Subgroups — C₅×#74394 #14327106

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4989	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4976	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×Dic₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4950	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4942	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4668	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×D₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4650	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4647	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2349	—	3	1	no	maximal, Hall
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
19	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₅×#217	C₂²	1	1	yes	characteristic
29	C₄×C₅×#67	—	2	4	no	—
30	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
43	C₅×#67⋊C₄	—	2	4	no	—
44	C₅×#67⋊C₄	C₄	1	8	yes	complemented
45	C₃×C₅×#95	C₂²	1	1	yes	characteristic
46	C₃×C₅×#95	C₂²	1	1	yes	characteristic
47	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
48	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
49	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
50	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
51	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
52	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
53	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
54	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
55	#74394	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
56	C₂×C₄×C₅×D₄	—	3	1	no	—
57	C₂×C₄×C₅×D₄	—	3	1	no	—
58	C₂×C₄×C₅×D₄	—	3	1	no	—
59	C₅×#389	—	3	1	no	—
60	C₅×#389	—	3	1	no	—
61	C₅×#385	—	3	1	no	—
62	C₅×#385	—	3	1	no	—
63	C₅×#385	—	3	1	no	—
64	C₅×#385	D₃	1	1	yes	characteristic, complemented
65	C₅×#382	—	3	1	no	—
66	C₅×#380	—	3	1	no	—
67	C₅×#380	—	3	1	no	—
68	C₄×C₅×C₄⋊C₄	—	3	1	no	—
69	C₂×C₅×#95	—	3	1	no	—
70	C₂×C₅×#95	—	3	1	no	—
71	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
72	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	—	2	2	no	—
74	C₂²×C₃×C₄×C₅	—	2	2	no	—
75	C₂²×C₃×C₄×C₅	—	4	1	no	—
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₅×#67	C₂×C₄	1	4	yes	—
83	C₂×C₅×#67	D₄	1	4	yes	—
84	C₂×C₅×#67	Q₈	1	4	yes	—
85	C₂²×C₅×Dic₃	—	2	2	no	—
86	C₂²×C₅×Dic₃	—	2	2	no	—
87	C₂²×C₅×Dic₃	—	4	1	no	—
88	C₂²×C₅×Dic₃	—	4	1	no	—
89	C₂²×C₅×Dic₃	—	4	1	no	—
90	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
91	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
93	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
94	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
96	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
97	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₂×C₄×C₅×D₃	—	2	2	no	—
99	C₂×C₄×C₅×D₃	—	2	2	no	—
100	C₂×C₄×C₅×D₃	—	2	2	no	—
101	C₂×C₄×C₅×D₃	—	2	2	no	—
102	C₂×C₄×C₅×D₃	—	4	1	no	—
103	C₂×C₄×C₅×D₃	—	4	1	no	—
104	C₂×C₄×C₅×D₃	—	4	1	no	—
105	C₂×C₄×C₅×D₃	—	4	1	no	—
106	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
107	C₃×C₅×C₄⋊C₄	—	2	2	no	—
108	C₃×C₅×C₄⋊C₄	—	4	1	no	—
109	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
110	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
111	C₅×#217	—	2	2	no	—
112	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
113	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
114	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
115	C₅×C₄⋊Dic₃	—	2	2	no	—
116	C₅×C₄⋊Dic₃	—	4	1	no	—
117	C₅×Dic₃⋊C₄	—	2	2	no	—
118	C₅×Dic₃⋊C₄	—	2	2	no	—
