Subgroups — C₃×#10617217 #14415460

Order 1920.

1004 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#704	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65920	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₂²⋊#170	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65775	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65774	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65773	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65773	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₄×#170	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65696	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65695	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65694	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65693	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65692	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65691	C₂	1	1	yes	maximal, characteristic, complemented
16	#10617217	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×#711	C₂²	1	1	yes	characteristic
19	C₂×C₃×#704	—	2	4	no	—
20	C₂×C₃×#704	C₂²	1	1	yes	characteristic
21	C₂×C₃×#704	C₂²	1	1	yes	characteristic
22	C₂×C₃×#704	C₂²	1	1	yes	characteristic
23	C₂×C₃×#704	C₂²	1	1	yes	characteristic
24	C₂×C₃×#704	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
26	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
27	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
28	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
29	C₂²×C₃×#170	C₂²	1	1	yes	characteristic, complemented
30	C₃×#4131	—	2	4	no	—
31	C₂×C₃×#700	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#120	C₄	1	1	yes	characteristic
34	C₃×#4099	C₄	1	1	yes	characteristic
35	C₃×#4085	C₄	1	1	yes	characteristic
36	C₃×#4085	C₄	1	1	yes	characteristic
37	C₃×#4081	C₄	1	1	yes	characteristic
38	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
39	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
40	C₃×#4032	C₄	1	1	yes	characteristic
41	C₃×#4027	C₂²	1	1	yes	characteristic
42	C₃×#4027	C₂²	1	1	yes	characteristic
43	C₃×#4024	C₄	1	1	yes	characteristic
44	C₃×#4024	C₄	1	1	yes	characteristic
45	C₃×#4023	C₂²	1	1	yes	characteristic
46	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic
47	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic
48	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic
49	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic
50	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic, complemented
52	C₃×#4004	C₂²	1	1	yes	characteristic, complemented
53	C₃×#4004	C₂²	1	1	yes	characteristic, complemented
54	C₃×#4003	C₂²	1	1	yes	characteristic, complemented
55	C₃×#4003	C₂²	1	1	yes	characteristic, complemented
56	C₃×#4002	C₂²	1	1	yes	characteristic, complemented
57	C₃×#4002	C₂²	1	1	yes	characteristic, complemented
58	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic, complemented
60	C₃×C₄×#170	C₂²	1	1	yes	characteristic, complemented
61	C₃×C₄×#170	C₂²	1	1	yes	characteristic, complemented
62	C₃×#2933	—	5	1	no	maximal, Hall
63	C₂²×#704	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×#4131	C₂×C₃	1	1	yes	characteristic, complemented
65	#65920	C₂×C₃	1	1	yes	characteristic
66	C₂×C₂²⋊#170	C₂×C₃	1	1	yes	characteristic, complemented
67	#65775	C₂×C₃	1	1	yes	characteristic, complemented
68	#65774	C₂×C₃	1	1	yes	characteristic, complemented
69	#65773	C₂×C₃	1	1	yes	characteristic, complemented
70	#65773	C₂×C₃	1	1	yes	characteristic, complemented
71	D₄×#170	C₂×C₃	1	1	yes	characteristic, complemented
72	#65696	C₂×C₃	1	1	yes	characteristic, complemented
73	#65695	C₂×C₃	1	1	yes	characteristic, complemented
74	#65694	C₂×C₃	1	1	yes	characteristic, complemented
