Subgroups — C₃×#10611736 #14424637

Order 1920.

1528 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4144	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4058	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4057	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65942	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#447	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65507	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65447	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65445	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65326	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65072	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65065	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65060	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×D₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65022	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65016	C₂	1	1	yes	maximal, characteristic, complemented
16	#10611736	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
19	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
20	C₃×#4144	—	2	4	no	—
21	C₃×#4144	—	2	4	no	—
22	C₂×C₃×#711	—	2	1	no	—
23	C₂×C₃×#711	C₂²	1	1	yes	characteristic
24	C₂×C₃×#711	C₂²	1	1	yes	characteristic
25	C₂×C₃×#711	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×D₄×D₅	—	2	1	no	—
27	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×#709	C₂²	1	1	yes	characteristic
30	C₂×C₃×#709	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
34	C₃×#4085	—	2	1	no	—
35	C₃×#4084	—	2	1	no	—
36	C₃×#4084	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×#687	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×#687	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×#687	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×#686	C₂²	1	1	yes	characteristic, complemented
41	C₃×#4070	C₂²	1	1	yes	characteristic, complemented
42	C₃×#4058	—	2	4	no	—
43	C₃×#4057	—	2	4	no	—
44	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×#677	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×#676	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic, complemented
48	C₃×#4043	C₂²	1	1	yes	characteristic, complemented
49	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₃×#4030	—	2	1	no	—
51	C₃×#4024	—	2	1	no	—
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₃×#3964	C₂²	1	1	yes	characteristic, complemented
56	C₃×#3964	C₂²	1	1	yes	characteristic, complemented
57	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic, complemented
58	C₃×#3953	C₂²	1	1	yes	characteristic, complemented
59	C₃×#3952	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3952	C₂²	1	1	yes	characteristic, complemented
61	C₃×#3948	C₂²	1	1	yes	characteristic, complemented
62	C₃×#3942	C₂²	1	1	yes	characteristic, complemented
63	C₃×#3941	C₂²	1	1	yes	characteristic, complemented
64	C₃×#3012	—	5	1	no	maximal, Hall
65	C₂×#4144	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×#4058	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂×#4057	C₂×C₃	1	1	yes	characteristic, complemented
68	#65942	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#447	C₂×C₃	1	1	yes	characteristic, complemented
70	#65507	C₂×C₃	1	1	yes	characteristic, complemented
71	#65447	C₂×C₃	1	1	yes	characteristic, complemented
72	#65445	C₂×C₃	1	1	yes	characteristic, complemented
73	#65326	C₂×C₃	1	1	yes	characteristic, complemented
74	#65072	C₂×C₃	1	1	yes	characteristic, complemented
75	#65065	C₂×C₃	1	1	yes	characteristic, complemented
76	#65060	C₂×C₃	1	1	yes	characteristic, complemented
77	D₅×#102	C₂×C₃	1	1	yes	characteristic, complemented
78	#65022	C₂×C₃	1	1	yes	characteristic, complemented
79	#65016	C₂×C₃	1	1	yes	characteristic, complemented
80	C₂⁴×C₃×C₅	—	2	1	no	—
81	C₂³×C₃×D₅	—	2	1	no	—
82	C₂³×C₃×D₅	—	2	1	no	—
83	C₂×C₃×C₅×D₄	—	2	2	no	—
84	C₂×C₃×C₅×D₄	—	2	2	no	—
85	C₂×C₃×C₅×D₄	—	2	1	no	—
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
92	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
93	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
94	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
