Subgroups — C₅×#60297 #11983017

Order 1280.

1684 conjugacy classes of subgroups.

The subgroup lattice has 942 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×#2987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2986	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2981	C₂	1	2	yes	maximal, 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	1	yes	characteristic
72	C₅×#433	C₂²	1	1	yes	characteristic
73	C₅×#433	C₂²	1	2	yes	—
74	C₅×#433	C₂²	1	1	yes	characteristic
75	C₅×#433	C₂²	1	1	yes	characteristic
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	—
80	C₅×#433	C₂²	1	2	yes	—
81	C₅×#433	C₂²	1	1	yes	characteristic, complemented
82	C₅×#433	C₂²	1	1	yes	characteristic, complemented
83	C₅×#433	C₂²	1	1	yes	characteristic, complemented
84	C₅×#433	C₂²	1	1	yes	characteristic, complemented
85	C₅×#433	C₂²	1	2	yes	complemented
86	C₅×#433	C₂²	1	2	yes	complemented
87	C₅×#432	C₂²	1	2	yes	—
88	C₅×#432	C₂²	1	2	yes	—
89	C₅×#432	C₂²	1	2	yes	complemented
90	C₅×#432	C₂²	1	2	yes	complemented
91	C₅×#431	C₂²	1	2	yes	—
92	C₅×#431	C₂²	1	2	yes	—
93	C₅×#431	C₂²	1	2	yes	complemented
94	C₅×#431	C₂²	1	2	yes	complemented
95	C₅×#424	C₂²	1	2	yes	—
96	C₅×#424	C₂²	1	2	yes	—
97	C₅×#424	C₂²	1	2	yes	complemented
98	C₅×#424	C₂²	1	2	yes	complemented
99	C₅×#423	C₂²	1	2	yes	complemented
100	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
101	C₅×#408	C₂²	1	2	yes	—
102	C₅×#408	C₂²	1	2	yes	—
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	#60297	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	2	yes	—
120	C₂×C₅×M₁₆	C₂³	1	2	yes	—
121	C₂×C₅×M₁₆	C₂³	1	2	yes	—
122	C₂×C₅×M₁₆	C₂³	1	2	yes	—
123	C₂×C₅×M₁₆	C₂³	1	2	yes	—
124	C₂×C₅×M₁₆	C₂³	1	2	yes	—
125	C₂²×C₅×C₈	C₂³	1	2	yes	—
126	C₂²×C₅×C₈	C₂³	1	2	yes	—
127	C₂²×C₅×C₈	C₂³	1	2	yes	—
128	C₂²×C₅×C₈	C₂³	1	2	yes	—
129	C₂²×C₅×C₈	C₂³	1	2	yes	—
130	C₂²×C₅×C₈	C₂³	1	2	yes	—
131	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
132	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
133	C₅×#127	C₂×C₄	1	1	yes	characteristic
134	C₅×#126	C₂×C₄	1	2	yes	—
135	C₅×#126	C₂×C₄	1	2	yes	—
136	C₅×#126	C₂×C₄	1	2	yes	—
137	C₅×#126	C₂×C₄	1	2	yes	—
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×#125	C₂×C₄	1	2	yes	—
143	C₅×#125	C₂×C₄	1	2	yes	—
144	C₅×#125	C₂×C₄	1	2	yes	—
145	C₅×#125	C₂×C₄	1	2	yes	—
146	C₅×#125	C₂×C₄	1	2	yes	—
147	C₅×#124	C₂×C₄	1	2	yes	—
148	C₅×#124	C₂×C₄	1	2	yes	—
149	C₅×#124	C₂×C₄	1	2	yes	—
150	C₅×#124	C₂×C₄	1	2	yes	—
151	C₅×#124	C₂×C₄	1	1	yes	characteristic
152	C₅×#124	C₂×C₄	1	1	yes	characteristic
153	C₅×#123	C₂×C₄	1	1	yes	characteristic
154	C₅×#123	C₂×C₄	1	1	yes	characteristic
155	C₅×#123	C₂×C₄	1	2	yes	—
156	C₅×#123	C₂×C₄	1	2	yes	—
157	C₅×#123	C₂×C₄	1	2	yes	—
158	C₅×#123	C₂×C₄	1	2	yes	—
159	C₅×#123	C₂×C₄	1	2	yes	—
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×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
165	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
166	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
167	C₅×C₂²⋊Q₈	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×#121	C₂×C₄	1	2	yes	—
173	C₅×#121	C₂×C₄	1	2	yes	—
174	C₅×#121	C₂×C₄	1	2	yes	—
175	C₅×#121	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×#120	C₂×C₄	1	1	yes	characteristic
181	C₅×#120	C₂×C₄	1	1	yes	characteristic
182	C₅×#120	C₂×C₄	1	2	yes	—
183	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
184	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
185	C₄×C₅×Q₈	C₂³	1	2	yes	—
186	C₄×C₅×Q₈	C₂³	1	2	yes	—
187	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
188	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
