no	—
376	C₂×C₃×D₄	—	4	1	no	—
377	C₂×C₃×D₄	—	4	1	no	—
378	C₂×C₃×D₄	C₅×Q₈	1	4	yes	complemented
379	C₂²×C₃×C₄	—	2	2	no	—
380	C₂²×C₃×C₄	—	2	2	no	—
381	C₂²×C₃×C₄	—	2	2	no	—
382	C₂²×C₃×C₄	—	4	1	no	—
383	C₂²×C₃×C₄	—	4	1	no	—
384	C₂²×C₃×C₄	—	4	1	no	—
385	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
390	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
392	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
393	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
394	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
395	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
396	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
397	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
398	C₃×C₄⋊C₄	—	2	2	no	—
399	C₃×C₄⋊C₄	—	2	2	no	—
400	C₃×C₄⋊C₄	—	2	2	no	—
401	C₃×C₄⋊C₄	—	2	2	no	—
402	C₃×C₄⋊C₄	—	4	1	no	—
403	C₃×C₄⋊C₄	—	4	1	no	—
404	C₃×C₄⋊C₄	—	4	1	no	—
405	C₃×C₄⋊C₄	—	4	1	no	—
406	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	complemented
407	C₃×C₂²⋊C₄	—	2	2	no	—
408	C₃×C₂²⋊C₄	—	2	2	no	—
409	C₃×C₂²⋊C₄	—	2	2	no	—
410	C₃×C₂²⋊C₄	—	2	2	no	—
411	C₃×C₂²⋊C₄	—	2	2	no	—
412	C₃×C₂²⋊C₄	—	4	1	no	—
413	C₃×C₂²⋊C₄	—	4	1	no	—
414	C₃×C₂²⋊C₄	—	4	1	no	—
415	C₃×C₂²⋊C₄	—	4	1	no	—
416	C₃×C₂²⋊C₄	—	4	1	no	—
417	C₃×C₄²	—	4	1	no	—
418	C₂³×C₅	—	2	1	no	—
419	C₂³×C₅	—	2	1	no	—
420	C₂³×C₅	—	2	1	no	—
421	C₂³×C₅	—	2	1	no	—
422	C₂³×C₅	—	2	1	no	—
423	C₂³×C₅	—	2	1	no	—
424	C₂³×C₅	—	2	1	no	—
425	C₂³×C₅	—	2	1	no	—
426	C₂³×C₅	—	2	1	no	—
427	C₂³×C₅	—	2	1	no	—
428	C₂³×C₅	—	2	1	no	—
429	C₂³×C₅	—	2	1	no	—
430	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
431	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
432	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
433	C₅×Q₈	—	4	4	no	—
434	C₅×Q₈	—	4	4	no	—
435	C₅×D₄	—	4	4	no	—
436	C₂×C₄×C₅	—	2	1	no	—
437	C₂×C₄×C₅	—	2	1	no	—
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	—	2	1	no	—
449	C₂×C₄×C₅	—	2	1	no	—
450	C₂×C₄×C₅	—	2	1	no	—
451	C₂×C₄×C₅	—	2	1	no	—
452	C₂×C₄×C₅	—	2	1	no	—
453	C₂×C₄×C₅	—	2	1	no	—
454	C₂×C₄×C₅	—	2	1	no	—
455	C₂×C₄×C₅	—	2	1	no	—
456	C₂×C₄×C₅	—	2	1	no	—
457	C₂×C₄×C₅	—	2	1	no	—
458	C₂×C₄×C₅	—	2	1	no	—
459	C₂×C₄×C₅	—	2	1	no	—
460	C₂×C₄×C₅	—	2	1	no	—
461	C₂×C₄×C₅	—	2	1	no	—
462	C₂×C₄×C₅	—	2	1	no	—
463	C₂×C₄×C₅	—	2	1	no	—
464	C₂×C₄×C₅	—	2	1	no	—
465	C₂×C₄×C₅	—	2	1	no	—
466	C₂×C₄×C₅	—	2	1	no	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	—	2	1	no	—
470	C₂×C₄×C₅	—	4	4	no	—
471	C₂×C₄×C₅	—	4	4	no	—
472	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
473	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
474	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
475	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
476	C₂×C₄×C₅	C₃×#41	1	2	yes	—
477	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
478	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
479	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
480	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
481	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
482	C₂²⋊Q₈	—	2	4	no	—
483	C₂²⋊Q₈	—	2	4	no	—
484	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
503	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
504	#95	C₂²×C₃×C₅	1	1	yes	characteristic
505	#95	C₂²×C₃×C₅	1	1	yes	characteristic
506	#95	C₂²×C₃×C₅	1	1	yes	characteristic
507	#95	C₂²×C₃×C₅	1	1	yes	characteristic
508	#95	C₂²×C₃×C₅	1	1	yes	characteristic
509	#95	C₂²×C₃×C₅	1	1	yes	characteristic
