Subgroups — C₅×#80301 #14457795

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5838	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5837	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5779	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5778	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#456	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5204	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5203	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5095	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5086	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4827	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4825	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4823	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4823	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4755	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4754	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3289	—	3	1	no	maximal, Hall
17	C₃×C₅×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
18	C₅×#1010	C₂²	1	1	yes	characteristic, complemented
19	C₅×#1009	C₂²	1	1	yes	characteristic
20	C₅×#1007	C₂²	1	1	yes	characteristic
21	C₃×C₅×#137	C₂²	1	1	yes	characteristic
22	C₃×C₅×#137	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₅×#951	—	2	1	no	—
25	C₅×#951	C₂²	1	1	yes	characteristic
26	C₅×#950	—	2	1	no	—
27	C₅×#950	—	2	1	no	—
28	C₅×#950	C₂²	1	1	yes	characteristic
29	C₅×#950	C₂²	1	1	yes	characteristic
30	C₅×#949	—	2	1	no	—
31	C₅×#949	C₂²	1	1	yes	characteristic
32	C₅×#948	C₂²	1	1	yes	characteristic
33	C₅×#948	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₅×#216	—	2	1	no	—
35	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
37	C₅×#942	—	2	1	no	—
38	C₅×#942	—	2	1	no	—
39	C₅×#942	C₂²	1	1	yes	characteristic
40	C₅×#942	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₅×#215	—	2	1	no	—
42	C₂×C₅×#215	C₂²	1	1	yes	characteristic
43	C₂×C₅×#215	C₂²	1	1	yes	characteristic
44	C₅×#919	—	2	1	no	—
45	C₅×#918	—	2	1	no	—
46	C₅×#918	—	2	1	no	—
47	C₅×D₃×Q₁₆	—	2	1	no	—
48	C₅×#916	—	2	1	no	—
49	C₅×#915	—	2	1	no	—
50	C₅×#914	—	2	1	no	—
51	C₅×D₃×SD₁₆	—	2	1	no	—
52	C₅×#909	C₂²	1	1	yes	characteristic
53	C₅×#908	C₂²	1	1	yes	characteristic
54	C₅×#907	C₂²	1	1	yes	characteristic
55	C₅×#907	C₂²	1	1	yes	characteristic, complemented
56	C₅×#875	C₂²	1	1	yes	characteristic
57	C₃×C₅×#104	C₂²	1	1	yes	characteristic
58	C₃×C₅×#104	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₅×#101	C₂²	1	1	yes	characteristic, complemented
60	C₅×#836	C₂²	1	1	yes	characteristic, complemented
61	C₅×#824	C₂²	1	1	yes	characteristic, complemented
62	C₅×#823	C₂²	1	1	yes	characteristic
63	C₅×#822	C₂²	1	1	yes	characteristic, complemented
64	C₅×#822	C₂²	1	1	yes	characteristic, complemented
65	C₅×#805	C₂²	1	1	yes	characteristic
66	C₅×#805	C₂²	1	1	yes	characteristic, complemented
67	C₅×#803	C₂²	1	1	yes	characteristic, complemented
68	#80301	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#578	—	3	1	no	—
70	C₅×#578	—	3	1	no	—
71	C₅×#577	—	3	1	no	—
72	C₅×#577	—	3	1	no	—
73	C₅×#497	—	3	1	no	—
74	C₅×#473	—	3	1	no	—
75	C₅×#473	—	3	1	no	—
76	C₅×#471	—	3	1	no	—
77	C₅×#471	—	3	1	no	—
78	C₅×#456	—	3	1	no	—
79	C₅×#456	D₃	1	1	yes	characteristic, complemented
80	C₅×#455	—	3	1	no	—
81	C₅×#454	—	3	1	no	—
82	C₅×#444	—	3	1	no	—
83	C₅×#444	—	3	1	no	—
84	C₃×C₅×#41	—	2	1	no	—
85	C₃×C₅×#41	—	2	1	no	—
86	C₃×C₅×#41	—	4	1	no	—
87	C₃×C₅×#41	C₂³	1	1	yes	characteristic
88	C₃×C₅×#41	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×Q₈	—	2	1	no	—
90	C₂×C₃×C₅×Q₈	—	2	1	no	—
91	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