95	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
96	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
97	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
98	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
99	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
100	C₂×C₃×C₂²⋊D₅	D₄	1	1	yes	characteristic
101	C₂×C₃×C₂²⋊D₅	D₄	1	1	yes	characteristic
102	C₂²×C₃×Dic₅	—	2	1	no	—
103	C₂²×C₃×Dic₅	—	2	1	no	—
104	C₂²×C₃×Dic₅	—	2	1	no	—
105	C₃×#711	—	2	8	no	—
106	C₃×#711	—	2	2	no	—
107	C₃×#711	—	2	2	no	—
108	C₃×#711	—	2	2	no	—
109	C₃×#711	—	2	2	no	—
110	C₃×#711	—	2	2	no	—
111	C₃×#711	D₄	1	4	yes	complemented
112	C₃×D₄×D₅	—	2	8	no	—
113	C₃×D₄×D₅	—	2	2	no	—
114	C₃×D₄×D₅	—	2	2	no	—
115	C₃×D₄×D₅	—	2	2	no	—
116	C₃×D₄×D₅	D₄	1	4	yes	complemented
117	C₃×#709	—	2	2	no	—
118	C₃×#709	—	2	2	no	—
119	C₃×#709	—	2	2	no	—
120	C₃×#709	—	2	2	no	—
121	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
122	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₄×D₅	—	2	1	no	—
124	C₂×C₃×C₄×D₅	—	2	1	no	—
125	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
126	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
127	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
128	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
129	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
130	C₃×C₅×D₈	—	2	2	no	—
131	C₃×C₅×D₈	—	2	2	no	—
132	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
134	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
136	C₃×C₂²⋊Dic₅	—	2	1	no	—
137	C₃×C₂²⋊Dic₅	—	2	1	no	—
138	C₃×#687	—	2	2	no	—
139	C₃×#687	—	2	2	no	—
140	C₃×#687	—	2	2	no	—
141	C₃×#686	—	2	2	no	—
142	C₃×#685	—	2	1	no	—
143	C₃×C₄⋊Dic₅	—	2	1	no	—
144	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
145	C₃×#683	—	2	1	no	—
146	C₃×#683	—	2	1	no	—
147	C₂×C₃×#168	C₂³	1	1	yes	characteristic
148	C₂×C₃×#168	C₂³	1	1	yes	characteristic
149	C₃×Dic₂₀	—	2	2	no	—
150	C₃×#677	—	2	2	no	—
151	C₃×#676	—	2	2	no	—
152	C₃×C₈×D₅	—	2	2	no	—
153	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
154	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
155	C₂×C₃×#135	—	5	1	no	—
156	C₃×#537	—	5	1	no	—
157	C₃×#452	—	5	1	no	—
158	C₃×#452	—	5	1	no	—
159	C₃×#450	—	5	1	no	—
160	C₃×#450	—	5	1	no	—
161	C₃×#449	—	5	1	no	—
162	C₃×#449	—	5	1	no	—
163	C₃×#447	—	5	1	no	—
164	C₃×#447	D₅	1	1	yes	characteristic, complemented
165	C₃×#417	—	5	1	no	—
166	C₂×C₃×#102	—	5	1	no	—
167	C₃×#408	—	5	1	no	—
168	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
169	C₂²×C₂²⋊D₅	—	2	1	no	—
170	C₂²×C₂²⋊D₅	—	2	1	no	—
171	#4144	—	2	4	no	—
172	#4144	—	2	4	no	—
173	C₂×#711	—	2	1	no	—
174	C₂×#711	C₂²×C₃	1	1	yes	characteristic
175	C₂×#711	C₂²×C₃	1	1	yes	characteristic
176	C₂×#711	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₂×D₄×D₅	—	2	1	no	—
178	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
179	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
180	C₂×#709	C₂²×C₃	1	1	yes	characteristic
181	C₂×#709	C₂²×C₃	1	1	yes	characteristic
182	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
185	#4085	—	2	1	no	—
186	#4084	—	2	1	no	—
187	#4084	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₂×#687	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₂×#687	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₂×#687	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₂×#686	C₂²×C₃	1	1	yes	characteristic, complemented
192	#4070	C₂²×C₃	1	1	yes	characteristic, complemented
193	#4058	—	2	4	no	—
194	#4057	—	2	4	no	—
195	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₂×#677	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₂×#676	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
199	#4043	C₂²×C₃	1	1	yes	characteristic, complemented
200	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
201	#4030	—	2	1	no	—
202	#4024	—	2	1	no	—
203	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
204	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
205	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
206	#3964	C₂²×C₃	1	1	yes	characteristic, complemented
207	#3964	C₂²×C₃	1	1	yes	characteristic, complemented
