Subgroups — C₅×#60339 #11983059

Order 1280.

1710 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3461	C₂	1	1	yes	maximal, characteristic
2	C₅×#2994	C₂	1	2	yes	maximal, complemented
3	C₅×#2994	C₂	1	4	yes	maximal, complemented
4	C₅×#2993	C₂	1	2	yes	maximal, complemented
5	C₅×#2989	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2986	C₂	1	2	yes	maximal, complemented
8	C₅×#2985	C₂	1	2	yes	maximal, complemented
9	C₅×#2982	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2969	C₂	1	2	yes	maximal, complemented
11	C₅×#2968	C₂	1	4	yes	maximal, complemented
12	C₅×#2966	C₂	1	2	yes	maximal, complemented
13	C₅×#2965	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×C₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2962	C₂	1	2	yes	maximal, complemented
16	C₅×#2960	C₂	1	2	yes	maximal, complemented
17	C₂×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#544	C₄	1	1	yes	characteristic
19	C₅×#542	C₄	1	2	yes	—
20	C₅×#542	C₄	1	2	yes	—
21	C₅×#541	C₄	1	2	yes	—
22	C₅×#541	C₄	1	2	yes	—
23	C₅×#539	C₄	1	4	yes	—
24	C₅×#537	C₄	1	1	yes	characteristic
25	C₅×#536	C₄	1	1	yes	characteristic
26	C₅×#536	C₄	1	1	yes	characteristic
27	C₅×#533	C₂²	1	2	yes	—
28	C₅×#533	C₂²	1	2	yes	—
29	C₅×#529	C₂²	1	2	yes	—
30	C₅×#529	C₂²	1	4	yes	—
31	C₅×#529	C₂²	1	2	yes	—
32	C₄×C₅×#41	C₂²	1	1	yes	characteristic
33	C₄×C₅×#41	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
35	C₅×#446	C₂²	1	1	yes	characteristic
36	C₅×#446	C₂²	1	4	yes	—
37	C₅×#446	C₂²	1	2	yes	—
38	C₅×#446	C₂²	1	4	yes	—
39	C₅×#446	C₂²	1	2	yes	—
40	C₅×#446	C₂²	1	2	yes	—
41	C₅×#446	C₂²	1	2	yes	—
42	C₅×#446	C₂²	1	2	yes	—
43	C₅×#446	C₂²	1	1	yes	characteristic
44	C₅×#446	C₂²	1	4	yes	—
45	C₅×C₈×Q₈	C₂²	1	2	yes	—
46	C₅×C₈×Q₈	C₂²	1	2	yes	—
47	C₅×C₈×Q₈	C₂²	1	2	yes	—
48	C₅×C₈×Q₈	C₂²	1	2	yes	—
49	C₅×C₈×Q₈	C₂²	1	2	yes	—
50	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
51	C₅×C₈×Q₈	C₂²	1	4	yes	—
52	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
53	C₅×#436	C₂²	1	2	yes	—
54	C₅×#436	C₂²	1	1	yes	characteristic
55	C₅×#436	C₂²	1	4	yes	—
56	C₅×#436	C₂²	1	1	yes	characteristic
57	C₅×#435	C₂²	1	4	yes	—
58	C₅×#435	C₂²	1	4	yes	—
59	C₅×#435	C₂²	1	2	yes	—
60	C₅×#435	C₂²	1	2	yes	—
61	C₅×#435	C₂²	1	4	yes	—
62	C₅×C₈×D₄	C₂²	1	2	yes	—
63	C₅×C₈×D₄	C₂²	1	4	yes	—
64	C₅×C₈×D₄	C₂²	1	2	yes	—
65	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
66	C₅×C₈×D₄	C₂²	1	4	yes	—
67	C₅×C₈×D₄	C₂²	1	2	yes	—
68	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
69	C₅×#433	C₂²	1	4	yes	—
70	C₅×#433	C₂²	1	4	yes	—
71	C₅×#433	C₂²	1	4	yes	—
72	C₅×#433	C₂²	1	4	yes	—
73	C₅×#432	C₂²	1	2	yes	—
74	C₅×#431	C₂²	1	1	yes	characteristic
75	C₅×#431	C₂²	1	1	yes	characteristic
76	C₅×#431	C₂²	1	4	yes	—
77	C₅×#431	C₂²	1	2	yes	—
78	C₅×#431	C₂²	1	2	yes	—
79	C₅×#431	C₂²	1	2	yes	—
80	C₅×#424	C₂²	1	4	yes	—
81	C₅×#424	C₂²	1	4	yes	—
82	C₅×#423	C₂²	1	2	yes	—
83	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
85	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
86	C₅×#405	C₂²	1	4	yes	—
87	C₅×#405	C₂²	1	4	yes	—
88	C₄×C₅×M₁₆	C₂²	1	2	yes	—
89	C₂×C₅×#97	C₂²	1	2	yes	—
90	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
91	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
92	#60339	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
94	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
96	C₂×C₅×M₁₆	C₂³	1	2	yes	—
97	C₂×C₅×M₁₆	C₂³	1	2	yes	—
98	C₂×C₅×M₁₆	C₂³	1	4	yes	—
99	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₂²×C₅×C₈	C₂³	1	2	yes	—
101	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₂²×C₅×C₈	C₂³	1	2	yes	—
103	C₂²×C₅×C₈	C₂³	1	2	yes	—
104	C₂²×C₅×C₈	C₂³	1	4	yes	—
105	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