75	#65693	C₂×C₃	1	1	yes	characteristic, complemented
76	#65692	C₂×C₃	1	1	yes	characteristic, complemented
77	#65691	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
83	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
84	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
85	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₃×Dic₅	—	2	2	no	—
87	C₂²×C₃×Dic₅	—	2	2	no	—
88	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
91	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
94	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
95	C₃×#711	—	2	2	no	—
96	C₃×#711	—	2	2	no	—
97	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
98	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
99	C₃×#704	—	2	2	no	—
100	C₃×#704	—	2	2	no	—
101	C₃×#704	—	2	2	no	—
102	C₃×#704	—	2	2	no	—
103	C₃×#704	D₄	1	4	yes	complemented
104	C₂×C₃×#170	—	2	2	no	—
105	C₂×C₃×#170	—	2	2	no	—
106	C₂×C₃×#170	—	2	2	no	—
107	C₂×C₃×#170	—	2	2	no	—
108	C₂×C₃×#170	—	2	2	no	—
109	C₂×C₃×#170	C₂³	1	1	yes	characteristic
110	C₂×C₃×#170	C₂³	1	1	yes	characteristic
111	C₂×C₃×#170	C₂³	1	1	yes	characteristic
112	C₂×C₃×#170	C₂³	1	1	yes	characteristic
113	C₂×C₃×#170	C₂³	1	1	yes	characteristic
114	C₂×C₃×#170	C₂³	1	1	yes	characteristic
115	C₂×C₃×#170	C₂³	1	1	yes	characteristic
116	C₂×C₃×#170	C₂³	1	1	yes	characteristic
117	C₃×#700	—	2	2	no	—
118	C₃×D₅⋊C₈	—	2	2	no	—
119	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
121	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
122	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
123	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
124	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
125	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
126	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
127	C₃×#685	C₂×C₄	1	1	yes	characteristic
128	C₃×#685	C₂×C₄	1	1	yes	characteristic
129	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
130	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
131	C₃×#683	C₂×C₄	1	1	yes	characteristic
132	C₃×#683	C₂×C₄	1	1	yes	characteristic
133	C₃×#683	C₂×C₄	1	1	yes	characteristic
134	C₃×#683	C₂×C₄	1	1	yes	characteristic
135	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
136	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
137	C₂×C₃×#131	—	5	1	no	—
138	C₂²×C₃×M₁₆	—	5	1	no	—
139	C₃×#525	—	5	1	no	—
140	C₃×#436	—	5	1	no	—
141	C₃×#436	—	5	1	no	—
142	C₃×#435	—	5	1	no	—
143	C₃×#435	—	5	1	no	—
144	C₃×#435	—	5	1	no	—
145	C₃×#435	—	5	1	no	—
146	C₃×C₈×D₄	—	5	1	no	—
147	C₃×C₈×D₄	—	5	1	no	—
148	C₃×#424	—	5	1	no	—
149	C₃×#408	—	5	1	no	—
150	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
151	C₃×#405	—	5	1	no	—
152	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
153	C₂×#711	C₂²×C₃	1	1	yes	characteristic
154	C₂×#704	—	2	4	no	—
155	C₂×#704	C₂²×C₃	1	1	yes	characteristic
156	C₂×#704	C₂²×C₃	1	1	yes	characteristic
157	C₂×#704	C₂²×C₃	1	1	yes	characteristic
158	C₂×#704	C₂²×C₃	1	1	yes	characteristic
159	C₂×#704	C₂²×C₃	1	1	yes	characteristic, complemented
160	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
161	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
162	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
163	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
164	C₂²×#170	C₂²×C₃	1	1	yes	characteristic, complemented
165	#4131	—	2	4	no	—
166	C₂×#700	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₅×#120	C₃×C₄	1	1	yes	characteristic
169	#4099	C₃×C₄	1	1	yes	characteristic
170	#4085	C₃×C₄	1	1	yes	characteristic
171	#4085	C₃×C₄	1	1	yes	characteristic
172	#4081	C₃×C₄	1	1	yes	characteristic