208	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
209	#3953	C₂²×C₃	1	1	yes	characteristic, complemented
210	#3952	C₂²×C₃	1	1	yes	characteristic, complemented
211	#3952	C₂²×C₃	1	1	yes	characteristic, complemented
212	#3948	C₂²×C₃	1	1	yes	characteristic, complemented
213	#3942	C₂²×C₃	1	1	yes	characteristic, complemented
214	#3941	C₂²×C₃	1	1	yes	characteristic, complemented
215	#3012	—	5	1	no	Sylow
216	C₂³×C₃×C₅	—	2	4	no	—
217	C₂³×C₃×C₅	—	2	1	no	—
218	C₂³×C₃×C₅	—	2	1	no	—
219	C₂³×C₃×C₅	—	2	1	no	—
220	C₂³×C₃×C₅	—	8	1	no	—
221	C₂³×C₃×C₅	—	8	1	no	—
222	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₃×D₅	—	2	1	no	—
224	C₂²×C₃×D₅	—	2	4	no	—
225	C₂²×C₃×D₅	—	2	4	no	—
226	C₂²×C₃×D₅	—	8	1	no	—
227	C₂²×C₃×D₅	—	8	1	no	—
228	C₂²×C₃×D₅	—	8	1	no	—
229	C₂²×C₃×D₅	—	8	1	no	—
230	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
232	C₃×C₅×D₄	—	2	4	no	—
233	C₃×C₅×D₄	—	2	1	no	—
234	C₃×C₅×D₄	—	2	1	no	—
235	C₃×C₅×D₄	—	2	1	no	—
236	C₃×C₅×D₄	—	2	1	no	—
237	C₃×C₅×D₄	—	8	1	no	—
238	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
239	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
240	C₂×C₃×C₄×C₅	—	2	1	no	—
241	C₂×C₃×C₄×C₅	—	2	1	no	—
242	C₂×C₃×C₄×C₅	—	2	1	no	—
243	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
245	C₃×C₂²⋊D₅	—	2	4	no	—
246	C₃×C₂²⋊D₅	—	2	4	no	—
247	C₃×C₂²⋊D₅	—	2	4	no	—
248	C₃×C₂²⋊D₅	—	2	2	no	—
249	C₃×C₂²⋊D₅	—	2	4	no	—
250	C₃×C₂²⋊D₅	—	2	2	no	—
251	C₃×C₂²⋊D₅	—	2	4	no	—
252	C₃×C₂²⋊D₅	—	4	2	no	—
253	C₃×C₂²⋊D₅	—	8	1	no	—
254	C₂×C₃×Dic₅	—	2	4	no	—
255	C₂×C₃×Dic₅	—	2	1	no	—
256	C₂×C₃×Dic₅	—	2	4	no	—
257	C₂×C₃×Dic₅	—	2	1	no	—
258	C₂×C₃×Dic₅	—	2	1	no	—
259	C₂×C₃×Dic₅	—	4	2	no	—
260	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
261	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
262	C₃×D₂₀	—	2	2	no	—
263	C₃×D₂₀	—	2	1	no	—
264	C₃×D₂₀	C₂×D₄	1	2	yes	—
265	C₃×C₄×D₅	—	2	4	no	—
266	C₃×C₄×D₅	—	2	1	no	—
267	C₃×C₄×D₅	—	2	1	no	—
268	C₃×C₄×D₅	—	8	1	no	—
269	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
270	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
271	C₃×Dic₁₀	—	2	1	no	—
272	C₃×Dic₁₀	—	2	2	no	—
273	C₃×Dic₁₀	—	2	1	no	—
274	C₃×Dic₁₀	—	2	1	no	—
275	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
276	C₃×C₅×C₈	—	2	1	no	—
277	C₃×C₅×C₈	—	2	1	no	—
278	C₃×#168	—	2	1	no	—
279	C₃×#168	—	2	1	no	—
280	C₃×H(5,𝔽₂)	—	10	4	no	—
281	C₃×H(5,𝔽₂)	—	10	4	no	—
282	C₂×C₃×#41	—	5	1	no	—
283	C₂×C₃×#41	—	5	1	no	—
284	C₂×C₃×#41	—	5	1	no	—
285	C₂×C₃×#41	—	5	1	no	—
286	C₂×C₃×#41	—	5	1	no	—
287	C₂×C₃×#41	—	10	1	no	—
288	C₂²×C₃×D₄	—	5	1	no	—
289	C₂²×C₃×D₄	—	5	1	no	—
290	C₂²×C₃×D₄	—	10	1	no	—
291	C₂²×C₃×D₄	—	10	1	no	—
292	C₂²×C₃×D₄	—	10	1	no	—
293	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
294	C₃×AGL(1,ℤ/8)	—	10	4	no	—
295	C₃×#135	—	10	4	no	—
296	C₂×C₃×Q₁₆	—	5	1	no	—
297	C₂×C₃×SD₁₆	—	5	1	no	—
298	C₂×C₃×SD₁₆	—	5	1	no	—
299	C₂×C₃×SD₁₆	—	5	1	no	—
300	C₂×C₃×SD₁₆	—	5	1	no	—
301	C₂×C₃×D₈	—	5	1	no	—
302	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
303	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
304	C₂×C₃×M₁₆	—	5	1	no	—
305	C₂²×C₃×C₈	—	5	1	no	—
306	C₃×C₂²⋊Q₈	—	5	1	no	—
307	C₃×C₂²⋊Q₈	—	5	1	no	—
308	C₃×C₂²⋊Q₈	—	10	1	no	—
309	C₃×#121	—	5	1	no	—
310	C₃×#121	—	10	1	no	—
311	C₃×#121	—	10	1	no	—
312	C₃×#121	—	10	1	no	—
313	C₃×#121	C₂×D₅	1	1	yes	characteristic, complemented
314	C₂×C₃×C₄⋊C₄	—	5	1	no	—
315	C₃×#103	—	5	1	no	—
316	C₃×#103	—	5	1	no	—
317	C₃×#102	—	5	1	no	—
318	C₃×#102	—	5	1	no	—
319	C₃×#102	—	5	1	no	—
320	C₃×#102	—	5	1	no	—
321	C₃×#102	C₂×D₅	1	1	yes	characteristic, complemented
322	C₃×#102	C₂×D₅	1	1	yes	characteristic, complemented
323	C₃×C₂²⋊C₈	—	5	1	no	—
324	C₃×C₂²⋊C₈	—	5	1	no	—
325	C₃×C₂²⋊C₈	—	5	1	no	—
326	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
327	C₂⁴×C₅	—	2	1	no	—
328	C₂³×D₅	—	2	1	no	—
329	C₂³×D₅	—	2	1	no	—
330	C₂×C₅×D₄	—	2	2	no	—
331	C₂×C₅×D₄	—	2	2	no	—
332	C₂×C₅×D₄	—	2	1	no	—
333	C₂×C₅×D₄	—	2	1	no	—
334	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
335	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
336	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
337	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
338	C₂×C₂²⋊D₅	—	2	8	no	—