106	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
107	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
108	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
109	C₅×#126	C₂×C₄	1	4	yes	—
110	C₅×#126	C₂×C₄	1	4	yes	—
111	C₅×#126	C₂×C₄	1	4	yes	—
112	C₅×#126	C₂×C₄	1	4	yes	—
113	C₅×#125	C₂×C₄	1	4	yes	—
114	C₅×#125	C₂×C₄	1	2	yes	—
115	C₅×#125	C₂×C₄	1	2	yes	—
116	C₅×#125	C₂×C₄	1	4	yes	—
117	C₅×#125	C₂×C₄	1	4	yes	—
118	C₅×#124	C₂×C₄	1	2	yes	—
119	C₅×#124	C₂×C₄	1	2	yes	—
120	C₅×#124	C₂×C₄	1	4	yes	—
121	C₅×#123	C₂×C₄	1	4	yes	—
122	C₅×#123	C₂×C₄	1	4	yes	—
123	C₅×#123	C₂×C₄	1	4	yes	—
124	C₅×#123	C₂×C₄	1	4	yes	—
125	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
126	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
127	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
128	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
129	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
130	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
131	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
132	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
133	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
134	C₅×#121	C₂×C₄	1	4	yes	—
135	C₅×#121	C₂×C₄	1	2	yes	—
136	C₅×#121	C₂×C₄	1	2	yes	—
137	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
138	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
139	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
140	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
141	C₄×C₅×Q₈	C₂³	1	2	yes	—
142	C₄×C₅×Q₈	C₂³	1	2	yes	—
143	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
145	C₄×C₅×Q₈	C₂³	1	4	yes	—
146	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
147	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
148	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
149	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
150	C₄×C₅×D₄	C₂³	1	2	yes	—
151	C₄×C₅×D₄	C₂³	1	2	yes	—
152	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
153	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
154	C₄×C₅×D₄	C₂³	1	4	yes	—
155	C₅×#117	C₂×C₄	1	1	yes	characteristic
156	C₅×#117	C₂×C₄	1	1	yes	characteristic
157	C₅×#117	C₂×C₄	1	2	yes	—
158	C₅×#117	C₂×C₄	1	2	yes	—
159	C₅×#117	C₂³	1	4	yes	—
160	C₅×#117	C₂³	1	4	yes	—
161	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
162	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
163	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₅	C₂³	1	2	yes	—
165	C₂×C₄²×C₅	C₂³	1	2	yes	—
166	C₂×C₄²×C₅	C₂³	1	2	yes	—
167	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
168	C₅×C₄⋊C₈	C₂³	1	2	yes	—
169	C₅×C₄⋊C₈	C₂³	1	2	yes	—
170	C₅×C₄⋊C₈	C₂³	1	4	yes	—
171	C₅×C₄⋊C₈	C₂³	1	4	yes	—
172	C₅×C₄⋊C₈	C₂³	1	4	yes	—
173	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
174	C₅×C₄⋊C₈	C₂³	1	4	yes	—
175	C₅×C₄⋊C₈	C₂³	1	2	yes	—
176	C₅×C₄⋊C₈	C₂³	1	4	yes	—
177	C₅×C₄⋊C₈	C₂³	1	2	yes	—
178	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
179	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
180	C₅×C₄⋊C₈	C₂³	1	2	yes	—
181	C₅×C₄⋊C₈	C₂³	1	4	yes	—
182	C₅×C₄⋊C₈	C₂³	1	2	yes	—
183	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
184	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
185	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
186	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
187	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
191	C₅×#97	C₂³	1	4	yes	—
192	C₅×#97	C₂³	1	4	yes	—
193	C₅×#97	C₂³	1	2	yes	—
194	C₅×#97	C₂³	1	2	yes	—
195	C₅×#97	C₂³	1	4	yes	—
196	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
197	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
198	C₄×C₅×C₈	C₂³	1	2	yes	—
199	C₄×C₅×C₈	C₂³	1	2	yes	—
200	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
