Subgroups — C₂×C₃×#65983 #14479767

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4085	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4075	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65983	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4044	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4038	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4035	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#4033	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#4031	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#4027	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#4027	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#4025	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#4024	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#4023	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#65983	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
22	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
23	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
24	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
26	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
27	C₃×C₅×#123	C₂²	1	8	yes	complemented
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
36	C₃×#4085	C₂²	1	8	yes	—
37	C₃×D₄×Dic₅	C₂²	1	8	yes	complemented
38	C₃×#4075	C₂²	1	8	yes	complemented
39	C₂×C₃×#685	C₂²	1	1	yes	characteristic
40	C₂×C₃×#685	C₂²	1	1	yes	characteristic
41	C₂×C₃×#685	C₂²	1	1	yes	characteristic
42	C₂×C₃×#685	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
45	C₂×C₃×#683	C₂²	1	1	yes	characteristic
46	C₂×C₃×#683	C₂²	1	1	yes	characteristic
47	C₂×C₃×#683	C₂²	1	1	yes	characteristic
48	C₂×C₃×#683	C₂²	1	1	yes	characteristic
49	C₂×C₃×#683	C₂²	1	1	yes	characteristic
50	C₂×C₃×#683	C₂²	1	1	yes	characteristic
51	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
52	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
53	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
54	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
55	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
56	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
57	C₂×C₃×C₄×Dic₅	C₂²	1	8	yes	complemented
58	C₃×#4044	C₂²	1	8	yes	complemented
59	C₃×#4038	C₂²	1	8	yes	complemented
60	C₃×#4035	C₂²	1	8	yes	complemented
61	C₃×#4033	C₂²	1	8	yes	complemented
62	C₃×#4031	C₂²	1	8	yes	complemented
63	C₃×#4027	C₂²	1	8	yes	complemented
64	C₃×#4027	C₂²	1	8	yes	complemented
65	C₃×#4025	C₂²	1	8	yes	complemented
66	C₃×#4024	C₂²	1	8	yes	complemented
67	C₃×#4023	C₂²	1	8	yes	complemented
68	C₂×C₃×#529	—	5	1	no	maximal, Hall
69	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂×#4085	C₂×C₃	1	1	yes	characteristic
71	C₂×D₄×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂×#4075	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂²×C₄×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
74	#65983	C₂×C₃	1	16	yes	direct product factor
75	C₂×#4044	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×#4038	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂×#4035	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂×#4033	C₂×C₃	1	1	yes	characteristic, complemented
79	C₂×#4031	C₂×C₃	1	1	yes	characteristic, complemented
80	C₂×#4027	C₂×C₃	1	1	yes	characteristic, complemented
81	C₂×#4027	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂×#4025	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×#4024	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂×#4023	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
86	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
87	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₅×D₄	—	2	4	no	—
89	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
90	C₂²×C₃×C₄×C₅	—	2	4	no	—
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
97	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