510	#95	C₂²×C₃×C₅	1	1	yes	characteristic
511	#95	C₂²×C₃×C₅	1	1	yes	characteristic
512	#95	C₂²×C₃×C₅	1	1	yes	characteristic
513	#95	C₂²×C₃×C₅	1	1	yes	characteristic
514	C₂×C₃×C₅	—	4	2	no	—
515	C₂×C₃×C₅	—	4	2	no	—
516	C₂×C₃×C₅	#535	1	1	yes	characteristic
517	C₂×C₃×C₅	#542	1	1	yes	characteristic
518	C₂×C₃×C₅	#543	1	1	yes	characteristic
519	C₂×C₃×C₅	#546	1	1	yes	characteristic
520	C₂×C₃×C₅	D₄×Q₈	1	1	yes	characteristic
521	C₂×C₃×C₅	#554	1	1	yes	characteristic
522	C₂×C₃×C₅	#562	1	1	yes	characteristic
523	C₂³×C₃	—	2	1	no	—
524	C₂³×C₃	—	2	1	no	—
525	C₂³×C₃	—	2	1	no	—
526	C₂³×C₃	—	2	1	no	—
527	C₂³×C₃	—	2	1	no	—
528	C₂³×C₃	—	2	1	no	—
529	C₂³×C₃	—	2	1	no	—
530	C₂³×C₃	—	2	1	no	—
531	C₂³×C₃	—	2	1	no	—
532	C₂³×C₃	—	2	1	no	—
533	C₂³×C₃	—	2	1	no	—
534	C₂³×C₃	—	2	1	no	—
535	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
536	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
537	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
538	C₃×Q₈	—	4	4	no	—
539	C₃×Q₈	—	4	4	no	—
540	C₃×D₄	—	4	4	no	—
541	C₂×C₃×C₄	—	2	1	no	—
542	C₂×C₃×C₄	—	2	1	no	—
543	C₂×C₃×C₄	—	2	1	no	—
544	C₂×C₃×C₄	—	2	1	no	—
545	C₂×C₃×C₄	—	2	1	no	—
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	1	no	—
549	C₂×C₃×C₄	—	2	1	no	—
550	C₂×C₃×C₄	—	2	1	no	—
551	C₂×C₃×C₄	—	2	1	no	—
552	C₂×C₃×C₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	—	2	1	no	—
555	C₂×C₃×C₄	—	2	1	no	—
556	C₂×C₃×C₄	—	2	1	no	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	1	no	—
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	—	2	1	no	—
561	C₂×C₃×C₄	—	2	1	no	—
562	C₂×C₃×C₄	—	2	1	no	—
563	C₂×C₃×C₄	—	2	1	no	—
564	C₂×C₃×C₄	—	2	1	no	—
565	C₂×C₃×C₄	—	2	1	no	—
566	C₂×C₃×C₄	—	2	1	no	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	2	1	no	—
569	C₂×C₃×C₄	—	2	1	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	—	4	4	no	—
576	C₂×C₃×C₄	—	4	4	no	—
577	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
578	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
579	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
580	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
581	C₂×C₃×C₄	C₅×#41	1	2	yes	—
582	C₂²×C₅	—	2	2	no	—
583	C₂²×C₅	—	2	2	no	—
584	C₂²×C₅	—	2	2	no	—
585	C₂²×C₅	—	2	2	no	—
586	C₂²×C₅	—	2	2	no	—
587	C₂²×C₅	—	2	2	no	—
588	C₂²×C₅	—	4	1	no	—
589	C₂²×C₅	—	4	1	no	—
590	C₂²×C₅	—	4	1	no	—
591	C₂²×C₅	—	4	1	no	—
592	C₂²×C₅	—	4	1	no	—
593	C₂²×C₅	—	4	1	no	—
594	C₂²×C₅	—	4	1	no	—
595	C₂²×C₅	—	4	1	no	—
596	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
597	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
598	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
599	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
600	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
601	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
603	C₄×C₅	—	2	2	no	—
604	C₄×C₅	—	2	2	no	—
605	C₄×C₅	—	2	2	no	—
606	C₄×C₅	—	2	2	no	—
607	C₄×C₅	—	2	2	no	—
608	C₄×C₅	—	4	1	no	—
609	C₄×C₅	—	4	1	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	—	4	1	no	—
616	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
617	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	—	2	2	no	—
621	C₂×Q₈	—	4	1	no	—
622	C₂×Q₈	—	4	1	no	—
623	C₂×Q₈	—	4	1	no	—
624	C₂×D₄	—	4	1	no	—
625	C₂×D₄	—	4	1	no	—
626	C₂×D₄	C₃×C₅×Q₈	1	4	yes	complemented
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	4	1	no	—
631	C₂²×C₄	—	4	1	no	—
632	C₂²×C₄	—	4	1	no	—