119	C₅×Dic₃⋊C₄	—	4	1	no	—
120	C₅×Dic₃⋊C₄	—	4	1	no	—
121	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	complemented
122	C₄×C₅×Dic₃	—	2	2	no	—
123	C₄×C₅×Dic₃	—	2	2	no	—
124	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
125	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic
126	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic
127	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic
128	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
129	C₂×C₃⋊#95	C₂×C₅	1	1	yes	characteristic, complemented
130	#4989	C₂×C₅	1	1	yes	characteristic, complemented
131	#4987	C₂×C₅	1	1	yes	characteristic, complemented
132	#4976	C₂×C₅	1	1	yes	characteristic, complemented
133	Dic₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
134	#4950	C₂×C₅	1	1	yes	characteristic, complemented
135	#4942	C₂×C₅	1	1	yes	characteristic, complemented
136	#4668	C₂×C₅	1	1	yes	characteristic, complemented
137	D₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
138	#4650	C₂×C₅	1	1	yes	characteristic, complemented
139	#4647	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂²×C₅×D₄	—	3	1	no	—
141	C₂³×C₄×C₅	—	3	1	no	—
142	C₂³×C₄×C₅	—	3	1	no	—
143	C₂³×C₄×C₅	—	3	1	no	—
144	C₂³×C₄×C₅	—	3	1	no	—
145	C₂³×C₄×C₅	—	3	1	no	—
146	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
147	C₄×C₅×D₄	—	3	8	no	—
148	C₄×C₅×D₄	—	6	4	no	—
149	C₄×C₅×D₄	—	6	4	no	—
150	C₂×C₅×C₄⋊C₄	—	3	1	no	—
151	C₂×C₅×C₄⋊C₄	—	3	1	no	—
152	C₂×C₅×C₄⋊C₄	—	3	1	no	—
153	C₂×C₅×C₄⋊C₄	—	3	1	no	—
154	C₂×C₅×C₄⋊C₄	—	3	1	no	—
155	C₂×C₅×C₄⋊C₄	—	3	1	no	—
156	C₂×C₅×C₄⋊C₄	—	3	1	no	—
157	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
158	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
159	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
160	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
161	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
162	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
163	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
164	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
165	C₂×C₄²×C₅	—	3	1	no	—
166	C₂×C₄²×C₅	—	3	1	no	—
167	C₂×C₄²×C₅	—	3	1	no	—
168	C₅×#95	—	3	1	no	—
169	C₅×#95	—	3	1	no	—
170	C₅×#95	—	3	1	no	—
171	C₅×#95	—	3	1	no	—
172	C₅×#95	—	3	1	no	—
173	C₅×#95	—	3	1	no	—
174	C₅×#95	—	3	1	no	—
175	C₅×#95	—	3	1	no	—
176	C₅×#95	C₂×D₃	1	1	yes	characteristic
177	C₅×#95	C₂×D₃	1	1	yes	characteristic
178	#2349	—	3	1	no	Sylow
179	C₂³×C₃×C₅	—	2	1	no	—
180	C₂³×C₃×C₅	—	2	1	no	—
181	C₂³×C₃×C₅	—	2	1	no	—
182	C₂³×C₃×C₅	—	2	1	no	—
183	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
184	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
185	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
186	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
187	C₂²×C₅×D₃	—	2	1	no	—
188	C₂²×C₅×D₃	—	2	1	no	—
189	C₂²×C₅×D₃	—	2	1	no	—
190	C₂²×C₅×D₃	—	2	1	no	—
191	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
192	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
193	C₂²×C₅×D₃	C₂×Q₈	1	2	yes	—
194	C₂×C₃×C₄×C₅	—	2	1	no	—
195	C₂×C₃×C₄×C₅	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	2	1	no	—
200	C₂×C₃×C₄×C₅	—	2	1	no	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	4	4	no	—
210	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
211	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
212	C₂×C₃×C₄×C₅	#41	1	2	yes	—
213	C₅×#67	C₄⋊C₄	1	16	yes	complemented
214	C₂×C₅×Dic₃	—	2	1	no	—
215	C₂×C₅×Dic₃	—	2	1	no	—
216	C₂×C₅×Dic₃	—	2	1	no	—
217	C₂×C₅×Dic₃	—	2	1	no	—