98	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
99	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
100	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
101	C₂²×C₃×Dic₅	—	2	4	no	—
102	C₂²×C₃×Dic₅	—	2	4	no	—
103	C₂²×C₃×Dic₅	—	2	4	no	—
104	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
105	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
106	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
107	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
108	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
109	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
110	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
111	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
112	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
113	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
114	C₂×C₃×C₄×D₅	—	2	4	no	—
115	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
116	C₂×C₃×Dic₁₀	—	2	4	no	—
117	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
118	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
119	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
120	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
124	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
125	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
126	C₃×#685	C₂³	1	4	yes	—
127	C₃×#685	C₂³	1	4	yes	—
128	C₃×#685	C₂³	1	4	yes	—
129	C₃×#685	C₂³	1	4	yes	—
130	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
131	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
132	C₃×#683	C₂³	1	4	yes	—
133	C₃×#683	C₂³	1	4	yes	—
134	C₃×#683	C₂³	1	4	yes	—
135	C₃×#683	C₂³	1	4	yes	—
136	C₃×#683	C₂³	1	4	yes	—
137	C₃×#683	C₂³	1	4	yes	—
138	C₃×C₄×Dic₅	C₂³	1	4	yes	—
139	C₃×C₄×Dic₅	C₂³	1	4	yes	—
140	C₃×C₄×Dic₅	C₂³	1	4	yes	—
141	C₃×C₄×Dic₅	C₂³	1	4	yes	—
142	C₃×C₄×Dic₅	C₂³	1	4	yes	—
143	C₃×C₄×Dic₅	C₂³	1	4	yes	—
144	C₃×#529	—	5	16	no	—
145	C₂×C₃×#126	—	5	1	no	—
146	C₂×C₃×#126	—	5	1	no	—
147	C₂×C₃×#125	—	5	1	no	—
148	C₂×C₃×#124	—	5	1	no	—
149	C₂×C₃×#123	—	5	1	no	—
150	C₂×C₃×#123	D₅	1	1	yes	characteristic, complemented
151	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
152	C₂×C₃×#121	—	5	1	no	—
153	C₂×C₃×C₄×Q₈	—	5	1	no	—
154	C₂×C₃×C₄×D₄	—	5	1	no	—
155	C₂×C₃×C₄×D₄	—	5	1	no	—
156	C₂×C₃×C₄×D₄	—	5	1	no	—
157	C₂×C₃×#117	—	5	1	no	—
158	C₂×C₃×#117	—	5	1	no	—
159	C₂²×C₃×C₄²	—	5	1	no	—
160	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
161	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
162	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
163	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
164	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
165	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
166	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
167	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
168	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
169	C₅×#123	C₂²×C₃	1	8	yes	complemented
170	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
176	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
177	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
178	#4085	C₂²×C₃	1	8	yes	—
179	D₄×Dic₅	C₂²×C₃	1	8	yes	complemented
180	#4075	C₂²×C₃	1	8	yes	complemented
181	C₂×#685	C₂²×C₃	1	1	yes	characteristic
182	C₂×#685	C₂²×C₃	1	1	yes	characteristic
183	C₂×#685	C₂²×C₃	1	1	yes	characteristic
184	C₂×#685	C₂²×C₃	1	1	yes	characteristic
185	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
186	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
187	C₂×#683	C₂²×C₃	1	1	yes	characteristic
188	C₂×#683	C₂²×C₃	1	1	yes	characteristic
189	C₂×#683	C₂²×C₃	1	1	yes	characteristic
190	C₂×#683	C₂²×C₃	1	1	yes	characteristic
191	C₂×#683	C₂²×C₃	1	1	yes	characteristic
192	C₂×#683	C₂²×C₃	1	1	yes	characteristic
193	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