173	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
174	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
175	#4032	C₃×C₄	1	1	yes	characteristic
176	#4027	C₂²×C₃	1	1	yes	characteristic
177	#4027	C₂²×C₃	1	1	yes	characteristic
178	#4024	C₃×C₄	1	1	yes	characteristic
179	#4024	C₃×C₄	1	1	yes	characteristic
180	#4023	C₂²×C₃	1	1	yes	characteristic
181	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic
182	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic
183	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic
184	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic
185	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic, complemented
186	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic, complemented
187	#4004	C₂²×C₃	1	1	yes	characteristic, complemented
188	#4004	C₂²×C₃	1	1	yes	characteristic, complemented
189	#4003	C₂²×C₃	1	1	yes	characteristic, complemented
190	#4003	C₂²×C₃	1	1	yes	characteristic, complemented
191	#4002	C₂²×C₃	1	1	yes	characteristic, complemented
192	#4002	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic, complemented
194	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₄×#170	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₄×#170	C₂²×C₃	1	1	yes	characteristic, complemented
197	#2933	—	5	1	no	Sylow
198	C₂³×C₃×C₅	—	2	2	no	—
199	C₂³×C₃×C₅	—	2	2	no	—
200	C₂³×C₃×C₅	—	4	1	no	—
201	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
202	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
203	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
204	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
206	C₃×C₅×D₄	—	2	2	no	—
207	C₃×C₅×D₄	—	2	2	no	—
208	C₃×C₅×D₄	—	4	1	no	—
209	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
212	C₃×C₂²⋊D₅	—	2	2	no	—
213	C₃×C₂²⋊D₅	—	2	2	no	—
214	C₃×C₂²⋊D₅	—	2	2	no	—
215	C₃×C₂²⋊D₅	—	4	1	no	—
216	C₂×C₃×Dic₅	—	2	2	no	—
217	C₂×C₃×Dic₅	—	2	2	no	—
218	C₂×C₃×Dic₅	—	2	2	no	—
219	C₂×C₃×Dic₅	—	2	1	no	—
220	C₂×C₃×Dic₅	—	2	1	no	—
221	C₂×C₃×Dic₅	—	2	1	no	—
222	C₂×C₃×Dic₅	—	2	1	no	—
223	C₂×C₃×Dic₅	—	2	1	no	—
224	C₂×C₃×Dic₅	—	2	1	no	—
225	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
226	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
227	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
229	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
230	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
231	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
232	C₂×C₃×Dic₅	#41	1	2	yes	—
233	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
234	C₃×C₄×D₅	—	2	1	no	—
235	C₃×C₄×D₅	—	2	1	no	—
236	C₃×Dic₁₀	—	2	2	no	—
237	C₃×#170	—	2	1	no	—
238	C₃×#170	—	2	1	no	—
239	C₃×#170	—	2	1	no	—
240	C₃×#170	—	2	1	no	—
241	C₃×#170	—	2	1	no	—
242	C₃×#170	—	2	1	no	—
243	C₃×#170	C₂×D₄	1	2	yes	—
244	C₃×#170	C₂×D₄	1	2	yes	—
245	C₂×C₃×#41	—	5	1	no	—
246	C₂³×C₃×C₄	—	5	1	no	—
247	C₃×#131	—	10	4	no	—
248	C₂×C₃×M₁₆	—	5	1	no	—
249	C₂×C₃×M₁₆	—	5	1	no	—
250	C₂×C₃×M₁₆	—	5	1	no	—
251	C₂×C₃×M₁₆	—	5	1	no	—
252	C₂×C₃×M₁₆	—	5	1	no	—
253	C₂×C₃×M₁₆	—	5	1	no	—
254	C₂×C₃×M₁₆	—	10	4	no	—
255	C₂²×C₃×C₈	—	5	1	no	—
256	C₂²×C₃×C₈	—	5	1	no	—
257	C₂²×C₃×C₈	—	5	1	no	—
258	C₂²×C₃×C₈	—	5	1	no	—
259	C₂²×C₃×C₈	—	5	1	no	—
260	C₂²×C₃×C₈	—	5	1	no	—
261	C₃×#123	—	5	1	no	—
262	C₃×#123	—	5	1	no	—
263	C₃×C₂²⋊Q₈	—	5	1	no	—
264	C₃×C₂²⋊Q₈	—	5	1	no	—
265	C₃×#121	—	5	1	no	—
266	C₃×#121	—	5	1	no	—
267	C₃×#120	—	5	1	no	—
268	C₃×#120	AGL(1,𝔽₅)	1	1	yes	characteristic
269	C₃×C₄×D₄	—	5	1	no	—
270	C₃×C₄×D₄	—	5	1	no	—
271	C₃×C₄×D₄	—	5	1	no	—
272	C₃×C₄×D₄	—	5	1	no	—
273	C₃×#117	—	5	1	no	—
274	C₃×C₄⋊C₈	—	5	1	no	—
275	C₃×C₄⋊C₈	—	5	1	no	—
276	C₃×C₄⋊C₈	—	5	1	no	—
277	C₃×C₄⋊C₈	—	5	1	no	—
278	C₃×C₂²⋊C₈	—	5	1	no	—
279	C₃×C₂²⋊C₈	—	5	1	no	—