201	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
202	C₄×C₅×C₈	C₂³	1	2	yes	—
203	C₄×C₅×C₈	C₂³	1	2	yes	—
204	C₄×C₅×C₈	C₂³	1	4	yes	—
205	C₄×C₅×C₈	C₂³	1	4	yes	—
206	C₄×C₅×C₈	C₂³	1	4	yes	—
207	#3461	C₂×C₅	1	1	yes	characteristic
208	#2994	C₂×C₅	1	4	yes	complemented
209	#2994	C₂×C₅	1	2	yes	complemented
210	#2993	C₂×C₅	1	2	yes	complemented
211	#2989	C₂×C₅	1	1	yes	characteristic, complemented
212	#2988	C₂×C₅	1	1	yes	characteristic, complemented
213	#2986	C₂×C₅	1	2	yes	complemented
214	#2985	C₂×C₅	1	2	yes	complemented
215	#2982	C₂×C₅	1	1	yes	characteristic, complemented
216	#2969	C₂×C₅	1	2	yes	complemented
217	#2968	C₂×C₅	1	4	yes	complemented
218	#2966	C₂×C₅	1	2	yes	complemented
219	#2965	C₂×C₅	1	1	yes	characteristic, complemented
220	C₈×#41	C₂×C₅	1	1	yes	characteristic, complemented
221	#2962	C₂×C₅	1	2	yes	complemented
222	#2960	C₂×C₅	1	2	yes	complemented
223	C₂×#446	C₂×C₅	1	1	yes	characteristic, complemented
224	C₅×#41	—	2	4	no	—
225	C₅×#41	—	2	4	no	—
226	C₂×C₅×Q₈	—	2	4	no	—
227	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
228	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
229	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
230	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
231	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
232	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
233	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
234	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
235	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
236	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
237	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
238	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
239	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
240	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
241	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
242	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
243	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
244	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
245	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
248	C₅×M₁₆	—	2	4	no	—
249	C₅×M₁₆	—	4	4	no	—
250	C₅×M₁₆	—	4	2	no	—
251	C₂×C₅×C₈	—	2	2	no	—
252	C₂×C₅×C₈	—	2	4	no	—
253	C₂×C₅×C₈	—	4	2	no	—
254	C₂×C₅×C₈	—	4	4	no	—
255	C₂×C₅×C₈	—	4	1	no	—
256	C₂×C₅×C₈	—	4	2	no	—
257	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
258	C₂×C₅×C₈	C₂⁴	1	2	yes	—
259	C₂×C₅×C₈	C₂⁴	1	4	yes	—
260	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
261	C₂×C₅×C₈	C₂⁴	1	2	yes	—
262	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
263	C₂×C₅×C₈	C₂⁴	1	2	yes	—
264	C₂×C₅×C₈	C₂⁴	1	2	yes	—
265	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
266	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
267	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
268	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
269	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
270	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
271	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
272	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
273	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
274	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
275	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
276	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
277	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
278	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
279	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
280	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
281	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