93	C₅×#239	—	2	1	no	—
94	C₅×#239	—	2	1	no	—
95	C₅×#239	—	2	1	no	—
96	C₅×D₃×Q₈	—	2	1	no	—
97	C₅×D₃×Q₈	—	2	1	no	—
98	C₅×D₃×Q₈	—	2	1	no	—
99	C₅×#237	—	2	1	no	—
100	C₅×#237	—	4	1	no	—
101	C₅×D₃×D₄	—	2	1	no	—
102	C₅×D₃×D₄	—	4	1	no	—
103	C₅×#235	—	2	1	no	—
104	C₅×#235	—	2	1	no	—
105	C₅×#235	—	4	1	no	—
106	C₅×#235	C₂³	1	1	yes	characteristic
107	C₅×#235	C₂³	1	1	yes	characteristic
108	C₂×C₅×D₁₂	—	2	1	no	—
109	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
110	C₂×C₅×Dic₆	—	2	1	no	—
111	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
112	C₃×C₅×Q₁₆	—	2	1	no	—
113	C₃×C₅×Q₁₆	—	2	1	no	—
114	C₃×C₅×SD₁₆	—	2	1	no	—
115	C₃×C₅×SD₁₆	—	2	1	no	—
116	C₃×C₅×M₁₆	C₂³	1	1	yes	characteristic
117	C₃×C₅×M₁₆	C₂³	1	1	yes	characteristic
118	C₃×C₅×C₄⋊C₄	—	4	1	no	—
119	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
120	C₅×#216	—	2	1	no	—
121	C₅×#216	—	2	1	no	—
122	C₅×#216	—	2	1	no	—
123	C₅×#216	—	2	1	no	—
124	C₅×#216	—	2	1	no	—
125	C₅×#216	—	2	1	no	—
126	C₅×#216	—	2	1	no	—
127	C₅×#216	D₄	1	1	yes	characteristic
128	C₅×#216	D₄	1	1	yes	characteristic
129	C₅×#215	—	2	1	no	—
130	C₅×#215	—	2	1	no	—
131	C₅×#215	—	2	1	no	—
132	C₅×#215	—	2	1	no	—
133	C₅×#215	—	2	1	no	—
134	C₅×#215	—	2	1	no	—
135	C₅×#215	—	2	1	no	—
136	C₅×#215	D₄	1	1	yes	characteristic
137	C₅×#215	D₄	1	1	yes	characteristic
138	C₅×#214	—	2	1	no	—
139	C₅×#214	D₄	1	1	yes	characteristic
140	C₅×#214	D₄	1	1	yes	characteristic
141	C₅×#213	—	2	1	no	—
142	C₅×#213	D₄	1	1	yes	characteristic
143	C₅×#213	D₄	1	1	yes	characteristic
144	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
145	C₅×#208	—	2	1	no	—
146	C₅×#208	—	2	1	no	—
147	C₅×#208	C₂³	1	1	yes	characteristic
148	C₅×#208	C₂³	1	1	yes	characteristic
149	C₂×C₅×C₃⋊C₈	—	2	1	no	—
150	C₂×C₅×C₃⋊C₈	—	2	1	no	—
151	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
152	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
153	C₅×Dic₁₂	—	2	1	no	—
154	C₅×D₂₄	—	2	1	no	—
155	C₅×#204	—	2	1	no	—
156	C₅×#204	—	2	1	no	—
157	C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
158	C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
159	C₅×D₃×C₈	—	2	1	no	—
160	C₅×D₃×C₈	—	2	1	no	—
161	#5838	C₂×C₅	1	1	yes	characteristic, complemented
162	#5837	C₂×C₅	1	1	yes	characteristic, complemented
163	#5779	C₂×C₅	1	1	yes	characteristic, complemented
164	#5778	C₂×C₅	1	1	yes	characteristic, complemented
165	C₃×#456	C₂×C₅	1	1	yes	characteristic, complemented
166	#5204	C₂×C₅	1	1	yes	characteristic, complemented
167	#5203	C₂×C₅	1	1	yes	characteristic, complemented
168	#5095	C₂×C₅	1	1	yes	characteristic, complemented
169	#5086	C₂×C₅	1	1	yes	characteristic, complemented
170	#4827	C₂×C₅	1	1	yes	characteristic, complemented
171	#4825	C₂×C₅	1	1	yes	characteristic, complemented
172	#4823	C₂×C₅	1	1	yes	characteristic, complemented
173	#4823	C₂×C₅	1	1	yes	characteristic, complemented
174	#4755	C₂×C₅	1	1	yes	characteristic, complemented
175	#4754	C₂×C₅	1	1	yes	characteristic, complemented
176	C₅×2₋¹⁺⁴	—	3	1	no	—
177	C₅×2₋¹⁺⁴	—	3	1	no	—
178	C₅×2₋¹⁺⁴	C₂×D₃	1	1	yes	characteristic
179	C₅×H(5,𝔽₂)	—	3	1	no	—
180	C₅×#137	—	3	1	no	—
181	C₅×#137	—	3	1	no	—
182	C₅×#137	—	3	1	no	—
183	C₅×#137	—	3	1	no	—
184	C₅×#137	—	6	1	no	—
185	C₅×#137	—	6	1	no	—
186	C₅×#137	—	6	1	no	—
187	C₅×#137	—	6	1	no	—
188	C₅×#137	—	6	1	no	—
189	C₅×#137	—	6	1	no	—
190	C₅×#137	C₂×D₃	1	1	yes	characteristic
191	C₅×#137	C₂×D₃	1	1	yes	characteristic, complemented
192	C₅×AGL(1,ℤ/8)	—	3	1	no	—
193	C₅×AGL(1,ℤ/8)	—	3	1	no	—
194	C₅×AGL(1,ℤ/8)	—	6	1	no	—
195	C₅×AGL(1,ℤ/8)	—	6	1	no	—
196	C₅×#135	—	3	1	no	—
197	C₅×#135	—	3	1	no	—
198	C₅×#135	—	6	1	no	—
199	C₅×#135	—	6	1	no	—
200	C₅×#135	—	6	1	no	—