194	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
195	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
196	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
197	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
198	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
199	C₂×C₄×Dic₅	C₂²×C₃	1	8	yes	complemented
200	#4044	C₂²×C₃	1	8	yes	complemented
201	#4038	C₂²×C₃	1	8	yes	complemented
202	#4035	C₂²×C₃	1	8	yes	complemented
203	#4033	C₂²×C₃	1	8	yes	complemented
204	#4031	C₂²×C₃	1	8	yes	complemented
205	#4027	C₂²×C₃	1	8	yes	complemented
206	#4027	C₂²×C₃	1	8	yes	complemented
207	#4025	C₂²×C₃	1	8	yes	complemented
208	#4024	C₂²×C₃	1	8	yes	complemented
209	#4023	C₂²×C₃	1	8	yes	complemented
210	C₂×#529	—	5	1	no	Sylow
211	C₂³×C₃×C₅	—	2	2	no	—
212	C₂³×C₃×C₅	—	2	2	no	—
213	C₂³×C₃×C₅	—	2	2	no	—
214	C₂³×C₃×C₅	—	2	2	no	—
215	C₂³×C₃×C₅	—	2	2	no	—
216	C₂³×C₃×C₅	#41	1	4	yes	—
217	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
218	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
219	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
220	C₂²×C₃×D₅	—	2	2	no	—
221	C₂²×C₃×D₅	—	2	2	no	—
222	C₂²×C₃×D₅	—	2	2	no	—
223	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
224	C₃×C₅×D₄	—	2	8	no	—
225	C₂×C₃×C₄×C₅	—	2	2	no	—
226	C₂×C₃×C₄×C₅	—	2	2	no	—
227	C₂×C₃×C₄×C₅	—	2	8	no	—
228	C₂×C₃×C₄×C₅	—	2	2	no	—
229	C₂×C₃×C₄×C₅	—	2	2	no	—
230	C₂×C₃×C₄×C₅	—	2	2	no	—
231	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
232	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
233	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
234	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
235	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
236	C₃×C₂²⋊D₅	—	2	8	no	—
237	C₃×C₂²⋊D₅	—	2	8	no	—
238	C₂×C₃×Dic₅	—	2	2	no	—
239	C₂×C₃×Dic₅	—	2	2	no	—
240	C₂×C₃×Dic₅	—	2	2	no	—
241	C₂×C₃×Dic₅	—	2	2	no	—
242	C₂×C₃×Dic₅	—	2	2	no	—
243	C₂×C₃×Dic₅	—	2	8	no	—
244	C₂×C₃×Dic₅	—	2	8	no	—
245	C₂×C₃×Dic₅	—	2	8	no	—
246	C₂×C₃×Dic₅	#41	1	4	yes	—
247	C₂×C₃×Dic₅	#41	1	4	yes	—
248	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
249	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
250	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
251	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
252	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
253	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
254	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
255	C₃×C₄×D₅	—	2	8	no	—
256	C₃×Dic₁₀	—	2	8	no	—
257	C₂²×C₃×Q₈	—	5	1	no	—
258	C₂²×C₃×D₄	—	5	1	no	—
259	C₂²×C₃×D₄	—	5	1	no	—
260	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
261	C₂³×C₃×C₄	—	5	1	no	—
262	C₂³×C₃×C₄	—	5	1	no	—
263	C₂³×C₃×C₄	—	5	1	no	—
264	C₂³×C₃×C₄	—	5	1	no	—
265	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
266	C₃×#126	—	5	8	no	—
267	C₃×#126	—	5	8	no	—
268	C₃×#125	—	5	8	no	—
269	C₃×#124	—	5	8	no	—
270	C₃×#123	—	5	8	no	—
271	C₃×#123	C₂×D₅	1	8	yes	complemented
272	C₃×C₂²⋊Q₈	—	5	8	no	—
273	C₃×#121	—	5	8	no	—
274	C₃×C₄×Q₈	—	5	8	no	—
275	C₃×C₄×D₄	—	5	8	no	—
276	C₃×C₄×D₄	—	5	8	no	—
277	C₃×C₄×D₄	—	5	8	no	—
278	C₃×#117	—	5	8	no	—
279	C₃×#117	—	5	8	no	—
280	C₂×C₃×C₄⋊C₄	—	5	1	no	—
281	C₂×C₃×C₄⋊C₄	—	5	1	no	—
282	C₂×C₃×C₄⋊C₄	—	5	1	no	—
283	C₂×C₃×C₄⋊C₄	—	5	1	no	—
284	C₂×C₃×C₄⋊C₄	—	5	1	no	—
285	C₂×C₃×C₄⋊C₄	—	5	1	no	—
286	C₂×C₃×C₄⋊C₄	—	5	1	no	—
287	C₂×C₃×C₄⋊C₄	—	5	1	no	—
288	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
289	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
290	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
291	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
292	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
293	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
294	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
295	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
296	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