282	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
283	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
284	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
285	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
286	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
287	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
288	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
289	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
290	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
291	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
292	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
293	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
294	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
295	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
296	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
297	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
298	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
299	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
300	C₄²×C₅	C₂²×C₄	1	2	yes	—
301	C₄²×C₅	C₂²×C₄	1	2	yes	—
302	C₄²×C₅	C₂²×C₄	1	2	yes	—
303	C₄²×C₅	C₂²×C₄	1	2	yes	—
304	C₄²×C₅	C₂²×C₄	1	4	yes	—
305	C₄²×C₅	C₂⁴	1	1	yes	characteristic
306	C₄²×C₅	C₂⁴	1	1	yes	characteristic
307	C₄²×C₅	C₂⁴	1	2	yes	—
308	C₄²×C₅	C₂⁴	1	4	yes	—
309	C₄²×C₅	C₂⁴	1	2	yes	—
310	#544	C₄×C₅	1	1	yes	characteristic
311	#542	C₄×C₅	1	2	yes	—
312	#542	C₄×C₅	1	2	yes	—
313	#541	C₄×C₅	1	2	yes	—
314	#541	C₄×C₅	1	2	yes	—
315	#539	C₄×C₅	1	4	yes	—
316	#537	C₄×C₅	1	1	yes	characteristic
317	#536	C₄×C₅	1	1	yes	characteristic
318	#536	C₄×C₅	1	1	yes	characteristic
319	#533	C₂²×C₅	1	2	yes	—
320	#533	C₂²×C₅	1	2	yes	—
321	#529	C₂²×C₅	1	2	yes	—
322	#529	C₂²×C₅	1	4	yes	—
323	#529	C₂²×C₅	1	2	yes	—
324	C₄×#41	C₂²×C₅	1	1	yes	characteristic
325	C₄×#41	C₂²×C₅	1	1	yes	characteristic
326	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
327	#446	C₂²×C₅	1	2	yes	—
328	#446	C₂²×C₅	1	2	yes	—
329	#446	C₂²×C₅	1	2	yes	—
330	#446	C₂²×C₅	1	2	yes	—
331	#446	C₂²×C₅	1	1	yes	characteristic
332	#446	C₂²×C₅	1	4	yes	—
333	#446	C₂²×C₅	1	4	yes	—
334	#446	C₂²×C₅	1	2	yes	—
335	#446	C₂²×C₅	1	1	yes	characteristic
336	#446	C₂²×C₅	1	4	yes	—
337	C₈×Q₈	C₂²×C₅	1	2	yes	—
338	C₈×Q₈	C₂²×C₅	1	2	yes	—
339	C₈×Q₈	C₂²×C₅	1	4	yes	—
340	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
341	C₈×Q₈	C₂²×C₅	1	2	yes	—
342	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
343	C₈×Q₈	C₂²×C₅	1	2	yes	—
344	C₈×Q₈	C₂²×C₅	1	2	yes	—
345	#436	C₂²×C₅	1	1	yes	characteristic
346	#436	C₂²×C₅	1	1	yes	characteristic
347	#436	C₂²×C₅	1	2	yes	—
348	#436	C₂²×C₅	1	4	yes	—
349	#435	C₂²×C₅	1	2	yes	—
350	#435	C₂²×C₅	1	2	yes	—
351	#435	C₂²×C₅	1	4	yes	—
352	#435	C₂²×C₅	1	4	yes	—
353	#435	C₂²×C₅	1	4	yes	—
354	C₈×D₄	C₂²×C₅	1	2	yes	—
355	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
356	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
357	C₈×D₄	C₂²×C₅	1	2	yes	—
358	C₈×D₄	C₂²×C₅	1	2	yes	—
359	C₈×D₄	C₂²×C₅	1	4	yes	—
360	C₈×D₄	C₂²×C₅	1	4	yes	—
361	#433	C₂²×C₅	1	4	yes	—
362	#433	C₂²×C₅	1	4	yes	—
363	#433	C₂²×C₅	1	4	yes	—
364	#433	C₂²×C₅	1	4	yes	—
365	#432	C₂²×C₅	1	2	yes	—
366	#431	C₂²×C₅	1	1	yes	characteristic
367	#431	C₂²×C₅	1	2	yes	—
368	#431	C₂²×C₅	1	1	yes	characteristic
369	#431	C₂²×C₅	1	2	yes	—
370	#431	C₂²×C₅	1	4	yes	—
371	#431	C₂²×C₅	1	2	yes	—
372	#424	C₂²×C₅	1	4	yes	—
373	#424	C₂²×C₅	1	4	yes	—
374	#423	C₂²×C₅	1	2	yes	—
375	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
376	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
377	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
378	#405	C₂²×C₅	1	4	yes	—
379	#405	C₂²×C₅	1	4	yes	—
380	C₄×M₁₆	C₂²×C₅	1	2	yes	—
