Subgroups — C₅×#60296 #11983016

Order 1280.

1684 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3455	C₂	1	1	yes	maximal, characteristic
2	C₅×#2995	C₂	1	2	yes	maximal, complemented
3	C₅×#2994	C₂	1	2	yes	maximal, complemented
4	C₅×#2993	C₂	1	2	yes	maximal, complemented
5	C₅×#2992	C₂	1	2	yes	maximal, complemented
6	C₅×#2985	C₂	1	2	yes	maximal, complemented
7	C₅×#2980	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2979	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2978	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2977	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2976	C₂	1	2	yes	maximal, complemented
12	C₅×#2969	C₂	1	2	yes	maximal, complemented
13	C₅×#2968	C₂	1	2	yes	maximal, complemented
14	C₅×#2967	C₂	1	2	yes	maximal, complemented
15	C₅×#2966	C₂	1	2	yes	maximal, complemented
16	C₅×#2925	C₂	1	2	yes	maximal, complemented
17	C₅×#2924	C₂	1	2	yes	maximal, complemented
18	C₅×#2923	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#542	C₄	1	2	yes	—
21	C₅×#542	C₄	1	2	yes	—
22	C₅×#541	C₄	1	2	yes	—
23	C₅×#540	C₄	1	2	yes	—
24	C₅×#539	C₄	1	2	yes	—
25	C₅×#539	C₄	1	2	yes	—
26	C₅×#538	C₄	1	2	yes	—
27	C₅×#538	C₄	1	2	yes	—
28	C₅×#533	C₂²	1	1	yes	characteristic
29	C₅×#532	C₂²	1	1	yes	characteristic
30	C₅×#529	C₂²	1	2	yes	—
31	C₅×#529	C₂²	1	2	yes	—
32	C₅×#529	C₂²	1	2	yes	—
33	C₅×#529	C₂²	1	2	yes	—
34	C₅×#525	C₂²	1	1	yes	characteristic
35	C₅×#525	C₂²	1	1	yes	characteristic
36	C₄×C₅×#41	C₂²	1	1	yes	characteristic
37	C₄×C₅×#41	C₂²	1	1	yes	characteristic
38	C₂×C₅×#117	C₂²	1	1	yes	characteristic
39	C₅×#446	C₂²	1	2	yes	complemented
40	C₅×#446	C₂²	1	2	yes	complemented
41	C₅×#446	C₂²	1	2	yes	complemented
42	C₅×#446	C₂²	1	2	yes	complemented
43	C₅×#446	C₂²	1	2	yes	complemented
44	C₅×#446	C₂²	1	2	yes	complemented
45	C₅×C₈×Q₈	C₂²	1	2	yes	complemented
46	C₅×C₈×Q₈	C₂²	1	2	yes	complemented
47	C₅×#436	C₂²	1	2	yes	—
48	C₅×#436	C₂²	1	2	yes	—
49	C₅×#436	C₂²	1	2	yes	—
50	C₅×#436	C₂²	1	2	yes	—
51	C₅×#436	C₂²	1	2	yes	complemented
52	C₅×#436	C₂²	1	2	yes	complemented
53	C₅×#435	C₂²	1	2	yes	—
54	C₅×#435	C₂²	1	2	yes	—
55	C₅×#435	C₂²	1	2	yes	—
56	C₅×#435	C₂²	1	2	yes	—
57	C₅×#435	C₂²	1	2	yes	—
58	C₅×#435	C₂²	1	2	yes	—
59	C₅×#435	C₂²	1	2	yes	—
60	C₅×#435	C₂²	1	2	yes	—
61	C₅×#435	C₂²	1	2	yes	complemented
62	C₅×#435	C₂²	1	2	yes	complemented
63	C₅×#435	C₂²	1	2	yes	complemented
64	C₅×#435	C₂²	1	2	yes	complemented
65	C₅×C₈×D₄	C₂²	1	2	yes	—
66	C₅×C₈×D₄	C₂²	1	2	yes	—
67	C₅×C₈×D₄	C₂²	1	2	yes	—
68	C₅×C₈×D₄	C₂²	1	2	yes	—
69	C₅×C₈×D₄	C₂²	1	2	yes	complemented
70	C₅×C₈×D₄	C₂²	1	2	yes	complemented
71	C₅×#433	C₂²	1	2	yes	—
72	C₅×#433	C₂²	1	2	yes	—
73	C₅×#433	C₂²	1	2	yes	—
74	C₅×#433	C₂²	1	2	yes	—
75	C₅×#433	C₂²	1	2	yes	—
76	C₅×#433	C₂²	1	2	yes	—
77	C₅×#433	C₂²	1	2	yes	—
78	C₅×#433	C₂²	1	2	yes	—
79	C₅×#433	C₂²	1	2	yes	complemented
80	C₅×#433	C₂²	1	2	yes	complemented
81	C₅×#433	C₂²	1	2	yes	complemented
82	C₅×#433	C₂²	1	2	yes	complemented
83	C₅×#432	C₂²	1	2	yes	—
84	C₅×#432	C₂²	1	2	yes	—
85	C₅×#432	C₂²	1	2	yes	complemented
86	C₅×#432	C₂²	1	2	yes	complemented
87	C₅×#431	C₂²	1	2	yes	—
88	C₅×#431	C₂²	1	2	yes	—
89	C₅×#431	C₂²	1	2	yes	complemented
90	C₅×#431	C₂²	1	2	yes	complemented
91	C₅×#424	C₂²	1	2	yes	—
92	C₅×#424	C₂²	1	2	yes	—
93	C₅×#424	C₂²	1	1	yes	characteristic, complemented
94	C₅×#424	C₂²	1	1	yes	characteristic, complemented
95	C₅×#424	C₂²	1	1	yes	characteristic, complemented
96	C₅×#424	C₂²	1	1	yes	characteristic, complemented
97	C₅×#423	C₂²	1	2	yes	complemented
98	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
99	C₅×#408	C₂²	1	1	yes	characteristic
100	C₅×#408	C₂²	1	1	yes	characteristic
101	C₅×#408	C₂²	1	1	yes	characteristic
102	C₅×#408	C₂²	1	1	yes	characteristic
103	C₅×#408	C₂²	1	2	yes	—
104	C₅×#408	C₂²	1	2	yes	—
105	C₅×#407	C₂²	1	2	yes	—
106	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
107	C₅×#405	C₂²	1	2	yes	—
108	C₅×#405	C₂²	1	2	yes	—
109	C₅×#405	C₂²	1	2	yes	complemented
110	C₅×#405	C₂²	1	2	yes	complemented
111	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
115	#60296	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂×C₅×#41	C₂³	1	1	yes	characteristic
117	C₂×C₅×#41	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
119	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
120	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₅×M₁₆	C₂³	1	2	yes	—
124	C₂×C₅×M₁₆	C₂³	1	2	yes	—
125	C₂×C₅×M₁₆	C₂³	1	2	yes	—
126	C₂×C₅×M₁₆	C₂³	1	2	yes	—
127	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
128	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
129	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
130	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
131	C₂²×C₅×C₈	C₂³	1	2	yes	—
132	C₂²×C₅×C₈	C₂³	1	2	yes	—
133	C₂²×C₅×C₈	C₂³	1	2	yes	—
134	C₂²×C₅×C₈	C₂³	1	2	yes	—
135	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