201	C₅×#135	—	6	1	no	—
202	C₂×C₅×Q₁₆	—	3	1	no	—
203	C₂×C₅×Q₁₆	—	3	1	no	—
204	C₂×C₅×Q₁₆	—	6	1	no	—
205	C₂×C₅×Q₁₆	—	6	1	no	—
206	C₂×C₅×SD₁₆	—	3	1	no	—
207	C₂×C₅×SD₁₆	—	3	1	no	—
208	C₂×C₅×SD₁₆	—	6	1	no	—
209	C₂×C₅×SD₁₆	—	6	1	no	—
210	C₅×#131	—	3	1	no	—
211	C₅×#131	—	3	1	no	—
212	C₅×#131	—	3	1	no	—
213	C₅×#131	—	3	1	no	—
214	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
215	C₅×#124	—	3	1	no	—
216	C₅×#108	—	3	1	no	—
217	C₅×#108	—	3	1	no	—
218	C₅×#104	—	3	1	no	—
219	C₅×#104	—	3	1	no	—
220	C₅×#104	C₂×D₃	1	1	yes	characteristic
221	C₅×#104	C₂×D₃	1	1	yes	characteristic, complemented
222	C₅×#101	—	3	1	no	—
223	C₅×#101	—	3	1	no	—
224	C₅×#101	C₂×D₃	1	1	yes	characteristic, complemented
225	C₅×#100	—	3	1	no	—
226	C₅×#97	—	3	1	no	—
227	#3289	—	3	1	no	Sylow
228	C₂²×C₅×D₃	—	2	1	no	—
229	C₂²×C₅×D₃	—	4	1	no	—
230	C₃×C₅×Q₈	—	2	1	no	—
231	C₃×C₅×Q₈	—	2	1	no	—
232	C₃×C₅×Q₈	—	2	1	no	—
233	C₃×C₅×Q₈	—	2	1	no	—
234	C₃×C₅×Q₈	—	4	1	no	—
235	C₃×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
236	C₃×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
237	C₃×C₅×D₄	—	2	1	no	—
238	C₃×C₅×D₄	—	2	1	no	—
239	C₃×C₅×D₄	—	4	1	no	—
240	C₃×C₅×D₄	C₂×D₄	1	1	yes	characteristic
241	C₃×C₅×D₄	C₂×D₄	1	1	yes	characteristic
242	C₂×C₃×C₄×C₅	—	2	1	no	—
243	C₂×C₃×C₄×C₅	—	2	1	no	—
244	C₂×C₃×C₄×C₅	—	2	1	no	—
245	C₂×C₃×C₄×C₅	—	2	1	no	—
246	C₂×C₃×C₄×C₅	—	2	1	no	—
247	C₂×C₃×C₄×C₅	—	4	1	no	—
248	C₂×C₃×C₄×C₅	—	4	1	no	—
249	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
250	C₅×#67	—	2	1	no	—
251	C₅×#67	—	2	1	no	—
252	C₅×#67	—	4	1	no	—
253	C₅×#67	—	4	1	no	—
254	C₂×C₅×Dic₃	—	2	1	no	—
255	C₂×C₅×Dic₃	—	4	1	no	—
256	C₅×D₁₂	—	2	1	no	—
257	C₅×D₁₂	—	2	1	no	—
258	C₅×D₁₂	—	4	1	no	—
259	C₅×D₁₂	—	4	1	no	—
260	C₅×D₁₂	C₂×D₄	1	1	yes	characteristic
261	C₅×D₁₂	C₂×D₄	1	1	yes	characteristic
262	C₄×C₅×D₃	—	2	1	no	—
263	C₄×C₅×D₃	—	2	1	no	—
264	C₄×C₅×D₃	—	4	1	no	—
265	C₄×C₅×D₃	—	4	1	no	—
266	C₄×C₅×D₃	—	4	1	no	—
267	C₄×C₅×D₃	—	4	1	no	—
268	C₅×Dic₆	—	2	1	no	—
269	C₅×Dic₆	—	2	1	no	—
270	C₅×Dic₆	—	4	1	no	—
271	C₅×Dic₆	—	4	1	no	—
272	C₅×Dic₆	C₂×D₄	1	1	yes	characteristic
273	C₅×Dic₆	C₂×D₄	1	1	yes	characteristic
274	C₃×C₅×C₈	—	2	1	no	—
275	C₃×C₅×C₈	—	2	1	no	—
276	C₅×C₃⋊C₈	—	2	1	no	—
277	C₅×C₃⋊C₈	—	2	1	no	—
278	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
279	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
280	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
281	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
282	C₃×2₋¹⁺⁴	C₂²×C₅	1	1	yes	characteristic
283	#1010	C₂²×C₅	1	1	yes	characteristic, complemented
284	#1009	C₂²×C₅	1	1	yes	characteristic
285	#1007	C₂²×C₅	1	1	yes	characteristic
286	C₃×#137	C₂²×C₅	1	1	yes	characteristic
287	C₃×#137	C₂²×C₅	1	1	yes	characteristic, complemented
288	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
289	#951	—	2	1	no	—
290	#951	C₂²×C₅	1	1	yes	characteristic
291	#950	—	2	1	no	—
292	#950	—	2	1	no	—
293	#950	C₂²×C₅	1	1	yes	characteristic
294	#950	C₂²×C₅	1	1	yes	characteristic
295	#949	—	2	1	no	—
296	#949	C₂²×C₅	1	1	yes	characteristic
297	#948	C₂²×C₅	1	1	yes	characteristic
298	#948	C₂²×C₅	1	1	yes	characteristic, complemented
299	C₂×#216	—	2	1	no	—
300	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
301	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
302	#942	—	2	1	no	—
303	#942	—	2	1	no	—
304	#942	C₂²×C₅	1	1	yes	characteristic
305	#942	C₂²×C₅	1	1	yes	characteristic, complemented
306	C₂×#215	—	2	1	no	—
307	C₂×#215	C₂²×C₅	1	1	yes	characteristic
308	C₂×#215	C₂²×C₅	1	1	yes	characteristic
309	#919	—	2	1	no	—
310	#918	—	2	1	no	—
311	#918	—	2	1	no	—
312	D₃×Q₁₆	—	2	1	no	—
313	#916	—	2	1	no	—
