Subgroups — C₅×#60596 #11983316

Order 1280.

2130 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3124	C₂	1	4	yes	maximal, complemented
4	C₅×#3118	C₂	1	4	yes	maximal, complemented
5	C₅×#3115	C₂	1	2	yes	maximal, complemented
6	C₅×#3110	C₂	1	2	yes	maximal, complemented
7	C₅×#3107	C₂	1	2	yes	maximal, complemented
8	C₅×#3100	C₂	1	2	yes	maximal, complemented
9	C₅×#3098	C₂	1	2	yes	maximal, complemented
10	C₅×#3079	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#3012	C₂	1	2	yes	maximal, complemented
15	C₅×#2951	C₂	1	2	yes	maximal, complemented
16	C₅×#2946	C₂	1	2	yes	maximal, complemented
17	C₅×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₅×#135	C₂²	1	2	yes	—
21	C₅×#556	—	2	1	no	—
22	C₅×#555	—	2	1	no	—
23	C₅×#554	—	2	1	no	—
24	C₅×#553	—	2	2	no	—
25	C₅×#548	—	2	2	no	—
26	C₅×#547	—	2	1	no	—
27	C₅×#542	C₂²	1	4	yes	complemented
28	C₅×#537	C₂²	1	2	yes	—
29	C₅×#533	C₂²	1	2	yes	complemented
30	C₅×#532	C₂²	1	1	yes	characteristic, complemented
31	C₅×#532	C₂²	1	2	yes	complemented
32	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₅×#520	—	2	1	no	—
34	C₅×#520	C₂²	1	2	yes	—
35	C₅×#520	C₂²	1	1	yes	characteristic
36	C₅×#520	C₂²	1	1	yes	characteristic
37	C₅×#520	C₂²	1	2	yes	complemented
38	C₅×#518	—	2	2	no	—
39	C₅×#518	—	2	1	no	—
40	C₅×#518	C₂²	1	2	yes	—
41	C₅×#518	C₂²	1	1	yes	characteristic
42	C₄×C₅×#41	—	2	1	no	—
43	C₄×C₅×#41	C₂²	1	1	yes	characteristic
44	C₄×C₅×#41	C₂²	1	2	yes	—
45	C₄×C₅×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₅×D₄	—	2	1	no	—
47	C₂×C₄×C₅×D₄	—	2	2	no	—
48	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
50	C₅×#485	C₂²	1	4	yes	complemented
51	C₅×#484	C₂²	1	4	yes	complemented
52	C₅×#482	C₂²	1	4	yes	complemented
53	C₅×#480	C₂²	1	4	yes	complemented
54	C₅×#477	C₂²	1	2	yes	complemented
55	C₅×#476	C₂²	1	2	yes	complemented
56	C₅×#475	C₂²	1	2	yes	complemented
57	C₅×#474	C₂²	1	2	yes	complemented
58	C₅×#474	C₂²	1	2	yes	complemented
59	C₅×#474	C₂²	1	4	yes	complemented
60	C₅×#474	C₂²	1	2	yes	complemented
61	C₅×#464	C₂²	1	2	yes	complemented
62	C₅×#463	C₂²	1	2	yes	complemented
63	C₅×#463	C₂²	1	4	yes	complemented
64	C₅×#462	C₂²	1	1	yes	characteristic, complemented
65	C₅×#461	C₂²	1	1	yes	characteristic, complemented
66	C₅×#461	C₂²	1	2	yes	complemented
67	C₅×#460	C₂²	1	1	yes	characteristic, complemented
68	C₅×#459	C₂²	1	1	yes	characteristic, complemented
69	C₅×#459	C₂²	1	2	yes	complemented
70	C₅×#452	C₂²	1	4	yes	—
71	C₅×#450	C₂²	1	4	yes	—
72	C₅×#449	C₂²	1	4	yes	—
73	C₅×#447	C₂²	1	4	yes	—
74	C₅×#442	C₂²	1	4	yes	complemented
75	C₅×#440	C₂²	1	4	yes	complemented
76	C₅×#440	C₂²	1	4	yes	complemented
77	C₅×#440	C₂²	1	4	yes	complemented
78	C₄×C₅×Q₁₆	C₂²	1	4	yes	complemented
79	C₄×C₅×SD₁₆	C₂²	1	4	yes	complemented
80	C₄×C₅×D₈	C₂²	1	4	yes	complemented
81	C₄×C₅×D₈	C₂²	1	4	yes	complemented
82	C₅×#433	C₂²	1	4	yes	complemented
83	C₅×#432	C₂²	1	2	yes	complemented
84	C₅×#431	C₂²	1	2	yes	complemented
85	C₅×#428	C₂²	1	2	yes	complemented
86	C₂×C₅×#107	C₂²	1	2	yes	complemented
87	C₅×#423	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
89	C₅×#417	C₂²	1	2	yes	—
90	C₅×#417	C₂²	1	2	yes	complemented
91	C₅×#416	C₂²	1	2	yes	complemented
92	C₂×C₅×#102	C₂²	1	2	yes	—
93	C₅×#408	C₂²	1	2	yes	—
94	C₅×#405	C₂²	1	2	yes	complemented
95	#60596	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₅×H(5,𝔽₂)	—	2	4	no	—
97	C₅×H(5,𝔽₂)	—	2	4	no	—
98	C₂×C₅×#41	—	2	1	no	—
99	C₂×C₅×#41	—	2	2	no	—
100	C₂×C₅×#41	C₂³	1	2	yes	—
101	C₂×C₅×#41	C₂³	1	2	yes	—
102	C₂×C₅×#41	C₂³	1	1	yes	characteristic
103	C₂×C₅×#41	C₂³	1	1	yes	characteristic
104	C₂²×C₅×Q₈	—	2	1	no	—
105	C₂²×C₅×D₄	—	2	2	no	—
106	C₂²×C₅×D₄	—	2	1	no	—
107	C₂²×C₅×D₄	C₂³	1	2	yes	—
108	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₅	—	2	1	no	—