339	C₂×C₂²⋊D₅	—	2	8	no	—
340	C₂×C₂²⋊D₅	—	2	1	no	—
341	C₂×C₂²⋊D₅	—	2	1	no	—
342	C₂×C₂²⋊D₅	—	2	1	no	—
343	C₂×C₂²⋊D₅	—	2	1	no	—
344	C₂×C₂²⋊D₅	—	2	1	no	—
345	C₂×C₂²⋊D₅	—	2	1	no	—
346	C₂×C₂²⋊D₅	—	2	1	no	—
347	C₂×C₂²⋊D₅	C₃×D₄	1	1	yes	characteristic
348	C₂×C₂²⋊D₅	C₃×D₄	1	1	yes	characteristic
349	C₂²×Dic₅	—	2	1	no	—
350	C₂²×Dic₅	—	2	1	no	—
351	C₂²×Dic₅	—	2	1	no	—
352	#711	—	2	8	no	—
353	#711	—	2	2	no	—
354	#711	—	2	2	no	—
355	#711	—	2	2	no	—
356	#711	—	2	2	no	—
357	#711	—	2	2	no	—
358	#711	C₃×D₄	1	4	yes	complemented
359	D₄×D₅	—	2	8	no	—
360	D₄×D₅	—	2	2	no	—
361	D₄×D₅	—	2	2	no	—
362	D₄×D₅	—	2	2	no	—
363	D₄×D₅	C₃×D₄	1	4	yes	complemented
364	#709	—	2	2	no	—
365	#709	—	2	2	no	—
366	#709	—	2	2	no	—
367	#709	—	2	2	no	—
368	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
369	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
370	C₂×C₄×D₅	—	2	1	no	—
371	C₂×C₄×D₅	—	2	1	no	—
372	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
373	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
374	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
375	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
376	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
377	C₅×D₈	—	2	2	no	—
378	C₅×D₈	—	2	2	no	—
379	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
380	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
381	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
382	C₅×C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊Dic₅	—	2	1	no	—
384	C₂²⋊Dic₅	—	2	1	no	—
385	#687	—	2	2	no	—
386	#687	—	2	2	no	—
387	#687	—	2	2	no	—
388	#686	—	2	2	no	—
389	#685	—	2	1	no	—
390	C₄⋊Dic₅	—	2	1	no	—
391	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
392	#683	—	2	1	no	—
393	#683	—	2	1	no	—
394	C₂×#168	C₂³×C₃	1	1	yes	characteristic
395	C₂×#168	C₂³×C₃	1	1	yes	characteristic
396	Dic₂₀	—	2	2	no	—
397	#677	—	2	2	no	—
398	#676	—	2	2	no	—
399	C₈×D₅	—	2	2	no	—
400	C₂×H(5,𝔽₂)	—	5	1	no	—
401	C₂×AGL(1,ℤ/8)	—	5	1	no	—
402	C₂×#135	—	5	1	no	—
403	#537	—	5	1	no	—
404	#452	—	5	1	no	—
405	#452	—	5	1	no	—
406	#450	—	5	1	no	—
407	#450	—	5	1	no	—
408	#449	—	5	1	no	—
409	#449	—	5	1	no	—
410	#447	—	5	1	no	—
411	#447	C₃×D₅	1	1	yes	characteristic, complemented
412	#417	—	5	1	no	—
413	C₂×#102	—	5	1	no	—
414	#408	—	5	1	no	—
415	C₂²×C₃×C₅	—	2	2	no	—
416	C₂²×C₃×C₅	—	2	2	no	—
417	C₂²×C₃×C₅	—	2	1	no	—
418	C₂²×C₃×C₅	—	2	1	no	—
419	C₂²×C₃×C₅	—	2	1	no	—
420	C₂²×C₃×C₅	—	4	1	no	—
421	C₂²×C₃×C₅	—	4	1	no	—
422	C₂²×C₃×C₅	—	4	1	no	—
423	C₂²×C₃×C₅	—	4	1	no	—
424	C₂²×C₃×C₅	—	4	1	no	—
425	C₂²×C₃×C₅	—	4	1	no	—
426	C₂²×C₃×C₅	—	4	1	no	—
427	C₂²×C₃×C₅	—	8	4	no	—
428	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₃×D₅	—	2	1	no	—
430	C₂×C₃×D₅	—	2	1	no	—
431	C₂×C₃×D₅	—	2	1	no	—
432	C₂×C₃×D₅	—	2	2	no	—
433	C₂×C₃×D₅	—	2	1	no	—
434	C₂×C₃×D₅	—	2	1	no	—
435	C₂×C₃×D₅	—	4	1	no	—
436	C₂×C₃×D₅	—	4	1	no	—
437	C₂×C₃×D₅	—	8	4	no	—
438	C₂×C₃×D₅	—	8	4	no	—
439	C₂×C₃×D₅	#120	1	2	yes	—
440	C₃×C₄×C₅	—	2	1	no	—
441	C₃×C₄×C₅	—	4	1	no	—
442	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
443	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
444	C₃×Dic₅	—	2	1	no	—
445	C₃×Dic₅	—	2	2	no	—
446	C₃×Dic₅	—	4	1	no	—
447	C₃×Dic₅	—	4	1	no	—
448	C₃×Dic₅	#120	1	2	yes	—
449	C₂⁴×C₃	—	2	1	no	—
450	C₂⁴×C₃	—	10	1	no	—
451	C₂⁴×C₃	—	10	1	no	—
452	C₃×#41	—	5	4	no	—
453	C₃×#41	—	10	2	no	—
454	C₃×#41	—	10	2	no	—
455	C₃×#41	—	10	2	no	—
456	C₃×#41	—	10	2	no	—
457	C₃×#41	—	10	2	no	—
458	C₃×#41	—	10	2	no	—
459	C₃×#41	—	10	2	no	—
460	C₃×#41	—	10	2	no	—
461	C₃×#41	—	10	8	no	—
462	C₃×#41	—	10	2	no	—
463	C₂×C₃×Q₈	—	5	1	no	—
464	C₂×C₃×Q₈	—	5	1	no	—
465	C₂×C₃×Q₈	—	5	1	no	—
466	C₂×C₃×D₄	—	2	2	no	—
467	C₂×C₃×D₄	—	2	2	no	—
468	C₂×C₃×D₄	—	2	1	no	—
469	C₂×C₃×D₄	—	2	1	no	—
470	C₂×C₃×D₄	—	5	4	no	—
471	C₂×C₃×D₄	—	5	1	no	—
472	C₂×C₃×D₄	—	5	1	no	—
473	C₂×C₃×D₄	—	5	1	no	—
474	C₂×C₃×D₄	—	5	1	no	—
475	C₂×C₃×D₄	—	10	2	no	—
476	C₂×C₃×D₄	—	10	1	no	—
477	C₂×C₃×D₄	—	10	1	no	—
478	C₂×C₃×D₄	—	10	2	no	—
479	C₂×C₃×D₄	—	10	8	no	—
480	C₂×C₃×D₄	—	10	1	no	—
481	C₂×C₃×D₄	—	10	1	no	—
482	C₂×C₃×D₄	—	10	8	no	—
483	C₂×C₃×D₄	—	10	8	no	—
484	C₂×C₃×D₄	—	10	1	no	—
485	C₂×C₃×D₄	—	10	2	no	—
486	C₂×C₃×D₄	—	10	1	no	—
