Subgroups — C₃×C₅×#3266 #14276300

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 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×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic
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×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#461	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×#450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#448	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×#3266	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, complemented
20	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₃×C₅×#137	—	2	4	no	—
22	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
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×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, complemented
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, complemented
36	C₃×C₅×#124	C₂²	1	1	yes	characteristic
37	C₃×C₅×#123	—	2	1	no	—
38	C₃×C₅×C₂²⋊Q₈	—	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, complemented
43	C₃×C₅×#121	—	2	1	no	—
44	C₃×C₅×#121	C₂²	1	1	yes	characteristic
45	C₃×C₅×#120	—	2	1	no	—
46	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
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×C₂²⋊C₄	—	2	1	no	—
51	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
56	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
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, complemented
61	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
62	C₃×#3266	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂²×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#546	C₂×C₃	1	1	yes	characteristic
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×#464	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#461	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×#450	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#448	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	C₂⁴×C₃×C₅	—	2	1	no	—
79	C₃×C₅×#41	—	2	2	no	—
80	C₃×C₅×#41	—	4	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	—	4	1	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	2	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	—	4	1	no	—
96	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
97	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
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	—	4	1	no	—
108	C₃×C₅×SD₁₆	—	2	2	no	—
109	C₃×C₅×SD₁₆	—	2	2	no	—
110	C₃×C₅×SD₁₆	—	2	2	no	—
111	C₃×C₅×SD₁₆	—	2	2	no	—
112	C₃×C₅×SD₁₆	—	4	1	no	—
113	C₃×C₅×SD₁₆	D₄	1	4	yes	complemented
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	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
143	C₃×#546	C₂×C₅	1	1	yes	characteristic
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×#464	C₂×C₅	1	1	yes	characteristic, complemented
148	C₃×#461	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×#450	C₂×C₅	1	1	yes	characteristic, complemented
152	C₃×#448	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	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
157	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
159	C₅×#137	—	2	4	no	—
160	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₂×C₅×SD₁₆	—	2	4	no	—
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×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, complemented
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, complemented
174	C₅×#124	C₂²×C₃	1	1	yes	characteristic
175	C₅×#123	—	2	1	no	—
176	C₅×C₂²⋊Q₈	—	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, complemented
181	C₅×#121	—	2	1	no	—
182	C₅×#121	C₂²×C₃	1	1	yes	characteristic
183	C₅×#120	—	2	1	no	—
184	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
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×C₂²⋊C₄	—	2	1	no	—
189	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
194	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