633	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
634	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
635	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
636	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
637	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
638	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
639	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
640	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
641	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
642	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
643	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
644	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
645	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	4	1	no	—
651	C₄⋊C₄	—	4	1	no	—
652	C₄⋊C₄	—	4	1	no	—
653	C₄⋊C₄	—	4	1	no	—
654	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	4	1	no	—
661	C₂²⋊C₄	—	4	1	no	—
662	C₂²⋊C₄	—	4	1	no	—
663	C₂²⋊C₄	—	4	1	no	—
664	C₂²⋊C₄	—	4	1	no	—
665	C₄²	—	4	1	no	—
666	C₃×C₅	#2692	1	1	yes	characteristic, direct product factor, Hall
667	C₂²×C₃	—	2	2	no	—
668	C₂²×C₃	—	2	2	no	—
669	C₂²×C₃	—	2	2	no	—
670	C₂²×C₃	—	2	2	no	—
671	C₂²×C₃	—	2	2	no	—
672	C₂²×C₃	—	2	2	no	—
673	C₂²×C₃	—	4	1	no	—
674	C₂²×C₃	—	4	1	no	—
675	C₂²×C₃	—	4	1	no	—
676	C₂²×C₃	—	4	1	no	—
677	C₂²×C₃	—	4	1	no	—
678	C₂²×C₃	—	4	1	no	—
679	C₂²×C₃	—	4	1	no	—
680	C₂²×C₃	—	4	1	no	—
681	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
682	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
683	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
684	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
686	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
687	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
688	C₃×C₄	—	2	2	no	—
689	C₃×C₄	—	2	2	no	—
690	C₃×C₄	—	2	2	no	—
691	C₃×C₄	—	2	2	no	—
692	C₃×C₄	—	2	2	no	—
693	C₃×C₄	—	4	1	no	—
694	C₃×C₄	—	4	1	no	—
695	C₃×C₄	—	4	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	C₂×C₅	—	4	2	no	—
702	C₂×C₅	—	4	2	no	—
703	C₂×C₅	C₃×#535	1	1	yes	characteristic
704	C₂×C₅	C₃×#542	1	1	yes	characteristic
705	C₂×C₅	C₃×#543	1	1	yes	characteristic
706	C₂×C₅	C₃×#546	1	1	yes	characteristic
707	C₂×C₅	C₃×D₄×Q₈	1	1	yes	characteristic
708	C₂×C₅	C₃×#554	1	1	yes	characteristic
709	C₂×C₅	C₃×#562	1	1	yes	characteristic
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
723	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
724	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
725	Q₈	—	4	4	no	—
726	Q₈	—	4	4	no	—
727	D₄	—	4	4	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	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	—	2	1	no	—
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	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
765	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
766	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
767	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
768	C₂×C₄	C₃×C₅×#41	1	2	yes	—
769	C₂×C₃	—	4	2	no	—
770	C₂×C₃	—	4	2	no	—
771	C₂×C₃	C₅×#535	1	1	yes	characteristic
772	C₂×C₃	C₅×#542	1	1	yes	characteristic
773	C₂×C₃	C₅×#543	1	1	yes	characteristic
774	C₂×C₃	C₅×#546	1	1	yes	characteristic
775	C₂×C₃	C₅×D₄×Q₈	1	1	yes	characteristic
776	C₂×C₃	C₅×#554	1	1	yes	characteristic
777	C₂×C₃	C₅×#562	1	1	yes	characteristic
778	C₅	C₃×#2692	1	1	yes	characteristic, direct product factor, Sylow
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