280	C₃×C₂²⋊C₈	—	5	1	no	—
281	C₃×C₂²⋊C₈	—	5	1	no	—
282	C₃×C₂²⋊C₈	—	5	1	no	—
283	C₃×C₂²⋊C₈	—	5	1	no	—
284	C₃×C₂²⋊C₈	—	5	1	no	—
285	C₃×C₂²⋊C₈	—	5	1	no	—
286	C₃×#97	—	5	1	no	—
287	C₃×#97	—	5	1	no	—
288	C₃×C₄×C₈	—	5	1	no	—
289	C₃×C₄×C₈	—	5	1	no	—
290	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
291	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
292	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
293	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
294	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
295	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
296	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
297	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
298	C₂²×Dic₅	—	2	2	no	—
299	C₂²×Dic₅	—	2	2	no	—
300	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
301	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
302	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
303	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
304	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
305	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
306	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
307	#711	—	2	2	no	—
308	#711	—	2	2	no	—
309	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
310	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
311	#704	—	2	2	no	—
312	#704	—	2	2	no	—
313	#704	—	2	2	no	—
314	#704	—	2	2	no	—
315	#704	C₃×D₄	1	4	yes	complemented
316	C₂×#170	—	2	2	no	—
317	C₂×#170	—	2	2	no	—
318	C₂×#170	—	2	2	no	—
319	C₂×#170	—	2	2	no	—
320	C₂×#170	—	2	2	no	—
321	C₂×#170	C₂³×C₃	1	1	yes	characteristic
322	C₂×#170	C₂³×C₃	1	1	yes	characteristic
323	C₂×#170	C₂³×C₃	1	1	yes	characteristic
324	C₂×#170	C₂³×C₃	1	1	yes	characteristic
325	C₂×#170	C₂³×C₃	1	1	yes	characteristic
326	C₂×#170	C₂³×C₃	1	1	yes	characteristic
327	C₂×#170	C₂³×C₃	1	1	yes	characteristic
328	C₂×#170	C₂³×C₃	1	1	yes	characteristic
329	#700	—	2	2	no	—
330	D₅⋊C₈	—	2	2	no	—
331	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
332	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
333	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
334	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
335	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
336	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
337	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
338	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
339	#685	C₂×C₃×C₄	1	1	yes	characteristic
340	#685	C₂×C₃×C₄	1	1	yes	characteristic
341	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
342	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
343	#683	C₂×C₃×C₄	1	1	yes	characteristic
344	#683	C₂×C₃×C₄	1	1	yes	characteristic
345	#683	C₂×C₃×C₄	1	1	yes	characteristic
346	#683	C₂×C₃×C₄	1	1	yes	characteristic
347	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
348	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
349	C₂×#131	—	5	1	no	—
350	C₂²×M₁₆	—	5	1	no	—
351	#525	—	5	1	no	—
352	#436	—	5	1	no	—
353	#436	—	5	1	no	—
354	#435	—	5	1	no	—
355	#435	—	5	1	no	—
356	#435	—	5	1	no	—
357	#435	—	5	1	no	—
358	C₈×D₄	—	5	1	no	—
359	C₈×D₄	—	5	1	no	—
360	#424	—	5	1	no	—
361	#408	—	5	1	no	—
362	C₂×C₂²⋊C₈	—	5	1	no	—
363	#405	—	5	1	no	—
364	C₂²×C₃×C₅	—	2	1	no	—
365	C₂²×C₃×C₅	—	2	1	no	—
366	C₂²×C₃×C₅	—	2	1	no	—
367	C₂²×C₃×C₅	—	2	1	no	—
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	—	2	1	no	—
374	C₂²×C₃×C₅	—	4	4	no	—
375	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
376	C₂²×C₃×C₅	#131	1	2	yes	complemented
377	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
378	C₂×C₃×D₅	—	2	1	no	—
379	C₂×C₃×D₅	—	2	1	no	—