218	C₂×C₅×Dic₃	—	2	1	no	—
219	C₂×C₅×Dic₃	—	2	1	no	—
220	C₂×C₅×Dic₃	—	2	1	no	—
221	C₂×C₅×Dic₃	—	2	1	no	—
222	C₂×C₅×Dic₃	—	2	1	no	—
223	C₂×C₅×Dic₃	—	2	1	no	—
224	C₂×C₅×Dic₃	—	2	1	no	—
225	C₂×C₅×Dic₃	—	2	1	no	—
226	C₂×C₅×Dic₃	—	2	1	no	—
227	C₂×C₅×Dic₃	—	2	1	no	—
228	C₂×C₅×Dic₃	—	2	1	no	—
229	C₂×C₅×Dic₃	—	4	4	no	—
230	C₂×C₅×Dic₃	—	4	4	no	—
231	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
232	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
233	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
234	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
235	C₂×C₅×Dic₃	C₂×Q₈	1	2	yes	—
236	C₂×C₅×Dic₃	#41	1	2	yes	—
237	C₄×C₅×D₃	—	4	4	no	—
238	C₄×C₅×D₃	—	4	4	no	—
239	C₄×C₅×D₃	—	4	4	no	—
240	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
241	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
242	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
243	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
244	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
245	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
246	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₂×#217	C₂²×C₅	1	1	yes	characteristic
252	C₄×#67	—	2	4	no	—
253	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
254	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
258	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
259	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
260	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
261	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
262	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
266	#67⋊C₄	—	2	4	no	—
267	#67⋊C₄	C₄×C₅	1	8	yes	complemented
268	C₃×#95	C₂²×C₅	1	1	yes	characteristic
269	C₃×#95	C₂²×C₅	1	1	yes	characteristic
270	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
271	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
272	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
273	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
274	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
275	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
276	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
277	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
278	C₂⁴×C₅	—	3	1	no	—
279	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
280	C₂×C₅×D₄	—	3	4	no	—
281	C₂×C₅×D₄	—	3	4	no	—
282	C₂×C₅×D₄	—	3	4	no	—
283	C₂²×C₄×C₅	—	2	2	no	—
284	C₂²×C₄×C₅	—	2	2	no	—
285	C₂²×C₄×C₅	—	3	1	no	—
286	C₂²×C₄×C₅	—	3	1	no	—
287	C₂²×C₄×C₅	—	3	1	no	—
288	C₂²×C₄×C₅	—	3	1	no	—
289	C₂²×C₄×C₅	—	3	4	no	—
290	C₂²×C₄×C₅	—	3	4	no	—
291	C₂²×C₄×C₅	—	3	1	no	—
292	C₂²×C₄×C₅	—	3	1	no	—
293	C₂²×C₄×C₅	—	3	1	no	—
294	C₂²×C₄×C₅	—	4	1	no	—
295	C₂²×C₄×C₅	—	6	2	no	—
296	C₂²×C₄×C₅	—	6	2	no	—
297	C₂²×C₄×C₅	—	6	2	no	—
298	C₂²×C₄×C₅	—	6	2	no	—
299	C₂²×C₄×C₅	—	6	2	no	—
300	C₂²×C₄×C₅	—	6	2	no	—
301	C₂²×C₄×C₅	—	12	1	no	—
302	C₂²×C₄×C₅	—	12	1	no	—
303	C₂²×C₄×C₅	—	12	1	no	—
304	C₂²×C₄×C₅	—	12	1	no	—
305	C₂²×C₄×C₅	—	12	1	no	—
306	C₂²×C₄×C₅	—	12	1	no	—
307	C₂²×C₄×C₅	—	12	1	no	—
308	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
309	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
310	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
311	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
312	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
313	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
314	C₅×C₄⋊C₄	—	2	2	no	—
315	C₅×C₄⋊C₄	—	3	4	no	—
316	C₅×C₄⋊C₄	—	4	1	no	—
317	C₅×C₄⋊C₄	—	6	2	no	—
318	C₅×C₄⋊C₄	—	6	2	no	—