189	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
190	C₄×C₅×D₄	C₂×C₄	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	C₂³	1	2	yes	—
194	C₄×C₅×D₄	C₂³	1	2	yes	—
195	C₄×C₅×D₄	C₂³	1	2	yes	—
196	C₄×C₅×D₄	C₂³	1	2	yes	—
197	C₄×C₅×D₄	C₂³	1	2	yes	—
198	C₄×C₅×D₄	C₂³	1	2	yes	—
199	C₅×#117	C₂×C₄	1	2	yes	—
200	C₅×#117	C₂×C₄	1	2	yes	—
201	C₅×#117	C₂³	1	2	yes	—
202	C₅×#117	C₂³	1	2	yes	—
203	C₅×#117	C₂³	1	2	yes	—
204	C₅×#117	C₂³	1	1	yes	characteristic
205	C₅×#117	C₂³	1	1	yes	characteristic
206	C₅×#117	C₂³	1	1	yes	characteristic
207	C₅×#117	C₂³	1	1	yes	characteristic
208	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
209	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
210	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₅	C₂³	1	2	yes	—
213	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
215	C₅×C₄⋊C₈	C₂³	1	2	yes	—
216	C₅×C₄⋊C₈	C₂³	1	2	yes	—
217	C₅×C₄⋊C₈	C₂³	1	2	yes	—
218	C₅×C₄⋊C₈	C₂³	1	2	yes	—
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×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
233	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
234	C₅×C₂²⋊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×#97	C₂³	1	2	yes	—
248	C₅×#97	C₂³	1	1	yes	characteristic
249	C₅×#97	C₂³	1	1	yes	characteristic
250	C₅×#97	C₂³	1	2	yes	—
251	C₅×#97	C₂³	1	1	yes	characteristic
252	C₅×#97	C₂³	1	1	yes	characteristic
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	C₄×C₅×C₈	C₂³	1	2	yes	—
258	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
259	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
260	C₄×C₅×C₈	C₂³	1	2	yes	—
261	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
262	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
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	#2987	C₂×C₅	1	1	yes	characteristic, complemented
273	#2986	C₂×C₅	1	1	yes	characteristic, complemented
274	#2981	C₂×C₅	1	2	yes	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	2	no	—
288	C₅×#41	—	4	2	no	—
289	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
290	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
291	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
292	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
293	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
294	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
295	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
296	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
297	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
298	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
299	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
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	C₂²×C₄×C₅	—	4	2	no	—
305	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
306	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
307	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
312	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
318	C₅×M₁₆	—	4	2	no	—
319	C₅×M₁₆	—	4	2	no	—
320	C₅×M₁₆	—	4	2	no	—
321	C₅×M₁₆	—	4	2	no	—
322	C₅×M₁₆	—	4	2	no	—
323	C₅×M₁₆	—	4	2	no	—
324	C₂×C₅×C₈	—	4	2	no	—
325	C₂×C₅×C₈	—	4	2	no	—
326	C₂×C₅×C₈	—	4	2	no	—
327	C₂×C₅×C₈	—	4	2	no	—
328	C₂×C₅×C₈	—	4	2	no	—
329	C₂×C₅×C₈	—	4	2	no	—
330	C₂×C₅×C₈	C₂⁴	1	2	yes	—
331	C₂×C₅×C₈	C₂⁴	1	2	yes	—
332	C₂×C₅×C₈	C₂⁴	1	2	yes	—
333	C₂×C₅×C₈	C₂⁴	1	2	yes	—
334	C₂×C₅×C₈	C₂⁴	1	2	yes	—
335	C₂×C₅×C₈	C₂⁴	1	2	yes	—
336	C₂×C₅×C₈	C₂⁴	1	2	yes	—
337	C₂×C₅×C₈	C₂⁴	1	2	yes	—
338	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