487	C₂×C₃×D₄	—	10	1	no	—
488	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
489	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
490	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
491	C₂²×C₃×C₄	—	5	1	no	—
492	C₂²×C₃×C₄	—	5	1	no	—
493	C₂²×C₃×C₄	—	10	1	no	—
494	C₂²×C₃×C₄	—	10	1	no	—
495	C₂²×C₃×C₄	—	10	1	no	—
496	C₂²×C₃×C₄	—	10	1	no	—
497	C₂²×C₃×C₄	—	10	1	no	—
498	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
499	C₃×Q₁₆	—	10	2	no	—
500	C₃×SD₁₆	—	10	2	no	—
501	C₃×SD₁₆	—	10	2	no	—
502	C₃×SD₁₆	—	10	2	no	—
503	C₃×SD₁₆	—	10	2	no	—
504	C₃×D₈	—	2	2	no	—
505	C₃×D₈	—	2	2	no	—
506	C₃×D₈	—	10	2	no	—
507	C₃×M₁₆	—	10	2	no	—
508	C₂×C₃×C₈	—	5	1	no	—
509	C₂×C₃×C₈	—	5	1	no	—
510	C₂×C₃×C₈	—	10	2	no	—
511	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
512	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
513	C₃×C₄⋊C₄	—	5	1	no	—
514	C₃×C₄⋊C₄	—	10	1	no	—
515	C₃×C₄⋊C₄	—	10	1	no	—
516	C₃×C₄⋊C₄	—	10	1	no	—
517	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
518	C₃×C₂²⋊C₄	—	2	1	no	—
519	C₃×C₂²⋊C₄	—	10	1	no	—
520	C₃×C₂²⋊C₄	—	10	1	no	—
521	C₃×C₂²⋊C₄	—	10	1	no	—
522	C₂³×C₅	—	2	4	no	—
523	C₂³×C₅	—	2	1	no	—
524	C₂³×C₅	—	2	1	no	—
525	C₂³×C₅	—	2	1	no	—
526	C₂³×C₅	—	8	1	no	—
527	C₂³×C₅	—	8	1	no	—
528	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
529	C₂²×D₅	—	2	1	no	—
530	C₂²×D₅	—	2	4	no	—
531	C₂²×D₅	—	2	4	no	—
532	C₂²×D₅	—	8	1	no	—
533	C₂²×D₅	—	8	1	no	—
534	C₂²×D₅	—	8	1	no	—
535	C₂²×D₅	—	8	1	no	—
536	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
537	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
538	C₅×D₄	—	2	4	no	—
539	C₅×D₄	—	2	1	no	—
540	C₅×D₄	—	2	1	no	—
541	C₅×D₄	—	2	1	no	—
542	C₅×D₄	—	2	1	no	—
543	C₅×D₄	—	8	1	no	—
544	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
545	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
546	C₂×C₄×C₅	—	2	1	no	—
547	C₂×C₄×C₅	—	2	1	no	—
548	C₂×C₄×C₅	—	2	1	no	—
549	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
550	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
551	C₂²⋊D₅	—	2	4	no	—
552	C₂²⋊D₅	—	2	4	no	—
553	C₂²⋊D₅	—	2	4	no	—
554	C₂²⋊D₅	—	2	2	no	—
555	C₂²⋊D₅	—	2	4	no	—
556	C₂²⋊D₅	—	2	2	no	—
557	C₂²⋊D₅	—	2	4	no	—
558	C₂²⋊D₅	—	4	2	no	—
559	C₂²⋊D₅	—	8	1	no	—
560	C₂×Dic₅	—	2	4	no	—
561	C₂×Dic₅	—	2	1	no	—
562	C₂×Dic₅	—	2	4	no	—
563	C₂×Dic₅	—	2	1	no	—
564	C₂×Dic₅	—	2	1	no	—
565	C₂×Dic₅	—	4	2	no	—
566	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
567	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
568	D₂₀	—	2	2	no	—
569	D₂₀	—	2	1	no	—
570	D₂₀	C₂×C₃×D₄	1	2	yes	—
571	C₄×D₅	—	2	4	no	—
572	C₄×D₅	—	2	1	no	—
573	C₄×D₅	—	2	1	no	—
574	C₄×D₅	—	8	1	no	—
575	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
576	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
577	Dic₁₀	—	2	1	no	—
578	Dic₁₀	—	2	2	no	—
579	Dic₁₀	—	2	1	no	—
580	Dic₁₀	—	2	1	no	—
581	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
582	C₅×C₈	—	2	1	no	—
583	C₅×C₈	—	2	1	no	—
584	#168	—	2	1	no	—
585	#168	—	2	1	no	—
586	H(5,𝔽₂)	—	10	4	no	—
587	H(5,𝔽₂)	—	10	4	no	—
588	C₂×#41	—	5	1	no	—
589	C₂×#41	—	5	1	no	—
590	C₂×#41	—	5	1	no	—
591	C₂×#41	—	5	1	no	—
592	C₂×#41	—	5	1	no	—
593	C₂×#41	—	10	1	no	—
594	C₂²×D₄	—	5	1	no	—
595	C₂²×D₄	—	5	1	no	—
596	C₂²×D₄	—	10	1	no	—
597	C₂²×D₄	—	10	1	no	—
598	C₂²×D₄	—	10	1	no	—
599	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
600	AGL(1,ℤ/8)	—	10	4	no	—
601	#135	—	10	4	no	—
602	C₂×Q₁₆	—	5	1	no	—
603	C₂×SD₁₆	—	5	1	no	—
604	C₂×SD₁₆	—	5	1	no	—
605	C₂×SD₁₆	—	5	1	no	—
606	C₂×SD₁₆	—	5	1	no	—
607	C₂×D₈	—	5	1	no	—
608	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
609	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
610	C₂×M₁₆	—	5	1	no	—
611	C₂²×C₈	—	5	1	no	—
612	C₂²⋊Q₈	—	5	1	no	—
613	C₂²⋊Q₈	—	5	1	no	—
614	C₂²⋊Q₈	—	10	1	no	—
615	#121	—	5	1	no	—
616	#121	—	10	1	no	—
617	#121	—	10	1	no	—
618	#121	—	10	1	no	—
619	#121	C₂×C₃×D₅	1	1	yes	characteristic, complemented
620	C₂×C₄⋊C₄	—	5	1	no	—
621	#103	—	5	1	no	—
622	#103	—	5	1	no	—
623	#102	—	5	1	no	—
624	#102	—	5	1	no	—
625	#102	—	5	1	no	—
626	#102	—	5	1	no	—
627	#102	C₂×C₃×D₅	1	1	yes	characteristic, complemented
628	#102	C₂×C₃×D₅	1	1	yes	characteristic, complemented