319	C₅×C₄⋊C₄	—	6	2	no	—
320	C₅×C₄⋊C₄	—	12	1	no	—
321	C₅×C₄⋊C₄	—	12	1	no	—
322	C₅×C₄⋊C₄	—	12	1	no	—
323	C₅×C₂²⋊C₄	—	2	2	no	—
324	C₅×C₂²⋊C₄	—	3	4	no	—
325	C₅×C₂²⋊C₄	—	6	2	no	—
326	C₅×C₂²⋊C₄	—	6	2	no	—
327	C₅×C₂²⋊C₄	—	6	2	no	—
328	C₅×C₂²⋊C₄	C₄×D₃	1	4	yes	complemented
329	C₄²×C₅	—	3	4	no	—
330	C₄²×C₅	—	6	2	no	—
331	C₄²×C₅	—	6	2	no	—
332	C₂×C₄×D₄	—	3	1	no	—
333	C₂×C₄×D₄	—	3	1	no	—
334	C₂×C₄×D₄	—	3	1	no	—
335	#389	—	3	1	no	—
336	#389	—	3	1	no	—
337	#385	—	3	1	no	—
338	#385	—	3	1	no	—
339	#385	—	3	1	no	—
340	#385	C₅×D₃	1	1	yes	characteristic, complemented
341	#382	—	3	1	no	—
342	#380	—	3	1	no	—
343	#380	—	3	1	no	—
344	C₄×C₄⋊C₄	—	3	1	no	—
345	C₂×#95	—	3	1	no	—
346	C₂×#95	—	3	1	no	—
347	C₂²×C₃×C₅	—	2	2	no	—
348	C₂²×C₃×C₅	—	2	2	no	—
349	C₂²×C₃×C₅	—	2	2	no	—
350	C₂²×C₃×C₅	—	2	2	no	—
351	C₂²×C₃×C₅	—	2	2	no	—
352	C₂²×C₃×C₅	—	2	2	no	—
353	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	4	yes	—
354	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
355	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
356	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
357	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
358	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
359	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
360	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₅×D₃	—	2	2	no	—
362	C₂×C₅×D₃	—	2	2	no	—
363	C₂×C₅×D₃	—	2	2	no	—
364	C₂×C₅×D₃	—	2	2	no	—
365	C₂×C₅×D₃	—	2	2	no	—
366	C₂×C₅×D₃	—	2	2	no	—
367	C₂×C₅×D₃	C₂×C₄⋊C₄	1	4	yes	—
368	C₃×C₄×C₅	—	2	2	no	—
369	C₃×C₄×C₅	—	2	2	no	—
370	C₃×C₄×C₅	—	2	2	no	—
371	C₃×C₄×C₅	—	4	1	no	—
372	C₃×C₄×C₅	—	4	1	no	—
373	C₃×C₄×C₅	—	4	1	no	—
374	C₅×Dic₃	—	2	2	no	—
375	C₅×Dic₃	—	2	2	no	—
376	C₅×Dic₃	—	2	2	no	—
377	C₅×Dic₃	—	4	1	no	—
378	C₅×Dic₃	—	4	1	no	—
379	C₅×Dic₃	—	4	1	no	—
380	C₅×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
381	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
382	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
383	C₂²×C₃×C₄	—	2	2	no	—
384	C₂²×C₃×C₄	—	2	2	no	—
385	C₂²×C₃×C₄	—	4	1	no	—
386	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
390	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
392	C₂×#67	C₂×C₄×C₅	1	4	yes	—
393	C₂×#67	C₅×D₄	1	4	yes	—
394	C₂×#67	C₅×Q₈	1	4	yes	—
395	C₂²×Dic₃	—	2	2	no	—
396	C₂²×Dic₃	—	2	2	no	—
397	C₂²×Dic₃	—	4	1	no	—
398	C₂²×Dic₃	—	4	1	no	—
399	C₂²×Dic₃	—	4	1	no	—
400	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
401	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
402	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
403	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
404	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
405	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
406	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
407	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
408	C₂×C₄×D₃	—	2	2	no	—
409	C₂×C₄×D₃	—	2	2	no	—
410	C₂×C₄×D₃	—	2	2	no	—
411	C₂×C₄×D₃	—	2	2	no	—
412	C₂×C₄×D₃	—	4	1	no	—
413	C₂×C₄×D₃	—	4	1	no	—
414	C₂×C₄×D₃	—	4	1	no	—
415	C₂×C₄×D₃	—	4	1	no	—
416	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
417	C₃×C₄⋊C₄	—	2	2	no	—
418	C₃×C₄⋊C₄	—	4	1	no	—
419	C₃×C₂²⋊C₄	—	2	2	no	—
420	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
421	#217	—	2	2	no	—
422	(C₂×D₃)⋊C₄	—	2	2	no	—
423	(C₂×D₃)⋊C₄	—	2	2	no	—
424	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
425	C₄⋊Dic₃	—	2	2	no	—
426	C₄⋊Dic₃	—	4	1	no	—
427	Dic₃⋊C₄	—	2	2	no	—
428	Dic₃⋊C₄	—	2	2	no	—
429	Dic₃⋊C₄	—	4	1	no	—
430	Dic₃⋊C₄	—	4	1	no	—