297	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
298	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
299	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
300	C₂×C₃×C₄²	—	5	1	no	—
301	C₂×C₃×C₄²	—	5	1	no	—
302	C₂×C₃×C₄²	—	5	1	no	—
303	C₂×C₃×C₄²	—	5	1	no	—
304	C₂×C₃×C₄²	—	5	8	no	—
305	C₂×C₃×C₄²	—	5	1	no	—
306	C₂×C₃×C₄²	—	5	1	no	—
307	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
308	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
309	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
310	C₂×C₅×D₄	—	2	4	no	—
311	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
312	C₂²×C₄×C₅	—	2	4	no	—
313	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
314	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
315	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
316	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
317	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
319	C₂×C₂²⋊D₅	—	2	4	no	—
320	C₂×C₂²⋊D₅	—	2	4	no	—
321	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
322	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
323	C₂²×Dic₅	—	2	4	no	—
324	C₂²×Dic₅	—	2	4	no	—
325	C₂²×Dic₅	—	2	4	no	—
326	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
327	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
328	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
329	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
330	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
331	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
332	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
333	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
334	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
335	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
336	C₂×C₄×D₅	—	2	4	no	—
337	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
338	C₂×Dic₁₀	—	2	4	no	—
339	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
340	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
341	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
342	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
343	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
344	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
345	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
346	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
347	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
348	#685	C₂³×C₃	1	4	yes	—
349	#685	C₂³×C₃	1	4	yes	—
350	#685	C₂³×C₃	1	4	yes	—
351	#685	C₂³×C₃	1	4	yes	—
352	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
353	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
354	#683	C₂³×C₃	1	4	yes	—
355	#683	C₂³×C₃	1	4	yes	—
356	#683	C₂³×C₃	1	4	yes	—
357	#683	C₂³×C₃	1	4	yes	—
358	#683	C₂³×C₃	1	4	yes	—
359	#683	C₂³×C₃	1	4	yes	—
360	C₄×Dic₅	C₂³×C₃	1	4	yes	—
361	C₄×Dic₅	C₂³×C₃	1	4	yes	—
362	C₄×Dic₅	C₂³×C₃	1	4	yes	—
363	C₄×Dic₅	C₂³×C₃	1	4	yes	—
364	C₄×Dic₅	C₂³×C₃	1	4	yes	—
365	C₄×Dic₅	C₂³×C₃	1	4	yes	—
366	#529	—	5	16	no	—
367	C₂×#126	—	5	1	no	—
368	C₂×#126	—	5	1	no	—
369	C₂×#125	—	5	1	no	—
370	C₂×#124	—	5	1	no	—
371	C₂×#123	—	5	1	no	—
372	C₂×#123	C₃×D₅	1	1	yes	characteristic, complemented
373	C₂×C₂²⋊Q₈	—	5	1	no	—
374	C₂×#121	—	5	1	no	—
375	C₂×C₄×Q₈	—	5	1	no	—
376	C₂×C₄×D₄	—	5	1	no	—
377	C₂×C₄×D₄	—	5	1	no	—
378	C₂×C₄×D₄	—	5	1	no	—
379	C₂×#117	—	5	1	no	—
380	C₂×#117	—	5	1	no	—
381	C₂²×C₄²	—	5	1	no	—
382	C₂²×C₃×C₅	—	2	8	no	—
383	C₂²×C₃×C₅	—	2	2	no	—
384	C₂²×C₃×C₅	—	2	2	no	—
385	C₂²×C₃×C₅	—	2	2	no	—
386	C₂²×C₃×C₅	—	2	2	no	—
387	C₂²×C₃×C₅	—	2	2	no	—
388	C₂²×C₃×C₅	—	4	4	no	—
389	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
390	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
391	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
392	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
393	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
394	C₂×C₃×D₅	—	2	2	no	—