629	C₂²⋊C₈	—	5	1	no	—
630	C₂²⋊C₈	—	5	1	no	—
631	C₂²⋊C₈	—	5	1	no	—
632	C₂²⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
633	C₂×C₃×C₅	—	4	2	no	—
634	C₂×C₃×C₅	—	4	2	no	—
635	C₂×C₃×C₅	—	4	1	no	—
636	C₂×C₃×C₅	—	8	1	no	—
637	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
638	C₂×C₃×C₅	#576	1	1	yes	characteristic
639	C₂×C₃×C₅	#577	1	1	yes	characteristic
640	C₃×D₅	—	2	2	no	—
641	C₃×D₅	—	4	1	no	—
642	C₃×D₅	—	4	2	no	—
643	C₂³×C₃	—	2	4	no	—
644	C₂³×C₃	—	2	1	no	—
645	C₂³×C₃	—	2	1	no	—
646	C₂³×C₃	—	2	1	no	—
647	C₂³×C₃	—	5	1	no	—
648	C₂³×C₃	—	5	1	no	—
649	C₂³×C₃	—	8	1	no	—
650	C₂³×C₃	—	8	1	no	—
651	C₂³×C₃	—	10	4	no	—
652	C₂³×C₃	—	10	4	no	—
653	C₂³×C₃	—	10	1	no	—
654	C₂³×C₃	—	40	1	no	—
655	C₂³×C₃	—	40	1	no	—
656	C₂³×C₃	—	40	1	no	—
657	C₂³×C₃	—	40	1	no	—
658	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
659	C₃×Q₈	—	5	2	no	—
660	C₃×Q₈	—	10	2	no	—
661	C₃×Q₈	—	10	1	no	—
662	C₃×Q₈	—	10	1	no	—
663	C₃×Q₈	—	10	1	no	—
664	C₃×D₄	—	2	4	no	—
665	C₃×D₄	—	2	1	no	—
666	C₃×D₄	—	2	1	no	—
667	C₃×D₄	—	2	1	no	—
668	C₃×D₄	—	2	1	no	—
669	C₃×D₄	—	5	2	no	—
670	C₃×D₄	—	8	1	no	—
671	C₃×D₄	—	10	2	no	—
672	C₃×D₄	—	10	2	no	—
673	C₃×D₄	—	10	4	no	—
674	C₃×D₄	—	10	2	no	—
675	C₃×D₄	—	10	4	no	—
676	C₃×D₄	—	10	4	no	—
677	C₃×D₄	—	10	4	no	—
678	C₃×D₄	—	10	4	no	—
679	C₃×D₄	—	10	1	no	—
680	C₃×D₄	—	20	2	no	—
681	C₃×D₄	—	40	1	no	—
682	C₃×D₄	D₄×D₅	1	2	yes	—
683	C₃×D₄	D₄×D₅	1	2	yes	—
684	C₂×C₃×C₄	—	2	1	no	—
685	C₂×C₃×C₄	—	2	1	no	—
686	C₂×C₃×C₄	—	2	1	no	—
687	C₂×C₃×C₄	—	5	1	no	—
688	C₂×C₃×C₄	—	5	2	no	—
689	C₂×C₃×C₄	—	5	2	no	—
690	C₂×C₃×C₄	—	5	1	no	—
691	C₂×C₃×C₄	—	10	4	no	—
692	C₂×C₃×C₄	—	10	4	no	—
693	C₂×C₃×C₄	—	10	4	no	—
694	C₂×C₃×C₄	—	10	1	no	—
695	C₂×C₃×C₄	—	10	1	no	—
696	C₂×C₃×C₄	—	10	1	no	—
697	C₂×C₃×C₄	—	10	1	no	—
698	C₂×C₃×C₄	—	10	1	no	—
699	C₂×C₃×C₄	—	20	2	no	—
700	C₂×C₃×C₄	—	40	1	no	—
701	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
702	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
703	C₃×C₈	—	2	1	no	—
704	C₃×C₈	—	2	1	no	—
705	C₃×C₈	—	10	1	no	—
706	C₃×C₈	—	10	1	no	—
707	C₂²×C₅	—	2	1	no	—
708	C₂²×C₅	—	2	1	no	—
709	C₂²×C₅	—	2	2	no	—
710	C₂²×C₅	—	2	2	no	—
711	C₂²×C₅	—	2	1	no	—
712	C₂²×C₅	—	4	1	no	—
713	C₂²×C₅	—	4	1	no	—
714	C₂²×C₅	—	4	1	no	—
715	C₂²×C₅	—	4	1	no	—
716	C₂²×C₅	—	4	1	no	—
717	C₂²×C₅	—	4	1	no	—
718	C₂²×C₅	—	4	1	no	—
719	C₂²×C₅	—	8	4	no	—
720	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
721	C₂×D₅	—	2	1	no	—
722	C₂×D₅	—	2	1	no	—
723	C₂×D₅	—	2	1	no	—
724	C₂×D₅	—	2	1	no	—
725	C₂×D₅	—	2	1	no	—
726	C₂×D₅	—	2	2	no	—
727	C₂×D₅	—	4	1	no	—
728	C₂×D₅	—	4	1	no	—
729	C₂×D₅	—	8	4	no	—
730	C₂×D₅	—	8	4	no	—
731	C₂×D₅	C₃×#120	1	2	yes	—
732	C₄×C₅	—	2	1	no	—
733	C₄×C₅	—	4	1	no	—
734	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
735	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
736	Dic₅	—	2	1	no	—
737	Dic₅	—	2	2	no	—
738	Dic₅	—	4	1	no	—
739	Dic₅	—	4	1	no	—
740	Dic₅	C₃×#120	1	2	yes	—
741	C₂⁴	—	2	1	no	—
742	C₂⁴	—	10	1	no	—
743	C₂⁴	—	10	1	no	—
744	#41	—	5	4	no	—
745	#41	—	10	2	no	—
746	#41	—	10	2	no	—
747	#41	—	10	2	no	—
748	#41	—	10	2	no	—
749	#41	—	10	2	no	—
750	#41	—	10	2	no	—
751	#41	—	10	2	no	—
752	#41	—	10	2	no	—
753	#41	—	10	8	no	—
754	#41	—	10	2	no	—
755	C₂×Q₈	—	5	1	no	—
756	C₂×Q₈	—	5	1	no	—
757	C₂×Q₈	—	5	1	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	1	no	—
761	C₂×D₄	—	2	1	no	—
762	C₂×D₄	—	5	4	no	—
763	C₂×D₄	—	5	1	no	—
764	C₂×D₄	—	5	1	no	—
765	C₂×D₄	—	5	1	no	—
766	C₂×D₄	—	5	1	no	—
767	C₂×D₄	—	10	2	no	—
768	C₂×D₄	—	10	1	no	—
769	C₂×D₄	—	10	1	no	—
770	C₂×D₄	—	10	2	no	—
771	C₂×D₄	—	10	8	no	—
772	C₂×D₄	—	10	1	no	—
773	C₂×D₄	—	10	1	no	—
774	C₂×D₄	—	10	8	no	—
775	C₂×D₄	—	10	8	no	—
776	C₂×D₄	—	10	1	no	—
777	C₂×D₄	—	10	2	no	—
778	C₂×D₄	—	10	1	no	—
779	C₂×D₄	—	10	1	no	—
780	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
781	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
782	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
783	C₂²×C₄	—	5	1	no	—
784	C₂²×C₄	—	5	1	no	—
785	C₂²×C₄	—	10	1	no	—
786	C₂²×C₄	—	10	1	no	—
787	C₂²×C₄	—	10	1	no	—
788	C₂²×C₄	—	10	1	no	—
789	C₂²×C₄	—	10	1	no	—
790	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