431	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
432	C₄×Dic₃	—	2	2	no	—
433	C₄×Dic₃	—	2	2	no	—
434	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
435	C₂³×C₅	—	2	1	no	—
436	C₂³×C₅	—	2	1	no	—
437	C₂³×C₅	—	2	1	no	—
438	C₂³×C₅	—	2	1	no	—
439	C₂³×C₅	—	3	2	no	—
440	C₂³×C₅	—	3	2	no	—
441	C₂³×C₅	—	3	2	no	—
442	C₂³×C₅	—	6	1	no	—
443	C₂³×C₅	—	6	1	no	—
444	C₂³×C₅	—	6	1	no	—
445	C₂³×C₅	—	6	1	no	—
446	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
447	C₂³×C₅	D₃×D₄	1	2	yes	—
448	C₂³×C₅	D₃×Q₈	1	2	yes	—
449	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
450	C₅×D₄	—	3	16	no	—
451	C₂×C₄×C₅	—	2	1	no	—
452	C₂×C₄×C₅	—	2	1	no	—
453	C₂×C₄×C₅	—	2	1	no	—
454	C₂×C₄×C₅	—	2	1	no	—
455	C₂×C₄×C₅	—	2	1	no	—
456	C₂×C₄×C₅	—	2	1	no	—
457	C₂×C₄×C₅	—	2	1	no	—
458	C₂×C₄×C₅	—	2	1	no	—
459	C₂×C₄×C₅	—	2	1	no	—
460	C₂×C₄×C₅	—	2	1	no	—
461	C₂×C₄×C₅	—	2	1	no	—
462	C₂×C₄×C₅	—	2	1	no	—
463	C₂×C₄×C₅	—	2	1	no	—
464	C₂×C₄×C₅	—	2	1	no	—
465	C₂×C₄×C₅	—	2	1	no	—
466	C₂×C₄×C₅	—	3	2	no	—
467	C₂×C₄×C₅	—	3	2	no	—
468	C₂×C₄×C₅	—	3	2	no	—
469	C₂×C₄×C₅	—	3	2	no	—
470	C₂×C₄×C₅	—	3	2	no	—
471	C₂×C₄×C₅	—	3	2	no	—
472	C₂×C₄×C₅	—	4	4	no	—
473	C₂×C₄×C₅	—	6	1	no	—
474	C₂×C₄×C₅	—	6	1	no	—
475	C₂×C₄×C₅	—	6	1	no	—
476	C₂×C₄×C₅	—	6	1	no	—
477	C₂×C₄×C₅	—	6	1	no	—
478	C₂×C₄×C₅	—	6	1	no	—
479	C₂×C₄×C₅	—	6	1	no	—
480	C₂×C₄×C₅	—	6	1	no	—
481	C₂×C₄×C₅	—	6	1	no	—
482	C₂×C₄×C₅	—	6	1	no	—
483	C₂×C₄×C₅	—	6	1	no	—
484	C₂×C₄×C₅	—	6	1	no	—
485	C₂×C₄×C₅	—	6	1	no	—
486	C₂×C₄×C₅	—	6	1	no	—
487	C₂×C₄×C₅	—	6	1	no	—
488	C₂×C₄×C₅	—	12	4	no	—
489	C₂×C₄×C₅	—	12	4	no	—
490	C₂×C₄×C₅	—	12	4	no	—
491	C₂×C₄×C₅	—	12	4	no	—
492	C₂×C₄×C₅	—	12	4	no	—
493	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
494	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
495	C₂×C₄×C₅	#237	1	2	yes	—
496	C₂²×D₄	—	3	1	no	—
497	C₂³×C₄	—	3	1	no	—
498	C₂³×C₄	—	3	1	no	—
499	C₂³×C₄	—	3	1	no	—
500	C₂³×C₄	—	3	1	no	—
501	C₂³×C₄	—	3	1	no	—
502	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
503	C₄×D₄	—	3	8	no	—
504	C₄×D₄	—	6	4	no	—
505	C₄×D₄	—	6	4	no	—
506	C₂×C₄⋊C₄	—	3	1	no	—
507	C₂×C₄⋊C₄	—	3	1	no	—
508	C₂×C₄⋊C₄	—	3	1	no	—
509	C₂×C₄⋊C₄	—	3	1	no	—
510	C₂×C₄⋊C₄	—	3	1	no	—
511	C₂×C₄⋊C₄	—	3	1	no	—
512	C₂×C₄⋊C₄	—	3	1	no	—
513	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	—	3	1	no	—
516	C₂×C₂²⋊C₄	—	3	1	no	—
517	C₂×C₂²⋊C₄	—	3	1	no	—
518	C₂×C₂²⋊C₄	—	3	1	no	—
519	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
521	C₂×C₄²	—	3	1	no	—
522	C₂×C₄²	—	3	1	no	—
523	C₂×C₄²	—	3	1	no	—
524	#95	—	3	1	no	—
525	#95	—	3	1	no	—
526	#95	—	3	1	no	—
527	#95	—	3	1	no	—
528	#95	—	3	1	no	—
529	#95	—	3	1	no	—
530	#95	—	3	1	no	—
531	#95	—	3	1	no	—
532	#95	C₂×C₅×D₃	1	1	yes	characteristic
533	#95	C₂×C₅×D₃	1	1	yes	characteristic
534	C₂×C₃×C₅	—	2	4	no	—
535	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
536	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
537	C₂×C₃×C₅	#518	1	1	yes	characteristic
538	C₂×C₃×C₅	#546	1	1	yes	characteristic
539	C₂×C₃×C₅	#546	1	1	yes	characteristic
540	C₂×C₃×C₅	#554	1	1	yes	characteristic
541	C₂×C₃×C₅	#554	1	1	yes	characteristic
542	C₅×D₃	—	2	4	no	—
543	C₂³×C₃	—	2	1	no	—
544	C₂³×C₃	—	2	1	no	—
545	C₂³×C₃	—	2	1	no	—
546	C₂³×C₃	—	2	1	no	—
547	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
548	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
549	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
550	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
551	C₂²×D₃	—	2	1	no	—
552	C₂²×D₃	—	2	1	no	—
553	C₂²×D₃	—	2	1	no	—