381	C₂×#97	C₂²×C₅	1	2	yes	—
382	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
383	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
384	C₂³×C₅	C₂³×C₄	1	2	yes	—
385	C₂³×C₅	C₂³×C₄	1	2	yes	—
386	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
387	C₅×Q₈	—	2	4	no	—
388	C₅×Q₈	—	2	4	no	—
389	C₅×Q₈	—	2	2	no	—
390	C₅×Q₈	—	2	2	no	—
391	C₅×Q₈	—	4	4	no	—
392	C₅×D₄	—	2	4	no	—
393	C₅×D₄	—	2	4	no	—
394	C₅×D₄	—	2	2	no	—
395	C₅×D₄	—	2	2	no	—
396	C₅×D₄	—	4	4	no	—
397	C₂×C₄×C₅	—	2	4	no	—
398	C₂×C₄×C₅	—	2	4	no	—
399	C₂×C₄×C₅	—	2	4	no	—
400	C₂×C₄×C₅	—	2	1	no	—
401	C₂×C₄×C₅	—	2	2	no	—
402	C₂×C₄×C₅	—	2	2	no	—
403	C₂×C₄×C₅	—	2	1	no	—
404	C₂×C₄×C₅	—	2	2	no	—
405	C₂×C₄×C₅	—	2	2	no	—
406	C₂×C₄×C₅	—	4	1	no	—
407	C₂×C₄×C₅	—	4	2	no	—
408	C₂×C₄×C₅	—	4	2	no	—
409	C₂×C₄×C₅	—	4	2	no	—
410	C₂×C₄×C₅	#131	1	4	yes	—
411	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
412	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
413	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
414	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
415	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
416	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
417	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
418	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
419	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
420	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
421	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
422	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
423	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
424	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
425	C₅×C₈	—	2	2	no	—
426	C₅×C₈	—	2	1	no	—
427	C₅×C₈	—	2	2	no	—
428	C₅×C₈	—	2	1	no	—
429	C₅×C₈	—	2	2	no	—
430	C₅×C₈	—	2	4	no	—
431	C₅×C₈	—	2	1	no	—
432	C₅×C₈	—	2	2	no	—
433	C₅×C₈	2₋¹⁺⁴	1	2	yes	—
434	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
435	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
436	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
437	C₂×M₁₆	C₂³×C₅	1	2	yes	—
438	C₂×M₁₆	C₂³×C₅	1	2	yes	—
439	C₂×M₁₆	C₂³×C₅	1	4	yes	—
440	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₅	1	2	yes	—
442	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₅	1	2	yes	—
444	C₂²×C₈	C₂³×C₅	1	2	yes	—
445	C₂²×C₈	C₂³×C₅	1	4	yes	—
446	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
447	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
448	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
449	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
450	#126	C₂×C₄×C₅	1	4	yes	—
451	#126	C₂×C₄×C₅	1	4	yes	—
452	#126	C₂×C₄×C₅	1	4	yes	—
453	#126	C₂×C₄×C₅	1	4	yes	—
454	#125	C₂×C₄×C₅	1	4	yes	—
455	#125	C₂×C₄×C₅	1	2	yes	—
456	#125	C₂×C₄×C₅	1	2	yes	—
457	#125	C₂×C₄×C₅	1	4	yes	—
458	#125	C₂×C₄×C₅	1	4	yes	—
459	#124	C₂×C₄×C₅	1	2	yes	—
460	#124	C₂×C₄×C₅	1	2	yes	—
461	#124	C₂×C₄×C₅	1	4	yes	—
462	#123	C₂×C₄×C₅	1	4	yes	—
463	#123	C₂×C₄×C₅	1	4	yes	—
464	#123	C₂×C₄×C₅	1	4	yes	—
465	#123	C₂×C₄×C₅	1	4	yes	—
466	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
467	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
468	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
469	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
470	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
471	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
472	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
473	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
474	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
475	#121	C₂×C₄×C₅	1	4	yes	—
476	#121	C₂×C₄×C₅	1	2	yes	—
477	#121	C₂×C₄×C₅	1	2	yes	—
478	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