314	#915	—	2	1	no	—
315	#914	—	2	1	no	—
316	D₃×SD₁₆	—	2	1	no	—
317	#909	C₂²×C₅	1	1	yes	characteristic
318	#908	C₂²×C₅	1	1	yes	characteristic
319	#907	C₂²×C₅	1	1	yes	characteristic
320	#907	C₂²×C₅	1	1	yes	characteristic, complemented
321	#875	C₂²×C₅	1	1	yes	characteristic
322	C₃×#104	C₂²×C₅	1	1	yes	characteristic
323	C₃×#104	C₂²×C₅	1	1	yes	characteristic, complemented
324	C₃×#101	C₂²×C₅	1	1	yes	characteristic, complemented
325	#836	C₂²×C₅	1	1	yes	characteristic, complemented
326	#824	C₂²×C₅	1	1	yes	characteristic, complemented
327	#823	C₂²×C₅	1	1	yes	characteristic
328	#822	C₂²×C₅	1	1	yes	characteristic, complemented
329	#822	C₂²×C₅	1	1	yes	characteristic, complemented
330	#805	C₂²×C₅	1	1	yes	characteristic
331	#805	C₂²×C₅	1	1	yes	characteristic, complemented
332	#803	C₂²×C₅	1	1	yes	characteristic, complemented
333	C₅×#41	—	2	1	no	—
334	C₅×#41	—	2	1	no	—
335	C₅×#41	—	3	1	no	—
336	C₅×#41	—	3	1	no	—
337	C₅×#41	—	4	1	no	—
338	C₅×#41	—	6	1	no	—
339	C₅×#41	—	6	1	no	—
340	C₅×#41	—	6	1	no	—
341	C₅×#41	—	6	1	no	—
342	C₅×#41	—	6	1	no	—
343	C₅×#41	—	6	1	no	—
344	C₅×#41	—	12	1	no	—
345	C₅×#41	—	12	1	no	—
346	C₅×#41	C₂²×D₃	1	1	yes	characteristic
347	C₅×#41	C₂²×D₃	1	1	yes	characteristic
348	C₂×C₅×Q₈	—	2	1	no	—
349	C₂×C₅×Q₈	—	2	1	no	—
350	C₂×C₅×Q₈	—	3	1	no	—
351	C₂×C₅×Q₈	—	6	1	no	—
352	C₂×C₅×Q₈	—	6	1	no	—
353	C₂×C₅×Q₈	—	6	1	no	—
354	C₂×C₅×Q₈	—	6	1	no	—
355	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
356	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
357	C₂×C₅×D₄	—	3	1	no	—
358	C₂×C₅×D₄	—	6	1	no	—
359	C₂×C₅×D₄	—	6	1	no	—
360	C₂×C₅×D₄	—	12	1	no	—
361	C₅×Q₁₆	—	2	1	no	—
362	C₅×Q₁₆	—	2	1	no	—
363	C₅×Q₁₆	—	3	1	no	—
364	C₅×Q₁₆	—	3	1	no	—
365	C₅×Q₁₆	—	6	1	no	—
366	C₅×Q₁₆	—	6	1	no	—
367	C₅×Q₁₆	—	6	1	no	—
368	C₅×Q₁₆	—	6	1	no	—
369	C₅×Q₁₆	—	6	1	no	—
370	C₅×Q₁₆	—	6	1	no	—
371	C₅×Q₁₆	—	6	1	no	—
372	C₅×Q₁₆	—	6	1	no	—
373	C₅×SD₁₆	—	2	1	no	—
374	C₅×SD₁₆	—	2	1	no	—
375	C₅×SD₁₆	—	3	1	no	—
376	C₅×SD₁₆	—	3	1	no	—
377	C₅×SD₁₆	—	3	1	no	—
378	C₅×SD₁₆	—	3	1	no	—
379	C₅×SD₁₆	—	6	1	no	—
380	C₅×SD₁₆	—	6	1	no	—
381	C₅×SD₁₆	—	6	1	no	—
382	C₅×SD₁₆	—	6	1	no	—
383	C₅×SD₁₆	—	6	1	no	—
384	C₅×SD₁₆	—	6	1	no	—
385	C₅×SD₁₆	—	6	1	no	—
386	C₅×SD₁₆	—	6	1	no	—
387	C₅×SD₁₆	—	6	1	no	—
388	C₅×SD₁₆	—	6	1	no	—
389	C₅×D₈	—	3	1	no	—
390	C₅×D₈	—	3	1	no	—
391	C₅×D₈	—	6	1	no	—
392	C₅×D₈	—	6	1	no	—
393	C₅×M₁₆	—	3	1	no	—
394	C₅×M₁₆	—	3	1	no	—
395	C₅×M₁₆	—	6	1	no	—
396	C₅×M₁₆	—	6	1	no	—
397	C₅×M₁₆	—	6	1	no	—
398	C₅×M₁₆	—	6	1	no	—
399	C₅×M₁₆	C₂²×D₃	1	1	yes	characteristic
400	C₅×M₁₆	C₂²×D₃	1	1	yes	characteristic
401	C₂×C₅×C₈	—	3	1	no	—
402	C₂×C₅×C₈	—	3	1	no	—
403	C₂×C₅×C₈	—	6	1	no	—
404	C₂×C₅×C₈	—	6	1	no	—
405	C₂×C₅×C₈	—	6	1	no	—
406	C₂×C₅×C₈	—	6	1	no	—
407	C₅×C₄⋊C₄	—	4	1	no	—
408	C₅×C₂²⋊C₄	—	12	1	no	—
409	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
410	#578	—	3	1	no	—
411	#578	—	3	1	no	—
412	#577	—	3	1	no	—
413	#577	—	3	1	no	—
414	#497	—	3	1	no	—
415	#473	—	3	1	no	—
416	#473	—	3	1	no	—
417	#471	—	3	1	no	—
418	#471	—	3	1	no	—
419	#456	—	3	1	no	—
420	#456	C₅×D₃	1	1	yes	characteristic, complemented
421	#455	—	3	1	no	—
422	#454	—	3	1	no	—
423	#444	—	3	1	no	—
424	#444	—	3	1	no	—
425	C₂²×C₃×C₅	—	2	1	no	—
426	C₂²×C₃×C₅	—	2	1	no	—
427	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
428	C₂×C₅×D₃	—	2	1	no	—
429	C₂×C₅×D₃	—	2	1	no	—
430	C₂×C₅×D₃	—	4	1	no	—
431	C₂×C₅×D₃	—	8	1	no	—
432	C₂×C₅×D₃	—	16	1	no	—
433	C₃×C₄×C₅	—	2	1	no	—
434	C₃×C₄×C₅	—	2	1	no	—
435	C₃×C₄×C₅	—	4	1	no	—
436	C₃×C₄×C₅	—	4	1	no	—
437	C₃×C₄×C₅	—	4	1	no	—
438	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
439	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
440	C₅×Dic₃	—	2	1	no	—