136	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
137	C₅×#127	C₂×C₄	1	1	yes	characteristic
138	C₅×#126	C₂×C₄	1	2	yes	—
139	C₅×#126	C₂×C₄	1	2	yes	—
140	C₅×#126	C₂×C₄	1	2	yes	—
141	C₅×#126	C₂×C₄	1	2	yes	—
142	C₅×#126	C₂×C₄	1	2	yes	—
143	C₅×#126	C₂×C₄	1	2	yes	—
144	C₅×#126	C₂×C₄	1	2	yes	—
145	C₅×#126	C₂×C₄	1	2	yes	—
146	C₅×#125	C₂×C₄	1	2	yes	—
147	C₅×#125	C₂×C₄	1	2	yes	—
148	C₅×#125	C₂×C₄	1	2	yes	—
149	C₅×#125	C₂×C₄	1	2	yes	—
150	C₅×#125	C₂×C₄	1	2	yes	—
151	C₅×#124	C₂×C₄	1	2	yes	—
152	C₅×#124	C₂×C₄	1	2	yes	—
153	C₅×#124	C₂×C₄	1	2	yes	—
154	C₅×#124	C₂×C₄	1	2	yes	—
155	C₅×#124	C₂×C₄	1	1	yes	characteristic
156	C₅×#124	C₂×C₄	1	1	yes	characteristic
157	C₅×#123	C₂×C₄	1	2	yes	—
158	C₅×#123	C₂×C₄	1	1	yes	characteristic
159	C₅×#123	C₂×C₄	1	1	yes	characteristic
160	C₅×#123	C₂×C₄	1	2	yes	—
161	C₅×#123	C₂×C₄	1	2	yes	—
162	C₅×#123	C₂×C₄	1	2	yes	—
163	C₅×#123	C₂×C₄	1	2	yes	—
164	C₅×#123	C₂×C₄	1	2	yes	—
165	C₅×#123	C₂×C₄	1	2	yes	—
166	C₅×#123	C₂×C₄	1	2	yes	—
167	C₅×#123	C₂×C₄	1	2	yes	—
168	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
169	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
170	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
171	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
172	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
173	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
174	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
175	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
176	C₅×#121	C₂×C₄	1	2	yes	—
177	C₅×#121	C₂×C₄	1	2	yes	—
178	C₅×#121	C₂×C₄	1	2	yes	—
179	C₅×#121	C₂×C₄	1	2	yes	—
180	C₅×#121	C₂×C₄	1	2	yes	—
181	C₅×#121	C₂×C₄	1	2	yes	—
182	C₅×#121	C₂×C₄	1	2	yes	—
183	C₅×#121	C₂×C₄	1	2	yes	—
184	C₅×#120	C₂×C₄	1	2	yes	—
185	C₅×#120	C₂×C₄	1	1	yes	characteristic
186	C₅×#120	C₂×C₄	1	1	yes	characteristic
187	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
188	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
189	C₄×C₅×Q₈	C₂³	1	2	yes	—
190	C₄×C₅×Q₈	C₂³	1	2	yes	—
191	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
192	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
193	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
194	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
195	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
196	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
197	C₄×C₅×D₄	C₂³	1	2	yes	—
198	C₄×C₅×D₄	C₂³	1	2	yes	—
199	C₄×C₅×D₄	C₂³	1	2	yes	—
200	C₄×C₅×D₄	C₂³	1	2	yes	—
201	C₄×C₅×D₄	C₂³	1	2	yes	—
202	C₄×C₅×D₄	C₂³	1	2	yes	—
203	C₅×#117	C₂×C₄	1	2	yes	—
204	C₅×#117	C₂×C₄	1	2	yes	—
205	C₅×#117	C₂³	1	2	yes	—
206	C₅×#117	C₂³	1	2	yes	—
207	C₅×#117	C₂³	1	2	yes	—
208	C₅×#117	C₂³	1	1	yes	characteristic
209	C₅×#117	C₂³	1	1	yes	characteristic
210	C₅×#117	C₂³	1	1	yes	characteristic
211	C₅×#117	C₂³	1	1	yes	characteristic
212	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
213	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
214	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₅	C₂³	1	2	yes	—
217	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
219	C₅×C₄⋊C₈	C₂³	1	2	yes	—
220	C₅×C₄⋊C₈	C₂³	1	2	yes	—
221	C₅×C₄⋊C₈	C₂³	1	2	yes	—
222	C₅×C₄⋊C₈	C₂³	1	2	yes	—
223	C₅×C₄⋊C₈	C₂³	1	2	yes	—
224	C₅×C₄⋊C₈	C₂³	1	2	yes	—
225	C₅×C₄⋊C₈	C₂³	1	2	yes	—
226	C₅×C₄⋊C₈	C₂³	1	2	yes	—
227	C₅×C₄⋊C₈	C₂³	1	2	yes	—
228	C₅×C₄⋊C₈	C₂³	1	2	yes	—
229	C₅×C₄⋊C₈	C₂³	1	2	yes	—
230	C₅×C₄⋊C₈	C₂³	1	2	yes	—
231	C₅×C₄⋊C₈	C₂³	1	2	yes	—
232	C₅×C₄⋊C₈	C₂³	1	2	yes	—
233	C₅×C₄⋊C₈	C₂³	1	2	yes	—
234	C₅×C₄⋊C₈	C₂³	1	2	yes	—
235	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
236	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
237	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
238	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
239	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
240	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
241	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
242	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
243	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
244	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
245	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
246	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
249	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
250	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
251	C₅×#97	C₂³	1	2	yes	—
252	C₅×#97	C₂³	1	2	yes	—
253	C₅×#97	C₂³	1	2	yes	—
254	C₅×#97	C₂³	1	2	yes	—
255	C₅×#97	C₂³	1	2	yes	—
256	C₅×#97	C₂³	1	2	yes	—
257	C₅×#97	C₂³	1	2	yes	—
258	C₅×#97	C₂³	1	2	yes	—
259	C₄×C₅×C₈	C₂³	1	2	yes	—
260	C₄×C₅×C₈	C₂³	1	2	yes	—
261	C₄×C₅×C₈	C₂³	1	2	yes	—
262	C₄×C₅×C₈	C₂³	1	2	yes	—
263	C₄×C₅×C₈	C₂³	1	2	yes	—
264	C₄×C₅×C₈	C₂³	1	2	yes	—
265	C₄×C₅×C₈	C₂³	1	2	yes	—
266	C₄×C₅×C₈	C₂³	1	2	yes	—
267	#3455	C₂×C₅	1	1	yes	characteristic
268	#2995	C₂×C₅	1	2	yes	complemented