479	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
480	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
481	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
482	C₄×Q₈	C₂³×C₅	1	2	yes	—
483	C₄×Q₈	C₂³×C₅	1	2	yes	—
484	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
485	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
486	C₄×Q₈	C₂³×C₅	1	4	yes	—
487	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
488	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
489	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
490	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
491	C₄×D₄	C₂³×C₅	1	2	yes	—
492	C₄×D₄	C₂³×C₅	1	2	yes	—
493	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
494	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
495	C₄×D₄	C₂³×C₅	1	4	yes	—
496	#117	C₂×C₄×C₅	1	1	yes	characteristic
497	#117	C₂×C₄×C₅	1	1	yes	characteristic
498	#117	C₂×C₄×C₅	1	2	yes	—
499	#117	C₂×C₄×C₅	1	2	yes	—
500	#117	C₂³×C₅	1	4	yes	—
501	#117	C₂³×C₅	1	4	yes	—
502	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
504	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₅	1	2	yes	—
506	C₂×C₄²	C₂³×C₅	1	2	yes	—
507	C₂×C₄²	C₂³×C₅	1	2	yes	—
508	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
509	C₄⋊C₈	C₂³×C₅	1	2	yes	—
510	C₄⋊C₈	C₂³×C₅	1	2	yes	—
511	C₄⋊C₈	C₂³×C₅	1	4	yes	—
512	C₄⋊C₈	C₂³×C₅	1	4	yes	—
513	C₄⋊C₈	C₂³×C₅	1	4	yes	—
514	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
515	C₄⋊C₈	C₂³×C₅	1	4	yes	—
516	C₄⋊C₈	C₂³×C₅	1	2	yes	—
517	C₄⋊C₈	C₂³×C₅	1	2	yes	—
518	C₄⋊C₈	C₂³×C₅	1	4	yes	—
519	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
520	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
521	C₄⋊C₈	C₂³×C₅	1	2	yes	—
522	C₄⋊C₈	C₂³×C₅	1	4	yes	—
523	C₄⋊C₈	C₂³×C₅	1	2	yes	—
524	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
525	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
526	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
527	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
528	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
529	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
530	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
531	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
532	#97	C₂³×C₅	1	4	yes	—
533	#97	C₂³×C₅	1	4	yes	—
534	#97	C₂³×C₅	1	2	yes	—
535	#97	C₂³×C₅	1	2	yes	—
536	#97	C₂³×C₅	1	4	yes	—
537	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
538	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
539	C₄×C₈	C₂³×C₅	1	2	yes	—
540	C₄×C₈	C₂³×C₅	1	2	yes	—
541	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
542	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
543	C₄×C₈	C₂³×C₅	1	2	yes	—
544	C₄×C₈	C₂³×C₅	1	2	yes	—
545	C₄×C₈	C₂³×C₅	1	4	yes	—
546	C₄×C₈	C₂³×C₅	1	4	yes	—
547	C₄×C₈	C₂³×C₅	1	4	yes	—
548	C₂²×C₅	—	2	1	no	—
549	C₂²×C₅	—	2	1	no	—
550	C₂²×C₅	—	2	2	no	—
551	C₂²×C₅	—	2	2	no	—
552	C₂²×C₅	—	2	2	no	—
553	C₂²×C₅	—	2	2	no	—
554	C₂²×C₅	—	2	2	no	—
555	C₂²×C₅	—	2	2	no	—
556	C₂²×C₅	C₂×#131	1	2	yes	—
557	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
558	C₄×C₅	—	2	1	no	—
559	C₄×C₅	—	2	2	no	—
560	C₄×C₅	—	2	2	no	—
561	C₄×C₅	—	2	2	no	—
562	C₄×C₅	—	2	2	no	—
563	C₄×C₅	—	2	4	no	—
564	C₄×C₅	—	2	1	no	—
565	C₄×C₅	—	2	1	no	—
566	C₄×C₅	—	2	4	no	—
567	C₄×C₅	—	2	2	no	—
568	C₄×C₅	—	2	2	no	—
569	C₄×C₅	C₂×#131	1	2	yes	—
570	C₄×C₅	C₂×#131	1	2	yes	—
571	C₄×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
572	C₄×C₅	#585	1	1	yes	characteristic
573	#41	—	2	4	no	—
574	#41	—	2	4	no	—
575	C₂×Q₈	—	2	4	no	—
576	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
577	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
578	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