554	C₂²×D₃	—	2	1	no	—
555	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
556	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
557	C₂²×D₃	C₂×C₅×Q₈	1	2	yes	—
558	C₂×C₃×C₄	—	2	1	no	—
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	—	2	1	no	—
561	C₂×C₃×C₄	—	2	1	no	—
562	C₂×C₃×C₄	—	2	1	no	—
563	C₂×C₃×C₄	—	2	1	no	—
564	C₂×C₃×C₄	—	2	1	no	—
565	C₂×C₃×C₄	—	2	1	no	—
566	C₂×C₃×C₄	—	2	1	no	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	2	1	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	1	no	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	4	4	no	—
574	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
575	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
576	C₂×C₃×C₄	C₅×#41	1	2	yes	—
577	#67	C₅×C₄⋊C₄	1	16	yes	complemented
578	C₂×Dic₃	—	2	1	no	—
579	C₂×Dic₃	—	2	1	no	—
580	C₂×Dic₃	—	2	1	no	—
581	C₂×Dic₃	—	2	1	no	—
582	C₂×Dic₃	—	2	1	no	—
583	C₂×Dic₃	—	2	1	no	—
584	C₂×Dic₃	—	2	1	no	—
585	C₂×Dic₃	—	2	1	no	—
586	C₂×Dic₃	—	2	1	no	—
587	C₂×Dic₃	—	2	1	no	—
588	C₂×Dic₃	—	2	1	no	—
589	C₂×Dic₃	—	2	1	no	—
590	C₂×Dic₃	—	2	1	no	—
591	C₂×Dic₃	—	2	1	no	—
592	C₂×Dic₃	—	2	1	no	—
593	C₂×Dic₃	—	4	4	no	—
594	C₂×Dic₃	—	4	4	no	—
595	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
596	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
597	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
598	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
599	C₂×Dic₃	C₂×C₅×Q₈	1	2	yes	—
600	C₂×Dic₃	C₅×#41	1	2	yes	—
601	C₄×D₃	—	4	4	no	—
602	C₄×D₃	—	4	4	no	—
603	C₄×D₃	—	4	4	no	—
604	C₂²×C₅	—	2	2	no	—
605	C₂²×C₅	—	2	2	no	—
606	C₂²×C₅	—	2	2	no	—
607	C₂²×C₅	—	2	2	no	—
608	C₂²×C₅	—	2	2	no	—
609	C₂²×C₅	—	2	2	no	—
610	C₂²×C₅	—	3	4	no	—
611	C₂²×C₅	—	6	2	no	—
612	C₂²×C₅	—	6	2	no	—
613	C₂²×C₅	—	6	2	no	—
614	C₂²×C₅	—	6	2	no	—
615	C₂²×C₅	—	6	2	no	—
616	C₂²×C₅	—	6	2	no	—
617	C₂²×C₅	D₃×C₄⋊C₄	1	4	yes	—
618	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
619	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
620	C₂²×C₅	C₂×#237	1	1	yes	characteristic
621	C₂²×C₅	#1004	1	1	yes	characteristic
622	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
623	C₂²×C₅	D₃×#41	1	1	yes	characteristic
624	C₂²×C₅	#1009	1	1	yes	characteristic
625	C₄×C₅	—	2	2	no	—
626	C₄×C₅	—	2	2	no	—
627	C₄×C₅	—	2	2	no	—
628	C₄×C₅	—	3	4	no	—
629	C₄×C₅	—	4	1	no	—
630	C₄×C₅	—	4	1	no	—
631	C₄×C₅	—	4	1	no	—
632	C₄×C₅	—	6	2	no	—
633	C₄×C₅	—	6	2	no	—
634	C₄×C₅	—	6	2	no	—
635	C₄×C₅	—	12	1	no	—
636	C₄×C₅	—	12	1	no	—
637	C₄×C₅	—	12	1	no	—
638	C₂⁴	—	3	1	no	—
639	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
640	C₂×D₄	—	3	4	no	—
641	C₂×D₄	—	3	4	no	—
642	C₂×D₄	—	3	4	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	3	1	no	—
646	C₂²×C₄	—	3	1	no	—
647	C₂²×C₄	—	3	1	no	—
648	C₂²×C₄	—	3	1	no	—
649	C₂²×C₄	—	3	4	no	—
650	C₂²×C₄	—	3	4	no	—
651	C₂²×C₄	—	3	1	no	—
652	C₂²×C₄	—	3	1	no	—
653	C₂²×C₄	—	3	1	no	—
654	C₂²×C₄	—	4	1	no	—
655	C₂²×C₄	—	6	2	no	—
656	C₂²×C₄	—	6	2	no	—
657	C₂²×C₄	—	6	2	no	—
658	C₂²×C₄	—	6	2	no	—
659	C₂²×C₄	—	6	2	no	—
660	C₂²×C₄	—	6	2	no	—
661	C₂²×C₄	—	12	1	no	—
662	C₂²×C₄	—	12	1	no	—
663	C₂²×C₄	—	12	1	no	—
664	C₂²×C₄	—	12	1	no	—
665	C₂²×C₄	—	12	1	no	—
666	C₂²×C₄	—	12	1	no	—
667	C₂²×C₄	—	12	1	no	—
668	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
669	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
670	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
671	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
672	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