339	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
340	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
341	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
342	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
343	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
344	C₅×C₄⋊C₄	C₂²×C₄	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×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
361	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
362	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
363	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
364	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
365	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
366	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
373	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
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	C₄²×C₅	C₂²×C₄	1	2	yes	—
384	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
385	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
386	C₄²×C₅	C₂²×C₄	1	2	yes	—
387	C₄²×C₅	C₂²×C₄	1	2	yes	—
388	C₄²×C₅	C₂²×C₄	1	2	yes	—
389	C₄²×C₅	C₂²×C₄	1	2	yes	—
390	C₄²×C₅	C₂⁴	1	1	yes	characteristic
391	C₄²×C₅	C₂⁴	1	1	yes	characteristic
392	C₄²×C₅	C₂⁴	1	2	yes	—
393	C₄²×C₅	C₂⁴	1	1	yes	characteristic
394	C₄²×C₅	C₂⁴	1	1	yes	characteristic
395	C₄²×C₅	C₂⁴	1	2	yes	—
396	#542	C₄×C₅	1	2	yes	—
397	#542	C₄×C₅	1	2	yes	—
398	#541	C₄×C₅	1	2	yes	—
399	#540	C₄×C₅	1	2	yes	—
400	#539	C₄×C₅	1	2	yes	—
401	#539	C₄×C₅	1	2	yes	—
402	#538	C₄×C₅	1	2	yes	—
403	#538	C₄×C₅	1	2	yes	—
404	#533	C₂²×C₅	1	1	yes	characteristic
405	#532	C₂²×C₅	1	1	yes	characteristic
406	#529	C₂²×C₅	1	2	yes	—
407	#529	C₂²×C₅	1	2	yes	—
408	#529	C₂²×C₅	1	2	yes	—
409	#529	C₂²×C₅	1	2	yes	—
410	#525	C₂²×C₅	1	1	yes	characteristic
411	#525	C₂²×C₅	1	1	yes	characteristic
412	C₄×#41	C₂²×C₅	1	1	yes	characteristic
413	C₄×#41	C₂²×C₅	1	1	yes	characteristic
414	C₂×#117	C₂²×C₅	1	1	yes	characteristic
415	#446	C₂²×C₅	1	2	yes	complemented
416	#446	C₂²×C₅	1	2	yes	complemented
417	#446	C₂²×C₅	1	2	yes	complemented
418	#446	C₂²×C₅	1	2	yes	complemented
419	#446	C₂²×C₅	1	2	yes	complemented
420	#446	C₂²×C₅	1	2	yes	complemented
421	C₈×Q₈	C₂²×C₅	1	2	yes	complemented
422	C₈×Q₈	C₂²×C₅	1	2	yes	complemented
423	#436	C₂²×C₅	1	2	yes	—
424	#436	C₂²×C₅	1	2	yes	—
425	#436	C₂²×C₅	1	2	yes	—
426	#436	C₂²×C₅	1	2	yes	—
427	#436	C₂²×C₅	1	2	yes	complemented
428	#436	C₂²×C₅	1	2	yes	complemented
429	#435	C₂²×C₅	1	2	yes	—
430	#435	C₂²×C₅	1	2	yes	—
431	#435	C₂²×C₅	1	2	yes	—
432	#435	C₂²×C₅	1	2	yes	—
433	#435	C₂²×C₅	1	2	yes	—
434	#435	C₂²×C₅	1	2	yes	—
435	#435	C₂²×C₅	1	2	yes	—
436	#435	C₂²×C₅	1	2	yes	—
437	#435	C₂²×C₅	1	2	yes	complemented
438	#435	C₂²×C₅	1	2	yes	complemented
439	#435	C₂²×C₅	1	2	yes	complemented
440	#435	C₂²×C₅	1	2	yes	complemented
441	C₈×D₄	C₂²×C₅	1	2	yes	—
442	C₈×D₄	C₂²×C₅	1	2	yes	—
443	C₈×D₄	C₂²×C₅	1	2	yes	—
444	C₈×D₄	C₂²×C₅	1	2	yes	—
445	C₈×D₄	C₂²×C₅	1	2	yes	complemented
446	C₈×D₄	C₂²×C₅	1	2	yes	complemented
447	#433	C₂²×C₅	1	1	yes	characteristic
448	#433	C₂²×C₅	1	1	yes	characteristic
449	#433	C₂²×C₅	1	1	yes	characteristic
450	#433	C₂²×C₅	1	1	yes	characteristic
451	#433	C₂²×C₅	1	2	yes	—
452	#433	C₂²×C₅	1	2	yes	—
453	#433	C₂²×C₅	1	2	yes	—
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	1	yes	characteristic, complemented
458	#433	C₂²×C₅	1	1	yes	characteristic, complemented
459	#433	C₂²×C₅	1	1	yes	characteristic, complemented
460	#433	C₂²×C₅	1	1	yes	characteristic, complemented
461	#433	C₂²×C₅	1	2	yes	complemented
462	#433	C₂²×C₅	1	2	yes	complemented
463	#432	C₂²×C₅	1	2	yes	—