269	#2994	C₂×C₅	1	2	yes	complemented
270	#2993	C₂×C₅	1	2	yes	complemented
271	#2992	C₂×C₅	1	2	yes	complemented
272	#2985	C₂×C₅	1	2	yes	complemented
273	#2980	C₂×C₅	1	1	yes	characteristic, complemented
274	#2979	C₂×C₅	1	1	yes	characteristic, complemented
275	#2978	C₂×C₅	1	1	yes	characteristic, complemented
276	#2977	C₂×C₅	1	1	yes	characteristic, complemented
277	#2976	C₂×C₅	1	2	yes	complemented
278	#2969	C₂×C₅	1	2	yes	complemented
279	#2968	C₂×C₅	1	2	yes	complemented
280	#2967	C₂×C₅	1	2	yes	complemented
281	#2966	C₂×C₅	1	2	yes	complemented
282	#2925	C₂×C₅	1	2	yes	complemented
283	#2924	C₂×C₅	1	2	yes	complemented
284	#2923	C₂×C₅	1	1	yes	characteristic, complemented
285	#2922	C₂×C₅	1	1	yes	characteristic, complemented
286	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
287	C₅×#41	—	4	1	no	—
288	C₅×#41	—	4	1	no	—
289	C₅×#41	—	4	1	no	—
290	C₅×#41	—	4	1	no	—
291	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
292	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
293	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
294	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
295	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
296	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
297	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
298	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
299	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
300	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
301	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
302	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
303	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
304	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
305	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
306	C₂²×C₄×C₅	—	4	1	no	—
307	C₂²×C₄×C₅	—	4	1	no	—
308	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
309	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
310	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
311	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
312	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
314	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
315	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
316	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
321	C₅×M₁₆	—	4	1	no	—
322	C₅×M₁₆	—	4	2	no	—
323	C₅×M₁₆	—	4	2	no	—
324	C₅×M₁₆	—	4	1	no	—
325	C₅×M₁₆	—	4	1	no	—
326	C₅×M₁₆	—	4	2	no	—
327	C₅×M₁₆	—	4	2	no	—
328	C₅×M₁₆	—	4	1	no	—
329	C₂×C₅×C₈	—	4	1	no	—
330	C₂×C₅×C₈	—	4	2	no	—
331	C₂×C₅×C₈	—	4	2	no	—
332	C₂×C₅×C₈	—	4	1	no	—
333	C₂×C₅×C₈	—	4	1	no	—
334	C₂×C₅×C₈	—	4	2	no	—
335	C₂×C₅×C₈	—	4	2	no	—
336	C₂×C₅×C₈	—	4	1	no	—
337	C₂×C₅×C₈	C₂⁴	1	2	yes	—
338	C₂×C₅×C₈	C₂⁴	1	2	yes	—
339	C₂×C₅×C₈	C₂⁴	1	2	yes	—
340	C₂×C₅×C₈	C₂⁴	1	2	yes	—
341	C₂×C₅×C₈	C₂⁴	1	2	yes	—
342	C₂×C₅×C₈	C₂⁴	1	2	yes	—
343	C₂×C₅×C₈	C₂⁴	1	2	yes	—
344	C₂×C₅×C₈	C₂⁴	1	2	yes	—
345	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
346	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
347	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
348	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
349	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
350	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
351	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
352	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
353	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
354	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
355	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
356	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
357	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
358	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
359	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
360	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
361	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
362	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
363	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
364	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
365	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
366	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
367	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
368	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
369	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
370	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
371	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
372	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
373	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
374	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
375	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
376	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
377	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