673	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	3	4	no	—
676	C₄⋊C₄	—	4	1	no	—
677	C₄⋊C₄	—	6	2	no	—
678	C₄⋊C₄	—	6	2	no	—
679	C₄⋊C₄	—	6	2	no	—
680	C₄⋊C₄	—	12	1	no	—
681	C₄⋊C₄	—	12	1	no	—
682	C₄⋊C₄	—	12	1	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	3	4	no	—
685	C₂²⋊C₄	—	6	2	no	—
686	C₂²⋊C₄	—	6	2	no	—
687	C₂²⋊C₄	—	6	2	no	—
688	C₂²⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
689	C₄²	—	3	4	no	—
690	C₄²	—	6	2	no	—
691	C₄²	—	6	2	no	—
692	C₃×C₅	#2349	1	1	yes	characteristic, complemented, Hall
693	C₂²×C₃	—	2	2	no	—
694	C₂²×C₃	—	2	2	no	—
695	C₂²×C₃	—	2	2	no	—
696	C₂²×C₃	—	2	2	no	—
697	C₂²×C₃	—	2	2	no	—
698	C₂²×C₃	—	2	2	no	—
699	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
700	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
701	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
702	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
703	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
704	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
705	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
707	C₂×D₃	—	2	2	no	—
708	C₂×D₃	—	2	2	no	—
709	C₂×D₃	—	2	2	no	—
710	C₂×D₃	—	2	2	no	—
711	C₂×D₃	—	2	2	no	—
712	C₂×D₃	—	2	2	no	—
713	C₂×D₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
714	C₃×C₄	—	2	2	no	—
715	C₃×C₄	—	2	2	no	—
716	C₃×C₄	—	2	2	no	—
717	C₃×C₄	—	4	1	no	—
718	C₃×C₄	—	4	1	no	—
719	C₃×C₄	—	4	1	no	—
720	Dic₃	—	2	2	no	—
721	Dic₃	—	2	2	no	—
722	Dic₃	—	2	2	no	—
723	Dic₃	—	4	1	no	—
724	Dic₃	—	4	1	no	—
725	Dic₃	—	4	1	no	—
726	Dic₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
727	C₂×C₅	—	2	4	no	—
728	C₂×C₅	—	6	4	no	—
729	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
730	C₂×C₅	C₄×#237	1	1	yes	characteristic
731	C₂×C₅	#5545	1	1	yes	characteristic
732	C₂×C₅	#5591	1	1	yes	characteristic
733	C₂×C₅	#5635	1	1	yes	characteristic
734	C₂×C₅	#5636	1	1	yes	characteristic
735	C₂×C₅	#5654	1	1	yes	characteristic
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	3	2	no	—
741	C₂³	—	3	2	no	—
742	C₂³	—	3	2	no	—
743	C₂³	—	6	1	no	—
744	C₂³	—	6	1	no	—
745	C₂³	—	6	1	no	—
746	C₂³	—	6	1	no	—
747	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
748	C₂³	C₅×D₃×D₄	1	2	yes	—
749	C₂³	C₅×D₃×Q₈	1	2	yes	—
750	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
751	D₄	—	3	16	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	3	2	no	—
768	C₂×C₄	—	3	2	no	—
769	C₂×C₄	—	3	2	no	—
770	C₂×C₄	—	3	2	no	—
771	C₂×C₄	—	3	2	no	—
772	C₂×C₄	—	3	2	no	—
773	C₂×C₄	—	4	4	no	—
774	C₂×C₄	—	6	1	no	—
775	C₂×C₄	—	6	1	no	—
776	C₂×C₄	—	6	1	no	—
777	C₂×C₄	—	6	1	no	—
778	C₂×C₄	—	6	1	no	—
779	C₂×C₄	—	6	1	no	—
780	C₂×C₄	—	6	1	no	—
781	C₂×C₄	—	6	1	no	—
782	C₂×C₄	—	6	1	no	—
783	C₂×C₄	—	6	1	no	—
784	C₂×C₄	—	6	1	no	—
785	C₂×C₄	—	6	1	no	—
786	C₂×C₄	—	6	1	no	—
787	C₂×C₄	—	6	1	no	—
788	C₂×C₄	—	6	1	no	—
789	C₂×C₄	—	12	4	no	—
790	C₂×C₄	—	12	4	no	—
791	C₂×C₄	—	12	4	no	—
792	C₂×C₄	—	12	4	no	—
793	C₂×C₄	—	12	4	no	—
794	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
795	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
796	C₂×C₄	C₅×#237	1	2	yes	—
797	C₂×C₃	—	2	4	no	—
798	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
799	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
800	C₂×C₃	C₅×#518	1	1	yes	characteristic
801	C₂×C₃	C₅×#546	1	1	yes	characteristic
802	C₂×C₃	C₅×#546	1	1	yes	characteristic
803	C₂×C₃	C₅×#554	1	1	yes	characteristic
804	C₂×C₃	C₅×#554	1	1	yes	characteristic
805	D₃	—	2	4	no	—
806	C₅	#74394	1	1	yes	characteristic, direct product factor, Sylow