395	C₂×C₃×D₅	—	2	2	no	—
396	C₂×C₃×D₅	—	2	2	no	—
397	C₂×C₃×D₅	—	4	4	no	—
398	C₃×C₄×C₅	—	2	2	no	—
399	C₃×C₄×C₅	—	2	2	no	—
400	C₃×C₄×C₅	—	2	2	no	—
401	C₃×C₄×C₅	—	2	2	no	—
402	C₃×C₄×C₅	—	2	2	no	—
403	C₃×Dic₅	—	2	2	no	—
404	C₃×Dic₅	—	2	2	no	—
405	C₃×Dic₅	—	2	2	no	—
406	C₃×Dic₅	—	2	2	no	—
407	C₃×Dic₅	—	2	2	no	—
408	C₃×Dic₅	C₂×#41	1	4	yes	—
409	C₃×Dic₅	C₂×#41	1	4	yes	—
410	C₂⁴×C₃	—	5	1	no	—
411	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
412	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
413	C₂×C₃×Q₈	—	5	4	no	—
414	C₂×C₃×Q₈	—	10	4	no	—
415	C₂×C₃×D₄	—	2	4	no	—
416	C₂×C₃×D₄	—	5	4	no	—
417	C₂×C₃×D₄	—	5	4	no	—
418	C₂×C₃×D₄	—	10	4	no	—
419	C₂×C₃×D₄	—	10	4	no	—
420	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
421	C₂²×C₃×C₄	—	2	4	no	—
422	C₂²×C₃×C₄	—	5	1	no	—
423	C₂²×C₃×C₄	—	5	1	no	—
424	C₂²×C₃×C₄	—	5	4	no	—
425	C₂²×C₃×C₄	—	5	4	no	—
426	C₂²×C₃×C₄	—	5	4	no	—
427	C₂²×C₃×C₄	—	5	1	no	—
428	C₂²×C₃×C₄	—	5	1	no	—
429	C₂²×C₃×C₄	—	5	1	no	—
430	C₂²×C₃×C₄	—	5	1	no	—
431	C₂²×C₃×C₄	—	5	1	no	—
432	C₂²×C₃×C₄	—	5	4	no	—
433	C₂²×C₃×C₄	—	10	4	no	—
434	C₂²×C₃×C₄	—	10	4	no	—
435	C₂²×C₃×C₄	—	10	4	no	—
436	C₂²×C₃×C₄	—	10	4	no	—
437	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
438	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
439	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
440	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
441	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
442	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
443	C₃×C₄⋊C₄	—	5	4	no	—
444	C₃×C₄⋊C₄	—	5	4	no	—
445	C₃×C₄⋊C₄	—	5	4	no	—
446	C₃×C₄⋊C₄	—	5	4	no	—
447	C₃×C₄⋊C₄	—	5	4	no	—
448	C₃×C₄⋊C₄	—	5	4	no	—
449	C₃×C₄⋊C₄	—	5	4	no	—
450	C₃×C₄⋊C₄	—	5	4	no	—
451	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
452	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
453	C₃×C₂²⋊C₄	—	5	4	no	—
454	C₃×C₂²⋊C₄	—	5	4	no	—
455	C₃×C₂²⋊C₄	—	5	4	no	—
456	C₃×C₂²⋊C₄	—	5	4	no	—
457	C₃×C₂²⋊C₄	—	5	4	no	—
458	C₃×C₂²⋊C₄	—	5	4	no	—
459	C₃×C₂²⋊C₄	—	5	4	no	—
460	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
461	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
462	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
463	C₃×C₄²	—	5	4	no	—
464	C₃×C₄²	—	5	4	no	—
465	C₃×C₄²	—	5	4	no	—
466	C₃×C₄²	—	5	4	no	—
467	C₃×C₄²	—	5	4	no	—
468	C₃×C₄²	—	5	4	no	—
469	C₂³×C₅	—	2	2	no	—
470	C₂³×C₅	—	2	2	no	—
471	C₂³×C₅	—	2	2	no	—
472	C₂³×C₅	—	2	2	no	—
473	C₂³×C₅	—	2	2	no	—
474	C₂³×C₅	C₃×#41	1	4	yes	—
475	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
476	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
477	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
478	C₂²×D₅	—	2	2	no	—
479	C₂²×D₅	—	2	2	no	—
480	C₂²×D₅	—	2	2	no	—
481	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
482	C₅×D₄	—	2	8	no	—
483	C₂×C₄×C₅	—	2	2	no	—
484	C₂×C₄×C₅	—	2	2	no	—
485	C₂×C₄×C₅	—	2	8	no	—
486	C₂×C₄×C₅	—	2	2	no	—
487	C₂×C₄×C₅	—	2	2	no	—
488	C₂×C₄×C₅	—	2	2	no	—
489	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
490	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
491	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
492	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
493	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
494	C₂²⋊D₅	—	2	8	no	—
495	C₂²⋊D₅	—	2	8	no	—
496	C₂×Dic₅	—	2	2	no	—
497	C₂×Dic₅	—	2	2	no	—
498	C₂×Dic₅	—	2	2	no	—
499	C₂×Dic₅	—	2	2	no	—
500	C₂×Dic₅	—	2	2	no	—
501	C₂×Dic₅	—	2	8	no	—
502	C₂×Dic₅	—	2	8	no	—
503	C₂×Dic₅	—	2	8	no	—
504	C₂×Dic₅	C₃×#41	1	4	yes	—
505	C₂×Dic₅	C₃×#41	1	4	yes	—
506	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
507	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
508	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
509	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
510	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
511	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