464	#432	C₂²×C₅	1	2	yes	—
465	#432	C₂²×C₅	1	2	yes	complemented
466	#432	C₂²×C₅	1	2	yes	complemented
467	#431	C₂²×C₅	1	2	yes	—
468	#431	C₂²×C₅	1	2	yes	—
469	#431	C₂²×C₅	1	2	yes	complemented
470	#431	C₂²×C₅	1	2	yes	complemented
471	#424	C₂²×C₅	1	2	yes	—
472	#424	C₂²×C₅	1	2	yes	—
473	#424	C₂²×C₅	1	2	yes	complemented
474	#424	C₂²×C₅	1	2	yes	complemented
475	#423	C₂²×C₅	1	2	yes	complemented
476	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
477	#408	C₂²×C₅	1	2	yes	—
478	#408	C₂²×C₅	1	2	yes	—
479	#408	C₂²×C₅	1	2	yes	—
480	#408	C₂²×C₅	1	2	yes	—
481	#407	C₂²×C₅	1	2	yes	—
482	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
483	#405	C₂²×C₅	1	2	yes	—
484	#405	C₂²×C₅	1	2	yes	—
485	#405	C₂²×C₅	1	2	yes	complemented
486	#405	C₂²×C₅	1	2	yes	complemented
487	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
488	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
489	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
490	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
491	C₂³×C₅	—	4	1	no	—
492	C₂³×C₅	—	4	2	no	—
493	C₂³×C₅	C₂³×C₄	1	2	yes	—
494	C₂³×C₅	C₂³×C₄	1	2	yes	—
495	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
496	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
497	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
498	C₅×Q₈	—	4	2	no	—
499	C₅×Q₈	—	4	2	no	—
500	C₅×Q₈	—	4	1	no	—
501	C₅×Q₈	—	4	1	no	—
502	C₅×D₄	—	4	2	no	—
503	C₅×D₄	—	4	2	no	—
504	C₅×D₄	—	4	2	no	—
505	C₅×D₄	—	4	2	no	—
506	C₅×D₄	—	4	2	no	—
507	C₅×D₄	—	4	2	no	—
508	C₅×D₄	—	4	1	no	—
509	C₅×D₄	—	4	1	no	—
510	C₅×D₄	—	4	2	no	—
511	C₅×D₄	—	4	1	no	—
512	C₅×D₄	—	4	1	no	—
513	C₂×C₄×C₅	—	2	2	no	—
514	C₂×C₄×C₅	—	2	2	no	—
515	C₂×C₄×C₅	—	2	2	no	—
516	C₂×C₄×C₅	—	2	2	no	—
517	C₂×C₄×C₅	—	2	2	no	—
518	C₂×C₄×C₅	—	2	2	no	—
519	C₂×C₄×C₅	—	2	2	no	—
520	C₂×C₄×C₅	—	4	1	no	—
521	C₂×C₄×C₅	—	4	2	no	—
522	C₂×C₄×C₅	—	4	2	no	—
523	C₂×C₄×C₅	—	4	2	no	—
524	C₂×C₄×C₅	—	4	2	no	—
525	C₂×C₄×C₅	—	4	2	no	—
526	C₂×C₄×C₅	—	4	2	no	—
527	C₂×C₄×C₅	—	4	2	no	—
528	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
529	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
530	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
531	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
532	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
533	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
534	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
535	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
536	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
537	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
538	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
539	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
540	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
541	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
542	C₅×C₈	—	2	2	no	—
543	C₅×C₈	—	2	2	no	—
544	C₅×C₈	—	2	2	no	—
545	C₅×C₈	—	2	2	no	—
546	C₅×C₈	—	2	2	no	—
547	C₅×C₈	—	2	2	no	—
548	C₅×C₈	—	2	2	no	—
549	C₅×C₈	—	2	2	no	—
550	C₂×#41	C₂³×C₅	1	1	yes	characteristic
551	C₂×#41	C₂³×C₅	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
553	C₂×M₁₆	C₂³×C₅	1	2	yes	—
554	C₂×M₁₆	C₂³×C₅	1	2	yes	—
555	C₂×M₁₆	C₂³×C₅	1	2	yes	—
556	C₂×M₁₆	C₂³×C₅	1	2	yes	—
557	C₂×M₁₆	C₂³×C₅	1	2	yes	—
558	C₂×M₁₆	C₂³×C₅	1	2	yes	—
559	C₂²×C₈	C₂³×C₅	1	2	yes	—
560	C₂²×C₈	C₂³×C₅	1	2	yes	—
561	C₂²×C₈	C₂³×C₅	1	2	yes	—
562	C₂²×C₈	C₂³×C₅	1	2	yes	—
563	C₂²×C₈	C₂³×C₅	1	2	yes	—
564	C₂²×C₈	C₂³×C₅	1	2	yes	—
565	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
566	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