110	C₂³×C₄×C₅	—	2	2	no	—
111	C₅×AGL(1,ℤ/8)	—	2	8	no	—
112	C₅×#135	—	2	8	no	—
113	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
114	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₅×SD₁₆	C₂³	1	2	yes	—
116	C₂×C₅×SD₁₆	C₂³	1	2	yes	—
117	C₂×C₅×D₈	C₂³	1	2	yes	—
118	C₂×C₅×D₈	C₂³	1	4	yes	—
119	C₂×C₅×M₁₆	C₂³	1	2	yes	—
120	C₂²×C₅×C₈	C₂³	1	2	yes	—
121	C₅×C₄⋊Q₈	—	2	1	no	—
122	C₅×C₄⋊Q₈	—	2	1	no	—
123	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
125	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₅×#127	C₂³	1	1	yes	characteristic
127	C₅×#126	—	2	4	no	—
128	C₅×#125	—	2	2	no	—
129	C₅×#124	—	2	4	no	—
130	C₅×#124	—	2	2	no	—
131	C₅×#124	C₂³	1	2	yes	—
132	C₅×#123	—	2	4	no	—
133	C₅×C₂²⋊Q₈	—	2	2	no	—
134	C₅×C₂²⋊Q₈	—	2	2	no	—
135	C₅×C₂²⋊Q₈	—	2	4	no	—
136	C₅×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₅×#121	—	2	2	no	—
138	C₅×#121	—	2	4	no	—
139	C₅×#121	—	2	1	no	—
140	C₅×#121	—	2	1	no	—
141	C₅×#121	—	2	2	no	—
142	C₅×#121	C₂³	1	4	yes	—
143	C₄×C₅×Q₈	—	2	1	no	—
144	C₄×C₅×Q₈	—	2	2	no	—
145	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
146	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
147	C₄×C₅×Q₈	C₂³	1	4	yes	—
148	C₄×C₅×Q₈	C₂³	1	2	yes	—
149	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
150	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
151	C₄×C₅×D₄	—	2	2	no	—
152	C₄×C₅×D₄	—	2	1	no	—
153	C₄×C₅×D₄	—	2	1	no	—
154	C₄×C₅×D₄	—	2	2	no	—
155	C₄×C₅×D₄	—	2	1	no	—
156	C₄×C₅×D₄	—	2	2	no	—
157	C₄×C₅×D₄	—	2	1	no	—
158	C₄×C₅×D₄	—	2	2	no	—
159	C₄×C₅×D₄	—	2	1	no	—
160	C₄×C₅×D₄	—	2	2	no	—
161	C₄×C₅×D₄	—	2	2	no	—
162	C₄×C₅×D₄	—	2	2	no	—
163	C₄×C₅×D₄	—	2	2	no	—
164	C₄×C₅×D₄	—	2	4	no	—
165	C₄×C₅×D₄	—	2	1	no	—
166	C₄×C₅×D₄	—	2	2	no	—
167	C₄×C₅×D₄	—	2	2	no	—
168	C₄×C₅×D₄	—	2	1	no	—
169	C₄×C₅×D₄	—	2	1	no	—
170	C₄×C₅×D₄	—	2	2	no	—
171	C₄×C₅×D₄	—	2	1	no	—
172	C₄×C₅×D₄	D₄	1	1	yes	characteristic
173	C₄×C₅×D₄	D₄	1	2	yes	—
174	C₄×C₅×D₄	D₄	1	2	yes	—
175	C₄×C₅×D₄	D₄	1	1	yes	characteristic
176	C₄×C₅×D₄	C₂³	1	2	yes	—
177	C₄×C₅×D₄	C₂³	1	2	yes	—
178	C₄×C₅×D₄	C₂³	1	4	yes	—
179	C₄×C₅×D₄	C₂³	1	2	yes	—
180	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
181	C₄×C₅×D₄	C₂³	1	2	yes	—
182	C₄×C₅×D₄	C₂³	1	2	yes	—
183	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
184	C₅×#117	—	2	2	no	—
185	C₅×#117	—	2	1	no	—
186	C₅×#117	—	2	2	no	—
187	C₅×#117	—	2	2	no	—
188	C₅×#117	—	2	2	no	—
189	C₅×#117	—	2	1	no	—
190	C₅×#117	C₂³	1	1	yes	characteristic
191	C₅×#117	C₂³	1	2	yes	—
192	C₅×#117	C₂³	1	1	yes	characteristic
193	C₅×#117	C₂³	1	2	yes	—
194	C₂×C₅×C₄⋊C₄	—	2	1	no	—
195	C₂×C₅×C₄⋊C₄	—	2	1	no	—
196	C₂×C₅×C₄⋊C₄	—	2	2	no	—
197	C₂×C₅×C₄⋊C₄	—	2	2	no	—
198	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
202	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
203	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₄²×C₅	—	2	1	no	—
207	C₂×C₄²×C₅	—	2	2	no	—
208	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₅	C₂³	1	2	yes	—
210	C₅×#107	C₂³	1	4	yes	—
211	C₅×#107	C₂³	1	4	yes	—
212	C₅×#107	C₂³	1	4	yes	—
213	C₅×#106	C₂³	1	4	yes	—
214	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	2	yes	—
220	C₅×#103	C₂³	1	2	yes	—
221	C₅×#103	C₂³	1	4	yes	—
222	C₅×#103	C₂³	1	4	yes	—
223	C₅×#102	C₂³	1	4	yes	—
224	C₅×#102	C₂³	1	4	yes	—
225	C₅×#102	C₂³	1	2	yes	—
226	C₅×#102	C₂³	1	2	yes	—
227	C₅×#102	C₂³	1	4	yes	—
228	C₅×#102	C₂³	1	4	yes	—
229	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₅×#97	C₂³	1	4	yes	—
232	C₄×C₅×C₈	C₂³	1	4	yes	—
233	#3511	C₂×C₅	1	1	yes	characteristic, complemented
234	C₄×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic, complemented
235	#3124	C₂×C₅	1	4	yes	complemented
236	#3118	C₂×C₅	1	4	yes	complemented