380	C₂×C₃×D₅	—	2	1	no	—
381	C₃×C₄×C₅	—	2	1	no	—
382	C₃×C₄×C₅	—	2	1	no	—
383	C₃×C₄×C₅	—	2	1	no	—
384	C₃×Dic₅	—	2	1	no	—
385	C₃×Dic₅	—	2	1	no	—
386	C₃×Dic₅	—	2	1	no	—
387	C₃×Dic₅	—	2	1	no	—
388	C₃×Dic₅	—	2	1	no	—
389	C₃×Dic₅	C₄×D₄	1	2	yes	—
390	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
391	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
392	C₂⁴×C₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
393	C₃×#41	—	10	2	no	—
394	C₃×#41	—	10	2	no	—
395	C₂×C₃×Q₈	—	5	1	no	—
396	C₂×C₃×D₄	—	5	1	no	—
397	C₂×C₃×D₄	—	5	1	no	—
398	C₂×C₃×D₄	—	5	1	no	—
399	C₂×C₃×D₄	—	5	1	no	—
400	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
401	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
402	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
403	C₂²×C₃×C₄	—	5	1	no	—
404	C₂²×C₃×C₄	—	5	1	no	—
405	C₂²×C₃×C₄	—	5	1	no	—
406	C₂²×C₃×C₄	—	5	1	no	—
407	C₂²×C₃×C₄	—	5	1	no	—
408	C₂²×C₃×C₄	—	5	1	no	—
409	C₂²×C₃×C₄	—	5	1	no	—
410	C₂²×C₃×C₄	—	5	1	no	—
411	C₂²×C₃×C₄	—	10	2	no	—
412	C₂²×C₃×C₄	—	10	2	no	—
413	C₃×M₁₆	—	5	4	no	—
414	C₃×M₁₆	—	10	2	no	—
415	C₃×M₁₆	—	10	2	no	—
416	C₃×M₁₆	—	10	2	no	—
417	C₃×M₁₆	—	10	2	no	—
418	C₃×M₁₆	—	10	2	no	—
419	C₂×C₃×C₈	—	5	1	no	—
420	C₂×C₃×C₈	—	5	1	no	—
421	C₂×C₃×C₈	—	5	1	no	—
422	C₂×C₃×C₈	—	5	1	no	—
423	C₂×C₃×C₈	—	5	1	no	—
424	C₂×C₃×C₈	—	5	1	no	—
425	C₂×C₃×C₈	—	5	1	no	—
426	C₂×C₃×C₈	—	5	1	no	—
427	C₂×C₃×C₈	—	10	2	no	—
428	C₂×C₃×C₈	—	10	2	no	—
429	C₂×C₃×C₈	—	10	2	no	—
430	C₂×C₃×C₈	—	10	2	no	—
431	C₂×C₃×C₈	—	10	2	no	—
432	C₂×C₃×C₈	—	10	2	no	—
433	C₃×C₄⋊C₄	—	5	1	no	—
434	C₃×C₄⋊C₄	—	5	1	no	—
435	C₃×C₄⋊C₄	—	5	1	no	—
436	C₃×C₄⋊C₄	—	5	1	no	—
437	C₃×C₄⋊C₄	—	5	1	no	—
438	C₃×C₄⋊C₄	—	5	1	no	—
439	C₃×C₂²⋊C₄	—	5	1	no	—
440	C₃×C₂²⋊C₄	—	5	1	no	—
441	C₃×C₂²⋊C₄	—	5	1	no	—
442	C₃×C₂²⋊C₄	—	5	1	no	—
443	C₃×C₂²⋊C₄	—	5	1	no	—
444	C₃×C₂²⋊C₄	—	5	1	no	—
445	C₃×C₂²⋊C₄	—	5	1	no	—
446	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
447	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
448	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
449	C₃×C₄²	—	5	1	no	—
450	C₃×C₄²	—	5	1	no	—
451	C₂³×C₅	—	2	2	no	—
452	C₂³×C₅	—	2	2	no	—
453	C₂³×C₅	—	4	1	no	—
454	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
455	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
456	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
457	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
458	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
459	C₅×D₄	—	2	2	no	—
460	C₅×D₄	—	2	2	no	—
461	C₅×D₄	—	4	1	no	—
462	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
463	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
464	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
465	C₂²⋊D₅	—	2	2	no	—
466	C₂²⋊D₅	—	2	2	no	—
467	C₂²⋊D₅	—	2	2	no	—
468	C₂²⋊D₅	—	4	1	no	—
469	C₂×Dic₅	—	2	2	no	—
470	C₂×Dic₅	—	2	2	no	—
471	C₂×Dic₅	—	2	2	no	—
472	C₂×Dic₅	—	2	1	no	—
473	C₂×Dic₅	—	2	1	no	—
474	C₂×Dic₅	—	2	1	no	—
475	C₂×Dic₅	—	2	1	no	—
476	C₂×Dic₅	—	2	1	no	—
477	C₂×Dic₅	—	2	1	no	—
478	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
479	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
480	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
481	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
482	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
483	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
484	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
485	C₂×Dic₅	C₃×#41	1	2	yes	—
486	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
487	C₄×D₅	—	2	1	no	—
488	C₄×D₅	—	2	1	no	—
489	Dic₁₀	—	2	2	no	—
490	#170	—	2	1	no	—
491	#170	—	2	1	no	—
492	#170	—	2	1	no	—
493	#170	—	2	1	no	—
494	#170	—	2	1	no	—
495	#170	—	2	1	no	—