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	3	4	no	—
814	C₂²	—	6	2	no	—
815	C₂²	—	6	2	no	—
816	C₂²	—	6	2	no	—
817	C₂²	—	6	2	no	—
818	C₂²	—	6	2	no	—
819	C₂²	—	6	2	no	—
820	C₂²	C₅×D₃×C₄⋊C₄	1	4	yes	—
821	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
822	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
823	C₂²	C₂×C₅×#237	1	1	yes	characteristic
824	C₂²	C₅×#1004	1	1	yes	characteristic
825	C₂²	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
826	C₂²	C₅×D₃×#41	1	1	yes	characteristic
827	C₂²	C₅×#1009	1	1	yes	characteristic
828	C₄	—	2	2	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	2	no	—
831	C₄	—	3	4	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	1	no	—
835	C₄	—	6	2	no	—
836	C₄	—	6	2	no	—
837	C₄	—	6	2	no	—
838	C₄	—	12	1	no	—
839	C₄	—	12	1	no	—
840	C₄	—	12	1	no	—
841	C₃	C₅×#2349	1	1	yes	characteristic, complemented, Sylow
842	C₂	—	2	4	no	—
843	C₂	—	6	4	no	—
844	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
845	C₂	C₄×C₅×#237	1	1	yes	characteristic
846	C₂	C₅×#5545	1	1	yes	characteristic
847	C₂	C₅×#5591	1	1	yes	characteristic
848	C₂	C₅×#5635	1	1	yes	characteristic
849	C₂	C₅×#5636	1	1	yes	characteristic
850	C₂	C₅×#5654	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#385	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#67	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#385	D₃
hypocenter	C₃	C₅×#2349
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#385

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#385	C₂	semidirect
5. C₂×C₅×C₃⋊#95	C₂	semidirect
6. C₅×#4989	C₂	semidirect
7. C₅×#4987	C₂	semidirect
8. C₅×#4976	C₂	semidirect
9. C₅×Dic₃×C₄⋊C₄	C₂	semidirect
10. C₅×#4950	C₂	semidirect
11. C₅×#4942	C₂	semidirect
12. C₅×#4668	C₂	semidirect
13. C₅×D₃×#95	C₂	semidirect
14. C₅×#4650	C₂	semidirect
15. C₅×#4647	C₂	semidirect
44. C₅×#67⋊C₄	C₄	semidirect
55. #74394	C₅	direct (N × H)
64. C₅×#385	D₃	semidirect
90. C₂²×C₅×Dic₃	C₂×C₄	semidirect
106. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
110. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
114. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
121. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
124. C₄×C₅×Dic₃	C₂×C₄	semidirect
128. C₃×#385	C₂×C₅	semidirect
129. C₂×C₃⋊#95	C₂×C₅	semidirect
130. #4989	C₂×C₅	semidirect
131. #4987	C₂×C₅	semidirect
132. #4976	C₂×C₅	semidirect
133. Dic₃×C₄⋊C₄	C₂×C₅	semidirect
134. #4950	C₂×C₅	semidirect
135. #4942	C₂×C₅	semidirect
136. #4668	C₂×C₅	semidirect
137. D₃×#95	C₂×C₅	semidirect
138. #4650	C₂×C₅	semidirect
139. #4647	C₂×C₅	semidirect
213. C₅×#67	C₄⋊C₄	semidirect
267. #67⋊C₄	C₄×C₅	semidirect
328. C₅×C₂²⋊C₄	C₄×D₃	semidirect
340. #385	C₅×D₃	semidirect
400. C₂²×Dic₃	C₂×C₄×C₅	semidirect
416. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
420. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
424. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
431. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
434. C₄×Dic₃	C₂×C₄×C₅	semidirect
577. #67	C₅×C₄⋊C₄	semidirect
688. C₂²⋊C₄	C₄×C₅×D₃	semidirect
692. C₃×C₅	#2349	semidirect
806. C₅	#74394	direct (N × H)
841. C₃	C₅×#2349	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×#67	2
C₂×C₅×#67⋊C₄	2
C₃×C₅×#385	2
C₂×C₅×C₃⋊#95	2
C₅×#4989	2
C₅×#4987	2
C₅×#4976	2
C₅×Dic₃×C₄⋊C₄	2
C₅×#4950	2
C₅×#4942	2
C₅×#4668	2
C₅×D₃×#95	2
C₅×#4650	2
C₅×#4647	2
C₅×#2349	3
#74394	5

Subgroups — C5×#74394 #14327106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#74394 #14327106