Subgroups — C₄×C₅×#547 #11956879

Order 1280.

3268 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×#41	C₂	1	2	yes	maximal, complemented
3	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2362	C₂	1	2	yes	maximal, complemented
5	C₅×#2361	C₂	1	2	yes	maximal, complemented
6	C₅×#2359	C₂	1	4	yes	maximal, complemented
7	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2344	C₂	1	2	yes	maximal, complemented
10	C₅×#2339	C₂	1	2	yes	maximal, complemented
11	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
13	C₄×C₅×#123	C₂	1	4	yes	maximal, complemented
14	C₄×C₅×#121	C₂	1	2	yes	maximal, complemented
15	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
18	C₂²×C₅×#41	C₂²	1	2	yes	—
19	C₅×#547	C₄	1	16	yes	direct product factor
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#123	C₂²	1	4	yes	—
22	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₅×#121	C₂²	1	2	yes	—
24	C₄×C₅×#41	—	2	16	no	—
25	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
26	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
27	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
31	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
33	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×#117	C₂²	1	4	yes	—
37	C₂×C₅×#117	C₂²	1	2	yes	—
38	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₄²×C₅	C₂²	1	2	yes	—
41	C₂²×C₄²×C₅	C₂²	1	4	yes	—
42	C₂²×C₄²×C₅	C₂²	1	2	yes	—
43	C₅×#391	C₂²	1	2	yes	—
44	C₅×#391	C₂²	1	2	yes	—
45	C₅×#390	C₂²	1	2	yes	—
46	C₅×#389	C₂²	1	2	yes	—
47	C₅×#389	C₂²	1	2	yes	—
48	C₅×#389	C₂²	1	2	yes	—
49	C₅×#389	C₂²	1	2	yes	—
50	C₅×#388	C₂²	1	4	yes	—
51	C₅×#388	C₂²	1	4	yes	—
52	C₅×#388	C₂²	1	4	yes	—
53	C₅×#387	C₂²	1	4	yes	—
54	C₅×#387	C₂²	1	4	yes	—
55	C₅×#387	C₂²	1	4	yes	—
56	C₅×#386	C₂²	1	4	yes	—
57	C₅×#386	C₂²	1	4	yes	—
58	C₅×#385	C₂²	1	4	yes	—
59	C₅×#385	C₂²	1	4	yes	—
60	C₅×#384	C₂²	1	1	yes	characteristic
61	C₅×#381	C₂²	1	4	yes	—
62	C₅×#380	C₂²	1	2	yes	—
63	C₅×#380	C₂²	1	2	yes	—
64	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
66	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
67	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
68	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
69	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
70	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
74	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
76	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
77	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
78	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
79	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
83	C₂×C₅×#95	C₂²	1	4	yes	—
84	C₄³×C₅	C₂²	1	1	yes	characteristic
85	C₄×#547	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂×C₅×#41	—	2	8	no	—
87	C₂×C₅×#41	—	2	8	no	—
88	C₂×C₅×#41	C₂×C₄	1	16	yes	complemented
89	C₂²×C₅×Q₈	C₂³	1	2	yes	—
90	C₂²×C₅×D₄	C₂³	1	4	yes	—
91	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
92	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₅	C₂³	1	2	yes	—
94	C₂³×C₄×C₅	C₂³	1	2	yes	—
95	C₂³×C₄×C₅	C₂³	1	4	yes	—
96	C₂³×C₄×C₅	C₂³	1	2	yes	—
97	C₂³×C₄×C₅	C₂³	1	4	yes	—
98	C₂³×C₄×C₅	C₂³	1	2	yes	—
99	C₂³×C₄×C₅	C₂³	1	2	yes	—
100	C₂³×C₄×C₅	C₂³	1	2	yes	—
101	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
102	C₅×#123	C₂×C₄	1	32	yes	complemented
103	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