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, complemented
199	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
200	#3266	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	—	4	2	no	—
204	C₂³×C₃×C₅	—	4	2	no	—
205	C₂³×C₃×C₅	—	8	1	no	—
206	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
207	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
213	C₃×C₅×Q₈	—	2	1	no	—
214	C₃×C₅×Q₈	—	2	1	no	—
215	C₃×C₅×Q₈	—	4	2	no	—
216	C₃×C₅×Q₈	—	4	2	no	—
217	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
218	C₃×C₅×D₄	—	2	2	no	—
219	C₃×C₅×D₄	—	2	1	no	—
220	C₃×C₅×D₄	—	2	1	no	—
221	C₃×C₅×D₄	—	2	1	no	—
222	C₃×C₅×D₄	—	4	2	no	—
223	C₃×C₅×D₄	—	4	2	no	—
224	C₃×C₅×D₄	—	8	1	no	—
225	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
234	C₂×C₃×C₄×C₅	—	2	1	no	—
235	C₂×C₃×C₄×C₅	—	2	1	no	—
236	C₂×C₃×C₄×C₅	—	4	2	no	—
237	C₂×C₃×C₄×C₅	—	4	2	no	—
238	C₂×C₃×C₄×C₅	—	4	2	no	—
239	C₂×C₃×C₄×C₅	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
243	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
245	C₃×C₅×C₈	—	2	1	no	—
246	C₃×C₅×C₈	—	2	1	no	—
247	C₃×C₅×C₈	—	2	1	no	—
248	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
249	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
250	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
251	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
252	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
253	C₃×#137	—	2	4	no	—
254	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
256	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₂×C₃×SD₁₆	—	2	4	no	—
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×SD₁₆	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
265	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
266	C₃×C₄⋊Q₈	—	2	1	no	—
267	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₃×#124	C₂²×C₅	1	1	yes	characteristic
269	C₃×#123	—	2	1	no	—
270	C₃×C₂²⋊Q₈	—	2	1	no	—
271	C₃×C₂²⋊Q₈	—	2	1	no	—
272	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
273	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
274	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₃×#121	—	2	1	no	—
276	C₃×#121	C₂²×C₅	1	1	yes	characteristic
277	C₃×#120	—	2	1	no	—
278	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₃×C₄×D₄	—	2	1	no	—
280	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
281	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
282	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
283	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
284	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
288	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
289	C₃×#102	C₂²×C₅	1	1	yes	characteristic
290	C₃×#102	C₂²×C₅	1	1	yes	characteristic
291	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
292	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
294	C₂⁴×C₅	—	2	1	no	—
295	C₅×#41	—	2	2	no	—
296	C₅×#41	—	4	1	no	—
297	C₂×C₅×Q₈	—	2	1	no	—
298	C₂×C₅×Q₈	—	2	1	no	—
299	C₂×C₅×Q₈	—	2	2	no	—
300	C₂×C₅×Q₈	—	2	2	no	—
301	C₂×C₅×Q₈	—	4	1	no	—
302	C₂×C₅×Q₈	—	4	1	no	—
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	2	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	—	4	1	no	—
312	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
313	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
314	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
315	C₂²×C₄×C₅	—	2	1	no	—
316	C₂²×C₄×C₅	—	2	1	no	—
317	C₂²×C₄×C₅	—	2	1	no	—
318	C₂²×C₄×C₅	—	2	1	no	—
319	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
320	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
321	C₅×Q₁₆	—	2	2	no	—
322	C₅×Q₁₆	—	2	2	no	—
323	C₅×Q₁₆	—	4	1	no	—
324	C₅×SD₁₆	—	2	2	no	—
325	C₅×SD₁₆	—	2	2	no	—
326	C₅×SD₁₆	—	2	2	no	—
327	C₅×SD₁₆	—	2	2	no	—
328	C₅×SD₁₆	—	4	1	no	—
329	C₅×SD₁₆	C₃×D₄	1	4	yes	complemented
330	C₅×M₁₆	—	2	2	no	—
331	C₂×C₅×C₈	—	2	2	no	—
332	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