378	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
379	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
380	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
381	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
382	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
383	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
384	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
385	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
386	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
387	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
388	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
389	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
390	C₄²×C₅	C₂²×C₄	1	2	yes	—
391	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
392	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
393	C₄²×C₅	C₂²×C₄	1	2	yes	—
394	C₄²×C₅	C₂²×C₄	1	2	yes	—
395	C₄²×C₅	C₂²×C₄	1	2	yes	—
396	C₄²×C₅	C₂²×C₄	1	2	yes	—
397	C₄²×C₅	C₂⁴	1	1	yes	characteristic
398	C₄²×C₅	C₂⁴	1	1	yes	characteristic
399	C₄²×C₅	C₂⁴	1	2	yes	—
400	C₄²×C₅	C₂⁴	1	1	yes	characteristic
401	C₄²×C₅	C₂⁴	1	1	yes	characteristic
402	C₄²×C₅	C₂⁴	1	2	yes	—
403	#542	C₄×C₅	1	2	yes	—
404	#542	C₄×C₅	1	2	yes	—
405	#541	C₄×C₅	1	2	yes	—
406	#540	C₄×C₅	1	2	yes	—
407	#539	C₄×C₅	1	2	yes	—
408	#539	C₄×C₅	1	2	yes	—
409	#538	C₄×C₅	1	2	yes	—
410	#538	C₄×C₅	1	2	yes	—
411	#533	C₂²×C₅	1	1	yes	characteristic
412	#532	C₂²×C₅	1	1	yes	characteristic
413	#529	C₂²×C₅	1	2	yes	—
414	#529	C₂²×C₅	1	2	yes	—
415	#529	C₂²×C₅	1	2	yes	—
416	#529	C₂²×C₅	1	2	yes	—
417	#525	C₂²×C₅	1	1	yes	characteristic
418	#525	C₂²×C₅	1	1	yes	characteristic
419	C₄×#41	C₂²×C₅	1	1	yes	characteristic
420	C₄×#41	C₂²×C₅	1	1	yes	characteristic
421	C₂×#117	C₂²×C₅	1	1	yes	characteristic
422	#446	C₂²×C₅	1	2	yes	complemented
423	#446	C₂²×C₅	1	2	yes	complemented
424	#446	C₂²×C₅	1	2	yes	complemented
425	#446	C₂²×C₅	1	2	yes	complemented
426	#446	C₂²×C₅	1	2	yes	complemented
427	#446	C₂²×C₅	1	2	yes	complemented
428	C₈×Q₈	C₂²×C₅	1	2	yes	complemented
429	C₈×Q₈	C₂²×C₅	1	2	yes	complemented
430	#436	C₂²×C₅	1	2	yes	—
431	#436	C₂²×C₅	1	2	yes	—
432	#436	C₂²×C₅	1	2	yes	—
433	#436	C₂²×C₅	1	2	yes	—
434	#436	C₂²×C₅	1	2	yes	complemented
435	#436	C₂²×C₅	1	2	yes	complemented
436	#435	C₂²×C₅	1	2	yes	—
437	#435	C₂²×C₅	1	2	yes	—
438	#435	C₂²×C₅	1	2	yes	—
439	#435	C₂²×C₅	1	2	yes	—
440	#435	C₂²×C₅	1	2	yes	—
441	#435	C₂²×C₅	1	2	yes	—
442	#435	C₂²×C₅	1	2	yes	—
443	#435	C₂²×C₅	1	2	yes	—
444	#435	C₂²×C₅	1	2	yes	complemented
445	#435	C₂²×C₅	1	2	yes	complemented
446	#435	C₂²×C₅	1	2	yes	complemented
447	#435	C₂²×C₅	1	2	yes	complemented
448	C₈×D₄	C₂²×C₅	1	2	yes	—
449	C₈×D₄	C₂²×C₅	1	2	yes	—
450	C₈×D₄	C₂²×C₅	1	2	yes	—
451	C₈×D₄	C₂²×C₅	1	2	yes	—
452	C₈×D₄	C₂²×C₅	1	2	yes	complemented
453	C₈×D₄	C₂²×C₅	1	2	yes	complemented
454	#433	C₂²×C₅	1	2	yes	—
455	#433	C₂²×C₅	1	2	yes	—
456	#433	C₂²×C₅	1	2	yes	—
457	#433	C₂²×C₅	1	2	yes	—
458	#433	C₂²×C₅	1	2	yes	—
459	#433	C₂²×C₅	1	2	yes	—
460	#433	C₂²×C₅	1	2	yes	—
461	#433	C₂²×C₅	1	2	yes	—
462	#433	C₂²×C₅	1	2	yes	complemented
463	#433	C₂²×C₅	1	2	yes	complemented
464	#433	C₂²×C₅	1	2	yes	complemented
465	#433	C₂²×C₅	1	2	yes	complemented
466	#432	C₂²×C₅	1	2	yes	—
467	#432	C₂²×C₅	1	2	yes	—
468	#432	C₂²×C₅	1	2	yes	complemented
469	#432	C₂²×C₅	1	2	yes	complemented
470	#431	C₂²×C₅	1	2	yes	—
471	#431	C₂²×C₅	1	2	yes	—
472	#431	C₂²×C₅	1	2	yes	complemented
473	#431	C₂²×C₅	1	2	yes	complemented
474	#424	C₂²×C₅	1	2	yes	—
475	#424	C₂²×C₅	1	2	yes	—
476	#424	C₂²×C₅	1	1	yes	characteristic, complemented
477	#424	C₂²×C₅	1	1	yes	characteristic, complemented
478	#424	C₂²×C₅	1	1	yes	characteristic, complemented
479	#424	C₂²×C₅	1	1	yes	characteristic, complemented
480	#423	C₂²×C₅	1	2	yes	complemented
481	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
482	#408	C₂²×C₅	1	1	yes	characteristic
483	#408	C₂²×C₅	1	1	yes	characteristic
484	#408	C₂²×C₅	1	1	yes	characteristic
485	#408	C₂²×C₅	1	1	yes	characteristic
486	#408	C₂²×C₅	1	2	yes	—
487	#408	C₂²×C₅	1	2	yes	—
488	#407	C₂²×C₅	1	2	yes	—
489	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
490	#405	C₂²×C₅	1	2	yes	—
491	#405	C₂²×C₅	1	2	yes	—
492	#405	C₂²×C₅	1	2	yes	complemented
493	#405	C₂²×C₅	1	2	yes	complemented
494	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
495	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
496	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
497	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
498	C₂³×C₅	—	4	1	no	—
499	C₂³×C₅	—	4	2	no	—
500	C₂³×C₅	C₂³×C₄	1	2	yes	—
501	C₂³×C₅	C₂³×C₄	1	2	yes	—
502	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
503	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
504	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
505	C₅×Q₈	—	4	2	no	—
506	C₅×Q₈	—	4	2	no	—
507	C₅×Q₈	—	4	1	no	—