104	C₅×#121	C₂×C₄	1	16	yes	complemented
105	C₄×C₅×Q₈	—	2	8	no	—
106	C₄×C₅×Q₈	—	2	8	no	—
107	C₄×C₅×D₄	—	2	8	no	—
108	C₄×C₅×D₄	—	2	4	no	—
109	C₄×C₅×D₄	—	2	16	no	—
110	C₄×C₅×D₄	—	2	4	no	—
111	C₄×C₅×D₄	—	2	16	no	—
112	C₄×C₅×D₄	—	2	4	no	—
113	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
114	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
115	C₄×C₅×D₄	D₄	1	8	yes	complemented
116	C₅×#117	—	2	8	no	—
117	C₅×#117	—	2	16	no	—
118	C₂×C₅×C₄⋊C₄	—	2	8	no	—
119	C₂×C₅×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
120	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
126	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
127	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
130	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₄²×C₅	—	2	16	no	—
146	C₂×C₄²×C₅	—	2	8	no	—
147	C₂×C₄²×C₅	—	2	8	no	—
148	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₅	C₂³	1	2	yes	—
151	C₂×C₄²×C₅	C₂³	1	2	yes	—
152	C₂×C₄²×C₅	C₂³	1	2	yes	—
153	C₂×C₄²×C₅	C₂³	1	2	yes	—
154	C₂×C₄²×C₅	C₂³	1	4	yes	—
155	C₂×C₄²×C₅	C₂³	1	4	yes	—
156	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₅	C₂³	1	2	yes	—
158	C₂×C₄²×C₅	C₂³	1	2	yes	—
159	C₂×C₄²×C₅	C₂³	1	4	yes	—
160	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
164	C₅×#95	C₂³	1	2	yes	—
165	C₅×#95	C₂³	1	4	yes	—
166	C₅×#95	C₂³	1	4	yes	—
167	C₅×#95	C₂³	1	4	yes	—
168	C₅×#95	C₂³	1	2	yes	—
169	C₅×#95	C₂³	1	2	yes	—
170	C₅×#95	C₂³	1	2	yes	—
171	C₅×#95	C₂³	1	2	yes	—
172	C₅×#95	C₂³	1	2	yes	—
173	C₅×#95	C₂³	1	4	yes	—
174	C₅×#95	C₂³	1	4	yes	—
175	C₅×#95	C₂³	1	4	yes	—
176	C₂×#547	C₂×C₅	1	1	yes	characteristic
177	C₂×C₄×#41	C₂×C₅	1	2	yes	complemented
178	#2365	C₂×C₅	1	1	yes	characteristic, complemented
179	#2362	C₂×C₅	1	2	yes	complemented
180	#2361	C₂×C₅	1	2	yes	complemented
181	#2359	C₂×C₅	1	4	yes	complemented
182	#2354	C₂×C₅	1	1	yes	characteristic, complemented
183	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
184	#2344	C₂×C₅	1	2	yes	complemented
185	#2339	C₂×C₅	1	2	yes	complemented
186	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
187	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
188	C₄×#123	C₂×C₅	1	4	yes	complemented
189	C₄×#121	C₂×C₅	1	2	yes	complemented
190	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
191	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
192	C₂×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
193	C₂⁴×C₅	C₂⁴	1	2	yes	—
194	C₂⁴×C₅	C₂⁴	1	2	yes	—
195	C₅×#41	—	2	64	no	—
196	C₂×C₅×Q₈	—	2	4	no	—
197	C₂×C₅×Q₈	—	2	4	no	—
198	C₂×C₅×Q₈	C₂²×C₄	1	8	yes	—
199	C₂×C₅×D₄	—	2	8	no	—
200	C₂×C₅×D₄	—	2	8	no	—
201	C₂×C₅×D₄	—	2	2	no	—
202	C₂×C₅×D₄	—	2	2	no	—
203	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
204	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
205	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
206	C₂×C₅×D₄	C₂×D₄	1	4	yes	—
207	C₂×C₅×D₄	#41	1	4	yes	—
208	C₂²×C₄×C₅	—	2	8	no	—
209	C₂²×C₄×C₅	—	2	8	no	—
210	C₂²×C₄×C₅	—	2	4	no	—
211	C₂²×C₄×C₅	—	2	4	no	—
212	C₂²×C₄×C₅	—	2	4	no	—
213	C₂²×C₄×C₅	—	2	4	no	—
214	C₂²×C₄×C₅	—	2	4	no	—
215	C₂²×C₄×C₅	—	2	4	no	—
216	C₂²×C₄×C₅	—	2	8	no	—
217	C₂²×C₄×C₅	—	2	4	no	—
218	C₂²×C₄×C₅	—	2	4	no	—
219	C₂²×C₄×C₅	—	2	4	no	—
220	C₂²×C₄×C₅	—	2	4	no	—
221	C₂²×C₄×C₅	—	2	8	no	—
222	C₂²×C₄×C₅	—	2	4	no	—
223	C₂²×C₄×C₅	—	2	4	no	—
224	C₂²×C₄×C₅	—	2	4	no	—
225	C₂²×C₄×C₅	—	4	2	no	—
226	C₂²×C₄×C₅	—	4	2	no	—
227	C₂²×C₄×C₅	—	4	4	no	—