237	#3115	C₂×C₅	1	2	yes	complemented
238	#3110	C₂×C₅	1	2	yes	complemented
239	#3107	C₂×C₅	1	2	yes	complemented
240	#3100	C₂×C₅	1	2	yes	complemented
241	#3098	C₂×C₅	1	2	yes	complemented
242	#3079	C₂×C₅	1	1	yes	characteristic, complemented
243	C₂×#474	C₂×C₅	1	1	yes	characteristic, complemented
244	#3036	C₂×C₅	1	1	yes	characteristic, complemented
245	#3035	C₂×C₅	1	1	yes	characteristic, complemented
246	#3012	C₂×C₅	1	2	yes	complemented
247	#2951	C₂×C₅	1	2	yes	complemented
248	#2946	C₂×C₅	1	2	yes	complemented
249	#2925	C₂×C₅	1	1	yes	characteristic, complemented
250	C₂⁴×C₅	—	2	2	no	—
251	C₂⁴×C₅	—	2	1	no	—
252	C₅×#41	—	2	8	no	—
253	C₅×#41	—	2	4	no	—
254	C₅×#41	—	2	4	no	—
255	C₅×#41	—	2	2	no	—
256	C₅×#41	—	2	2	no	—
257	C₅×#41	—	2	2	no	—
258	C₅×#41	—	2	4	no	—
259	C₅×#41	—	2	4	no	—
260	C₅×#41	—	8	4	no	—
261	C₅×#41	#41	1	4	yes	complemented
262	C₂×C₅×Q₈	—	2	2	no	—
263	C₂×C₅×Q₈	—	2	2	no	—
264	C₂×C₅×Q₈	—	8	2	no	—
265	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
266	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
267	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
268	C₂×C₅×D₄	—	2	16	no	—
269	C₂×C₅×D₄	—	2	8	no	—
270	C₂×C₅×D₄	—	2	2	no	—
271	C₂×C₅×D₄	—	2	1	no	—
272	C₂×C₅×D₄	—	2	4	no	—
273	C₂×C₅×D₄	—	2	4	no	—
274	C₂×C₅×D₄	—	2	2	no	—
275	C₂×C₅×D₄	—	2	4	no	—
276	C₂×C₅×D₄	—	2	2	no	—
277	C₂×C₅×D₄	—	2	1	no	—
278	C₂×C₅×D₄	—	2	1	no	—
279	C₂×C₅×D₄	—	2	1	no	—
280	C₂×C₅×D₄	—	2	2	no	—
281	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
282	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
283	C₂×C₅×D₄	#41	1	4	yes	complemented
284	C₂×C₅×D₄	C₂⁴	1	2	yes	—
285	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
286	C₂×C₅×D₄	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₅	—	2	2	no	—
288	C₂²×C₄×C₅	—	2	1	no	—
289	C₂²×C₄×C₅	—	2	2	no	—
290	C₂²×C₄×C₅	—	2	1	no	—
291	C₂²×C₄×C₅	—	2	2	no	—
292	C₂²×C₄×C₅	—	2	1	no	—
293	C₂²×C₄×C₅	—	2	2	no	—
294	C₂²×C₄×C₅	—	2	2	no	—
295	C₂²×C₄×C₅	—	2	2	no	—
296	C₂²×C₄×C₅	—	2	1	no	—
297	C₂²×C₄×C₅	—	2	2	no	—
298	C₂²×C₄×C₅	—	2	2	no	—
299	C₂²×C₄×C₅	—	2	2	no	—
300	C₂²×C₄×C₅	—	2	4	no	—
301	C₂²×C₄×C₅	—	8	2	no	—
302	C₂²×C₄×C₅	—	8	4	no	—
303	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
305	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
307	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
309	C₅×Q₁₆	—	2	4	no	—
310	C₅×SD₁₆	—	2	4	no	—
311	C₅×SD₁₆	—	2	4	no	—
312	C₅×SD₁₆	—	2	8	no	—
313	C₅×D₈	—	2	4	no	—
314	C₅×D₈	—	2	8	no	—
315	C₅×M₁₆	—	2	4	no	—
316	C₂×C₅×C₈	—	2	4	no	—
317	C₂×C₅×C₈	C₂⁴	1	2	yes	—
318	C₂×C₅×C₈	C₂⁴	1	2	yes	—
319	C₂×C₅×C₈	C₂⁴	1	4	yes	—
320	C₅×C₄⋊C₄	—	2	1	no	—
321	C₅×C₄⋊C₄	—	2	2	no	—
322	C₅×C₄⋊C₄	—	2	2	no	—
323	C₅×C₄⋊C₄	—	2	1	no	—
324	C₅×C₄⋊C₄	—	2	2	no	—
325	C₅×C₄⋊C₄	—	2	2	no	—
326	C₅×C₄⋊C₄	—	2	4	no	—
327	C₅×C₄⋊C₄	—	2	2	no	—
328	C₅×C₄⋊C₄	—	2	1	no	—
329	C₅×C₄⋊C₄	—	2	1	no	—
330	C₅×C₄⋊C₄	—	2	1	no	—
331	C₅×C₄⋊C₄	—	2	4	no	—
332	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
333	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
334	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
335	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
336	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
337	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
338	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
339	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
340	C₅×C₂²⋊C₄	—	2	2	no	—
341	C₅×C₂²⋊C₄	—	2	1	no	—
342	C₅×C₂²⋊C₄	—	2	4	no	—
343	C₅×C₂²⋊C₄	—	2	1	no	—
344	C₅×C₂²⋊C₄	—	2	2	no	—
345	C₅×C₂²⋊C₄	—	2	2	no	—
346	C₅×C₂²⋊C₄	—	2	2	no	—
347	C₅×C₂²⋊C₄	—	2	2	no	—
348	C₅×C₂²⋊C₄	—	2	2	no	—
349	C₅×C₂²⋊C₄	—	2	1	no	—
350	C₅×C₂²⋊C₄	—	2	4	no	—
351	C₅×C₂²⋊C₄	—	2	4	no	—
352	C₅×C₂²⋊C₄	—	2	2	no	—
353	C₅×C₂²⋊C₄	—	2	2	no	—