508	C₅×Q₈	—	4	1	no	—
509	C₅×D₄	—	4	2	no	—
510	C₅×D₄	—	4	2	no	—
511	C₅×D₄	—	4	2	no	—
512	C₅×D₄	—	4	2	no	—
513	C₅×D₄	—	4	2	no	—
514	C₅×D₄	—	4	2	no	—
515	C₅×D₄	—	4	1	no	—
516	C₅×D₄	—	4	1	no	—
517	C₅×D₄	—	4	2	no	—
518	C₅×D₄	—	4	1	no	—
519	C₅×D₄	—	4	1	no	—
520	C₂×C₄×C₅	—	2	2	no	—
521	C₂×C₄×C₅	—	2	2	no	—
522	C₂×C₄×C₅	—	2	2	no	—
523	C₂×C₄×C₅	—	2	1	no	—
524	C₂×C₄×C₅	—	2	1	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	1	no	—
527	C₂×C₄×C₅	—	2	2	no	—
528	C₂×C₄×C₅	—	2	1	no	—
529	C₂×C₄×C₅	—	2	1	no	—
530	C₂×C₄×C₅	—	4	1	no	—
531	C₂×C₄×C₅	—	4	2	no	—
532	C₂×C₄×C₅	—	4	2	no	—
533	C₂×C₄×C₅	—	4	2	no	—
534	C₂×C₄×C₅	—	4	2	no	—
535	C₂×C₄×C₅	—	4	2	no	—
536	C₂×C₄×C₅	—	4	2	no	—
537	C₂×C₄×C₅	—	4	2	no	—
538	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
539	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
540	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
541	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
542	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
543	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
544	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
545	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
546	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
547	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
548	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
549	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
550	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
551	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
552	C₅×C₈	—	2	2	no	—
553	C₅×C₈	—	2	2	no	—
554	C₅×C₈	—	2	2	no	—
555	C₅×C₈	—	2	2	no	—
556	C₅×C₈	—	2	2	no	—
557	C₅×C₈	—	2	2	no	—
558	C₅×C₈	—	2	2	no	—
559	C₅×C₈	—	2	2	no	—
560	C₂×#41	C₂³×C₅	1	1	yes	characteristic
561	C₂×#41	C₂³×C₅	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
563	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
564	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
565	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
566	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
567	C₂×M₁₆	C₂³×C₅	1	2	yes	—
568	C₂×M₁₆	C₂³×C₅	1	2	yes	—
569	C₂×M₁₆	C₂³×C₅	1	2	yes	—
570	C₂×M₁₆	C₂³×C₅	1	2	yes	—
571	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
572	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
573	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
574	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
575	C₂²×C₈	C₂³×C₅	1	2	yes	—
576	C₂²×C₈	C₂³×C₅	1	2	yes	—
577	C₂²×C₈	C₂³×C₅	1	2	yes	—
578	C₂²×C₈	C₂³×C₅	1	2	yes	—
579	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
580	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
581	#127	C₂×C₄×C₅	1	1	yes	characteristic
582	#126	C₂×C₄×C₅	1	2	yes	—
583	#126	C₂×C₄×C₅	1	2	yes	—
584	#126	C₂×C₄×C₅	1	2	yes	—
585	#126	C₂×C₄×C₅	1	2	yes	—
586	#126	C₂×C₄×C₅	1	2	yes	—
587	#126	C₂×C₄×C₅	1	2	yes	—
588	#126	C₂×C₄×C₅	1	2	yes	—
589	#126	C₂×C₄×C₅	1	2	yes	—
590	#125	C₂×C₄×C₅	1	2	yes	—
591	#125	C₂×C₄×C₅	1	2	yes	—
592	#125	C₂×C₄×C₅	1	2	yes	—
593	#125	C₂×C₄×C₅	1	2	yes	—
594	#125	C₂×C₄×C₅	1	2	yes	—
595	#124	C₂×C₄×C₅	1	2	yes	—
596	#124	C₂×C₄×C₅	1	2	yes	—
597	#124	C₂×C₄×C₅	1	2	yes	—
598	#124	C₂×C₄×C₅	1	2	yes	—
599	#124	C₂×C₄×C₅	1	1	yes	characteristic
600	#124	C₂×C₄×C₅	1	1	yes	characteristic
601	#123	C₂×C₄×C₅	1	2	yes	—
602	#123	C₂×C₄×C₅	1	1	yes	characteristic
603	#123	C₂×C₄×C₅	1	1	yes	characteristic
604	#123	C₂×C₄×C₅	1	2	yes	—
605	#123	C₂×C₄×C₅	1	2	yes	—
606	#123	C₂×C₄×C₅	1	2	yes	—
607	#123	C₂×C₄×C₅	1	2	yes	—
608	#123	C₂×C₄×C₅	1	2	yes	—
609	#123	C₂×C₄×C₅	1	2	yes	—
610	#123	C₂×C₄×C₅	1	2	yes	—
611	#123	C₂×C₄×C₅	1	2	yes	—
612	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
613	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
614	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
615	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
616	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
617	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
618	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
619	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
620	#121	C₂×C₄×C₅	1	2	yes	—
621	#121	C₂×C₄×C₅	1	2	yes	—
622	#121	C₂×C₄×C₅	1	2	yes	—
623	#121	C₂×C₄×C₅	1	2	yes	—
624	#121	C₂×C₄×C₅	1	2	yes	—
625	#121	C₂×C₄×C₅	1	2	yes	—
626	#121	C₂×C₄×C₅	1	2	yes	—
627	#121	C₂×C₄×C₅	1	2	yes	—
628	#120	C₂×C₄×C₅	1	2	yes	—
629	#120	C₂×C₄×C₅	1	1	yes	characteristic
630	#120	C₂×C₄×C₅	1	1	yes	characteristic
631	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
632	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
633	C₄×Q₈	C₂³×C₅	1	2	yes	—
634	C₄×Q₈	C₂³×C₅	1	2	yes	—
635	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
636	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
637	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
638	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