228	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
229	C₂²×C₄×C₅	C₂²×C₄	1	16	yes	—
230	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
231	C₂²×C₄×C₅	C₂×D₄	1	8	yes	—
232	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
247	C₅×C₄⋊C₄	—	2	8	no	—
248	C₅×C₄⋊C₄	—	2	8	no	—
249	C₅×C₄⋊C₄	—	2	4	no	—
250	C₅×C₄⋊C₄	—	2	8	no	—
251	C₅×C₄⋊C₄	—	2	4	no	—
252	C₅×C₄⋊C₄	—	2	2	no	—
253	C₅×C₄⋊C₄	—	2	2	no	—
254	C₅×C₄⋊C₄	—	4	2	no	—
255	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
256	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
257	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	—
258	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
259	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
260	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
261	C₅×C₄⋊C₄	#41	1	4	yes	complemented
262	C₅×C₂²⋊C₄	—	2	8	no	—
263	C₅×C₂²⋊C₄	—	2	4	no	—
264	C₅×C₂²⋊C₄	—	2	8	no	—
265	C₅×C₂²⋊C₄	—	2	4	no	—
266	C₅×C₂²⋊C₄	—	2	4	no	—
267	C₅×C₂²⋊C₄	—	4	4	no	—
268	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
269	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
270	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
271	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
272	C₄²×C₅	—	2	4	no	—
273	C₄²×C₅	—	2	8	no	—
274	C₄²×C₅	—	2	4	no	—
275	C₄²×C₅	—	2	8	no	—
276	C₄²×C₅	—	2	4	no	—
277	C₄²×C₅	—	2	8	no	—
278	C₄²×C₅	—	2	4	no	—
279	C₄²×C₅	—	2	4	no	—
280	C₄²×C₅	—	2	4	no	—
281	C₄²×C₅	—	2	2	no	—
282	C₄²×C₅	—	2	2	no	—
283	C₄²×C₅	—	2	2	no	—
284	C₄²×C₅	—	4	1	no	—
285	C₄²×C₅	C₂²×C₄	1	4	yes	—
286	C₄²×C₅	C₂×D₄	1	4	yes	—
287	C₄²×C₅	#41	1	4	yes	complemented
288	C₂²×#41	C₂²×C₅	1	2	yes	—
289	#547	C₄×C₅	1	16	yes	direct product factor
290	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
291	C₂×#123	C₂²×C₅	1	4	yes	—
292	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
293	C₂×#121	C₂²×C₅	1	2	yes	—
294	C₄×#41	—	2	16	no	—
295	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
296	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
297	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
299	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
300	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
302	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
303	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
304	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
306	C₂×#117	C₂²×C₅	1	4	yes	—
307	C₂×#117	C₂²×C₅	1	2	yes	—
308	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
309	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
310	C₂²×C₄²	C₂²×C₅	1	4	yes	—
311	C₂²×C₄²	C₂²×C₅	1	2	yes	—
312	C₂²×C₄²	C₂²×C₅	1	2	yes	—
313	#391	C₂²×C₅	1	2	yes	—
314	#391	C₂²×C₅	1	2	yes	—
315	#390	C₂²×C₅	1	2	yes	—
316	#389	C₂²×C₅	1	2	yes	—
317	#389	C₂²×C₅	1	2	yes	—
318	#389	C₂²×C₅	1	2	yes	—
319	#389	C₂²×C₅	1	2	yes	—
320	#388	C₂²×C₅	1	4	yes	—
321	#388	C₂²×C₅	1	4	yes	—
322	#388	C₂²×C₅	1	4	yes	—
323	#387	C₂²×C₅	1	4	yes	—
324	#387	C₂²×C₅	1	4	yes	—
325	#387	C₂²×C₅	1	4	yes	—
326	#386	C₂²×C₅	1	4	yes	—
327	#386	C₂²×C₅	1	4	yes	—
328	#385	C₂²×C₅	1	4	yes	—
329	#385	C₂²×C₅	1	4	yes	—
330	#384	C₂²×C₅	1	1	yes	characteristic
331	#381	C₂²×C₅	1	4	yes	—
332	#380	C₂²×C₅	1	2	yes	—
333	#380	C₂²×C₅	1	2	yes	—
334	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
335	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
336	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