333	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
334	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
335	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
341	C₅×C₄⋊C₄	—	2	1	no	—
342	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
343	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
344	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	—	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	C₂³×C₃	1	1	yes	characteristic
356	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
357	C₂²×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
358	D₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
359	#546	C₂×C₃×C₅	1	1	yes	characteristic
360	#497	C₂×C₃×C₅	1	1	yes	characteristic, complemented
361	#468	C₂×C₃×C₅	1	1	yes	characteristic, complemented
362	#467	C₂×C₃×C₅	1	1	yes	characteristic, complemented
363	#464	C₂×C₃×C₅	1	1	yes	characteristic, complemented
364	#461	C₂×C₃×C₅	1	1	yes	characteristic, complemented
365	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
366	#451	C₂×C₃×C₅	1	1	yes	characteristic, complemented
367	#450	C₂×C₃×C₅	1	1	yes	characteristic, complemented
368	#448	C₂×C₃×C₅	1	1	yes	characteristic, complemented
369	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
370	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
371	C₂²×C₃×C₅	—	2	1	no	—
372	C₂²×C₃×C₅	—	2	1	no	—
373	C₂²×C₃×C₅	—	2	1	no	—
374	C₂²×C₃×C₅	—	2	2	no	—
375	C₂²×C₃×C₅	—	2	1	no	—
376	C₂²×C₃×C₅	—	2	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	—	4	1	no	—
382	C₂²×C₃×C₅	—	8	4	no	—
383	C₂²×C₃×C₅	#137	1	2	yes	complemented
384	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
385	C₃×C₄×C₅	—	2	1	no	—
386	C₃×C₄×C₅	—	2	1	no	—
387	C₃×C₄×C₅	—	2	2	no	—
388	C₃×C₄×C₅	—	2	1	no	—
389	C₃×C₄×C₅	—	2	1	no	—
390	C₃×C₄×C₅	—	4	1	no	—
391	C₃×C₄×C₅	—	4	1	no	—
392	C₃×C₄×C₅	—	4	1	no	—
393	C₃×C₄×C₅	—	4	1	no	—
394	C₃×C₄×C₅	—	4	1	no	—
395	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
396	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
397	C₂⁴×C₃	—	2	1	no	—
398	C₃×#41	—	2	2	no	—
399	C₃×#41	—	4	1	no	—
400	C₂×C₃×Q₈	—	2	1	no	—
401	C₂×C₃×Q₈	—	2	1	no	—
402	C₂×C₃×Q₈	—	2	2	no	—
403	C₂×C₃×Q₈	—	2	2	no	—
404	C₂×C₃×Q₈	—	4	1	no	—
405	C₂×C₃×Q₈	—	4	1	no	—
406	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
407	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
408	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
409	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₃×D₄	—	2	2	no	—
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	—	4	1	no	—
415	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
416	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
417	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
418	C₂²×C₃×C₄	—	2	1	no	—
419	C₂²×C₃×C₄	—	2	1	no	—
420	C₂²×C₃×C₄	—	2	1	no	—
421	C₂²×C₃×C₄	—	2	1	no	—
422	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
423	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
424	C₃×Q₁₆	—	2	2	no	—
425	C₃×Q₁₆	—	2	2	no	—
426	C₃×Q₁₆	—	4	1	no	—
427	C₃×SD₁₆	—	2	2	no	—
428	C₃×SD₁₆	—	2	2	no	—
429	C₃×SD₁₆	—	2	2	no	—
430	C₃×SD₁₆	—	2	2	no	—
431	C₃×SD₁₆	—	4	1	no	—
432	C₃×SD₁₆	C₅×D₄	1	4	yes	complemented
433	C₃×M₁₆	—	2	2	no	—
434	C₂×C₃×C₈	—	2	2	no	—
435	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
436	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
437	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
438	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
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	—	2	1	no	—
443	C₃×C₄⋊C₄	—	2	1	no	—
444	C₃×C₄⋊C₄	—	2	1	no	—
445	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
446	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
447	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	—	2	1	no	—
453	C₃×C₂²⋊C₄	—	2	1	no	—
454	C₃×C₂²⋊C₄	—	2	1	no	—
455	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