639	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
640	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
641	C₄×D₄	C₂³×C₅	1	2	yes	—
642	C₄×D₄	C₂³×C₅	1	2	yes	—
643	C₄×D₄	C₂³×C₅	1	2	yes	—
644	C₄×D₄	C₂³×C₅	1	2	yes	—
645	C₄×D₄	C₂³×C₅	1	2	yes	—
646	C₄×D₄	C₂³×C₅	1	2	yes	—
647	#117	C₂×C₄×C₅	1	2	yes	—
648	#117	C₂×C₄×C₅	1	2	yes	—
649	#117	C₂³×C₅	1	2	yes	—
650	#117	C₂³×C₅	1	2	yes	—
651	#117	C₂³×C₅	1	1	yes	characteristic
652	#117	C₂³×C₅	1	1	yes	characteristic
653	#117	C₂³×C₅	1	2	yes	—
654	#117	C₂³×C₅	1	1	yes	characteristic
655	#117	C₂³×C₅	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
658	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₅	1	2	yes	—
663	C₄⋊C₈	C₂³×C₅	1	2	yes	—
664	C₄⋊C₈	C₂³×C₅	1	2	yes	—
665	C₄⋊C₈	C₂³×C₅	1	2	yes	—
666	C₄⋊C₈	C₂³×C₅	1	2	yes	—
667	C₄⋊C₈	C₂³×C₅	1	2	yes	—
668	C₄⋊C₈	C₂³×C₅	1	2	yes	—
669	C₄⋊C₈	C₂³×C₅	1	2	yes	—
670	C₄⋊C₈	C₂³×C₅	1	2	yes	—
671	C₄⋊C₈	C₂³×C₅	1	2	yes	—
672	C₄⋊C₈	C₂³×C₅	1	2	yes	—
673	C₄⋊C₈	C₂³×C₅	1	2	yes	—
674	C₄⋊C₈	C₂³×C₅	1	2	yes	—
675	C₄⋊C₈	C₂³×C₅	1	2	yes	—
676	C₄⋊C₈	C₂³×C₅	1	2	yes	—
677	C₄⋊C₈	C₂³×C₅	1	2	yes	—
678	C₄⋊C₈	C₂³×C₅	1	2	yes	—
679	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
680	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
681	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
682	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
683	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
684	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
685	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
686	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
687	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
688	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
689	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
690	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
691	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
692	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
693	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
694	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
695	#97	C₂³×C₅	1	2	yes	—
696	#97	C₂³×C₅	1	2	yes	—
697	#97	C₂³×C₅	1	2	yes	—
698	#97	C₂³×C₅	1	2	yes	—
699	#97	C₂³×C₅	1	2	yes	—
700	#97	C₂³×C₅	1	2	yes	—
701	#97	C₂³×C₅	1	2	yes	—
702	#97	C₂³×C₅	1	2	yes	—
703	C₄×C₈	C₂³×C₅	1	2	yes	—
704	C₄×C₈	C₂³×C₅	1	2	yes	—
705	C₄×C₈	C₂³×C₅	1	2	yes	—
706	C₄×C₈	C₂³×C₅	1	2	yes	—
707	C₄×C₈	C₂³×C₅	1	2	yes	—
708	C₄×C₈	C₂³×C₅	1	2	yes	—
709	C₄×C₈	C₂³×C₅	1	2	yes	—
710	C₄×C₈	C₂³×C₅	1	2	yes	—
711	C₂²×C₅	—	2	1	no	—
712	C₂²×C₅	—	2	2	no	—
713	C₂²×C₅	—	2	2	no	—
714	C₂²×C₅	—	2	1	no	—
715	C₂²×C₅	—	2	1	no	—
716	C₂²×C₅	—	2	2	no	—
717	C₂²×C₅	—	2	2	no	—
718	C₂²×C₅	—	2	2	no	—
719	C₂²×C₅	—	2	2	no	—
720	C₂²×C₅	—	2	2	no	—
721	C₂²×C₅	—	2	2	no	—
722	C₂²×C₅	—	2	2	no	—
723	C₂²×C₅	—	8	2	no	—
724	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
725	C₄×C₅	—	2	2	no	—
726	C₄×C₅	—	2	1	no	—
727	C₄×C₅	—	2	2	no	—
728	C₄×C₅	—	2	1	no	—
729	C₄×C₅	—	2	1	no	—
730	C₄×C₅	—	2	2	no	—
731	C₄×C₅	—	2	2	no	—
732	C₄×C₅	—	2	2	no	—
733	C₄×C₅	—	2	2	no	—
734	C₄×C₅	—	2	2	no	—
735	C₄×C₅	—	2	2	no	—
736	C₄×C₅	—	2	2	no	—
737	C₄×C₅	—	2	2	no	—
738	C₄×C₅	#585	1	1	yes	characteristic
739	C₄×C₅	#585	1	1	yes	characteristic
740	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
741	#41	—	4	1	no	—
742	#41	—	4	1	no	—
743	#41	—	4	1	no	—
744	#41	—	4	1	no	—
745	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
746	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
747	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
748	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
749	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
750	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
751	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
752	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
753	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
754	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
755	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
756	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
757	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
758	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
759	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
760	C₂²×C₄	—	4	1	no	—
761	C₂²×C₄	—	4	1	no	—
762	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
763	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
764	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
765	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
766	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
767	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
768	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
769	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
775	M₁₆	—	4	1	no	—
776	M₁₆	—	4	2	no	—
777	M₁₆	—	4	2	no	—
778	M₁₆	—	4	1	no	—
779	M₁₆	—	4	1	no	—