496	#170	C₂×C₃×D₄	1	2	yes	—
497	#170	C₂×C₃×D₄	1	2	yes	—
498	C₂×#41	—	5	1	no	—
499	C₂³×C₄	—	5	1	no	—
500	#131	—	10	4	no	—
501	C₂×M₁₆	—	5	1	no	—
502	C₂×M₁₆	—	5	1	no	—
503	C₂×M₁₆	—	5	1	no	—
504	C₂×M₁₆	—	5	1	no	—
505	C₂×M₁₆	—	5	1	no	—
506	C₂×M₁₆	—	5	1	no	—
507	C₂×M₁₆	—	10	4	no	—
508	C₂²×C₈	—	5	1	no	—
509	C₂²×C₈	—	5	1	no	—
510	C₂²×C₈	—	5	1	no	—
511	C₂²×C₈	—	5	1	no	—
512	C₂²×C₈	—	5	1	no	—
513	C₂²×C₈	—	5	1	no	—
514	#123	—	5	1	no	—
515	#123	—	5	1	no	—
516	C₂²⋊Q₈	—	5	1	no	—
517	C₂²⋊Q₈	—	5	1	no	—
518	#121	—	5	1	no	—
519	#121	—	5	1	no	—
520	#120	—	5	1	no	—
521	#120	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
522	C₄×D₄	—	5	1	no	—
523	C₄×D₄	—	5	1	no	—
524	C₄×D₄	—	5	1	no	—
525	C₄×D₄	—	5	1	no	—
526	#117	—	5	1	no	—
527	C₄⋊C₈	—	5	1	no	—
528	C₄⋊C₈	—	5	1	no	—
529	C₄⋊C₈	—	5	1	no	—
530	C₄⋊C₈	—	5	1	no	—
531	C₂²⋊C₈	—	5	1	no	—
532	C₂²⋊C₈	—	5	1	no	—
533	C₂²⋊C₈	—	5	1	no	—
534	C₂²⋊C₈	—	5	1	no	—
535	C₂²⋊C₈	—	5	1	no	—
536	C₂²⋊C₈	—	5	1	no	—
537	C₂²⋊C₈	—	5	1	no	—
538	C₂²⋊C₈	—	5	1	no	—
539	#97	—	5	1	no	—
540	#97	—	5	1	no	—
541	C₄×C₈	—	5	1	no	—
542	C₄×C₈	—	5	1	no	—
543	C₂×C₃×C₅	—	2	2	no	—
544	C₂×C₃×C₅	—	2	2	no	—
545	C₂×C₃×C₅	—	4	1	no	—
546	C₂×C₃×C₅	—	4	1	no	—
547	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
548	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
549	C₂×C₃×C₅	#568	1	1	yes	characteristic
550	C₃×D₅	—	4	1	no	—
551	C₂³×C₃	—	2	2	no	—
552	C₂³×C₃	—	2	2	no	—
553	C₂³×C₃	—	4	1	no	—
554	C₂³×C₃	—	5	1	no	—
555	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
556	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
557	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
558	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
559	C₃×Q₈	—	10	2	no	—
560	C₃×D₄	—	2	2	no	—
561	C₃×D₄	—	2	2	no	—
562	C₃×D₄	—	4	1	no	—
563	C₃×D₄	—	10	2	no	—
564	C₃×D₄	—	10	2	no	—
565	C₃×D₄	—	10	2	no	—
566	C₃×D₄	—	20	1	no	—
567	C₂×C₃×C₄	—	5	2	no	—
568	C₂×C₃×C₄	—	5	2	no	—
569	C₂×C₃×C₄	—	5	1	no	—
570	C₂×C₃×C₄	—	5	1	no	—
571	C₂×C₃×C₄	—	5	1	no	—
572	C₂×C₃×C₄	—	5	1	no	—
573	C₂×C₃×C₄	—	5	1	no	—
574	C₂×C₃×C₄	—	5	1	no	—
575	C₂×C₃×C₄	—	5	1	no	—
576	C₂×C₃×C₄	—	10	1	no	—
577	C₂×C₃×C₄	—	10	1	no	—
578	C₂×C₃×C₄	—	10	1	no	—
579	C₂×C₃×C₄	—	10	1	no	—
580	C₂×C₃×C₄	—	10	1	no	—
581	C₂×C₃×C₄	—	10	2	no	—
582	C₂×C₃×C₄	—	10	2	no	—
583	C₂×C₃×C₄	—	10	1	no	—
584	C₂×C₃×C₄	—	10	1	no	—
585	C₂×C₃×C₄	—	10	1	no	—
586	C₂×C₃×C₄	—	10	2	no	—
587	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
588	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
589	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
590	C₃×C₈	—	5	2	no	—
591	C₃×C₈	—	5	2	no	—
592	C₃×C₈	—	10	1	no	—
593	C₃×C₈	—	10	1	no	—
594	C₃×C₈	—	10	1	no	—
595	C₃×C₈	—	10	1	no	—
596	C₃×C₈	—	10	1	no	—
597	C₃×C₈	—	10	1	no	—
598	C₂²×C₅	—	2	1	no	—
599	C₂²×C₅	—	2	1	no	—
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	1	no	—
607	C₂²×C₅	—	2	1	no	—
608	C₂²×C₅	—	4	4	no	—
609	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
610	C₂²×C₅	C₃×#131	1	2	yes	complemented
611	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
612	C₂×D₅	—	2	1	no	—
613	C₂×D₅	—	2	1	no	—
614	C₂×D₅	—	2	1	no	—
615	C₄×C₅	—	2	1	no	—
616	C₄×C₅	—	2	1	no	—
617	C₄×C₅	—	2	1	no	—
618	Dic₅	—	2	1	no	—
619	Dic₅	—	2	1	no	—
620	Dic₅	—	2	1	no	—
621	Dic₅	—	2	1	no	—
622	Dic₅	—	2	1	no	—
623	Dic₅	C₃×C₄×D₄	1	2	yes	—
624	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
625	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
626	C₂⁴	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
627	#41	—	10	2	no	—
628	#41	—	10	2	no	—
629	C₂×Q₈	—	5	1	no	—
630	C₂×D₄	—	5	1	no	—
631	C₂×D₄	—	5	1	no	—
632	C₂×D₄	—	5	1	no	—
633	C₂×D₄	—	5	1	no	—
634	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