579	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
580	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
581	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
582	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
583	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
584	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
585	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
586	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
587	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
588	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
589	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
590	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
591	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
592	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
593	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
597	M₁₆	—	2	4	no	—
598	M₁₆	—	4	4	no	—
599	M₁₆	—	4	2	no	—
600	C₂×C₈	—	2	2	no	—
601	C₂×C₈	—	2	4	no	—
602	C₂×C₈	—	4	2	no	—
603	C₂×C₈	—	4	4	no	—
604	C₂×C₈	—	4	1	no	—
605	C₂×C₈	—	4	2	no	—
606	C₂×C₈	C₂⁴×C₅	1	2	yes	—
607	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
608	C₂×C₈	C₂⁴×C₅	1	2	yes	—
609	C₂×C₈	C₂⁴×C₅	1	2	yes	—
610	C₂×C₈	C₂⁴×C₅	1	2	yes	—
611	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
612	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
613	C₂×C₈	C₂⁴×C₅	1	4	yes	—
614	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
615	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
616	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
617	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
618	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
619	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
620	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
621	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
622	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
623	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
624	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
625	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
626	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
627	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
628	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
629	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
630	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
631	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
632	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
633	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
634	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
635	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
636	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
637	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
638	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
639	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
640	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
641	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
642	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
643	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
644	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
645	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
646	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
647	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
648	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
649	C₄²	C₂²×C₄×C₅	1	2	yes	—
650	C₄²	C₂²×C₄×C₅	1	2	yes	—
651	C₄²	C₂²×C₄×C₅	1	2	yes	—
652	C₄²	C₂²×C₄×C₅	1	2	yes	—
653	C₄²	C₂²×C₄×C₅	1	4	yes	—
654	C₄²	C₂⁴×C₅	1	1	yes	characteristic
655	C₄²	C₂⁴×C₅	1	1	yes	characteristic
656	C₄²	C₂⁴×C₅	1	2	yes	—