567	#127	C₂×C₄×C₅	1	1	yes	characteristic
568	#126	C₂×C₄×C₅	1	2	yes	—
569	#126	C₂×C₄×C₅	1	2	yes	—
570	#126	C₂×C₄×C₅	1	2	yes	—
571	#126	C₂×C₄×C₅	1	2	yes	—
572	#126	C₂×C₄×C₅	1	2	yes	—
573	#126	C₂×C₄×C₅	1	2	yes	—
574	#126	C₂×C₄×C₅	1	2	yes	—
575	#126	C₂×C₄×C₅	1	2	yes	—
576	#125	C₂×C₄×C₅	1	2	yes	—
577	#125	C₂×C₄×C₅	1	2	yes	—
578	#125	C₂×C₄×C₅	1	2	yes	—
579	#125	C₂×C₄×C₅	1	2	yes	—
580	#125	C₂×C₄×C₅	1	2	yes	—
581	#124	C₂×C₄×C₅	1	2	yes	—
582	#124	C₂×C₄×C₅	1	2	yes	—
583	#124	C₂×C₄×C₅	1	2	yes	—
584	#124	C₂×C₄×C₅	1	2	yes	—
585	#124	C₂×C₄×C₅	1	1	yes	characteristic
586	#124	C₂×C₄×C₅	1	1	yes	characteristic
587	#123	C₂×C₄×C₅	1	1	yes	characteristic
588	#123	C₂×C₄×C₅	1	1	yes	characteristic
589	#123	C₂×C₄×C₅	1	2	yes	—
590	#123	C₂×C₄×C₅	1	2	yes	—
591	#123	C₂×C₄×C₅	1	2	yes	—
592	#123	C₂×C₄×C₅	1	2	yes	—
593	#123	C₂×C₄×C₅	1	2	yes	—
594	#123	C₂×C₄×C₅	1	2	yes	—
595	#123	C₂×C₄×C₅	1	2	yes	—
596	#123	C₂×C₄×C₅	1	2	yes	—
597	#123	C₂×C₄×C₅	1	2	yes	—
598	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
599	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
600	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
601	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
602	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
603	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
604	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
605	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
606	#121	C₂×C₄×C₅	1	2	yes	—
607	#121	C₂×C₄×C₅	1	2	yes	—
608	#121	C₂×C₄×C₅	1	2	yes	—
609	#121	C₂×C₄×C₅	1	2	yes	—
610	#121	C₂×C₄×C₅	1	2	yes	—
611	#121	C₂×C₄×C₅	1	2	yes	—
612	#121	C₂×C₄×C₅	1	2	yes	—
613	#121	C₂×C₄×C₅	1	2	yes	—
614	#120	C₂×C₄×C₅	1	1	yes	characteristic
615	#120	C₂×C₄×C₅	1	1	yes	characteristic
616	#120	C₂×C₄×C₅	1	2	yes	—
617	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
618	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
619	C₄×Q₈	C₂³×C₅	1	2	yes	—
620	C₄×Q₈	C₂³×C₅	1	2	yes	—
621	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
622	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
623	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
624	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
625	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
626	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
627	C₄×D₄	C₂³×C₅	1	2	yes	—
628	C₄×D₄	C₂³×C₅	1	2	yes	—
629	C₄×D₄	C₂³×C₅	1	2	yes	—
630	C₄×D₄	C₂³×C₅	1	2	yes	—
631	C₄×D₄	C₂³×C₅	1	2	yes	—
632	C₄×D₄	C₂³×C₅	1	2	yes	—
633	#117	C₂×C₄×C₅	1	2	yes	—
634	#117	C₂×C₄×C₅	1	2	yes	—
635	#117	C₂³×C₅	1	2	yes	—
636	#117	C₂³×C₅	1	2	yes	—
637	#117	C₂³×C₅	1	1	yes	characteristic
638	#117	C₂³×C₅	1	1	yes	characteristic
639	#117	C₂³×C₅	1	2	yes	—
640	#117	C₂³×C₅	1	1	yes	characteristic
641	#117	C₂³×C₅	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
644	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₅	1	2	yes	—
649	C₄⋊C₈	C₂³×C₅	1	2	yes	—
650	C₄⋊C₈	C₂³×C₅	1	2	yes	—
651	C₄⋊C₈	C₂³×C₅	1	2	yes	—
652	C₄⋊C₈	C₂³×C₅	1	2	yes	—
653	C₄⋊C₈	C₂³×C₅	1	2	yes	—
654	C₄⋊C₈	C₂³×C₅	1	2	yes	—
655	C₄⋊C₈	C₂³×C₅	1	2	yes	—
656	C₄⋊C₈	C₂³×C₅	1	2	yes	—
657	C₄⋊C₈	C₂³×C₅	1	2	yes	—
658	C₄⋊C₈	C₂³×C₅	1	2	yes	—
659	C₄⋊C₈	C₂³×C₅	1	2	yes	—
660	C₄⋊C₈	C₂³×C₅	1	2	yes	—
661	C₄⋊C₈	C₂³×C₅	1	2	yes	—
662	C₄⋊C₈	C₂³×C₅	1	2	yes	—
663	C₄⋊C₈	C₂³×C₅	1	2	yes	—
664	C₄⋊C₈	C₂³×C₅	1	2	yes	—
665	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
666	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
667	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
668	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
669	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