635	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
636	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
637	C₂²×C₄	—	5	1	no	—
638	C₂²×C₄	—	5	1	no	—
639	C₂²×C₄	—	5	1	no	—
640	C₂²×C₄	—	5	1	no	—
641	C₂²×C₄	—	5	1	no	—
642	C₂²×C₄	—	5	1	no	—
643	C₂²×C₄	—	5	1	no	—
644	C₂²×C₄	—	5	1	no	—
645	C₂²×C₄	—	10	2	no	—
646	C₂²×C₄	—	10	2	no	—
647	M₁₆	—	5	4	no	—
648	M₁₆	—	10	2	no	—
649	M₁₆	—	10	2	no	—
650	M₁₆	—	10	2	no	—
651	M₁₆	—	10	2	no	—
652	M₁₆	—	10	2	no	—
653	C₂×C₈	—	5	1	no	—
654	C₂×C₈	—	5	1	no	—
655	C₂×C₈	—	5	1	no	—
656	C₂×C₈	—	5	1	no	—
657	C₂×C₈	—	5	1	no	—
658	C₂×C₈	—	5	1	no	—
659	C₂×C₈	—	5	1	no	—
660	C₂×C₈	—	5	1	no	—
661	C₂×C₈	—	10	2	no	—
662	C₂×C₈	—	10	2	no	—
663	C₂×C₈	—	10	2	no	—
664	C₂×C₈	—	10	2	no	—
665	C₂×C₈	—	10	2	no	—
666	C₂×C₈	—	10	2	no	—
667	C₄⋊C₄	—	5	1	no	—
668	C₄⋊C₄	—	5	1	no	—
669	C₄⋊C₄	—	5	1	no	—
670	C₄⋊C₄	—	5	1	no	—
671	C₄⋊C₄	—	5	1	no	—
672	C₄⋊C₄	—	5	1	no	—
673	C₂²⋊C₄	—	5	1	no	—
674	C₂²⋊C₄	—	5	1	no	—
675	C₂²⋊C₄	—	5	1	no	—
676	C₂²⋊C₄	—	5	1	no	—
677	C₂²⋊C₄	—	5	1	no	—
678	C₂²⋊C₄	—	5	1	no	—
679	C₂²⋊C₄	—	5	1	no	—
680	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
681	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
682	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
683	C₄²	—	5	1	no	—
684	C₄²	—	5	1	no	—
685	C₃×C₅	#2933	1	1	yes	characteristic, complemented, Hall
686	C₂²×C₃	—	2	1	no	—
687	C₂²×C₃	—	2	1	no	—
688	C₂²×C₃	—	2	1	no	—
689	C₂²×C₃	—	2	1	no	—
690	C₂²×C₃	—	2	1	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	—	2	1	no	—
696	C₂²×C₃	—	4	4	no	—
697	C₂²×C₃	—	10	1	no	—
698	C₂²×C₃	—	10	1	no	—
699	C₂²×C₃	—	10	1	no	—
700	C₂²×C₃	#4131	1	2	yes	complemented
701	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	2	yes	—
702	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
703	C₃×C₄	—	2	1	no	—
704	C₃×C₄	—	2	1	no	—
705	C₃×C₄	—	2	1	no	—
706	C₃×C₄	—	5	2	no	—
707	C₃×C₄	—	5	1	no	—
708	C₃×C₄	—	5	1	no	—
709	C₃×C₄	—	10	1	no	—
710	C₃×C₄	—	10	1	no	—
711	C₃×C₄	—	10	1	no	—
712	C₃×C₄	—	10	1	no	—
713	C₃×C₄	—	10	1	no	—
714	C₂×C₅	—	2	2	no	—
715	C₂×C₅	—	2	2	no	—
716	C₂×C₅	—	4	1	no	—
717	C₂×C₅	—	4	1	no	—
718	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
719	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
720	C₂×C₅	C₃×#568	1	1	yes	characteristic
721	D₅	—	4	1	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	4	1	no	—
725	C₂³	—	5	1	no	—
726	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
727	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
728	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
729	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
730	Q₈	—	10	2	no	—
731	D₄	—	2	2	no	—
732	D₄	—	2	2	no	—
733	D₄	—	4	1	no	—
734	D₄	—	10	2	no	—
735	D₄	—	10	2	no	—
736	D₄	—	10	2	no	—
737	D₄	—	20	1	no	—
738	C₂×C₄	—	5	2	no	—
739	C₂×C₄	—	5	2	no	—
740	C₂×C₄	—	5	1	no	—
741	C₂×C₄	—	5	1	no	—
742	C₂×C₄	—	5	1	no	—
743	C₂×C₄	—	5	1	no	—
744	C₂×C₄	—	5	1	no	—
745	C₂×C₄	—	5	1	no	—
746	C₂×C₄	—	5	1	no	—
747	C₂×C₄	—	10	1	no	—
748	C₂×C₄	—	10	1	no	—
749	C₂×C₄	—	10	1	no	—
750	C₂×C₄	—	10	1	no	—
751	C₂×C₄	—	10	1	no	—
752	C₂×C₄	—	10	1	no	—
753	C₂×C₄	—	10	1	no	—
754	C₂×C₄	—	10	2	no	—
755	C₂×C₄	—	10	2	no	—
756	C₂×C₄	—	10	1	no	—
757	C₂×C₄	—	10	2	no	—
758	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
759	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
760	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
761	C₈	—	5	2	no	—
762	C₈	—	5	2	no	—
763	C₈	—	10	1	no	—
764	C₈	—	10	1	no	—
765	C₈	—	10	1	no	—
766	C₈	—	10	1	no	—
767	C₈	—	10	1	no	—
768	C₈	—	10	1	no	—
769	C₂×C₃	—	2	2	no	—
770	C₂×C₃	—	2	2	no	—
771	C₂×C₃	—	4	1	no	—
772	C₂×C₃	—	4	1	no	—
773	C₂×C₃	—	20	1	no	—
774	C₂×C₃	C₂×#4131	1	1	yes	characteristic