657	C₄²	C₂⁴×C₅	1	2	yes	—
658	C₄²	C₂⁴×C₅	1	4	yes	—
659	C₂×C₅	—	2	2	no	—
660	C₂×C₅	—	4	2	no	—
661	C₂×C₅	—	4	2	no	—
662	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
663	C₂×C₅	C₂²×#131	1	1	yes	characteristic
664	C₂×C₅	#3573	1	1	yes	characteristic
665	C₂³	C₂³×C₄×C₅	1	2	yes	—
666	C₂³	C₂³×C₄×C₅	1	2	yes	—
667	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
668	Q₈	—	2	4	no	—
669	Q₈	—	2	4	no	—
670	Q₈	—	2	2	no	—
671	Q₈	—	2	2	no	—
672	Q₈	—	4	4	no	—
673	D₄	—	2	4	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	2	no	—
676	D₄	—	2	2	no	—
677	D₄	—	4	4	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	C₅×#131	1	4	yes	—
692	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
693	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
694	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
695	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
696	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
697	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
698	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
699	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
700	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
701	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
702	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
703	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
704	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
705	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
706	C₈	—	2	2	no	—
707	C₈	—	2	1	no	—
708	C₈	—	2	2	no	—
709	C₈	—	2	1	no	—
710	C₈	—	2	2	no	—
711	C₈	—	2	4	no	—
712	C₈	—	2	1	no	—
713	C₈	—	2	2	no	—
714	C₈	C₅×2₋¹⁺⁴	1	2	yes	—
715	C₅	#60339	1	1	yes	characteristic, direct product factor, Sylow
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	C₂×C₅×#131	1	2	yes	—
725	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
726	C₄	—	2	1	no	—
727	C₄	—	2	2	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	2	no	—
737	C₄	C₂×C₅×#131	1	2	yes	—
738	C₄	C₂×C₅×#131	1	2	yes	—
739	C₄	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
740	C₄	C₅×#585	1	1	yes	characteristic
741	C₂	—	2	2	no	—
742	C₂	—	4	2	no	—
743	C₂	—	4	2	no	—
744	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
745	C₂	C₂²×C₅×#131	1	1	yes	characteristic
746	C₂	C₅×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂²×C₅	C₂⁴×C₄
prime radical	C₅×#537	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2994	C₂	semidirect
3. C₅×#2994	C₂	semidirect
4. C₅×#2993	C₂	semidirect
5. C₅×#2989	C₂	semidirect
6. C₅×#2988	C₂	semidirect
7. C₅×#2986	C₂	semidirect
8. C₅×#2985	C₂	semidirect
9. C₅×#2982	C₂	semidirect
10. C₅×#2969	C₂	semidirect
11. C₅×#2968	C₂	semidirect
12. C₅×#2966	C₂	semidirect
13. C₅×#2965	C₂	semidirect
14. C₅×C₈×#41	C₂	semidirect
15. C₅×#2962	C₂	semidirect
16. C₅×#2960	C₂	semidirect
17. C₂×C₅×#446	C₂	semidirect
92. #60339	C₅	direct (N × H)
208. #2994	C₂×C₅	semidirect
209. #2994	C₂×C₅	semidirect
210. #2993	C₂×C₅	semidirect
211. #2989	C₂×C₅	semidirect
212. #2988	C₂×C₅	semidirect
213. #2986	C₂×C₅	semidirect
214. #2985	C₂×C₅	semidirect
215. #2982	C₂×C₅	semidirect
216. #2969	C₂×C₅	semidirect
217. #2968	C₂×C₅	semidirect
218. #2966	C₂×C₅	semidirect
219. #2965	C₂×C₅	semidirect
220. C₈×#41	C₂×C₅	semidirect
221. #2962	C₂×C₅	semidirect
222. #2960	C₂×C₅	semidirect
223. C₂×#446	C₂×C₅	semidirect
715. C₅	#60339	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3461	2
C₅×#2994	2
C₅×#2993	2
C₅×#2989	2
C₅×#2988	2
C₅×#2986	2
C₅×#2985	2
C₅×#2982	2
C₅×#2969	2
C₅×#2968	2
C₅×#2966	2
C₅×#2965	2
C₅×C₈×#41	2
C₅×#2962	2
C₅×#2960	2
C₂×C₅×#446	2
#60339	5

Subgroups — C5×#60339 #11983059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60339 #11983059