670	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
671	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
672	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
673	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
674	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
678	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
679	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
680	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
681	#97	C₂³×C₅	1	2	yes	—
682	#97	C₂³×C₅	1	1	yes	characteristic
683	#97	C₂³×C₅	1	1	yes	characteristic
684	#97	C₂³×C₅	1	2	yes	—
685	#97	C₂³×C₅	1	1	yes	characteristic
686	#97	C₂³×C₅	1	1	yes	characteristic
687	#97	C₂³×C₅	1	2	yes	—
688	#97	C₂³×C₅	1	2	yes	—
689	#97	C₂³×C₅	1	2	yes	—
690	#97	C₂³×C₅	1	2	yes	—
691	C₄×C₈	C₂³×C₅	1	2	yes	—
692	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
693	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
694	C₄×C₈	C₂³×C₅	1	2	yes	—
695	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
696	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
697	C₄×C₈	C₂³×C₅	1	2	yes	—
698	C₄×C₈	C₂³×C₅	1	2	yes	—
699	C₄×C₈	C₂³×C₅	1	2	yes	—
700	C₄×C₈	C₂³×C₅	1	2	yes	—
701	C₂²×C₅	—	2	1	no	—
702	C₂²×C₅	—	2	2	no	—
703	C₂²×C₅	—	2	2	no	—
704	C₂²×C₅	—	2	1	no	—
705	C₂²×C₅	—	2	1	no	—
706	C₂²×C₅	—	2	2	no	—
707	C₂²×C₅	—	2	2	no	—
708	C₂²×C₅	—	2	2	no	—
709	C₂²×C₅	—	2	2	no	—
710	C₂²×C₅	—	2	2	no	—
711	C₂²×C₅	—	2	2	no	—
712	C₂²×C₅	—	2	2	no	—
713	C₂²×C₅	—	8	2	no	—
714	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
715	C₄×C₅	—	2	2	no	—
716	C₄×C₅	—	2	1	no	—
717	C₄×C₅	—	2	2	no	—
718	C₄×C₅	—	2	1	no	—
719	C₄×C₅	—	2	1	no	—
720	C₄×C₅	—	2	2	no	—
721	C₄×C₅	—	2	2	no	—
722	C₄×C₅	—	2	2	no	—
723	C₄×C₅	—	2	2	no	—
724	C₄×C₅	—	2	2	no	—
725	C₄×C₅	—	2	2	no	—
726	C₄×C₅	—	2	2	no	—
727	C₄×C₅	—	2	2	no	—
728	C₄×C₅	#585	1	2	yes	—
729	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
730	#41	—	4	2	no	—
731	#41	—	4	2	no	—
732	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
733	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
734	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
735	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
736	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
737	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
738	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
739	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
740	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
741	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
742	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
743	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
744	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
745	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
746	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
749	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
750	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
751	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
752	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
753	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
754	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
755	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
761	M₁₆	—	4	2	no	—
762	M₁₆	—	4	2	no	—
763	M₁₆	—	4	2	no	—
764	M₁₆	—	4	2	no	—
765	M₁₆	—	4	2	no	—
766	M₁₆	—	4	2	no	—
767	C₂×C₈	—	4	2	no	—
768	C₂×C₈	—	4	2	no	—
769	C₂×C₈	—	4	2	no	—
770	C₂×C₈	—	4	2	no	—
771	C₂×C₈	—	4	2	no	—
772	C₂×C₈	—	4	2	no	—
773	C₂×C₈	C₂⁴×C₅	1	2	yes	—
774	C₂×C₈	C₂⁴×C₅	1	2	yes	—