456	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
457	C₃×C₄²	—	2	1	no	—
458	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
459	C₂³×C₅	—	2	1	no	—
460	C₂³×C₅	—	2	1	no	—
461	C₂³×C₅	—	4	2	no	—
462	C₂³×C₅	—	4	2	no	—
463	C₂³×C₅	—	8	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	—	2	1	no	—
471	C₅×Q₈	—	2	1	no	—
472	C₅×Q₈	—	2	1	no	—
473	C₅×Q₈	—	4	2	no	—
474	C₅×Q₈	—	4	2	no	—
475	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
476	C₅×D₄	—	2	2	no	—
477	C₅×D₄	—	2	1	no	—
478	C₅×D₄	—	2	1	no	—
479	C₅×D₄	—	2	1	no	—
480	C₅×D₄	—	4	2	no	—
481	C₅×D₄	—	4	2	no	—
482	C₅×D₄	—	8	1	no	—
483	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
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	—	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	—	4	2	no	—
495	C₂×C₄×C₅	—	4	2	no	—
496	C₂×C₄×C₅	—	4	2	no	—
497	C₂×C₄×C₅	—	8	1	no	—
498	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
499	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
500	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
501	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
502	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
503	C₅×C₈	—	2	1	no	—
504	C₅×C₈	—	2	1	no	—
505	C₅×C₈	—	2	1	no	—
506	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
507	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
508	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
509	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
510	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
511	#137	—	2	4	no	—
512	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
513	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
514	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
515	C₂×SD₁₆	—	2	4	no	—
516	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
517	C₂×SD₁₆	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×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
523	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
524	C₄⋊Q₈	—	2	1	no	—
525	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
526	#124	C₂²×C₃×C₅	1	1	yes	characteristic
527	#123	—	2	1	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	1	no	—
530	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
531	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
532	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
533	#121	—	2	1	no	—
534	#121	C₂²×C₃×C₅	1	1	yes	characteristic
535	#120	—	2	1	no	—
536	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
539	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
542	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
543	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
544	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
545	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
546	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
547	#102	C₂²×C₃×C₅	1	1	yes	characteristic
548	#102	C₂²×C₃×C₅	1	1	yes	characteristic
549	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
550	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
551	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
552	C₂×C₃×C₅	—	2	2	no	—
553	C₂×C₃×C₅	—	4	1	no	—
554	C₂×C₃×C₅	—	4	2	no	—
555	C₂×C₃×C₅	—	8	1	no	—
556	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
557	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
558	C₂×C₃×C₅	#577	1	1	yes	characteristic
559	C₂³×C₃	—	2	1	no	—
560	C₂³×C₃	—	2	1	no	—
561	C₂³×C₃	—	4	2	no	—
562	C₂³×C₃	—	4	2	no	—
563	C₂³×C₃	—	8	1	no	—
564	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
565	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
566	C₃×Q₈	—	2	1	no	—
567	C₃×Q₈	—	2	1	no	—
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	—	2	1	no	—
573	C₃×Q₈	—	4	2	no	—
574	C₃×Q₈	—	4	2	no	—
575	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
576	C₃×D₄	—	2	2	no	—
577	C₃×D₄	—	2	1	no	—
578	C₃×D₄	—	2	1	no	—
579	C₃×D₄	—	2	1	no	—