441	C₅×Dic₃	—	2	1	no	—
442	C₅×Dic₃	—	4	1	no	—
443	C₃×#41	—	2	1	no	—
444	C₃×#41	—	2	1	no	—
445	C₃×#41	—	4	1	no	—
446	C₃×#41	C₂³×C₅	1	1	yes	characteristic
447	C₃×#41	C₂³×C₅	1	1	yes	characteristic
448	C₂×C₃×Q₈	—	2	1	no	—
449	C₂×C₃×Q₈	—	2	1	no	—
450	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
451	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
452	#239	—	2	1	no	—
453	#239	—	2	1	no	—
454	#239	—	2	1	no	—
455	D₃×Q₈	—	2	1	no	—
456	D₃×Q₈	—	2	1	no	—
457	D₃×Q₈	—	2	1	no	—
458	#237	—	2	1	no	—
459	#237	—	4	1	no	—
460	D₃×D₄	—	2	1	no	—
461	D₃×D₄	—	4	1	no	—
462	#235	—	2	1	no	—
463	#235	—	2	1	no	—
464	#235	—	4	1	no	—
465	#235	C₂³×C₅	1	1	yes	characteristic
466	#235	C₂³×C₅	1	1	yes	characteristic
467	C₂×D₁₂	—	2	1	no	—
468	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
469	C₂×Dic₆	—	2	1	no	—
470	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
471	C₃×Q₁₆	—	2	1	no	—
472	C₃×Q₁₆	—	2	1	no	—
473	C₃×SD₁₆	—	2	1	no	—
474	C₃×SD₁₆	—	2	1	no	—
475	C₃×M₁₆	C₂³×C₅	1	1	yes	characteristic
476	C₃×M₁₆	C₂³×C₅	1	1	yes	characteristic
477	C₃×C₄⋊C₄	—	4	1	no	—
478	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
479	#216	—	2	1	no	—
480	#216	—	2	1	no	—
481	#216	—	2	1	no	—
482	#216	—	2	1	no	—
483	#216	—	2	1	no	—
484	#216	—	2	1	no	—
485	#216	—	2	1	no	—
486	#216	C₅×D₄	1	1	yes	characteristic
487	#216	C₅×D₄	1	1	yes	characteristic
488	#215	—	2	1	no	—
489	#215	—	2	1	no	—
490	#215	—	2	1	no	—
491	#215	—	2	1	no	—
492	#215	—	2	1	no	—
493	#215	—	2	1	no	—
494	#215	—	2	1	no	—
495	#215	C₅×D₄	1	1	yes	characteristic
496	#215	C₅×D₄	1	1	yes	characteristic
497	#214	—	2	1	no	—
498	#214	C₅×D₄	1	1	yes	characteristic
499	#214	C₅×D₄	1	1	yes	characteristic
500	#213	—	2	1	no	—
501	#213	C₅×D₄	1	1	yes	characteristic
502	#213	C₅×D₄	1	1	yes	characteristic
503	(C₂×D₃)⋊C₄	—	4	1	no	—
504	#208	—	2	1	no	—
505	#208	—	2	1	no	—
506	#208	C₂³×C₅	1	1	yes	characteristic
507	#208	C₂³×C₅	1	1	yes	characteristic
508	C₂×C₃⋊C₈	—	2	1	no	—
509	C₂×C₃⋊C₈	—	2	1	no	—
510	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
511	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
512	Dic₁₂	—	2	1	no	—
513	D₂₄	—	2	1	no	—
514	#204	—	2	1	no	—
515	#204	—	2	1	no	—
516	ΓL(1,𝔽₂₅)	—	2	1	no	—
517	ΓL(1,𝔽₂₅)	—	2	1	no	—
518	D₃×C₈	—	2	1	no	—
519	D₃×C₈	—	2	1	no	—
520	C₂³×C₅	—	6	1	no	—
521	C₂³×C₅	—	12	1	no	—
522	C₅×Q₈	—	2	1	no	—
523	C₅×Q₈	—	2	1	no	—
524	C₅×Q₈	—	2	1	no	—
525	C₅×Q₈	—	2	1	no	—
526	C₅×Q₈	—	3	1	no	—
527	C₅×Q₈	—	3	1	no	—
528	C₅×Q₈	—	4	1	no	—
529	C₅×Q₈	—	6	1	no	—
530	C₅×Q₈	—	6	1	no	—
531	C₅×Q₈	—	12	1	no	—
532	C₅×Q₈	—	12	1	no	—
533	C₅×Q₈	D₃×D₄	1	1	yes	characteristic
534	C₅×Q₈	D₃×D₄	1	1	yes	characteristic
535	C₅×D₄	—	2	1	no	—
536	C₅×D₄	—	2	1	no	—
537	C₅×D₄	—	3	1	no	—
538	C₅×D₄	—	3	1	no	—
539	C₅×D₄	—	4	1	no	—
540	C₅×D₄	—	6	1	no	—
541	C₅×D₄	—	6	1	no	—
542	C₅×D₄	—	6	1	no	—
543	C₅×D₄	—	6	1	no	—
544	C₅×D₄	—	12	1	no	—
545	C₅×D₄	—	12	1	no	—
546	C₅×D₄	—	12	1	no	—
547	C₅×D₄	—	12	1	no	—
548	C₅×D₄	D₃×D₄	1	1	yes	characteristic
549	C₅×D₄	D₃×D₄	1	1	yes	characteristic
550	C₂×C₄×C₅	—	2	1	no	—
551	C₂×C₄×C₅	—	2	1	no	—
552	C₂×C₄×C₅	—	2	1	no	—
553	C₂×C₄×C₅	—	2	1	no	—
554	C₂×C₄×C₅	—	2	1	no	—
555	C₂×C₄×C₅	—	4	1	no	—
556	C₂×C₄×C₅	—	4	1	no	—
557	C₂×C₄×C₅	—	6	1	no	—
558	C₂×C₄×C₅	—	6	1	no	—
559	C₂×C₄×C₅	—	6	1	no	—
560	C₂×C₄×C₅	—	12	1	no	—
561	C₂×C₄×C₅	—	12	1	no	—
562	C₂×C₄×C₅	—	12	1	no	—
563	C₂×C₄×C₅	—	12	1	no	—
564	C₂×C₄×C₅	—	12	1	no	—
565	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
566	C₅×C₈	—	2	1	no	—
567	C₅×C₈	—	2	1	no	—
568	C₅×C₈	—	3	1	no	—
569	C₅×C₈	—	3	1	no	—
570	C₅×C₈	—	3	1	no	—
571	C₅×C₈	—	3	1	no	—
572	C₅×C₈	—	6	1	no	—
573	C₅×C₈	—	6	1	no	—
574	2₋¹⁺⁴	—	3	1	no	—
575	2₋¹⁺⁴	—	3	1	no	—