775	C₂×C₈	C₂⁴×C₅	1	2	yes	—
776	C₂×C₈	C₂⁴×C₅	1	2	yes	—
777	C₂×C₈	C₂⁴×C₅	1	2	yes	—
778	C₂×C₈	C₂⁴×C₅	1	2	yes	—
779	C₂×C₈	C₂⁴×C₅	1	2	yes	—
780	C₂×C₈	C₂⁴×C₅	1	2	yes	—
781	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
782	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
783	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
784	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
785	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
786	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
787	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
788	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
789	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
790	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
791	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
792	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
793	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
794	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
795	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
796	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
797	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
798	C₄⋊C₄	C₂²×C₄×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	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
804	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
805	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
806	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
807	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
808	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
811	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
812	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
813	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
814	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
815	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
816	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
817	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
818	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
819	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
820	C₂²⋊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	C₄²	C₂²×C₄×C₅	1	2	yes	—
827	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
828	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
829	C₄²	C₂²×C₄×C₅	1	2	yes	—
830	C₄²	C₂²×C₄×C₅	1	2	yes	—
831	C₄²	C₂²×C₄×C₅	1	2	yes	—
832	C₄²	C₂²×C₄×C₅	1	2	yes	—
833	C₄²	C₂⁴×C₅	1	1	yes	characteristic
834	C₄²	C₂⁴×C₅	1	2	yes	—
835	C₄²	C₂⁴×C₅	1	1	yes	characteristic
836	C₄²	C₂⁴×C₅	1	1	yes	characteristic
837	C₄²	C₂⁴×C₅	1	2	yes	—
838	C₄²	C₂⁴×C₅	1	1	yes	characteristic
839	C₂×C₅	—	4	2	no	—
840	C₂×C₅	—	4	1	no	—
841	C₂×C₅	—	4	1	no	—
842	C₂×C₅	—	4	1	no	—
843	C₂×C₅	—	4	2	no	—
844	C₂×C₅	#3428	1	1	yes	characteristic
845	C₂×C₅	#3573	1	2	yes	—
846	C₂³	—	4	1	no	—
847	C₂³	—	4	2	no	—
848	C₂³	C₂³×C₄×C₅	1	2	yes	—
849	C₂³	C₂³×C₄×C₅	1	2	yes	—
850	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
851	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
852	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
853	Q₈	—	4	1	no	—
854	Q₈	—	4	1	no	—
855	Q₈	—	4	2	no	—
856	Q₈	—	4	2	no	—
857	D₄	—	4	1	no	—
858	D₄	—	4	1	no	—
859	D₄	—	4	2	no	—
860	D₄	—	4	1	no	—
861	D₄	—	4	1	no	—
862	D₄	—	4	2	no	—
863	D₄	—	4	2	no	—
864	D₄	—	4	2	no	—
865	D₄	—	4	2	no	—
866	D₄	—	4	2	no	—
867	D₄	—	4	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	2	no	—
878	C₂×C₄	—	4	2	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	2	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	4	2	no	—