780	M₁₆	—	4	2	no	—
781	M₁₆	—	4	2	no	—
782	M₁₆	—	4	1	no	—
783	C₂×C₈	—	4	1	no	—
784	C₂×C₈	—	4	2	no	—
785	C₂×C₈	—	4	2	no	—
786	C₂×C₈	—	4	1	no	—
787	C₂×C₈	—	4	1	no	—
788	C₂×C₈	—	4	2	no	—
789	C₂×C₈	—	4	2	no	—
790	C₂×C₈	—	4	1	no	—
791	C₂×C₈	C₂⁴×C₅	1	2	yes	—
792	C₂×C₈	C₂⁴×C₅	1	2	yes	—
793	C₂×C₈	C₂⁴×C₅	1	2	yes	—
794	C₂×C₈	C₂⁴×C₅	1	2	yes	—
795	C₂×C₈	C₂⁴×C₅	1	2	yes	—
796	C₂×C₈	C₂⁴×C₅	1	2	yes	—
797	C₂×C₈	C₂⁴×C₅	1	2	yes	—
798	C₂×C₈	C₂⁴×C₅	1	2	yes	—
799	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
800	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
801	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
802	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
803	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
804	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
805	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
806	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
807	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
808	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
809	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
810	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
811	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
812	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
813	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
814	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
815	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
816	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
817	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
818	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
819	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
820	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
821	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
822	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
823	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
824	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
825	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
826	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
827	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
828	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
829	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
830	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
831	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
832	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
833	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
834	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
835	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
836	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
837	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
838	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
839	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
840	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
841	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
842	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
843	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
844	C₄²	C₂²×C₄×C₅	1	2	yes	—
845	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
846	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
847	C₄²	C₂²×C₄×C₅	1	2	yes	—
848	C₄²	C₂²×C₄×C₅	1	2	yes	—
849	C₄²	C₂²×C₄×C₅	1	2	yes	—
850	C₄²	C₂²×C₄×C₅	1	2	yes	—
851	C₄²	C₂⁴×C₅	1	1	yes	characteristic
852	C₄²	C₂⁴×C₅	1	2	yes	—
853	C₄²	C₂⁴×C₅	1	1	yes	characteristic
854	C₄²	C₂⁴×C₅	1	1	yes	characteristic
855	C₄²	C₂⁴×C₅	1	2	yes	—
856	C₄²	C₂⁴×C₅	1	1	yes	characteristic
857	C₂×C₅	—	4	2	no	—
858	C₂×C₅	—	4	1	no	—
859	C₂×C₅	—	4	1	no	—
860	C₂×C₅	—	4	1	no	—
861	C₂×C₅	—	4	2	no	—
862	C₂×C₅	#3428	1	1	yes	characteristic
863	C₂×C₅	#3573	1	2	yes	—
864	C₂³	—	4	1	no	—
865	C₂³	—	4	2	no	—
866	C₂³	C₂³×C₄×C₅	1	2	yes	—
867	C₂³	C₂³×C₄×C₅	1	2	yes	—
868	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
869	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
870	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
871	Q₈	—	4	1	no	—
872	Q₈	—	4	1	no	—
873	Q₈	—	4	2	no	—
874	Q₈	—	4	2	no	—
875	D₄	—	4	1	no	—
876	D₄	—	4	1	no	—
877	D₄	—	4	2	no	—
878	D₄	—	4	1	no	—
879	D₄	—	4	1	no	—
880	D₄	—	4	2	no	—
881	D₄	—	4	2	no	—
882	D₄	—	4	2	no	—
883	D₄	—	4	2	no	—
884	D₄	—	4	2	no	—
885	D₄	—	4	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	4	2	no	—
897	C₂×C₄	—	4	1	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	4	2	no	—
902	C₂×C₄	—	4	2	no	—
903	C₂×C₄	—	4	2	no	—
904	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
905	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
906	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
907	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
908	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
909	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