354	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
355	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
356	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
357	C₄²×C₅	—	2	1	no	—
358	C₄²×C₅	—	2	2	no	—
359	C₄²×C₅	—	2	1	no	—
360	C₄²×C₅	—	2	2	no	—
361	C₄²×C₅	—	2	1	no	—
362	C₄²×C₅	—	2	4	no	—
363	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
364	C₄²×C₅	C₂×D₄	1	2	yes	—
365	C₄²×C₅	C₂×D₄	1	2	yes	—
366	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
367	C₄²×C₅	C₂⁴	1	1	yes	characteristic
368	C₄²×C₅	C₂⁴	1	2	yes	—
369	C₄²×C₅	C₂⁴	1	1	yes	characteristic
370	C₂×H(5,𝔽₂)	C₂²×C₅	1	1	yes	characteristic
371	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	—
372	C₂×#135	C₂²×C₅	1	2	yes	—
373	#556	—	2	1	no	—
374	#555	—	2	1	no	—
375	#554	—	2	1	no	—
376	#553	—	2	2	no	—
377	#548	—	2	2	no	—
378	#547	—	2	1	no	—
379	#542	C₂²×C₅	1	4	yes	complemented
380	#537	C₂²×C₅	1	2	yes	—
381	#533	C₂²×C₅	1	2	yes	complemented
382	#532	C₂²×C₅	1	1	yes	characteristic, complemented
383	#532	C₂²×C₅	1	2	yes	complemented
384	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
385	#520	—	2	1	no	—
386	#520	C₂²×C₅	1	2	yes	—
387	#520	C₂²×C₅	1	1	yes	characteristic
388	#520	C₂²×C₅	1	1	yes	characteristic
389	#520	C₂²×C₅	1	2	yes	complemented
390	#518	—	2	2	no	—
391	#518	—	2	1	no	—
392	#518	C₂²×C₅	1	2	yes	—
393	#518	C₂²×C₅	1	1	yes	characteristic
394	C₄×#41	—	2	1	no	—
395	C₄×#41	C₂²×C₅	1	1	yes	characteristic
396	C₄×#41	C₂²×C₅	1	2	yes	—
397	C₄×#41	C₂²×C₅	1	1	yes	characteristic
398	C₂×C₄×D₄	—	2	1	no	—
399	C₂×C₄×D₄	—	2	2	no	—
400	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
401	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
402	#485	C₂²×C₅	1	4	yes	complemented
403	#484	C₂²×C₅	1	4	yes	complemented
404	#482	C₂²×C₅	1	4	yes	complemented
405	#480	C₂²×C₅	1	4	yes	complemented
406	#477	C₂²×C₅	1	2	yes	complemented
407	#476	C₂²×C₅	1	2	yes	complemented
408	#475	C₂²×C₅	1	2	yes	complemented
409	#474	C₂²×C₅	1	2	yes	complemented
410	#474	C₂²×C₅	1	2	yes	complemented
411	#474	C₂²×C₅	1	2	yes	complemented
412	#474	C₂²×C₅	1	4	yes	complemented
413	#464	C₂²×C₅	1	2	yes	complemented
414	#463	C₂²×C₅	1	2	yes	complemented
415	#463	C₂²×C₅	1	4	yes	complemented
416	#462	C₂²×C₅	1	1	yes	characteristic, complemented
417	#461	C₂²×C₅	1	2	yes	complemented
418	#461	C₂²×C₅	1	1	yes	characteristic, complemented
419	#460	C₂²×C₅	1	1	yes	characteristic, complemented
420	#459	C₂²×C₅	1	1	yes	characteristic, complemented
421	#459	C₂²×C₅	1	2	yes	complemented
422	#452	C₂²×C₅	1	4	yes	—
423	#450	C₂²×C₅	1	4	yes	—
424	#449	C₂²×C₅	1	4	yes	—
425	#447	C₂²×C₅	1	4	yes	—
426	#442	C₂²×C₅	1	4	yes	complemented
427	#440	C₂²×C₅	1	4	yes	complemented
428	#440	C₂²×C₅	1	4	yes	complemented
429	#440	C₂²×C₅	1	4	yes	complemented
430	C₄×Q₁₆	C₂²×C₅	1	4	yes	complemented
431	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
432	C₄×D₈	C₂²×C₅	1	4	yes	complemented
433	C₄×D₈	C₂²×C₅	1	4	yes	complemented
434	#433	C₂²×C₅	1	4	yes	complemented
435	#432	C₂²×C₅	1	2	yes	complemented
436	#431	C₂²×C₅	1	2	yes	complemented
437	#428	C₂²×C₅	1	2	yes	complemented
438	C₂×#107	C₂²×C₅	1	2	yes	complemented
439	#423	C₂²×C₅	1	1	yes	characteristic, complemented
440	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
441	#417	C₂²×C₅	1	2	yes	—
442	#417	C₂²×C₅	1	2	yes	complemented
443	#416	C₂²×C₅	1	2	yes	complemented
444	C₂×#102	C₂²×C₅	1	2	yes	—
445	#408	C₂²×C₅	1	2	yes	—
446	#405	C₂²×C₅	1	2	yes	complemented
447	C₂³×C₅	—	2	8	no	—
448	C₂³×C₅	—	2	2	no	—
449	C₂³×C₅	—	2	1	no	—
450	C₂³×C₅	—	2	4	no	—
451	C₂³×C₅	—	2	2	no	—
452	C₂³×C₅	—	8	1	no	—
453	C₂³×C₅	—	8	2	no	—
454	C₂³×C₅	—	8	1	no	—
455	C₂³×C₅	—	8	2	no	—
456	C₂³×C₅	C₂²×D₄	1	2	yes	—
457	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