337	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
338	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
339	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
340	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
341	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
342	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
345	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
346	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
347	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
348	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
349	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
351	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
352	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
353	C₂×#95	C₂²×C₅	1	4	yes	—
354	C₄³	C₂²×C₅	1	1	yes	characteristic
355	C₂³×C₅	—	2	2	no	—
356	C₂³×C₅	—	2	2	no	—
357	C₂³×C₅	—	2	2	no	—
358	C₂³×C₅	—	2	2	no	—
359	C₂³×C₅	—	2	2	no	—
360	C₂³×C₅	—	2	2	no	—
361	C₂³×C₅	—	2	2	no	—
362	C₂³×C₅	—	2	2	no	—
363	C₂³×C₅	—	2	2	no	—
364	C₂³×C₅	—	2	2	no	—
365	C₂³×C₅	C₂³×C₄	1	4	yes	—
366	C₂³×C₅	C₂³×C₄	1	4	yes	—
367	C₂³×C₅	C₂²×D₄	1	4	yes	—
368	C₂³×C₅	C₂×#41	1	4	yes	—
369	C₂³×C₅	C₂⁵	1	1	yes	characteristic
370	C₅×Q₈	—	2	16	no	—
371	C₅×D₄	—	2	32	no	—
372	C₅×D₄	—	2	8	no	—
373	C₅×D₄	C₄×D₄	1	16	yes	complemented
374	C₂×C₄×C₅	—	2	32	no	—
375	C₂×C₄×C₅	—	2	2	no	—
376	C₂×C₄×C₅	—	2	2	no	—
377	C₂×C₄×C₅	—	2	4	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	2	2	no	—
380	C₂×C₄×C₅	—	2	1	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	2	no	—
383	C₂×C₄×C₅	—	2	2	no	—
384	C₂×C₄×C₅	—	2	4	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	2	no	—
387	C₂×C₄×C₅	—	2	1	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	1	no	—
390	C₂×C₄×C₅	—	2	2	no	—
391	C₂×C₄×C₅	—	2	16	no	—
392	C₂×C₄×C₅	—	2	16	no	—
393	C₂×C₄×C₅	—	2	16	no	—
394	C₂×C₄×C₅	—	2	2	no	—
395	C₂×C₄×C₅	—	2	4	no	—
396	C₂×C₄×C₅	—	2	2	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	1	no	—
399	C₂×C₄×C₅	—	2	2	no	—
400	C₂×C₄×C₅	—	2	2	no	—
401	C₂×C₄×C₅	—	2	4	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	2	2	no	—
404	C₂×C₄×C₅	—	2	2	no	—
405	C₂×C₄×C₅	—	2	4	no	—
406	C₂×C₄×C₅	—	4	8	no	—
407	C₂×C₄×C₅	—	4	16	no	—
408	C₂×C₄×C₅	—	4	8	no	—
409	C₂×C₄×C₅	—	4	8	no	—
410	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
411	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
412	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
413	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
414	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
415	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
416	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
417	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₅	C₂×#41	1	2	yes	—
421	C₂×C₄×C₅	C₂×#41	1	4	yes	—
422	C₂×C₄×C₅	C₂×#41	1	2	yes	—
423	C₂×C₄×C₅	C₂×#41	1	2	yes	—
424	C₂×C₄×C₅	C₂×#41	1	2	yes	—
425	C₂×C₄×C₅	C₂×#41	1	2	yes	—
426	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
427	C₂×#41	—	2	8	no	—
428	C₂×#41	—	2	8	no	—
429	C₂×#41	C₂×C₄×C₅	1	16	yes	complemented
430	C₂²×Q₈	C₂³×C₅	1	2	yes	—
431	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₅	1	4	yes	—
433	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₅	1	2	yes	—
435	C₂³×C₄	C₂³×C₅	1	4	yes	—
436	C₂³×C₄	C₂³×C₅	1	2	yes	—
437	C₂³×C₄	C₂³×C₅	1	2	yes	—
438	C₂³×C₄	C₂³×C₅	1	2	yes	—
439	C₂³×C₄	C₂³×C₅	1	4	yes	—