791	Q₁₆	—	10	2	no	—
792	SD₁₆	—	10	2	no	—
793	SD₁₆	—	10	2	no	—
794	SD₁₆	—	10	2	no	—
795	SD₁₆	—	10	2	no	—
796	D₈	—	2	2	no	—
797	D₈	—	2	2	no	—
798	D₈	—	10	2	no	—
799	M₁₆	—	10	2	no	—
800	C₂×C₈	—	5	1	no	—
801	C₂×C₈	—	5	1	no	—
802	C₂×C₈	—	10	2	no	—
803	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
804	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
805	C₄⋊C₄	—	5	1	no	—
806	C₄⋊C₄	—	10	1	no	—
807	C₄⋊C₄	—	10	1	no	—
808	C₄⋊C₄	—	10	1	no	—
809	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
810	C₂²⋊C₄	—	2	1	no	—
811	C₂²⋊C₄	—	10	1	no	—
812	C₂²⋊C₄	—	10	1	no	—
813	C₂²⋊C₄	—	10	1	no	—
814	C₃×C₅	#3012	1	1	yes	characteristic, complemented, Hall
815	C₂²×C₃	—	2	1	no	—
816	C₂²×C₃	—	2	1	no	—
817	C₂²×C₃	—	2	1	no	—
818	C₂²×C₃	—	2	2	no	—
819	C₂²×C₃	—	2	2	no	—
820	C₂²×C₃	—	4	1	no	—
821	C₂²×C₃	—	4	1	no	—
822	C₂²×C₃	—	4	1	no	—
823	C₂²×C₃	—	4	1	no	—
824	C₂²×C₃	—	4	1	no	—
825	C₂²×C₃	—	4	1	no	—
826	C₂²×C₃	—	4	1	no	—
827	C₂²×C₃	—	5	2	no	—
828	C₂²×C₃	—	8	4	no	—
829	C₂²×C₃	—	10	1	no	—
830	C₂²×C₃	—	10	1	no	—
831	C₂²×C₃	—	10	1	no	—
832	C₂²×C₃	—	10	1	no	—
833	C₂²×C₃	—	10	2	no	—
834	C₂²×C₃	—	10	1	no	—
835	C₂²×C₃	—	20	1	no	—
836	C₂²×C₃	—	20	1	no	—
837	C₂²×C₃	—	40	4	no	—
838	C₂²×C₃	—	40	4	no	—
839	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
840	C₃×C₄	—	2	1	no	—
841	C₃×C₄	—	4	1	no	—
842	C₃×C₄	—	5	2	no	—
843	C₃×C₄	—	10	1	no	—
844	C₃×C₄	—	10	2	no	—
845	C₃×C₄	—	20	1	no	—
846	C₃×C₄	—	20	1	no	—
847	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
848	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
849	C₂×C₅	—	4	2	no	—
850	C₂×C₅	—	4	2	no	—
851	C₂×C₅	—	4	1	no	—
852	C₂×C₅	—	8	1	no	—
853	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
854	C₂×C₅	C₃×#576	1	1	yes	characteristic
855	C₂×C₅	C₃×#577	1	1	yes	characteristic
856	D₅	—	2	2	no	—
857	D₅	—	4	1	no	—
858	D₅	—	4	2	no	—
859	C₂³	—	2	4	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	5	1	no	—
864	C₂³	—	5	1	no	—
865	C₂³	—	8	1	no	—
866	C₂³	—	8	1	no	—
867	C₂³	—	10	4	no	—
868	C₂³	—	10	4	no	—
869	C₂³	—	10	1	no	—
870	C₂³	—	40	1	no	—
871	C₂³	—	40	1	no	—
872	C₂³	—	40	1	no	—
873	C₂³	—	40	1	no	—
874	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
875	Q₈	—	5	2	no	—
876	Q₈	—	10	2	no	—
877	Q₈	—	10	1	no	—
878	Q₈	—	10	1	no	—
879	Q₈	—	10	1	no	—
880	D₄	—	2	4	no	—
881	D₄	—	2	1	no	—
882	D₄	—	2	1	no	—
883	D₄	—	2	1	no	—
884	D₄	—	2	1	no	—
885	D₄	—	5	2	no	—
886	D₄	—	8	1	no	—
887	D₄	—	10	2	no	—
888	D₄	—	10	2	no	—
889	D₄	—	10	4	no	—
890	D₄	—	10	2	no	—
891	D₄	—	10	4	no	—
892	D₄	—	10	4	no	—
893	D₄	—	10	4	no	—
894	D₄	—	10	4	no	—
895	D₄	—	10	1	no	—
896	D₄	—	20	2	no	—
897	D₄	—	40	1	no	—
898	D₄	C₃×D₄×D₅	1	2	yes	—
899	D₄	C₃×D₄×D₅	1	2	yes	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	5	1	no	—
904	C₂×C₄	—	5	2	no	—
905	C₂×C₄	—	5	2	no	—
906	C₂×C₄	—	5	1	no	—
907	C₂×C₄	—	10	4	no	—
908	C₂×C₄	—	10	4	no	—
909	C₂×C₄	—	10	4	no	—
910	C₂×C₄	—	10	1	no	—
911	C₂×C₄	—	10	1	no	—
912	C₂×C₄	—	10	1	no	—
913	C₂×C₄	—	10	1	no	—
914	C₂×C₄	—	10	1	no	—
915	C₂×C₄	—	20	2	no	—
916	C₂×C₄	—	40	1	no	—
917	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
918	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
919	C₈	—	2	1	no	—
920	C₈	—	2	1	no	—
921	C₈	—	10	1	no	—
922	C₈	—	10	1	no	—
923	C₂×C₃	—	4	1	no	—
924	C₂×C₃	—	4	2	no	—
925	C₂×C₃	—	4	2	no	—
926	C₂×C₃	—	8	1	no	—
927	C₂×C₃	—	10	2	no	—
928	C₂×C₃	—	20	1	no	—
929	C₂×C₃	—	20	2	no	—
930	C₂×C₃	D₅×#120	1	1	yes	characteristic
931	C₂×C₃	#66091	1	1	yes	characteristic
932	C₂×C₃	#66109	1	1	yes	characteristic
933	C₅	C₃×#3012	1	1	yes	characteristic, complemented, Sylow
934	C₂²	—	2	1	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	5	2	no	—
947	C₂²	—	8	4	no	—
948	C₂²	—	10	1	no	—
949	C₂²	—	10	1	no	—
950	C₂²	—	10	1	no	—
951	C₂²	—	10	2	no	—
952	C₂²	—	10	1	no	—
953	C₂²	—	10	1	no	—
954	C₂²	—	20	1	no	—
955	C₂²	—	20	1	no	—
956	C₂²	—	40	4	no	—
957	C₂²	—	40	4	no	—
958	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
959	C₄	—	2	1	no	—
960	C₄	—	4	1	no	—
961	C₄	—	5	2	no	—
962	C₄	—	10	1	no	—
963	C₄	—	10	2	no	—
964	C₄	—	20	1	no	—
965	C₄	—	20	1	no	—
966	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
967	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