794	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
795	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
796	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
797	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
798	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
799	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	2	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	2	no	—
805	C₄	—	4	1	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	1	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	1	no	—
812	C₄	—	4	1	no	—
813	C₃	C₅×#2692	1	1	yes	characteristic, direct product factor, Sylow
814	C₂	—	4	2	no	—
815	C₂	—	4	2	no	—
816	C₂	C₃×C₅×#535	1	1	yes	characteristic
817	C₂	C₃×C₅×#542	1	1	yes	characteristic
818	C₂	C₃×C₅×#543	1	1	yes	characteristic
819	C₂	C₃×C₅×#546	1	1	yes	characteristic
820	C₂	C₃×C₅×D₄×Q₈	1	1	yes	characteristic
821	C₂	C₃×C₅×#554	1	1	yes	characteristic
822	C₂	C₃×C₅×#562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
2. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
3. C₃×C₅×#399	C₂	semidirect
4. C₃×C₅×#398	C₂	semidirect
5. C₃×C₅×#396	C₂	semidirect
6. C₃×C₅×#395	C₂	semidirect
7. C₃×C₅×#393	C₂	semidirect
8. C₃×C₅×#393	C₂	semidirect
9. C₃×C₅×#391	C₂	semidirect
11. C₃×C₅×#387	C₂	semidirect
14. C₃×C₅×#385	C₂	semidirect
15. C₃×C₅×#380	C₂	semidirect
16. C₅×#2692	C₃	direct (N × H)
54. C₃×#2692	C₅	direct (N × H)
55. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
56. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
57. C₅×#399	C₂×C₃	semidirect
58. C₅×#398	C₂×C₃	semidirect
59. C₅×#396	C₂×C₃	semidirect
60. C₅×#395	C₂×C₃	semidirect
61. C₅×#393	C₂×C₃	semidirect
62. C₅×#393	C₂×C₃	semidirect
63. C₅×#391	C₂×C₃	semidirect
65. C₅×#387	C₂×C₃	semidirect
68. C₅×#385	C₂×C₃	semidirect
69. C₅×#380	C₂×C₃	semidirect
80. C₂×C₃×C₅×D₄	Q₈	semidirect
108. C₃×C₅×C₄⋊C₄	D₄	semidirect
120. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
121. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
122. C₃×#399	C₂×C₅	semidirect
123. C₃×#398	C₂×C₅	semidirect
124. C₃×#396	C₂×C₅	semidirect
125. C₃×#395	C₂×C₅	semidirect
126. C₃×#393	C₂×C₅	semidirect
127. C₃×#393	C₂×C₅	semidirect
128. C₃×#391	C₂×C₅	semidirect
130. C₃×#387	C₂×C₅	semidirect
133. C₃×#385	C₂×C₅	semidirect
134. C₃×#380	C₂×C₅	semidirect
172. #2692	C₃×C₅	direct (N × H)
279. C₂×C₅×D₄	C₃×Q₈	semidirect
307. C₅×C₄⋊C₄	C₃×D₄	semidirect
319. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
320. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
321. #399	C₂×C₃×C₅	semidirect
322. #398	C₂×C₃×C₅	semidirect
323. #396	C₂×C₃×C₅	semidirect
324. #395	C₂×C₃×C₅	semidirect
325. #393	C₂×C₃×C₅	semidirect
326. #393	C₂×C₃×C₅	semidirect
327. #391	C₂×C₃×C₅	semidirect
329. #387	C₂×C₃×C₅	semidirect
332. #385	C₂×C₃×C₅	semidirect
333. #380	C₂×C₃×C₅	semidirect
378. C₂×C₃×D₄	C₅×Q₈	semidirect
406. C₃×C₄⋊C₄	C₅×D₄	semidirect
626. C₂×D₄	C₃×C₅×Q₈	semidirect
654. C₄⋊C₄	C₃×C₅×D₄	semidirect
666. C₃×C₅	#2692	direct (N × H)
778. C₅	C₃×#2692	direct (N × H)
813. C₃	C₅×#2692	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×C₂²⋊Q₈	2
C₃×C₅×#399	2
C₃×C₅×#398	2
C₃×C₅×#396	2
C₃×C₅×#395	2
C₃×C₅×#393	2
C₃×C₅×#391	2
C₃×C₅×#390	2
C₃×C₅×#387	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#380	2
C₅×#2692	3
C₃×#2692	5

Subgroups — C3×C5×#2692 #14275726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2692 #14275726