580	C₃×D₄	—	4	2	no	—
581	C₃×D₄	—	4	2	no	—
582	C₃×D₄	—	8	1	no	—
583	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
584	C₂×C₃×C₄	—	2	1	no	—
585	C₂×C₃×C₄	—	2	1	no	—
586	C₂×C₃×C₄	—	2	1	no	—
587	C₂×C₃×C₄	—	2	1	no	—
588	C₂×C₃×C₄	—	2	1	no	—
589	C₂×C₃×C₄	—	2	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	—	4	2	no	—
595	C₂×C₃×C₄	—	4	2	no	—
596	C₂×C₃×C₄	—	4	2	no	—
597	C₂×C₃×C₄	—	8	1	no	—
598	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
599	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
600	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
601	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
602	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
603	C₃×C₈	—	2	1	no	—
604	C₃×C₈	—	2	1	no	—
605	C₃×C₈	—	2	1	no	—
606	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
607	C₂²×C₅	—	2	1	no	—
608	C₂²×C₅	—	2	1	no	—
609	C₂²×C₅	—	2	1	no	—
610	C₂²×C₅	—	2	1	no	—
611	C₂²×C₅	—	2	1	no	—
612	C₂²×C₅	—	2	2	no	—
613	C₂²×C₅	—	4	1	no	—
614	C₂²×C₅	—	4	1	no	—
615	C₂²×C₅	—	4	1	no	—
616	C₂²×C₅	—	4	1	no	—
617	C₂²×C₅	—	4	1	no	—
618	C₂²×C₅	—	8	4	no	—
619	C₂²×C₅	C₃×#137	1	2	yes	complemented
620	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
621	C₄×C₅	—	2	1	no	—
622	C₄×C₅	—	2	1	no	—
623	C₄×C₅	—	2	1	no	—
624	C₄×C₅	—	2	1	no	—
625	C₄×C₅	—	2	2	no	—
626	C₄×C₅	—	4	1	no	—
627	C₄×C₅	—	4	1	no	—
628	C₄×C₅	—	4	1	no	—
629	C₄×C₅	—	4	1	no	—
630	C₄×C₅	—	4	1	no	—
631	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
632	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
633	C₂⁴	—	2	1	no	—
634	#41	—	2	2	no	—
635	#41	—	4	1	no	—
636	C₂×Q₈	—	2	1	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	2	2	no	—
640	C₂×Q₈	—	4	1	no	—
641	C₂×Q₈	—	4	1	no	—
642	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
643	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
644	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
645	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	4	1	no	—
651	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
652	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
653	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
659	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
660	Q₁₆	—	2	2	no	—
661	Q₁₆	—	2	2	no	—
662	Q₁₆	—	4	1	no	—
663	SD₁₆	—	2	2	no	—
664	SD₁₆	—	2	2	no	—
665	SD₁₆	—	2	2	no	—
666	SD₁₆	—	2	2	no	—
667	SD₁₆	—	4	1	no	—
668	SD₁₆	C₃×C₅×D₄	1	4	yes	complemented
669	M₁₆	—	2	2	no	—
670	C₂×C₈	—	2	2	no	—
671	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
672	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
673	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
674	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
682	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
683	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
684	C₂²⋊C₄	—	2	1	no	—
685	C₂²⋊C₄	—	2	1	no	—
686	C₂²⋊C₄	—	2	1	no	—
687	C₂²⋊C₄	—	2	1	no	—
688	C₂²⋊C₄	—	2	1	no	—
689	C₂²⋊C₄	—	2	1	no	—
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
692	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
693	C₄²	—	2	1	no	—
694	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
695	C₃×C₅	#3266	1	1	yes	characteristic, direct product factor, Hall
696	C₂²×C₃	—	2	1	no	—
697	C₂²×C₃	—	2	1	no	—
698	C₂²×C₃	—	2	1	no	—
699	C₂²×C₃	—	2	2	no	—
700	C₂²×C₃	—	2	1	no	—
701	C₂²×C₃	—	2	1	no	—
702	C₂²×C₃	—	4	1	no	—
703	C₂²×C₃	—	4	1	no	—
704	C₂²×C₃	—	4	1	no	—
705	C₂²×C₃	—	4	1	no	—
706	C₂²×C₃	—	4	1	no	—
707	C₂²×C₃	—	8	4	no	—
708	C₂²×C₃	C₅×#137	1	2	yes	complemented
709	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
710	C₃×C₄	—	2	1	no	—
711	C₃×C₄	—	2	1	no	—
712	C₃×C₄	—	2	2	no	—
713	C₃×C₄	—	2	1	no	—
714	C₃×C₄	—	2	1	no	—
715	C₃×C₄	—	4	1	no	—
716	C₃×C₄	—	4	1	no	—
717	C₃×C₄	—	4	1	no	—
718	C₃×C₄	—	4	1	no	—
719	C₃×C₄	—	4	1	no	—
720	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
721	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
722	C₂×C₅	—	2	2	no	—