775	C₂×C₃	#66256	1	1	yes	characteristic
776	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
777	C₅	C₃×#2933	1	1	yes	characteristic, complemented, Sylow
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	2	1	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	10	1	no	—
790	C₂²	—	10	1	no	—
791	C₂²	—	10	1	no	—
792	C₂²	C₃×#4131	1	2	yes	complemented
793	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
794	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	5	1	no	—
799	C₄	—	5	1	no	—
800	C₄	—	5	2	no	—
801	C₄	—	10	1	no	—
802	C₄	—	10	1	no	—
803	C₄	—	10	1	no	—
804	C₄	—	10	1	no	—
805	C₄	—	10	1	no	—
806	C₃	#10617217	1	1	yes	characteristic, direct product factor, Sylow
807	C₂	—	2	2	no	—
808	C₂	—	2	2	no	—
809	C₂	—	4	1	no	—
810	C₂	—	4	1	no	—
811	C₂	—	20	1	no	—
812	C₂	C₂×C₃×#4131	1	1	yes	characteristic
813	C₂	C₃×#66256	1	1	yes	characteristic
814	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#120	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#65920	C₂
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#120	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2933
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#120

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#704	C₂	semidirect
2. C₂×C₃×#4131	C₂	semidirect
4. C₂×C₃×C₂²⋊#170	C₂	semidirect
5. C₃×#65775	C₂	semidirect
6. C₃×#65774	C₂	semidirect
7. C₃×#65773	C₂	semidirect
8. C₃×#65773	C₂	semidirect
9. C₃×D₄×#170	C₂	semidirect
10. C₃×#65696	C₂	semidirect
11. C₃×#65695	C₂	semidirect
12. C₃×#65694	C₂	semidirect
13. C₃×#65693	C₂	semidirect
14. C₃×#65692	C₂	semidirect
15. C₃×#65691	C₂	semidirect
16. #10617217	C₃	direct (N × H)
24. C₂×C₃×#704	C₂²	semidirect
29. C₂²×C₃×#170	C₂²	semidirect
31. C₂×C₃×#700	C₂²	semidirect
32. C₂×C₃×D₅⋊C₈	C₂²	semidirect
50. C₃×C₂²⋊#170	C₂²	semidirect
51. C₃×C₂²⋊#170	C₂²	semidirect
52. C₃×#4004	C₂²	semidirect
53. C₃×#4004	C₂²	semidirect
54. C₃×#4003	C₂²	semidirect
55. C₃×#4003	C₂²	semidirect
56. C₃×#4002	C₂²	semidirect
57. C₃×#4002	C₂²	semidirect
58. C₃×C₄⋊#170	C₂²	semidirect
59. C₃×C₄⋊#170	C₂²	semidirect
60. C₃×C₄×#170	C₂²	semidirect
61. C₃×C₄×#170	C₂²	semidirect
63. C₂²×#704	C₂×C₃	semidirect
64. C₂×#4131	C₂×C₃	semidirect
66. C₂×C₂²⋊#170	C₂×C₃	semidirect
67. #65775	C₂×C₃	semidirect
68. #65774	C₂×C₃	semidirect
69. #65773	C₂×C₃	semidirect
70. #65773	C₂×C₃	semidirect
71. D₄×#170	C₂×C₃	semidirect
72. #65696	C₂×C₃	semidirect
73. #65695	C₂×C₃	semidirect
74. #65694	C₂×C₃	semidirect
75. #65693	C₂×C₃	semidirect
76. #65692	C₂×C₃	semidirect
77. #65691	C₂×C₃	semidirect
103. C₃×#704	D₄	semidirect
159. C₂×#704	C₂²×C₃	semidirect
164. C₂²×#170	C₂²×C₃	semidirect
166. C₂×#700	C₂²×C₃	semidirect
167. C₂×D₅⋊C₈	C₂²×C₃	semidirect
185. C₂²⋊#170	C₂²×C₃	semidirect
186. C₂²⋊#170	C₂²×C₃	semidirect
187. #4004	C₂²×C₃	semidirect
188. #4004	C₂²×C₃	semidirect
189. #4003	C₂²×C₃	semidirect
190. #4003	C₂²×C₃	semidirect
191. #4002	C₂²×C₃	semidirect
192. #4002	C₂²×C₃	semidirect
193. C₄⋊#170	C₂²×C₃	semidirect
194. C₄⋊#170	C₂²×C₃	semidirect
195. C₄×#170	C₂²×C₃	semidirect
196. C₄×#170	C₂²×C₃	semidirect
315. #704	C₃×D₄	semidirect
376. C₂²×C₃×C₅	#131	semidirect
610. C₂²×C₅	C₃×#131	semidirect
685. C₃×C₅	#2933	semidirect
700. C₂²×C₃	#4131	semidirect
777. C₅	C₃×#2933	semidirect
792. C₂²	C₃×#4131	semidirect
806. C₃	#10617217	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#704	2
C₂×C₃×#4131	2
C₃×#65920	2
C₂×C₃×C₂²⋊#170	2
C₃×#65775	2
C₃×#65774	2
C₃×#65773	2
C₃×D₄×#170	2
C₃×#65696	2
C₃×#65695	2
C₃×#65694	2
C₃×#65693	2
C₃×#65692	2
C₃×#65691	2
#10617217	3
C₃×#2933	5

Subgroups — C3×#10617217 #14415460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617217 #14415460