458	C₅×Q₈	—	2	2	no	—
459	C₅×Q₈	—	2	1	no	—
460	C₅×Q₈	—	2	2	no	—
461	C₅×Q₈	—	2	2	no	—
462	C₅×Q₈	—	4	4	no	—
463	C₅×Q₈	—	8	2	no	—
464	C₅×Q₈	C₂×#41	1	2	yes	—
465	C₅×D₄	—	2	8	no	—
466	C₅×D₄	—	2	8	no	—
467	C₅×D₄	—	2	4	no	—
468	C₅×D₄	—	2	4	no	—
469	C₅×D₄	—	2	2	no	—
470	C₅×D₄	—	2	4	no	—
471	C₅×D₄	—	2	2	no	—
472	C₅×D₄	—	2	1	no	—
473	C₅×D₄	—	2	2	no	—
474	C₅×D₄	—	2	2	no	—
475	C₅×D₄	—	4	2	no	—
476	C₅×D₄	—	4	4	no	—
477	C₅×D₄	—	4	2	no	—
478	C₅×D₄	—	8	4	no	—
479	C₅×D₄	C₂×#41	1	2	yes	—
480	C₅×D₄	C₂×#41	1	4	yes	—
481	C₂×C₄×C₅	—	2	8	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	2	4	no	—
484	C₂×C₄×C₅	—	2	2	no	—
485	C₂×C₄×C₅	—	2	4	no	—
486	C₂×C₄×C₅	—	2	2	no	—
487	C₂×C₄×C₅	—	2	2	no	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	2	no	—
490	C₂×C₄×C₅	—	2	2	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	4	no	—
493	C₂×C₄×C₅	—	4	1	no	—
494	C₂×C₄×C₅	—	4	2	no	—
495	C₂×C₄×C₅	—	4	4	no	—
496	C₂×C₄×C₅	—	4	4	no	—
497	C₂×C₄×C₅	—	4	2	no	—
498	C₂×C₄×C₅	—	8	2	no	—
499	C₂×C₄×C₅	—	8	1	no	—
500	C₂×C₄×C₅	—	8	2	no	—
501	C₂×C₄×C₅	—	8	2	no	—
502	C₂×C₄×C₅	—	8	2	no	—
503	C₂×C₄×C₅	—	8	4	no	—
504	C₂×C₄×C₅	—	8	1	no	—
505	C₂×C₄×C₅	—	8	2	no	—
506	C₂×C₄×C₅	—	8	2	no	—
507	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₅	C₂×#41	1	2	yes	—
516	C₂×C₄×C₅	C₂×#41	1	2	yes	—
517	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
518	C₅×C₈	—	2	2	no	—
519	C₅×C₈	—	2	2	no	—
520	C₅×C₈	—	2	4	no	—
521	H(5,𝔽₂)	—	2	4	no	—
522	H(5,𝔽₂)	—	2	4	no	—
523	C₂×#41	—	2	1	no	—
524	C₂×#41	—	2	2	no	—
525	C₂×#41	C₂³×C₅	1	2	yes	—
526	C₂×#41	C₂³×C₅	1	2	yes	—
527	C₂×#41	C₂³×C₅	1	1	yes	characteristic
528	C₂×#41	C₂³×C₅	1	1	yes	characteristic
529	C₂²×Q₈	—	2	1	no	—
530	C₂²×D₄	—	2	2	no	—
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	C₂³×C₅	1	2	yes	—
533	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
534	C₂³×C₄	—	2	1	no	—
535	C₂³×C₄	—	2	2	no	—
536	AGL(1,ℤ/8)	—	2	8	no	—
537	#135	—	2	8	no	—
538	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
539	C₂×SD₁₆	C₂³×C₅	1	2	yes	—
540	C₂×SD₁₆	C₂³×C₅	1	2	yes	—
541	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
542	C₂×D₈	C₂³×C₅	1	2	yes	—
543	C₂×D₈	C₂³×C₅	1	4	yes	—
544	C₂×M₁₆	C₂³×C₅	1	2	yes	—
545	C₂²×C₈	C₂³×C₅	1	2	yes	—
546	C₄⋊Q₈	—	2	1	no	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
551	#127	C₂³×C₅	1	1	yes	characteristic
552	#126	—	2	4	no	—
553	#125	—	2	2	no	—
554	#124	—	2	4	no	—
555	#124	—	2	2	no	—
556	#124	C₂³×C₅	1	2	yes	—
557	#123	—	2	4	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂²⋊Q₈	C₂³×C₅	1	4	yes	—
562	#121	—	2	2	no	—
563	#121	—	2	4	no	—
564	#121	—	2	1	no	—
565	#121	—	2	1	no	—
566	#121	—	2	2	no	—
567	#121	C₂³×C₅	1	4	yes	—
568	C₄×Q₈	—	2	1	no	—
569	C₄×Q₈	—	2	2	no	—
570	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
571	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
572	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
573	C₄×Q₈	C₂³×C₅	1	2	yes	—
574	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
575	C₄×Q₈	C₂³×C₅	1	4	yes	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	1	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	4	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	C₅×D₄	1	1	yes	characteristic
598	C₄×D₄	C₅×D₄	1	2	yes	—
599	C₄×D₄	C₅×D₄	1	2	yes	—
600	C₄×D₄	C₅×D₄	1	1	yes	characteristic
601	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
602	C₄×D₄	C₂³×C₅	1	2	yes	—
603	C₄×D₄	C₂³×C₅	1	2	yes	—
604	C₄×D₄	C₂³×C₅	1	2	yes	—
605	C₄×D₄	C₂³×C₅	1	2	yes	—
606	C₄×D₄	C₂³×C₅	1	2	yes	—
607	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
608	C₄×D₄	C₂³×C₅	1	4	yes	—
609	#117	—	2	2	no	—
610	#117	—	2	1	no	—
611	#117	—	2	2	no	—
612	#117	—	2	2	no	—
613	#117	—	2	2	no	—
614	#117	—	2	1	no	—