440	C₂³×C₄	C₂³×C₅	1	2	yes	—
441	C₂³×C₄	C₂³×C₅	1	2	yes	—
442	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
443	#123	C₂×C₄×C₅	1	32	yes	complemented
444	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
445	#121	C₂×C₄×C₅	1	16	yes	complemented
446	C₄×Q₈	—	2	8	no	—
447	C₄×Q₈	—	2	8	no	—
448	C₄×D₄	—	2	8	no	—
449	C₄×D₄	—	2	4	no	—
450	C₄×D₄	—	2	16	no	—
451	C₄×D₄	—	2	4	no	—
452	C₄×D₄	—	2	16	no	—
453	C₄×D₄	—	2	4	no	—
454	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
455	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
456	C₄×D₄	C₅×D₄	1	8	yes	complemented
457	#117	—	2	8	no	—
458	#117	—	2	16	no	—
459	C₂×C₄⋊C₄	—	2	8	no	—
460	C₂×C₄⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
461	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
486	C₂×C₄²	—	2	16	no	—
487	C₂×C₄²	—	2	8	no	—
488	C₂×C₄²	—	2	8	no	—
489	C₂×C₄²	C₂³×C₅	1	2	yes	—
490	C₂×C₄²	C₂³×C₅	1	4	yes	—
491	C₂×C₄²	C₂³×C₅	1	4	yes	—
492	C₂×C₄²	C₂³×C₅	1	2	yes	—
493	C₂×C₄²	C₂³×C₅	1	4	yes	—
494	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₅	1	2	yes	—
498	C₂×C₄²	C₂³×C₅	1	2	yes	—
499	C₂×C₄²	C₂³×C₅	1	2	yes	—
500	C₂×C₄²	C₂³×C₅	1	2	yes	—
501	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
502	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
505	#95	C₂³×C₅	1	2	yes	—
506	#95	C₂³×C₅	1	4	yes	—
507	#95	C₂³×C₅	1	4	yes	—
508	#95	C₂³×C₅	1	4	yes	—
509	#95	C₂³×C₅	1	2	yes	—
510	#95	C₂³×C₅	1	2	yes	—
511	#95	C₂³×C₅	1	2	yes	—
512	#95	C₂³×C₅	1	2	yes	—
513	#95	C₂³×C₅	1	2	yes	—
514	#95	C₂³×C₅	1	4	yes	—
515	#95	C₂³×C₅	1	4	yes	—
516	#95	C₂³×C₅	1	4	yes	—
517	C₂²×C₅	—	2	4	no	—
518	C₂²×C₅	—	2	4	no	—
519	C₂²×C₅	—	2	4	no	—
520	C₂²×C₅	—	2	4	no	—
521	C₂²×C₅	—	2	4	no	—
522	C₂²×C₅	—	2	4	no	—
523	C₂²×C₅	—	2	4	no	—
524	C₂²×C₅	—	2	4	no	—
525	C₂²×C₅	—	2	4	no	—
526	C₂²×C₅	—	4	2	no	—
527	C₂²×C₅	—	4	2	no	—
528	C₂²×C₅	—	4	2	no	—
529	C₂²×C₅	—	4	2	no	—
530	C₂²×C₅	C₂×C₄×D₄	1	8	yes	—
531	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
532	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
533	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
534	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
535	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
536	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
537	C₂²×C₅	#585	1	1	yes	characteristic
538	C₄×C₅	—	2	4	no	—
539	C₄×C₅	—	2	8	no	—
540	C₄×C₅	—	2	4	no	—
541	C₄×C₅	—	2	2	no	—
542	C₄×C₅	—	2	4	no	—
543	C₄×C₅	—	2	4	no	—
544	C₄×C₅	—	2	2	no	—
545	C₄×C₅	—	2	2	no	—
546	C₄×C₅	—	4	2	no	—
547	C₄×C₅	—	4	4	no	—
548	C₄×C₅	—	4	2	no	—
549	C₄×C₅	—	4	1	no	—
550	C₄×C₅	C₂×C₄×D₄	1	4	yes	—
551	C₄×C₅	C₄×#41	1	4	yes	complemented
552	C₄×C₅	#547	1	4	yes	direct product factor
553	C₂⁴	C₂⁴×C₅	1	2	yes	—
554	C₂⁴	C₂⁴×C₅	1	2	yes	—
555	#41	—	2	64	no	—
556	C₂×Q₈	—	2	4	no	—
557	C₂×Q₈	—	2	4	no	—
558	C₂×Q₈	C₂²×C₄×C₅	1	8	yes	—
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	2	8	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
564	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
565	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
566	C₂×D₄	C₂×C₅×D₄	1	4	yes	—
567	C₂×D₄	C₅×#41	1	4	yes	—
568	C₂²×C₄	—	2	8	no	—
569	C₂²×C₄	—	2	8	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	8	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
589	C₂²×C₄	C₂²×C₄×C₅	1	16	yes	—
590	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
591	C₂²×C₄	C₂×C₅×D₄	1	8	yes	—