512	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
513	C₄×D₅	—	2	8	no	—
514	Dic₁₀	—	2	8	no	—
515	C₂²×Q₈	—	5	1	no	—
516	C₂²×D₄	—	5	1	no	—
517	C₂²×D₄	—	5	1	no	—
518	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
519	C₂³×C₄	—	5	1	no	—
520	C₂³×C₄	—	5	1	no	—
521	C₂³×C₄	—	5	1	no	—
522	C₂³×C₄	—	5	1	no	—
523	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
524	#126	—	5	8	no	—
525	#126	—	5	8	no	—
526	#125	—	5	8	no	—
527	#124	—	5	8	no	—
528	#123	—	5	8	no	—
529	#123	C₂×C₃×D₅	1	8	yes	complemented
530	C₂²⋊Q₈	—	5	8	no	—
531	#121	—	5	8	no	—
532	C₄×Q₈	—	5	8	no	—
533	C₄×D₄	—	5	8	no	—
534	C₄×D₄	—	5	8	no	—
535	C₄×D₄	—	5	8	no	—
536	#117	—	5	8	no	—
537	#117	—	5	8	no	—
538	C₂×C₄⋊C₄	—	5	1	no	—
539	C₂×C₄⋊C₄	—	5	1	no	—
540	C₂×C₄⋊C₄	—	5	1	no	—
541	C₂×C₄⋊C₄	—	5	1	no	—
542	C₂×C₄⋊C₄	—	5	1	no	—
543	C₂×C₄⋊C₄	—	5	1	no	—
544	C₂×C₄⋊C₄	—	5	1	no	—
545	C₂×C₄⋊C₄	—	5	1	no	—
546	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	—	5	1	no	—
549	C₂×C₂²⋊C₄	—	5	1	no	—
550	C₂×C₂²⋊C₄	—	5	1	no	—
551	C₂×C₂²⋊C₄	—	5	1	no	—
552	C₂×C₂²⋊C₄	—	5	1	no	—
553	C₂×C₂²⋊C₄	—	5	1	no	—
554	C₂×C₂²⋊C₄	—	5	1	no	—
555	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
558	C₂×C₄²	—	5	1	no	—
559	C₂×C₄²	—	5	1	no	—
560	C₂×C₄²	—	5	1	no	—
561	C₂×C₄²	—	5	1	no	—
562	C₂×C₄²	—	5	1	no	—
563	C₂×C₄²	—	5	1	no	—
564	C₂×C₄²	—	5	8	no	—
565	C₂×C₃×C₅	—	2	4	no	—
566	C₂×C₃×C₅	—	4	2	no	—
567	C₂×C₃×C₅	#529	1	4	yes	complemented
568	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
569	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
570	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
571	C₃×D₅	—	4	2	no	—
572	C₂³×C₃	—	2	2	no	—
573	C₂³×C₃	—	2	2	no	—
574	C₂³×C₃	—	2	2	no	—
575	C₂³×C₃	—	2	2	no	—
576	C₂³×C₃	—	2	2	no	—
577	C₂³×C₃	—	5	2	no	—
578	C₂³×C₃	—	10	2	no	—
579	C₂³×C₃	—	10	2	no	—
580	C₂³×C₃	—	10	2	no	—
581	C₂³×C₃	#711	1	4	yes	—
582	C₂³×C₃	C₂³×D₅	1	2	yes	—
583	C₂³×C₃	C₂³×D₅	1	2	yes	—
584	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
585	C₃×Q₈	—	10	8	no	—
586	C₃×D₄	—	2	8	no	—
587	C₃×D₄	—	10	8	no	—
588	C₃×D₄	—	10	8	no	—
589	C₂×C₃×C₄	—	2	8	no	—
590	C₂×C₃×C₄	—	2	2	no	—
591	C₂×C₃×C₄	—	2	2	no	—
592	C₂×C₃×C₄	—	2	2	no	—
593	C₂×C₃×C₄	—	2	2	no	—
594	C₂×C₃×C₄	—	2	2	no	—
595	C₂×C₃×C₄	—	5	4	no	—
596	C₂×C₃×C₄	—	5	4	no	—
597	C₂×C₃×C₄	—	5	2	no	—
598	C₂×C₃×C₄	—	5	2	no	—
599	C₂×C₃×C₄	—	5	2	no	—
600	C₂×C₃×C₄	—	5	2	no	—
601	C₂×C₃×C₄	—	5	2	no	—
602	C₂×C₃×C₄	—	5	2	no	—
603	C₂×C₃×C₄	—	5	2	no	—
604	C₂×C₃×C₄	—	10	8	no	—
605	C₂×C₃×C₄	—	10	8	no	—
606	C₂×C₃×C₄	—	10	8	no	—
607	C₂×C₃×C₄	—	10	8	no	—
608	C₂×C₃×C₄	—	10	2	no	—
609	C₂×C₃×C₄	—	10	2	no	—
610	C₂×C₃×C₄	—	10	2	no	—
611	C₂×C₃×C₄	—	10	2	no	—
612	C₂×C₃×C₄	—	10	2	no	—
613	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
614	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
615	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
616	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
617	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
618	C₂²×C₅	—	2	2	no	—
619	C₂²×C₅	—	2	2	no	—
620	C₂²×C₅	—	2	8	no	—
621	C₂²×C₅	—	2	2	no	—
622	C₂²×C₅	—	2	2	no	—
623	C₂²×C₅	—	2	2	no	—
624	C₂²×C₅	—	4	4	no	—
625	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
626	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
627	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
628	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
629	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
630	C₂×D₅	—	2	2	no	—
631	C₂×D₅	—	2	2	no	—
632	C₂×D₅	—	2	2	no	—
633	C₂×D₅	—	4	4	no	—
634	C₄×C₅	—	2	2	no	—
635	C₄×C₅	—	2	2	no	—
636	C₄×C₅	—	2	2	no	—
637	C₄×C₅	—	2	2	no	—
638	C₄×C₅	—	2	2	no	—
639	Dic₅	—	2	2	no	—
640	Dic₅	—	2	2	no	—
641	Dic₅	—	2	2	no	—
642	Dic₅	—	2	2	no	—
643	Dic₅	—	2	2	no	—
644	Dic₅	C₂×C₃×#41	1	4	yes	—
645	Dic₅	C₂×C₃×#41	1	4	yes	—
646	C₂⁴	—	5	1	no	—
647	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
648	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