910	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
911	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
912	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
913	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
914	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
915	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
916	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
917	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
918	C₈	—	2	2	no	—
919	C₈	—	2	2	no	—
920	C₈	—	2	2	no	—
921	C₈	—	2	2	no	—
922	C₈	—	2	2	no	—
923	C₈	—	2	2	no	—
924	C₈	—	2	2	no	—
925	C₈	—	2	2	no	—
926	C₅	#60296	1	1	yes	characteristic, direct product factor, Sylow
927	C₂²	—	2	1	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	8	2	no	—
940	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
941	C₄	—	2	1	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	1	no	—
945	C₄	—	2	1	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	2	no	—
954	C₄	C₅×#585	1	1	yes	characteristic
955	C₄	C₅×#585	1	1	yes	characteristic
956	C₂	—	4	1	no	—
957	C₂	—	4	2	no	—
958	C₂	—	4	2	no	—
959	C₂	—	4	1	no	—
960	C₂	—	4	1	no	—
961	C₂	C₅×#3428	1	1	yes	characteristic
962	C₂	C₅×#3573	1	2	yes	—

	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×#3455	C₂
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×#2995	C₂	semidirect
3. C₅×#2994	C₂	semidirect
4. C₅×#2993	C₂	semidirect
5. C₅×#2992	C₂	semidirect
6. C₅×#2985	C₂	semidirect
7. C₅×#2980	C₂	semidirect
8. C₅×#2979	C₂	semidirect
9. C₅×#2978	C₂	semidirect
10. C₅×#2977	C₂	semidirect
11. C₅×#2976	C₂	semidirect
12. C₅×#2969	C₂	semidirect
13. C₅×#2968	C₂	semidirect
14. C₅×#2967	C₂	semidirect
15. C₅×#2966	C₂	semidirect
16. C₅×#2925	C₂	semidirect
17. C₅×#2924	C₂	semidirect
18. C₅×#2923	C₂	semidirect
19. C₅×#2922	C₂	semidirect
39. C₅×#446	C₂²	semidirect
40. C₅×#446	C₂²	semidirect
41. C₅×#446	C₂²	semidirect
42. C₅×#446	C₂²	semidirect
43. C₅×#446	C₂²	semidirect
44. C₅×#446	C₂²	semidirect
45. C₅×C₈×Q₈	C₂²	semidirect
46. C₅×C₈×Q₈	C₂²	semidirect
51. C₅×#436	C₂²	semidirect
52. C₅×#436	C₂²	semidirect
61. C₅×#435	C₂²	semidirect
62. C₅×#435	C₂²	semidirect
63. C₅×#435	C₂²	semidirect
64. C₅×#435	C₂²	semidirect
69. C₅×C₈×D₄	C₂²	semidirect
70. C₅×C₈×D₄	C₂²	semidirect
79. C₅×#433	C₂²	semidirect
80. C₅×#433	C₂²	semidirect
81. C₅×#433	C₂²	semidirect
82. C₅×#433	C₂²	semidirect
85. C₅×#432	C₂²	semidirect
86. C₅×#432	C₂²	semidirect
89. C₅×#431	C₂²	semidirect
90. C₅×#431	C₂²	semidirect
93. C₅×#424	C₂²	semidirect
94. C₅×#424	C₂²	semidirect
95. C₅×#424	C₂²	semidirect
96. C₅×#424	C₂²	semidirect
97. C₅×#423	C₂²	semidirect
98. C₂×C₅×C₄⋊C₈	C₂²	semidirect
109. C₅×#405	C₂²	semidirect
110. C₅×#405	C₂²	semidirect
111. C₄×C₅×M₁₆	C₂²	semidirect
112. C₄×C₅×M₁₆	C₂²	semidirect
113. C₂×C₅×#97	C₂²	semidirect
114. C₂×C₄×C₅×C₈	C₂²	semidirect
115. #60296	C₅	direct (N × H)
268. #2995	C₂×C₅	semidirect
269. #2994	C₂×C₅	semidirect
270. #2993	C₂×C₅	semidirect
271. #2992	C₂×C₅	semidirect
272. #2985	C₂×C₅	semidirect
273. #2980	C₂×C₅	semidirect
274. #2979	C₂×C₅	semidirect
275. #2978	C₂×C₅	semidirect
276. #2977	C₂×C₅	semidirect
277. #2976	C₂×C₅	semidirect
278. #2969	C₂×C₅	semidirect
279. #2968	C₂×C₅	semidirect
280. #2967	C₂×C₅	semidirect
281. #2966	C₂×C₅	semidirect
282. #2925	C₂×C₅	semidirect
283. #2924	C₂×C₅	semidirect
284. #2923	C₂×C₅	semidirect
285. #2922	C₂×C₅	semidirect
422. #446	C₂²×C₅	semidirect
423. #446	C₂²×C₅	semidirect
424. #446	C₂²×C₅	semidirect
425. #446	C₂²×C₅	semidirect
426. #446	C₂²×C₅	semidirect
427. #446	C₂²×C₅	semidirect
428. C₈×Q₈	C₂²×C₅	semidirect
429. C₈×Q₈	C₂²×C₅	semidirect
434. #436	C₂²×C₅	semidirect
435. #436	C₂²×C₅	semidirect
444. #435	C₂²×C₅	semidirect
445. #435	C₂²×C₅	semidirect
446. #435	C₂²×C₅	semidirect
447. #435	C₂²×C₅	semidirect
452. C₈×D₄	C₂²×C₅	semidirect
453. C₈×D₄	C₂²×C₅	semidirect
462. #433	C₂²×C₅	semidirect
463. #433	C₂²×C₅	semidirect
464. #433	C₂²×C₅	semidirect
465. #433	C₂²×C₅	semidirect
468. #432	C₂²×C₅	semidirect
469. #432	C₂²×C₅	semidirect
472. #431	C₂²×C₅	semidirect
473. #431	C₂²×C₅	semidirect
476. #424	C₂²×C₅	semidirect
477. #424	C₂²×C₅	semidirect
478. #424	C₂²×C₅	semidirect
479. #424	C₂²×C₅	semidirect
480. #423	C₂²×C₅	semidirect
481. C₂×C₄⋊C₈	C₂²×C₅	semidirect
492. #405	C₂²×C₅	semidirect
493. #405	C₂²×C₅	semidirect
494. C₄×M₁₆	C₂²×C₅	semidirect
495. C₄×M₁₆	C₂²×C₅	semidirect
496. C₂×#97	C₂²×C₅	semidirect
497. C₂×C₄×C₈	C₂²×C₅	semidirect
926. C₅	#60296	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×#3455	2
C₅×#2995	2
C₅×#2994	2
C₅×#2993	2
C₅×#2992	2
C₅×#2985	2
C₅×#2980	2
C₅×#2979	2
C₅×#2978	2
C₅×#2977	2
C₅×#2976	2
C₅×#2969	2
C₅×#2968	2
C₅×#2967	2
C₅×#2966	2
C₅×#2925	2
C₅×#2924	2
C₅×#2923	2
C₅×#2922	2
#60296	5

Subgroups — C5×#60296 #11983016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60296 #11983016