592	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
596	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
607	C₄⋊C₄	—	2	8	no	—
608	C₄⋊C₄	—	2	8	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	8	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
616	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
617	C₄⋊C₄	C₂²×C₄×C₅	1	16	yes	—
618	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
619	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
620	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
621	C₄⋊C₄	C₅×#41	1	4	yes	complemented
622	C₂²⋊C₄	—	2	8	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	8	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	4	4	no	—
628	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
629	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
630	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
631	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	8	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	8	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	8	no	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	2	no	—
644	C₄²	—	4	1	no	—
645	C₄²	C₂²×C₄×C₅	1	4	yes	—
646	C₄²	C₂×C₅×D₄	1	4	yes	—
647	C₄²	C₅×#41	1	4	yes	complemented
648	C₂×C₅	—	2	8	no	—
649	C₂×C₅	—	4	4	no	—
650	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
651	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
652	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
653	C₂×C₅	C₂×#547	1	1	yes	characteristic
654	C₂×C₅	D₄×#41	1	1	yes	characteristic
655	C₂×C₅	#3475	1	1	yes	characteristic
656	C₂×C₅	#3482	1	1	yes	characteristic
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	C₂³×C₄×C₅	1	4	yes	—
668	C₂³	C₂³×C₄×C₅	1	4	yes	—
669	C₂³	C₂²×C₅×D₄	1	4	yes	—
670	C₂³	C₂×C₅×#41	1	4	yes	—
671	C₂³	C₂⁵×C₅	1	1	yes	characteristic
672	Q₈	—	2	16	no	—
673	D₄	—	2	32	no	—
674	D₄	—	2	8	no	—
675	D₄	C₄×C₅×D₄	1	16	yes	complemented
676	C₂×C₄	—	2	32	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	16	no	—
694	C₂×C₄	—	2	16	no	—
695	C₂×C₄	—	2	16	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	16	no	—
710	C₂×C₄	—	4	8	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
713	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
714	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
715	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
716	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
717	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
718	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
719	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
720	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
721	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
722	C₂×C₄	C₂×C₅×#41	1	2	yes	—
723	C₂×C₄	C₂×C₅×#41	1	4	yes	—
724	C₂×C₄	C₂×C₅×#41	1	2	yes	—
725	C₂×C₄	C₂×C₅×#41	1	2	yes	—
726	C₂×C₄	C₂×C₅×#41	1	2	yes	—
727	C₂×C₄	C₂×C₅×#41	1	2	yes	—
728	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
729	C₅	C₄×#547	1	1	yes	characteristic, direct product factor, Sylow
730	C₂²	—	2	4	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	C₂×C₄×C₅×D₄	1	8	yes	—
744	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
745	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
746	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
747	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