649	C₂×Q₈	—	5	4	no	—
650	C₂×Q₈	—	10	4	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	5	4	no	—
653	C₂×D₄	—	5	4	no	—
654	C₂×D₄	—	10	4	no	—
655	C₂×D₄	—	10	4	no	—
656	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	5	1	no	—
659	C₂²×C₄	—	5	1	no	—
660	C₂²×C₄	—	5	1	no	—
661	C₂²×C₄	—	5	1	no	—
662	C₂²×C₄	—	5	4	no	—
663	C₂²×C₄	—	5	4	no	—
664	C₂²×C₄	—	5	1	no	—
665	C₂²×C₄	—	5	1	no	—
666	C₂²×C₄	—	5	1	no	—
667	C₂²×C₄	—	5	4	no	—
668	C₂²×C₄	—	5	4	no	—
669	C₂²×C₄	—	10	4	no	—
670	C₂²×C₄	—	10	4	no	—
671	C₂²×C₄	—	10	4	no	—
672	C₂²×C₄	—	10	4	no	—
673	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
674	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
675	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
676	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
677	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
678	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
679	C₄⋊C₄	—	5	4	no	—
680	C₄⋊C₄	—	5	4	no	—
681	C₄⋊C₄	—	5	4	no	—
682	C₄⋊C₄	—	5	4	no	—
683	C₄⋊C₄	—	5	4	no	—
684	C₄⋊C₄	—	5	4	no	—
685	C₄⋊C₄	—	5	4	no	—
686	C₄⋊C₄	—	5	4	no	—
687	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
688	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
689	C₂²⋊C₄	—	5	4	no	—
690	C₂²⋊C₄	—	5	4	no	—
691	C₂²⋊C₄	—	5	4	no	—
692	C₂²⋊C₄	—	5	4	no	—
693	C₂²⋊C₄	—	5	4	no	—
694	C₂²⋊C₄	—	5	4	no	—
695	C₂²⋊C₄	—	5	4	no	—
696	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
697	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
698	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
699	C₄²	—	5	4	no	—
700	C₄²	—	5	4	no	—
701	C₄²	—	5	4	no	—
702	C₄²	—	5	4	no	—
703	C₄²	—	5	4	no	—
704	C₄²	—	5	4	no	—
705	C₃×C₅	C₂×#529	1	1	yes	characteristic, complemented, Hall
706	C₂²×C₃	—	2	8	no	—
707	C₂²×C₃	—	2	2	no	—
708	C₂²×C₃	—	2	2	no	—
709	C₂²×C₃	—	2	2	no	—
710	C₂²×C₃	—	2	2	no	—
711	C₂²×C₃	—	2	2	no	—
712	C₂²×C₃	—	4	4	no	—
713	C₂²×C₃	—	10	2	no	—
714	C₂²×C₃	—	10	2	no	—
715	C₂²×C₃	—	10	2	no	—
716	C₂²×C₃	—	20	4	no	—
717	C₂²×C₃	C₂×#711	1	4	yes	—
718	C₂²×C₃	C₂×#711	1	2	yes	—
719	C₂²×C₃	D₅×#41	1	2	yes	—
720	C₂²×C₃	D₅×#41	1	2	yes	—
721	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
722	C₃×C₄	—	2	2	no	—
723	C₃×C₄	—	2	2	no	—
724	C₃×C₄	—	2	2	no	—
725	C₃×C₄	—	2	2	no	—
726	C₃×C₄	—	2	2	no	—
727	C₃×C₄	—	5	4	no	—
728	C₃×C₄	—	5	4	no	—
729	C₃×C₄	—	10	2	no	—
730	C₃×C₄	—	10	2	no	—
731	C₃×C₄	—	10	2	no	—
732	C₃×C₄	—	10	2	no	—
733	C₃×C₄	—	10	2	no	—
734	C₂×C₅	—	2	4	no	—
735	C₂×C₅	—	4	2	no	—
736	C₂×C₅	C₃×#529	1	4	yes	complemented
737	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
738	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
739	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
740	D₅	—	4	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	5	2	no	—
747	C₂³	—	10	2	no	—
748	C₂³	—	10	2	no	—
749	C₂³	—	10	2	no	—
750	C₂³	C₃×#711	1	4	yes	—
751	C₂³	C₂³×C₃×D₅	1	2	yes	—
752	C₂³	C₂³×C₃×D₅	1	2	yes	—
753	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
754	Q₈	—	10	8	no	—
755	D₄	—	2	8	no	—
756	D₄	—	10	8	no	—
757	D₄	—	10	8	no	—
758	C₂×C₄	—	2	8	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	5	4	no	—
765	C₂×C₄	—	5	4	no	—
766	C₂×C₄	—	5	2	no	—
767	C₂×C₄	—	5	2	no	—
768	C₂×C₄	—	5	2	no	—
769	C₂×C₄	—	5	2	no	—
770	C₂×C₄	—	5	2	no	—
771	C₂×C₄	—	5	2	no	—
772	C₂×C₄	—	5	2	no	—
773	C₂×C₄	—	10	8	no	—
774	C₂×C₄	—	10	8	no	—
775	C₂×C₄	—	10	8	no	—
776	C₂×C₄	—	10	8	no	—
777	C₂×C₄	—	10	2	no	—
778	C₂×C₄	—	10	2	no	—
779	C₂×C₄	—	10	2	no	—
780	C₂×C₄	—	10	2	no	—
781	C₂×C₄	—	10	2	no	—
782	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
783	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
784	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
785	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
786	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
787	C₂×C₃	—	2	4	no	—
788	C₂×C₃	—	4	2	no	—
789	C₂×C₃	—	20	2	no	—