576	2₋¹⁺⁴	C₂×C₅×D₃	1	1	yes	characteristic
577	H(5,𝔽₂)	—	3	1	no	—
578	#137	—	3	1	no	—
579	#137	—	3	1	no	—
580	#137	—	3	1	no	—
581	#137	—	3	1	no	—
582	#137	—	6	1	no	—
583	#137	—	6	1	no	—
584	#137	—	6	1	no	—
585	#137	—	6	1	no	—
586	#137	—	6	1	no	—
587	#137	—	6	1	no	—
588	#137	C₂×C₅×D₃	1	1	yes	characteristic
589	#137	C₂×C₅×D₃	1	1	yes	characteristic, complemented
590	AGL(1,ℤ/8)	—	3	1	no	—
591	AGL(1,ℤ/8)	—	3	1	no	—
592	AGL(1,ℤ/8)	—	6	1	no	—
593	AGL(1,ℤ/8)	—	6	1	no	—
594	#135	—	3	1	no	—
595	#135	—	3	1	no	—
596	#135	—	6	1	no	—
597	#135	—	6	1	no	—
598	#135	—	6	1	no	—
599	#135	—	6	1	no	—
600	C₂×Q₁₆	—	3	1	no	—
601	C₂×Q₁₆	—	3	1	no	—
602	C₂×Q₁₆	—	6	1	no	—
603	C₂×Q₁₆	—	6	1	no	—
604	C₂×SD₁₆	—	3	1	no	—
605	C₂×SD₁₆	—	3	1	no	—
606	C₂×SD₁₆	—	6	1	no	—
607	C₂×SD₁₆	—	6	1	no	—
608	#131	—	3	1	no	—
609	#131	—	3	1	no	—
610	#131	—	3	1	no	—
611	#131	—	3	1	no	—
612	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
613	#124	—	3	1	no	—
614	#108	—	3	1	no	—
615	#108	—	3	1	no	—
616	#104	—	3	1	no	—
617	#104	—	3	1	no	—
618	#104	C₂×C₅×D₃	1	1	yes	characteristic
619	#104	C₂×C₅×D₃	1	1	yes	characteristic, complemented
620	#101	—	3	1	no	—
621	#101	—	3	1	no	—
622	#101	C₂×C₅×D₃	1	1	yes	characteristic, complemented
623	#100	—	3	1	no	—
624	#97	—	3	1	no	—
625	C₂×C₃×C₅	—	2	1	no	—
626	C₂×C₃×C₅	—	4	1	no	—
627	C₂×C₃×C₅	—	4	1	no	—
628	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
629	C₅×D₃	—	4	1	no	—
630	C₅×D₃	—	4	1	no	—
631	C₅×D₃	—	8	1	no	—
632	C₂²×D₃	—	2	1	no	—
633	C₂²×D₃	—	4	1	no	—
634	C₃×Q₈	—	2	1	no	—
635	C₃×Q₈	—	2	1	no	—
636	C₃×Q₈	—	2	1	no	—
637	C₃×Q₈	—	2	1	no	—
638	C₃×Q₈	—	4	1	no	—
639	C₃×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
640	C₃×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
641	C₃×D₄	—	2	1	no	—
642	C₃×D₄	—	2	1	no	—
643	C₃×D₄	—	4	1	no	—
644	C₃×D₄	C₂×C₅×D₄	1	1	yes	characteristic
645	C₃×D₄	C₂×C₅×D₄	1	1	yes	characteristic
646	C₂×C₃×C₄	—	2	1	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	2	1	no	—
649	C₂×C₃×C₄	—	2	1	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	4	1	no	—
652	C₂×C₃×C₄	—	4	1	no	—
653	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
654	#67	—	2	1	no	—
655	#67	—	2	1	no	—
656	#67	—	4	1	no	—
657	#67	—	4	1	no	—
658	C₂×Dic₃	—	2	1	no	—
659	C₂×Dic₃	—	4	1	no	—
660	D₁₂	—	2	1	no	—
661	D₁₂	—	2	1	no	—
662	D₁₂	—	4	1	no	—
663	D₁₂	—	4	1	no	—
664	D₁₂	C₂×C₅×D₄	1	1	yes	characteristic
665	D₁₂	C₂×C₅×D₄	1	1	yes	characteristic
666	C₄×D₃	—	2	1	no	—
667	C₄×D₃	—	2	1	no	—
668	C₄×D₃	—	4	1	no	—
669	C₄×D₃	—	4	1	no	—
670	C₄×D₃	—	4	1	no	—
671	C₄×D₃	—	4	1	no	—
672	Dic₆	—	2	1	no	—
673	Dic₆	—	2	1	no	—
674	Dic₆	—	4	1	no	—
675	Dic₆	—	4	1	no	—
676	Dic₆	C₂×C₅×D₄	1	1	yes	characteristic
677	Dic₆	C₂×C₅×D₄	1	1	yes	characteristic
678	C₃×C₈	—	2	1	no	—
679	C₃×C₈	—	2	1	no	—
680	C₃⋊C₈	—	2	1	no	—
681	C₃⋊C₈	—	2	1	no	—
682	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
683	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
684	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
685	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
686	C₂²×C₅	—	2	1	no	—
687	C₂²×C₅	—	2	1	no	—
688	C₂²×C₅	—	6	1	no	—
689	C₂²×C₅	—	6	1	no	—
690	C₂²×C₅	—	12	1	no	—
691	C₂²×C₅	—	24	1	no	—
692	C₂²×C₅	—	48	1	no	—
693	C₂²×C₅	#1004	1	1	yes	characteristic
694	C₄×C₅	—	2	1	no	—
695	C₄×C₅	—	2	1	no	—
696	C₄×C₅	—	4	1	no	—
697	C₄×C₅	—	4	1	no	—
698	C₄×C₅	—	4	1	no	—
699	C₄×C₅	—	6	1	no	—
700	C₄×C₅	—	6	1	no	—
701	C₄×C₅	—	12	1	no	—
702	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
703	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
704	#41	—	2	1	no	—
705	#41	—	2	1	no	—
706	#41	—	3	1	no	—
707	#41	—	3	1	no	—
708	#41	—	4	1	no	—