968	C₃	#10611736	1	1	yes	characteristic, direct product factor, Sylow
969	C₂	—	4	1	no	—
970	C₂	—	4	2	no	—
971	C₂	—	4	2	no	—
972	C₂	—	8	1	no	—
973	C₂	—	10	2	no	—
974	C₂	—	20	1	no	—
975	C₂	—	20	2	no	—
976	C₂	C₃×D₅×#120	1	1	yes	characteristic
977	C₂	C₃×#66091	1	1	yes	characteristic
978	C₂	C₃×#66109	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#447	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#447	D₅
hypocenter	C₅	C₃×#3012
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#447

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4144	C₂	semidirect
2. C₂×C₃×#4058	C₂	semidirect
3. C₂×C₃×#4057	C₂	semidirect
4. C₃×#65942	C₂	semidirect
5. C₃×C₅×#447	C₂	semidirect
6. C₃×#65507	C₂	semidirect
7. C₃×#65447	C₂	semidirect
8. C₃×#65445	C₂	semidirect
9. C₃×#65326	C₂	semidirect
10. C₃×#65072	C₂	semidirect
11. C₃×#65065	C₂	semidirect
12. C₃×#65060	C₂	semidirect
13. C₃×D₅×#102	C₂	semidirect
14. C₃×#65022	C₂	semidirect
15. C₃×#65016	C₂	semidirect
16. #10611736	C₃	direct (N × H)
25. C₂×C₃×#711	C₂²	semidirect
31. C₂×C₃×C₅×D₈	C₂²	semidirect
32. C₂×C₃×C₅×D₈	C₂²	semidirect
33. C₃×C₅×#121	C₂²	semidirect
36. C₃×#4084	C₂²	semidirect
37. C₂×C₃×#687	C₂²	semidirect
38. C₂×C₃×#687	C₂²	semidirect
39. C₂×C₃×#687	C₂²	semidirect
40. C₂×C₃×#686	C₂²	semidirect
41. C₃×#4070	C₂²	semidirect
44. C₂×C₃×Dic₂₀	C₂²	semidirect
45. C₂×C₃×#677	C₂²	semidirect
46. C₂×C₃×#676	C₂²	semidirect
47. C₂×C₃×C₈×D₅	C₂²	semidirect
48. C₃×#4043	C₂²	semidirect
49. C₃×D₅×C₄⋊C₄	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
55. C₃×#3964	C₂²	semidirect
56. C₃×#3964	C₂²	semidirect
57. C₃×C₂²⋊#168	C₂²	semidirect
58. C₃×#3953	C₂²	semidirect
59. C₃×#3952	C₂²	semidirect
60. C₃×#3952	C₂²	semidirect
61. C₃×#3948	C₂²	semidirect
62. C₃×#3942	C₂²	semidirect
63. C₃×#3941	C₂²	semidirect
65. C₂×#4144	C₂×C₃	semidirect
66. C₂×#4058	C₂×C₃	semidirect
67. C₂×#4057	C₂×C₃	semidirect
68. #65942	C₂×C₃	semidirect
69. C₅×#447	C₂×C₃	semidirect
70. #65507	C₂×C₃	semidirect
71. #65447	C₂×C₃	semidirect
72. #65445	C₂×C₃	semidirect
73. #65326	C₂×C₃	semidirect
74. #65072	C₂×C₃	semidirect
75. #65065	C₂×C₃	semidirect
76. #65060	C₂×C₃	semidirect
77. D₅×#102	C₂×C₃	semidirect
78. #65022	C₂×C₃	semidirect
79. #65016	C₂×C₃	semidirect
111. C₃×#711	D₄	semidirect
116. C₃×D₄×D₅	D₄	semidirect
164. C₃×#447	D₅	semidirect
176. C₂×#711	C₂²×C₃	semidirect
182. C₂×C₅×D₈	C₂²×C₃	semidirect
183. C₂×C₅×D₈	C₂²×C₃	semidirect
184. C₅×#121	C₂²×C₃	semidirect
187. #4084	C₂²×C₃	semidirect
188. C₂×#687	C₂²×C₃	semidirect
189. C₂×#687	C₂²×C₃	semidirect
190. C₂×#687	C₂²×C₃	semidirect
191. C₂×#686	C₂²×C₃	semidirect
192. #4070	C₂²×C₃	semidirect
195. C₂×Dic₂₀	C₂²×C₃	semidirect
196. C₂×#677	C₂²×C₃	semidirect
197. C₂×#676	C₂²×C₃	semidirect
198. C₂×C₈×D₅	C₂²×C₃	semidirect
199. #4043	C₂²×C₃	semidirect
200. D₅×C₄⋊C₄	C₂²×C₃	semidirect
203. C₅×#102	C₂²×C₃	semidirect
204. C₅×#102	C₂²×C₃	semidirect
205. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
206. #3964	C₂²×C₃	semidirect
207. #3964	C₂²×C₃	semidirect
208. C₂²⋊#168	C₂²×C₃	semidirect
209. #3953	C₂²×C₃	semidirect
210. #3952	C₂²×C₃	semidirect
211. #3952	C₂²×C₃	semidirect
212. #3948	C₂²×C₃	semidirect
213. #3942	C₂²×C₃	semidirect
214. #3941	C₂²×C₃	semidirect
302. C₂×C₃×D₈	C₂×D₅	semidirect
303. C₂×C₃×D₈	C₂×D₅	semidirect
313. C₃×#121	C₂×D₅	semidirect
321. C₃×#102	C₂×D₅	semidirect
322. C₃×#102	C₂×D₅	semidirect
326. C₃×C₂²⋊C₈	C₂×D₅	semidirect
358. #711	C₃×D₄	semidirect
363. D₄×D₅	C₃×D₄	semidirect
411. #447	C₃×D₅	semidirect
608. C₂×D₈	C₂×C₃×D₅	semidirect
609. C₂×D₈	C₂×C₃×D₅	semidirect
619. #121	C₂×C₃×D₅	semidirect
627. #102	C₂×C₃×D₅	semidirect
628. #102	C₂×C₃×D₅	semidirect
632. C₂²⋊C₈	C₂×C₃×D₅	semidirect
814. C₃×C₅	#3012	semidirect
933. C₅	C₃×#3012	semidirect
968. C₃	#10611736	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×#4144	2
C₂×C₃×#4058	2
C₂×C₃×#4057	2
C₃×#65942	2
C₃×C₅×#447	2
C₃×#65507	2
C₃×#65447	2
C₃×#65445	2
C₃×#65326	2
C₃×#65072	2
C₃×#65065	2
C₃×#65060	2
C₃×D₅×#102	2
C₃×#65022	2
C₃×#65016	2
#10611736	3
C₃×#3012	5

Subgroups — C3×#10611736 #14424637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611736 #14424637