723	C₂×C₅	—	4	1	no	—
724	C₂×C₅	—	4	2	no	—
725	C₂×C₅	—	8	1	no	—
726	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
727	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
728	C₂×C₅	C₃×#577	1	1	yes	characteristic
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	8	1	no	—
734	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
735	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
736	Q₈	—	2	1	no	—
737	Q₈	—	2	1	no	—
738	Q₈	—	2	1	no	—
739	Q₈	—	2	1	no	—
740	Q₈	—	2	1	no	—
741	Q₈	—	2	1	no	—
742	Q₈	—	2	1	no	—
743	Q₈	—	4	2	no	—
744	Q₈	—	4	2	no	—
745	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
746	D₄	—	2	2	no	—
747	D₄	—	2	1	no	—
748	D₄	—	2	1	no	—
749	D₄	—	2	1	no	—
750	D₄	—	4	2	no	—
751	D₄	—	4	2	no	—
752	D₄	—	8	1	no	—
753	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
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	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	8	1	no	—
768	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
769	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
770	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
771	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
772	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
773	C₈	—	2	1	no	—
774	C₈	—	2	1	no	—
775	C₈	—	2	1	no	—
776	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
777	C₂×C₃	—	2	2	no	—
778	C₂×C₃	—	4	1	no	—
779	C₂×C₃	—	4	2	no	—
780	C₂×C₃	—	8	1	no	—
781	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
782	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
783	C₂×C₃	C₅×#577	1	1	yes	characteristic
784	C₅	C₃×#3266	1	1	yes	characteristic, direct product factor, Sylow
785	C₂²	—	2	1	no	—
786	C₂²	—	2	1	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	8	4	no	—
797	C₂²	C₃×C₅×#137	1	2	yes	complemented
798	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
799	C₄	—	2	1	no	—
800	C₄	—	2	1	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	4	1	no	—
805	C₄	—	4	1	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	1	no	—
808	C₄	—	4	1	no	—
809	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
810	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
811	C₃	C₅×#3266	1	1	yes	characteristic, direct product factor, Sylow
812	C₂	—	2	2	no	—
813	C₂	—	4	1	no	—
814	C₂	—	4	2	no	—
815	C₂	—	8	1	no	—
816	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
817	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
818	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
prime radical	C₃×C₅×#546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#137	C₂	semidirect
2. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
3. C₃×C₅×D₄×Q₈	C₂	semidirect
5. C₃×C₅×#497	C₂	semidirect
6. C₃×C₅×#468	C₂	semidirect
7. C₃×C₅×#467	C₂	semidirect
8. C₃×C₅×#464	C₂	semidirect
9. C₃×C₅×#461	C₂	semidirect
10. C₃×C₅×#452	C₂	semidirect
11. C₃×C₅×#451	C₂	semidirect
12. C₃×C₅×#450	C₂	semidirect
13. C₃×C₅×#448	C₂	semidirect
14. C₃×C₅×#440	C₂	semidirect
15. C₃×C₅×#435	C₂	semidirect
16. C₅×#3266	C₃	direct (N × H)
19. C₂²×C₃×C₅×Q₈	C₂²	semidirect
22. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
23. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
24. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
32. C₂×C₃×C₅×M₁₆	C₂²	semidirect
35. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
42. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
46. C₃×C₄×C₅×Q₈	C₂²	semidirect
51. C₃×C₅×#107	C₂²	semidirect
52. C₃×C₅×C₄⋊C₈	C₂²	semidirect
53. C₃×C₅×#103	C₂²	semidirect
54. C₃×C₅×#103	C₂²	semidirect
55. C₃×C₅×#103	C₂²	semidirect
56. C₃×C₅×#103	C₂²	semidirect
60. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
61. C₃×C₅×#97	C₂²	semidirect
62. C₃×#3266	C₅	direct (N × H)
63. C₂×C₅×#137	C₂×C₃	semidirect
64. C₂²×C₅×SD₁₆	C₂×C₃	semidirect
65. C₅×D₄×Q₈	C₂×C₃	semidirect
67. C₅×#497	C₂×C₃	semidirect
68. C₅×#468	C₂×C₃	semidirect
69. C₅×#467	C₂×C₃	semidirect