709	#41	—	6	1	no	—
710	#41	—	6	1	no	—
711	#41	—	6	1	no	—
712	#41	—	6	1	no	—
713	#41	—	6	1	no	—
714	#41	—	6	1	no	—
715	#41	—	12	1	no	—
716	#41	—	12	1	no	—
717	#41	C₂²×C₅×D₃	1	1	yes	characteristic
718	#41	C₂²×C₅×D₃	1	1	yes	characteristic
719	C₂×Q₈	—	2	1	no	—
720	C₂×Q₈	—	2	1	no	—
721	C₂×Q₈	—	3	1	no	—
722	C₂×Q₈	—	6	1	no	—
723	C₂×Q₈	—	6	1	no	—
724	C₂×Q₈	—	6	1	no	—
725	C₂×Q₈	—	6	1	no	—
726	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
727	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
728	C₂×D₄	—	3	1	no	—
729	C₂×D₄	—	6	1	no	—
730	C₂×D₄	—	6	1	no	—
731	C₂×D₄	—	12	1	no	—
732	Q₁₆	—	2	1	no	—
733	Q₁₆	—	2	1	no	—
734	Q₁₆	—	3	1	no	—
735	Q₁₆	—	3	1	no	—
736	Q₁₆	—	6	1	no	—
737	Q₁₆	—	6	1	no	—
738	Q₁₆	—	6	1	no	—
739	Q₁₆	—	6	1	no	—
740	Q₁₆	—	6	1	no	—
741	Q₁₆	—	6	1	no	—
742	Q₁₆	—	6	1	no	—
743	Q₁₆	—	6	1	no	—
744	SD₁₆	—	2	1	no	—
745	SD₁₆	—	2	1	no	—
746	SD₁₆	—	3	1	no	—
747	SD₁₆	—	3	1	no	—
748	SD₁₆	—	3	1	no	—
749	SD₁₆	—	3	1	no	—
750	SD₁₆	—	6	1	no	—
751	SD₁₆	—	6	1	no	—
752	SD₁₆	—	6	1	no	—
753	SD₁₆	—	6	1	no	—
754	SD₁₆	—	6	1	no	—
755	SD₁₆	—	6	1	no	—
756	SD₁₆	—	6	1	no	—
757	SD₁₆	—	6	1	no	—
758	SD₁₆	—	6	1	no	—
759	SD₁₆	—	6	1	no	—
760	D₈	—	3	1	no	—
761	D₈	—	3	1	no	—
762	D₈	—	6	1	no	—
763	D₈	—	6	1	no	—
764	M₁₆	—	3	1	no	—
765	M₁₆	—	3	1	no	—
766	M₁₆	—	6	1	no	—
767	M₁₆	—	6	1	no	—
768	M₁₆	—	6	1	no	—
769	M₁₆	—	6	1	no	—
770	M₁₆	C₂²×C₅×D₃	1	1	yes	characteristic
771	M₁₆	C₂²×C₅×D₃	1	1	yes	characteristic
772	C₂×C₈	—	3	1	no	—
773	C₂×C₈	—	3	1	no	—
774	C₂×C₈	—	6	1	no	—
775	C₂×C₈	—	6	1	no	—
776	C₂×C₈	—	6	1	no	—
777	C₂×C₈	—	6	1	no	—
778	C₄⋊C₄	—	4	1	no	—
779	C₂²⋊C₄	—	12	1	no	—
780	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
781	C₃×C₅	#3289	1	1	yes	characteristic, complemented, Hall
782	C₂²×C₃	—	2	1	no	—
783	C₂²×C₃	—	2	1	no	—
784	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
785	C₂×D₃	—	2	1	no	—
786	C₂×D₃	—	2	1	no	—
787	C₂×D₃	—	4	1	no	—
788	C₂×D₃	—	8	1	no	—
789	C₂×D₃	—	16	1	no	—
790	C₃×C₄	—	2	1	no	—
791	C₃×C₄	—	2	1	no	—
792	C₃×C₄	—	4	1	no	—
793	C₃×C₄	—	4	1	no	—
794	C₃×C₄	—	4	1	no	—
795	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
796	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
797	Dic₃	—	2	1	no	—
798	Dic₃	—	2	1	no	—
799	Dic₃	—	4	1	no	—
800	C₂×C₅	—	2	1	no	—
801	C₂×C₅	—	4	1	no	—
802	C₂×C₅	—	4	1	no	—
803	C₂×C₅	—	12	1	no	—
804	C₂×C₅	—	12	1	no	—
805	C₂×C₅	—	24	1	no	—
806	C₂×C₅	#5590	1	1	yes	characteristic
807	C₂³	—	6	1	no	—
808	C₂³	—	12	1	no	—
809	Q₈	—	2	1	no	—
810	Q₈	—	2	1	no	—
811	Q₈	—	2	1	no	—
812	Q₈	—	2	1	no	—
813	Q₈	—	3	1	no	—
814	Q₈	—	3	1	no	—
815	Q₈	—	4	1	no	—
816	Q₈	—	6	1	no	—
817	Q₈	—	6	1	no	—
818	Q₈	—	12	1	no	—
819	Q₈	—	12	1	no	—
820	Q₈	C₅×D₃×D₄	1	1	yes	characteristic
821	Q₈	C₅×D₃×D₄	1	1	yes	characteristic
822	D₄	—	2	1	no	—
823	D₄	—	2	1	no	—
824	D₄	—	3	1	no	—
825	D₄	—	3	1	no	—
826	D₄	—	4	1	no	—
827	D₄	—	6	1	no	—
828	D₄	—	6	1	no	—
829	D₄	—	6	1	no	—
830	D₄	—	6	1	no	—
831	D₄	—	12	1	no	—
832	D₄	—	12	1	no	—
833	D₄	—	12	1	no	—
834	D₄	—	12	1	no	—
835	D₄	C₅×D₃×D₄	1	1	yes	characteristic
836	D₄	C₅×D₃×D₄	1	1	yes	characteristic
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	6	1	no	—
845	C₂×C₄	—	6	1	no	—
846	C₂×C₄	—	6	1	no	—
847	C₂×C₄	—	12	1	no	—
848	C₂×C₄	—	12	1	no	—
849	C₂×C₄	—	12	1	no	—
850	C₂×C₄	—	12	1	no	—
851	C₂×C₄	—	12	1	no	—
852	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
853	C₈	—	2	1	no	—
854	C₈	—	2	1	no	—
855	C₈	—	3	1	no	—
856	C₈	—	3	1	no	—
857	C₈	—	3	1	no	—
858	C₈	—	3	1	no	—
859	C₈	—	6	1	no	—
860	C₈	—	6	1	no	—
861	C₂×C₃	—	2	1	no	—
862	C₂×C₃	—	4	1	no	—
863	C₂×C₃	—	4	1	no	—
864	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
865	D₃	—	4	1	no	—
866	D₃	—	4	1	no	—
867	D₃	—	8	1	no	—