615	#117	C₂³×C₅	1	1	yes	characteristic
616	#117	C₂³×C₅	1	2	yes	—
617	#117	C₂³×C₅	1	1	yes	characteristic
618	#117	C₂³×C₅	1	2	yes	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	2	no	—
622	C₂×C₄⋊C₄	—	2	2	no	—
623	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₂²⋊C₄	—	2	2	no	—
631	C₂×C₄²	—	2	1	no	—
632	C₂×C₄²	—	2	2	no	—
633	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₅	1	2	yes	—
635	#107	C₂³×C₅	1	4	yes	—
636	#107	C₂³×C₅	1	4	yes	—
637	#107	C₂³×C₅	1	4	yes	—
638	#106	C₂³×C₅	1	4	yes	—
639	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
640	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
641	C₄⋊C₈	C₂³×C₅	1	2	yes	—
642	C₄⋊C₈	C₂³×C₅	1	2	yes	—
643	C₄⋊C₈	C₂³×C₅	1	2	yes	—
644	#103	C₂³×C₅	1	2	yes	—
645	#103	C₂³×C₅	1	2	yes	—
646	#103	C₂³×C₅	1	4	yes	—
647	#103	C₂³×C₅	1	4	yes	—
648	#102	C₂³×C₅	1	4	yes	—
649	#102	C₂³×C₅	1	4	yes	—
650	#102	C₂³×C₅	1	2	yes	—
651	#102	C₂³×C₅	1	2	yes	—
652	#102	C₂³×C₅	1	4	yes	—
653	#102	C₂³×C₅	1	4	yes	—
654	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
655	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
656	#97	C₂³×C₅	1	4	yes	—
657	C₄×C₈	C₂³×C₅	1	4	yes	—
658	C₂²×C₅	—	2	1	no	—
659	C₂²×C₅	—	2	1	no	—
660	C₂²×C₅	—	2	2	no	—
661	C₂²×C₅	—	2	2	no	—
662	C₂²×C₅	—	2	4	no	—
663	C₂²×C₅	—	2	2	no	—
664	C₂²×C₅	—	2	2	no	—
665	C₂²×C₅	—	4	2	no	—
666	C₂²×C₅	—	4	1	no	—
667	C₂²×C₅	—	4	2	no	—
668	C₂²×C₅	—	4	1	no	—
669	C₂²×C₅	—	4	2	no	—
670	C₂²×C₅	—	4	2	no	—
671	C₂²×C₅	—	4	2	no	—
672	C₂²×C₅	—	8	4	no	—
673	C₂²×C₅	—	8	8	no	—
674	C₂²×C₅	#525	1	2	yes	—
675	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
676	C₄×C₅	—	2	1	no	—
677	C₄×C₅	—	2	2	no	—
678	C₄×C₅	—	2	1	no	—
679	C₄×C₅	—	2	2	no	—
680	C₄×C₅	—	2	2	no	—
681	C₄×C₅	—	2	2	no	—
682	C₄×C₅	—	2	1	no	—
683	C₄×C₅	—	4	1	no	—
684	C₄×C₅	—	4	2	no	—
685	C₄×C₅	—	4	1	no	—
686	C₄×C₅	—	4	2	no	—
687	C₄×C₅	—	4	4	no	—
688	C₄×C₅	#525	1	2	yes	—
689	C₄×C₅	#576	1	2	yes	—
690	C₄×C₅	C₂²×#41	1	1	yes	characteristic
691	C₄×C₅	C₂²×#41	1	1	yes	characteristic
692	C₂⁴	—	2	2	no	—
693	C₂⁴	—	2	1	no	—
694	#41	—	2	8	no	—
695	#41	—	2	4	no	—
696	#41	—	2	4	no	—
697	#41	—	2	2	no	—
698	#41	—	2	2	no	—
699	#41	—	2	2	no	—
700	#41	—	2	4	no	—
701	#41	—	2	4	no	—
702	#41	—	8	4	no	—
703	#41	C₅×#41	1	4	yes	complemented
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	2	2	no	—
706	C₂×Q₈	—	8	2	no	—
707	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
708	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
709	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
710	C₂×D₄	—	2	16	no	—
711	C₂×D₄	—	2	8	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
724	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
725	C₂×D₄	C₅×#41	1	4	yes	complemented
726	C₂×D₄	C₂⁴×C₅	1	2	yes	—
727	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
728	C₂×D₄	C₂⁴×C₅	1	2	yes	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	8	2	no	—
744	C₂²×C₄	—	8	4	no	—
745	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
746	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
747	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
748	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
751	Q₁₆	—	2	4	no	—
752	SD₁₆	—	2	4	no	—
753	SD₁₆	—	2	4	no	—
754	SD₁₆	—	2	8	no	—
755	D₈	—	2	4	no	—
756	D₈	—	2	8	no	—
757	M₁₆	—	2	4	no	—
758	C₂×C₈	—	2	4	no	—
759	C₂×C₈	C₂⁴×C₅	1	2	yes	—
760	C₂×C₈	C₂⁴×C₅	1	4	yes	—
761	C₂×C₈	C₂⁴×C₅	1	2	yes	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
775	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
776	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
777	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
778	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
779	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