883	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
884	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
885	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
886	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
887	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
888	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
889	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
890	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
891	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
892	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
893	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
894	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
895	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
896	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
897	C₈	—	2	2	no	—
898	C₈	—	2	2	no	—
899	C₈	—	2	2	no	—
900	C₈	—	2	2	no	—
901	C₈	—	2	2	no	—
902	C₈	—	2	2	no	—
903	C₈	—	2	2	no	—
904	C₈	—	2	2	no	—
905	C₅	#60297	1	1	yes	characteristic, direct product factor, Sylow
906	C₂²	—	2	1	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	8	2	no	—
919	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
920	C₄	—	2	1	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	2	2	no	—
928	C₄	—	2	2	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	C₅×#585	1	2	yes	—
934	C₂	—	4	1	no	—
935	C₂	—	4	2	no	—
936	C₂	—	4	2	no	—
937	C₂	—	4	1	no	—
938	C₂	—	4	1	no	—
939	C₂	C₅×#3428	1	1	yes	characteristic
940	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×#2987	C₂	semidirect
7. C₅×#2986	C₂	semidirect
8. C₅×#2981	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
81. C₅×#433	C₂²	semidirect
82. C₅×#433	C₂²	semidirect
83. C₅×#433	C₂²	semidirect
84. C₅×#433	C₂²	semidirect
85. C₅×#433	C₂²	semidirect
86. C₅×#433	C₂²	semidirect
89. C₅×#432	C₂²	semidirect
90. C₅×#432	C₂²	semidirect
93. C₅×#431	C₂²	semidirect
94. C₅×#431	C₂²	semidirect
97. C₅×#424	C₂²	semidirect
98. C₅×#424	C₂²	semidirect
99. C₅×#423	C₂²	semidirect
100. 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. #60297	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. #2987	C₂×C₅	semidirect
273. #2986	C₂×C₅	semidirect
274. #2981	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
415. #446	C₂²×C₅	semidirect
416. #446	C₂²×C₅	semidirect
417. #446	C₂²×C₅	semidirect
418. #446	C₂²×C₅	semidirect
419. #446	C₂²×C₅	semidirect
420. #446	C₂²×C₅	semidirect
421. C₈×Q₈	C₂²×C₅	semidirect
422. C₈×Q₈	C₂²×C₅	semidirect
427. #436	C₂²×C₅	semidirect
428. #436	C₂²×C₅	semidirect
437. #435	C₂²×C₅	semidirect
438. #435	C₂²×C₅	semidirect
439. #435	C₂²×C₅	semidirect
440. #435	C₂²×C₅	semidirect
445. C₈×D₄	C₂²×C₅	semidirect
446. C₈×D₄	C₂²×C₅	semidirect
457. #433	C₂²×C₅	semidirect
458. #433	C₂²×C₅	semidirect
459. #433	C₂²×C₅	semidirect
460. #433	C₂²×C₅	semidirect
461. #433	C₂²×C₅	semidirect
462. #433	C₂²×C₅	semidirect
465. #432	C₂²×C₅	semidirect
466. #432	C₂²×C₅	semidirect
469. #431	C₂²×C₅	semidirect
470. #431	C₂²×C₅	semidirect
473. #424	C₂²×C₅	semidirect
474. #424	C₂²×C₅	semidirect
475. #423	C₂²×C₅	semidirect
476. C₂×C₄⋊C₈	C₂²×C₅	semidirect
485. #405	C₂²×C₅	semidirect
486. #405	C₂²×C₅	semidirect
487. C₄×M₁₆	C₂²×C₅	semidirect
488. C₄×M₁₆	C₂²×C₅	semidirect
489. C₂×#97	C₂²×C₅	semidirect
490. C₂×C₄×C₈	C₂²×C₅	semidirect
905. C₅	#60297	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×#2987	2
C₅×#2986	2
C₅×#2981	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
#60297	5

Subgroups — C5×#60297 #11983017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60297 #11983017