868	C₅	#80301	1	1	yes	characteristic, direct product factor, Sylow
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	6	1	no	—
872	C₂²	—	6	1	no	—
873	C₂²	—	12	1	no	—
874	C₂²	—	24	1	no	—
875	C₂²	—	48	1	no	—
876	C₂²	C₅×#1004	1	1	yes	characteristic
877	C₄	—	2	1	no	—
878	C₄	—	2	1	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	1	no	—
882	C₄	—	6	1	no	—
883	C₄	—	6	1	no	—
884	C₄	—	12	1	no	—
885	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
886	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
887	C₃	C₅×#3289	1	1	yes	characteristic, complemented, Sylow
888	C₂	—	2	1	no	—
889	C₂	—	4	1	no	—
890	C₂	—	4	1	no	—
891	C₂	—	12	1	no	—
892	C₂	—	12	1	no	—
893	C₂	—	24	1	no	—
894	C₂	C₅×#5590	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#5590
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#456	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₅×#456	D₃
hypocenter	C₃	C₅×#3289
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#456

Complements

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

N	H ≅ G/N	type
1. C₅×#5838	C₂	semidirect
2. C₅×#5837	C₂	semidirect
3. C₅×#5779	C₂	semidirect
4. C₅×#5778	C₂	semidirect
5. C₃×C₅×#456	C₂	semidirect
6. C₅×#5204	C₂	semidirect
7. C₅×#5203	C₂	semidirect
8. C₅×#5095	C₂	semidirect
9. C₅×#5086	C₂	semidirect
10. C₅×#4827	C₂	semidirect
11. C₅×#4825	C₂	semidirect
12. C₅×#4823	C₂	semidirect
13. C₅×#4823	C₂	semidirect
14. C₅×#4755	C₂	semidirect
15. C₅×#4754	C₂	semidirect
18. C₅×#1010	C₂²	semidirect
22. C₃×C₅×#137	C₂²	semidirect
23. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
33. C₅×#948	C₂²	semidirect
35. C₂×C₅×#216	C₂²	semidirect
36. C₂×C₅×#216	C₂²	semidirect
40. C₅×#942	C₂²	semidirect
55. C₅×#907	C₂²	semidirect
58. C₃×C₅×#104	C₂²	semidirect
59. C₃×C₅×#101	C₂²	semidirect
60. C₅×#836	C₂²	semidirect
61. C₅×#824	C₂²	semidirect
63. C₅×#822	C₂²	semidirect
64. C₅×#822	C₂²	semidirect
66. C₅×#805	C₂²	semidirect
67. C₅×#803	C₂²	semidirect
68. #80301	C₅	direct (N × H)
79. C₅×#456	D₃	semidirect
161. #5838	C₂×C₅	semidirect
162. #5837	C₂×C₅	semidirect
163. #5779	C₂×C₅	semidirect
164. #5778	C₂×C₅	semidirect
165. C₃×#456	C₂×C₅	semidirect
166. #5204	C₂×C₅	semidirect
167. #5203	C₂×C₅	semidirect
168. #5095	C₂×C₅	semidirect
169. #5086	C₂×C₅	semidirect
170. #4827	C₂×C₅	semidirect
171. #4825	C₂×C₅	semidirect
172. #4823	C₂×C₅	semidirect
173. #4823	C₂×C₅	semidirect
174. #4755	C₂×C₅	semidirect
175. #4754	C₂×C₅	semidirect
191. C₅×#137	C₂×D₃	semidirect
214. C₅×C₄⋊Q₈	C₂×D₃	semidirect
221. C₅×#104	C₂×D₃	semidirect
224. C₅×#101	C₂×D₃	semidirect
283. #1010	C₂²×C₅	semidirect
287. C₃×#137	C₂²×C₅	semidirect
288. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
298. #948	C₂²×C₅	semidirect
300. C₂×#216	C₂²×C₅	semidirect
301. C₂×#216	C₂²×C₅	semidirect
305. #942	C₂²×C₅	semidirect
320. #907	C₂²×C₅	semidirect
323. C₃×#104	C₂²×C₅	semidirect
324. C₃×#101	C₂²×C₅	semidirect
325. #836	C₂²×C₅	semidirect
326. #824	C₂²×C₅	semidirect
328. #822	C₂²×C₅	semidirect
329. #822	C₂²×C₅	semidirect
331. #805	C₂²×C₅	semidirect
332. #803	C₂²×C₅	semidirect
420. #456	C₅×D₃	semidirect
589. #137	C₂×C₅×D₃	semidirect
612. C₄⋊Q₈	C₂×C₅×D₃	semidirect
619. #104	C₂×C₅×D₃	semidirect
622. #101	C₂×C₅×D₃	semidirect
781. C₃×C₅	#3289	semidirect
868. C₅	#80301	direct (N × H)
887. C₃	C₅×#3289	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5838	2
C₅×#5837	2
C₅×#5779	2
C₅×#5778	2
C₃×C₅×#456	2
C₅×#5204	2
C₅×#5203	2
C₅×#5095	2
C₅×#5086	2
C₅×#4827	2
C₅×#4825	2
C₅×#4823	2
C₅×#4755	2
C₅×#4754	2
C₅×#3289	3
#80301	5

Subgroups — C5×#80301 #14457795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80301 #14457795