70. C₅×#464	C₂×C₃	semidirect
71. C₅×#461	C₂×C₃	semidirect
72. C₅×#452	C₂×C₃	semidirect
73. C₅×#451	C₂×C₃	semidirect
74. C₅×#450	C₂×C₃	semidirect
75. C₅×#448	C₂×C₃	semidirect
76. C₅×#440	C₂×C₃	semidirect
77. C₅×#435	C₂×C₃	semidirect
113. C₃×C₅×SD₁₆	D₄	semidirect
140. C₂×C₃×#137	C₂×C₅	semidirect
141. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
142. C₃×D₄×Q₈	C₂×C₅	semidirect
144. C₃×#497	C₂×C₅	semidirect
145. C₃×#468	C₂×C₅	semidirect
146. C₃×#467	C₂×C₅	semidirect
147. C₃×#464	C₂×C₅	semidirect
148. C₃×#461	C₂×C₅	semidirect
149. C₃×#452	C₂×C₅	semidirect
150. C₃×#451	C₂×C₅	semidirect
151. C₃×#450	C₂×C₅	semidirect
152. C₃×#448	C₂×C₅	semidirect
153. C₃×#440	C₂×C₅	semidirect
154. C₃×#435	C₂×C₅	semidirect
157. C₂²×C₅×Q₈	C₂²×C₃	semidirect
160. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
161. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
162. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
170. C₂×C₅×M₁₆	C₂²×C₃	semidirect
173. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
180. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
184. C₄×C₅×Q₈	C₂²×C₃	semidirect
189. C₅×#107	C₂²×C₃	semidirect
190. C₅×C₄⋊C₈	C₂²×C₃	semidirect
191. C₅×#103	C₂²×C₃	semidirect
192. C₅×#103	C₂²×C₃	semidirect
193. C₅×#103	C₂²×C₃	semidirect
194. C₅×#103	C₂²×C₃	semidirect
198. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
199. C₅×#97	C₂²×C₃	semidirect
200. #3266	C₃×C₅	direct (N × H)
251. C₂²×C₃×Q₈	C₂²×C₅	semidirect
254. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
255. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
256. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
264. C₂×C₃×M₁₆	C₂²×C₅	semidirect
267. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
274. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
278. C₃×C₄×Q₈	C₂²×C₅	semidirect
283. C₃×#107	C₂²×C₅	semidirect
284. C₃×C₄⋊C₈	C₂²×C₅	semidirect
285. C₃×#103	C₂²×C₅	semidirect
286. C₃×#103	C₂²×C₅	semidirect
287. C₃×#103	C₂²×C₅	semidirect
288. C₃×#103	C₂²×C₅	semidirect
292. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
293. C₃×#97	C₂²×C₅	semidirect
329. C₅×SD₁₆	C₃×D₄	semidirect
356. C₂×#137	C₂×C₃×C₅	semidirect
357. C₂²×SD₁₆	C₂×C₃×C₅	semidirect
358. D₄×Q₈	C₂×C₃×C₅	semidirect
360. #497	C₂×C₃×C₅	semidirect
361. #468	C₂×C₃×C₅	semidirect
362. #467	C₂×C₃×C₅	semidirect
363. #464	C₂×C₃×C₅	semidirect
364. #461	C₂×C₃×C₅	semidirect
365. #452	C₂×C₃×C₅	semidirect
366. #451	C₂×C₃×C₅	semidirect
367. #450	C₂×C₃×C₅	semidirect
368. #448	C₂×C₃×C₅	semidirect
369. #440	C₂×C₃×C₅	semidirect
370. #435	C₂×C₃×C₅	semidirect
383. C₂²×C₃×C₅	#137	semidirect
432. C₃×SD₁₆	C₅×D₄	semidirect
509. C₂²×Q₈	C₂²×C₃×C₅	semidirect
512. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
513. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
514. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
522. C₂×M₁₆	C₂²×C₃×C₅	semidirect
525. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
532. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
536. C₄×Q₈	C₂²×C₃×C₅	semidirect
541. #107	C₂²×C₃×C₅	semidirect
542. C₄⋊C₈	C₂²×C₃×C₅	semidirect
543. #103	C₂²×C₃×C₅	semidirect
544. #103	C₂²×C₃×C₅	semidirect
545. #103	C₂²×C₃×C₅	semidirect
546. #103	C₂²×C₃×C₅	semidirect
550. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
551. #97	C₂²×C₃×C₅	semidirect
619. C₂²×C₅	C₃×#137	semidirect
668. SD₁₆	C₃×C₅×D₄	semidirect
695. C₃×C₅	#3266	direct (N × H)
708. C₂²×C₃	C₅×#137	semidirect
784. C₅	C₃×#3266	direct (N × H)
797. C₂²	C₃×C₅×#137	semidirect
811. C₃	C₅×#3266	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×SD₁₆	2
C₃×C₅×D₄×Q₈	2
C₃×C₅×#546	2
C₃×C₅×#497	2
C₃×C₅×#468	2
C₃×C₅×#467	2
C₃×C₅×#464	2
C₃×C₅×#461	2
C₃×C₅×#452	2
C₃×C₅×#451	2
C₃×C₅×#450	2
C₃×C₅×#448	2
C₃×C₅×#440	2
C₃×C₅×#435	2
C₅×#3266	3
C₃×#3266	5

Subgroups — C3×C5×#3266 #14276300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3266 #14276300