790	C₂×C₃	#65983	1	4	yes	direct product factor
791	C₂×C₃	C₂²×#711	1	1	yes	characteristic
792	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
793	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
794	C₅	C₂×C₃×#529	1	1	yes	characteristic, complemented, Sylow
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	8	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	4	4	no	—
802	C₂²	—	10	2	no	—
803	C₂²	—	10	2	no	—
804	C₂²	—	10	2	no	—
805	C₂²	—	20	4	no	—
806	C₂²	C₂×C₃×#711	1	4	yes	—
807	C₂²	C₂×C₃×#711	1	2	yes	—
808	C₂²	C₃×D₅×#41	1	2	yes	—
809	C₂²	C₃×D₅×#41	1	2	yes	—
810	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
811	C₄	—	2	2	no	—
812	C₄	—	2	2	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	5	4	no	—
817	C₄	—	5	4	no	—
818	C₄	—	10	2	no	—
819	C₄	—	10	2	no	—
820	C₄	—	10	2	no	—
821	C₄	—	10	2	no	—
822	C₄	—	10	2	no	—
823	C₃	C₂×#65983	1	1	yes	characteristic, direct product factor, Sylow
824	C₂	—	2	4	no	—
825	C₂	—	4	2	no	—
826	C₂	—	20	2	no	—
827	C₂	C₃×#65983	1	4	yes	direct product factor
828	C₂	C₂²×C₃×#711	1	1	yes	characteristic
829	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
830	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#123	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₃×#4085	C₂
hypercenter	C₂×C₃×#123	D₅
hypocenter	C₅	C₂×C₃×#529
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#123	C₂	semidirect
3. C₂×C₃×D₄×Dic₅	C₂	semidirect
4. C₂×C₃×#4075	C₂	semidirect
5. C₂²×C₃×C₄×Dic₅	C₂	semidirect
6. C₃×#65983	C₂	direct (N × H)
7. C₂×C₃×#4044	C₂	semidirect
8. C₂×C₃×#4038	C₂	semidirect
9. C₂×C₃×#4035	C₂	semidirect
10. C₂×C₃×#4033	C₂	semidirect
11. C₂×C₃×#4031	C₂	semidirect
12. C₂×C₃×#4027	C₂	semidirect
13. C₂×C₃×#4027	C₂	semidirect
14. C₂×C₃×#4025	C₂	semidirect
15. C₂×C₃×#4024	C₂	semidirect
16. C₂×C₃×#4023	C₂	semidirect
17. C₂×#65983	C₃	direct (N × H)
27. C₃×C₅×#123	C₂²	semidirect
37. C₃×D₄×Dic₅	C₂²	semidirect
38. C₃×#4075	C₂²	semidirect
57. C₂×C₃×C₄×Dic₅	C₂²	semidirect
58. C₃×#4044	C₂²	semidirect
59. C₃×#4038	C₂²	semidirect
60. C₃×#4035	C₂²	semidirect
61. C₃×#4033	C₂²	semidirect
62. C₃×#4031	C₂²	semidirect
63. C₃×#4027	C₂²	semidirect
64. C₃×#4027	C₂²	semidirect
65. C₃×#4025	C₂²	semidirect
66. C₃×#4024	C₂²	semidirect
67. C₃×#4023	C₂²	semidirect
69. C₂×C₅×#123	C₂×C₃	semidirect
71. C₂×D₄×Dic₅	C₂×C₃	semidirect
72. C₂×#4075	C₂×C₃	semidirect
73. C₂²×C₄×Dic₅	C₂×C₃	semidirect
74. #65983	C₂×C₃	direct (N × H)
75. C₂×#4044	C₂×C₃	semidirect
76. C₂×#4038	C₂×C₃	semidirect
77. C₂×#4035	C₂×C₃	semidirect
78. C₂×#4033	C₂×C₃	semidirect
79. C₂×#4031	C₂×C₃	semidirect
80. C₂×#4027	C₂×C₃	semidirect
81. C₂×#4027	C₂×C₃	semidirect
82. C₂×#4025	C₂×C₃	semidirect
83. C₂×#4024	C₂×C₃	semidirect
84. C₂×#4023	C₂×C₃	semidirect
150. C₂×C₃×#123	D₅	semidirect
169. C₅×#123	C₂²×C₃	semidirect
179. D₄×Dic₅	C₂²×C₃	semidirect
180. #4075	C₂²×C₃	semidirect
199. C₂×C₄×Dic₅	C₂²×C₃	semidirect
200. #4044	C₂²×C₃	semidirect
201. #4038	C₂²×C₃	semidirect
202. #4035	C₂²×C₃	semidirect
203. #4033	C₂²×C₃	semidirect
204. #4031	C₂²×C₃	semidirect
205. #4027	C₂²×C₃	semidirect
206. #4027	C₂²×C₃	semidirect
207. #4025	C₂²×C₃	semidirect
208. #4024	C₂²×C₃	semidirect
209. #4023	C₂²×C₃	semidirect
271. C₃×#123	C₂×D₅	semidirect
372. C₂×#123	C₃×D₅	semidirect
529. #123	C₂×C₃×D₅	semidirect
567. C₂×C₃×C₅	#529	semidirect
705. C₃×C₅	C₂×#529	semidirect
736. C₂×C₅	C₃×#529	semidirect
790. C₂×C₃	#65983	direct (N × H)
794. C₅	C₂×C₃×#529	semidirect
823. C₃	C₂×#65983	direct (N × H)
827. C₂	C₃×#65983	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×#123	2
C₂×C₃×#4085	2
C₂×C₃×D₄×Dic₅	2
C₂×C₃×#4075	2
C₂²×C₃×C₄×Dic₅	2
C₃×#65983	2
C₂×C₃×#4044	2
C₂×C₃×#4038	2
C₂×C₃×#4035	2
C₂×C₃×#4033	2
C₂×C₃×#4031	2
C₂×C₃×#4027	2
C₂×C₃×#4025	2
C₂×C₃×#4024	2
C₂×C₃×#4023	2
C₂×#65983	3
C₂×C₃×#529	5

Subgroups — C2×C3×#65983 #14479767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65983 #14479767