748	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
749	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
750	C₂²	C₅×#585	1	1	yes	characteristic
751	C₄	—	2	4	no	—
752	C₄	—	2	8	no	—
753	C₄	—	2	4	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	4	no	—
756	C₄	—	2	4	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	1	no	—
763	C₄	C₂×C₄×C₅×D₄	1	4	yes	—
764	C₄	C₄×C₅×#41	1	4	yes	complemented
765	C₄	C₅×#547	1	4	yes	direct product factor
766	C₂	—	2	8	no	—
767	C₂	—	4	4	no	—
768	C₂	C₂²×C₄×C₅×D₄	1	1	yes	characteristic
769	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
770	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
771	C₂	C₂×C₅×#547	1	1	yes	characteristic
772	C₂	C₅×D₄×#41	1	1	yes	characteristic
773	C₂	C₅×#3475	1	1	yes	characteristic
774	C₂	C₅×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₂×C₅×#547	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×#41	C₂	semidirect
3. C₅×#2365	C₂	semidirect
4. C₅×#2362	C₂	semidirect
5. C₅×#2361	C₂	semidirect
6. C₅×#2359	C₂	semidirect
7. C₅×#2354	C₂	semidirect
8. C₅×D₄×C₄⋊C₄	C₂	semidirect
9. C₅×#2344	C₂	semidirect
10. C₅×#2339	C₂	semidirect
11. C₄×C₅×C₄⋊Q₈	C₂	semidirect
12. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
13. C₄×C₅×#123	C₂	semidirect
14. C₄×C₅×#121	C₂	semidirect
15. C₄²×C₅×D₄	C₂	semidirect
16. C₄²×C₅×D₄	C₂	semidirect
17. C₂×C₄×C₅×C₄⋊C₄	C₂	semidirect
19. C₅×#547	C₄	direct (N × H)
85. C₄×#547	C₅	direct (N × H)
88. C₂×C₅×#41	C₂×C₄	semidirect
101. C₅×C₄⋊Q₈	C₂×C₄	semidirect
102. C₅×#123	C₂×C₄	semidirect
103. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
104. C₅×#121	C₂×C₄	semidirect
113. C₄×C₅×D₄	C₂×C₄	semidirect
114. C₄×C₅×D₄	C₂×C₄	semidirect
115. C₄×C₅×D₄	D₄	semidirect
119. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
177. C₂×C₄×#41	C₂×C₅	semidirect
178. #2365	C₂×C₅	semidirect
179. #2362	C₂×C₅	semidirect
180. #2361	C₂×C₅	semidirect
181. #2359	C₂×C₅	semidirect
182. #2354	C₂×C₅	semidirect
183. D₄×C₄⋊C₄	C₂×C₅	semidirect
184. #2344	C₂×C₅	semidirect
185. #2339	C₂×C₅	semidirect
186. C₄×C₄⋊Q₈	C₂×C₅	semidirect
187. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
188. C₄×#123	C₂×C₅	semidirect
189. C₄×#121	C₂×C₅	semidirect
190. C₄²×D₄	C₂×C₅	semidirect
191. C₄²×D₄	C₂×C₅	semidirect
192. C₂×C₄×C₄⋊C₄	C₂×C₅	semidirect
261. C₅×C₄⋊C₄	#41	semidirect
287. C₄²×C₅	#41	semidirect
289. #547	C₄×C₅	direct (N × H)
373. C₅×D₄	C₄×D₄	semidirect
429. C₂×#41	C₂×C₄×C₅	semidirect
442. C₄⋊Q₈	C₂×C₄×C₅	semidirect
443. #123	C₂×C₄×C₅	semidirect
444. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
445. #121	C₂×C₄×C₅	semidirect
454. C₄×D₄	C₂×C₄×C₅	semidirect
455. C₄×D₄	C₂×C₄×C₅	semidirect
456. C₄×D₄	C₅×D₄	semidirect
460. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
551. C₄×C₅	C₄×#41	semidirect
552. C₄×C₅	#547	direct (N × H)
621. C₄⋊C₄	C₅×#41	semidirect
647. C₄²	C₅×#41	semidirect
675. D₄	C₄×C₅×D₄	semidirect
729. C₅	C₄×#547	direct (N × H)
764. C₄	C₄×C₅×#41	semidirect
765. C₄	C₅×#547	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×C₅×#547	2
C₂×C₄×C₅×#41	2
C₅×#2365	2
C₅×#2362	2
C₅×#2361	2
C₅×#2359	2
C₅×#2354	2
C₅×D₄×C₄⋊C₄	2
C₅×#2344	2
C₅×#2339	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×C₂²⋊Q₈	2
C₄×C₅×#123	2
C₄×C₅×#121	2
C₄²×C₅×D₄	2
C₂×C₄×C₅×C₄⋊C₄	2
C₄×#547	5

Subgroups — C4×C5×#547 #11956879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#547 #11956879