780	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
781	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
797	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
798	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	1	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	1	no	—
804	C₄²	—	2	4	no	—
805	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
806	C₄²	C₂×C₅×D₄	1	2	yes	—
807	C₄²	C₂×C₅×D₄	1	2	yes	—
808	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
809	C₄²	C₂⁴×C₅	1	2	yes	—
810	C₄²	C₂⁴×C₅	1	1	yes	characteristic
811	C₄²	C₂⁴×C₅	1	1	yes	characteristic
812	C₂×C₅	—	2	2	no	—
813	C₂×C₅	—	4	2	no	—
814	C₂×C₅	—	4	4	no	—
815	C₂×C₅	—	4	2	no	—
816	C₂×C₅	—	8	2	no	—
817	C₂×C₅	C₂×#525	1	1	yes	characteristic
818	C₂×C₅	C₂×#576	1	1	yes	characteristic
819	C₂×C₅	#3586	1	1	yes	characteristic
820	C₂³	—	2	8	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	4	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	8	1	no	—
826	C₂³	—	8	2	no	—
827	C₂³	—	8	1	no	—
828	C₂³	—	8	2	no	—
829	C₂³	C₂²×C₅×D₄	1	2	yes	—
830	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
831	Q₈	—	2	2	no	—
832	Q₈	—	2	1	no	—
833	Q₈	—	2	2	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	4	4	no	—
836	Q₈	—	8	2	no	—
837	Q₈	C₂×C₅×#41	1	2	yes	—
838	D₄	—	2	8	no	—
839	D₄	—	2	8	no	—
840	D₄	—	2	4	no	—
841	D₄	—	2	4	no	—
842	D₄	—	2	2	no	—
843	D₄	—	2	4	no	—
844	D₄	—	2	2	no	—
845	D₄	—	2	1	no	—
846	D₄	—	2	2	no	—
847	D₄	—	2	2	no	—
848	D₄	—	4	2	no	—
849	D₄	—	4	4	no	—
850	D₄	—	4	2	no	—
851	D₄	—	8	4	no	—
852	D₄	C₂×C₅×#41	1	2	yes	—
853	D₄	C₂×C₅×#41	1	4	yes	—
854	C₂×C₄	—	2	8	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	4	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	4	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	4	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	8	2	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	—	8	2	no	—
874	C₂×C₄	—	8	4	no	—
875	C₂×C₄	—	8	2	no	—
876	C₂×C₄	—	8	1	no	—
877	C₂×C₄	—	8	1	no	—
878	C₂×C₄	—	8	2	no	—
879	C₂×C₄	—	8	2	no	—
880	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
881	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
882	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
883	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
884	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
885	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
886	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
887	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
888	C₂×C₄	C₂×C₅×#41	1	2	yes	—
889	C₂×C₄	C₂×C₅×#41	1	2	yes	—
890	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
891	C₈	—	2	2	no	—
892	C₈	—	2	2	no	—
893	C₈	—	2	4	no	—
894	C₅	#60596	1	1	yes	characteristic, direct product factor, Sylow
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	8	4	no	—
910	C₂²	—	8	8	no	—
911	C₂²	C₅×#525	1	2	yes	—
912	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	4	no	—
924	C₄	—	4	1	no	—
925	C₄	C₅×#525	1	2	yes	—
926	C₄	C₅×#576	1	2	yes	—
927	C₄	C₂²×C₅×#41	1	1	yes	characteristic
928	C₄	C₂²×C₅×#41	1	1	yes	characteristic
929	C₂	—	2	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	4	4	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₂×C₅×#525	1	1	yes	characteristic
935	C₂	C₂×C₅×#576	1	1	yes	characteristic
936	C₂	C₅×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3511	C₂	semidirect
2. C₄×C₅×H(5,𝔽₂)	C₂	semidirect
3. C₅×#3124	C₂	semidirect
4. C₅×#3118	C₂	semidirect
5. C₅×#3115	C₂	semidirect
6. C₅×#3110	C₂	semidirect
7. C₅×#3107	C₂	semidirect
8. C₅×#3100	C₂	semidirect
9. C₅×#3098	C₂	semidirect
10. C₅×#3079	C₂	semidirect
11. C₂×C₅×#474	C₂	semidirect
12. C₅×#3036	C₂	semidirect
13. C₅×#3035	C₂	semidirect
14. C₅×#3012	C₂	semidirect
15. C₅×#2951	C₂	semidirect
16. C₅×#2946	C₂	semidirect
17. C₅×#2925	C₂	semidirect
27. C₅×#542	C₂²	semidirect
29. C₅×#533	C₂²	semidirect
30. C₅×#532	C₂²	semidirect
31. C₅×#532	C₂²	semidirect
32. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
37. C₅×#520	C₂²	semidirect
50. C₅×#485	C₂²	semidirect
51. C₅×#484	C₂²	semidirect
52. C₅×#482	C₂²	semidirect
53. C₅×#480	C₂²	semidirect
54. C₅×#477	C₂²	semidirect
55. C₅×#476	C₂²	semidirect
56. C₅×#475	C₂²	semidirect
57. C₅×#474	C₂²	semidirect
58. C₅×#474	C₂²	semidirect
59. C₅×#474	C₂²	semidirect
60. C₅×#474	C₂²	semidirect
61. C₅×#464	C₂²	semidirect
62. C₅×#463	C₂²	semidirect
63. C₅×#463	C₂²	semidirect
64. C₅×#462	C₂²	semidirect
65. C₅×#461	C₂²	semidirect
66. C₅×#461	C₂²	semidirect
67. C₅×#460	C₂²	semidirect
68. C₅×#459	C₂²	semidirect
69. C₅×#459	C₂²	semidirect
74. C₅×#442	C₂²	semidirect
75. C₅×#440	C₂²	semidirect
76. C₅×#440	C₂²	semidirect
77. C₅×#440	C₂²	semidirect
78. C₄×C₅×Q₁₆	C₂²	semidirect
79. C₄×C₅×SD₁₆	C₂²	semidirect
80. C₄×C₅×D₈	C₂²	semidirect
81. C₄×C₅×D₈	C₂²	semidirect
82. C₅×#433	C₂²	semidirect
83. C₅×#432	C₂²	semidirect
84. C₅×#431	C₂²	semidirect
85. C₅×#428	C₂²	semidirect
86. C₂×C₅×#107	C₂²	semidirect
87. C₅×#423	C₂²	semidirect
88. C₂×C₅×C₄⋊C₈	C₂²	semidirect
90. C₅×#417	C₂²	semidirect
91. C₅×#416	C₂²	semidirect
94. C₅×#405	C₂²	semidirect
95. #60596	C₅	direct (N × H)
233. #3511	C₂×C₅	semidirect
234. C₄×H(5,𝔽₂)	C₂×C₅	semidirect
235. #3124	C₂×C₅	semidirect
236. #3118	C₂×C₅	semidirect
237. #3115	C₂×C₅	semidirect
238. #3110	C₂×C₅	semidirect
239. #3107	C₂×C₅	semidirect
240. #3100	C₂×C₅	semidirect
241. #3098	C₂×C₅	semidirect
242. #3079	C₂×C₅	semidirect
243. C₂×#474	C₂×C₅	semidirect
244. #3036	C₂×C₅	semidirect
245. #3035	C₂×C₅	semidirect
246. #3012	C₂×C₅	semidirect
247. #2951	C₂×C₅	semidirect
248. #2946	C₂×C₅	semidirect
249. #2925	C₂×C₅	semidirect
261. C₅×#41	#41	semidirect
283. C₂×C₅×D₄	#41	semidirect
379. #542	C₂²×C₅	semidirect
381. #533	C₂²×C₅	semidirect
382. #532	C₂²×C₅	semidirect
383. #532	C₂²×C₅	semidirect
384. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
389. #520	C₂²×C₅	semidirect
402. #485	C₂²×C₅	semidirect
403. #484	C₂²×C₅	semidirect
404. #482	C₂²×C₅	semidirect
405. #480	C₂²×C₅	semidirect
406. #477	C₂²×C₅	semidirect
407. #476	C₂²×C₅	semidirect
408. #475	C₂²×C₅	semidirect
409. #474	C₂²×C₅	semidirect
410. #474	C₂²×C₅	semidirect
411. #474	C₂²×C₅	semidirect
412. #474	C₂²×C₅	semidirect
413. #464	C₂²×C₅	semidirect
414. #463	C₂²×C₅	semidirect
415. #463	C₂²×C₅	semidirect
416. #462	C₂²×C₅	semidirect
417. #461	C₂²×C₅	semidirect
418. #461	C₂²×C₅	semidirect
419. #460	C₂²×C₅	semidirect
420. #459	C₂²×C₅	semidirect
421. #459	C₂²×C₅	semidirect
426. #442	C₂²×C₅	semidirect
427. #440	C₂²×C₅	semidirect
428. #440	C₂²×C₅	semidirect
429. #440	C₂²×C₅	semidirect
430. C₄×Q₁₆	C₂²×C₅	semidirect
431. C₄×SD₁₆	C₂²×C₅	semidirect
432. C₄×D₈	C₂²×C₅	semidirect
433. C₄×D₈	C₂²×C₅	semidirect
434. #433	C₂²×C₅	semidirect
435. #432	C₂²×C₅	semidirect
436. #431	C₂²×C₅	semidirect
437. #428	C₂²×C₅	semidirect
438. C₂×#107	C₂²×C₅	semidirect
439. #423	C₂²×C₅	semidirect
440. C₂×C₄⋊C₈	C₂²×C₅	semidirect
442. #417	C₂²×C₅	semidirect
443. #416	C₂²×C₅	semidirect
446. #405	C₂²×C₅	semidirect
703. #41	C₅×#41	semidirect
725. C₂×D₄	C₅×#41	semidirect
894. C₅	#60596	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×#3511	2
C₄×C₅×H(5,𝔽₂)	2
C₅×#3124	2
C₅×#3118	2
C₅×#3115	2
C₅×#3110	2
C₅×#3107	2
C₅×#3100	2
C₅×#3098	2
C₅×#3079	2
C₂×C₅×#474	2
C₅×#3036	2
C₅×#3035	2
C₅×#3012	2
C₅×#2951	2
C₅×#2946	2
C₅×#2925	2
#60596	5

Subgroups — C5×#60596 #11983316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60596 #11983316