Subgroups — C₅×#23717 #11946437

Order 1280.

752 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#137	C₂	1	2	yes	maximal
2	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2922	C₂	1	1	yes	maximal, characteristic
4	C₅×#2089	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2078	C₂	1	1	yes	maximal, characteristic
6	C₅×#2064	C₂	1	2	yes	maximal, complemented
7	C₅×#2052	C₂	1	2	yes	maximal
8	C₅×#2047	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2020	C₂	1	1	yes	maximal, characteristic
10	C₄×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#101	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#137	C₂²	1	2	yes	—
13	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
14	C₄×C₅×#41	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₅×#441	—	2	2	no	—
17	C₅×#440	—	2	2	no	—
18	C₄×C₅×Q₁₆	—	2	2	no	—
19	C₄×C₅×Q₁₆	—	2	2	no	—
20	C₄×C₅×Q₁₆	—	2	2	no	—
21	C₄×C₅×SD₁₆	—	2	2	no	—
22	C₅×#433	—	2	2	no	—
23	C₅×#431	—	2	2	no	—
24	C₂×C₅×#108	C₂²	1	2	yes	—
25	C₅×#428	C₂²	1	2	yes	—
26	C₂×C₅×#107	C₂²	1	1	yes	characteristic
27	C₅×#424	C₂²	1	1	yes	characteristic
28	C₅×#424	C₂²	1	1	yes	characteristic
29	C₅×#419	C₂²	1	2	yes	—
30	C₅×#417	C₂²	1	2	yes	—
31	C₂×C₅×#103	C₂²	1	2	yes	—
32	C₂×C₅×#101	C₂²	1	2	yes	—
33	C₂×C₅×#101	C₂²	1	2	yes	—
34	C₅×#408	C₂²	1	1	yes	characteristic
35	C₅×#408	C₂²	1	1	yes	characteristic
36	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
37	C₄×C₅×M₁₆	C₂²	1	2	yes	—
38	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₅×#343	C₂²	1	2	yes	—
40	C₅×#343	C₂²	1	2	yes	—
41	C₅×#341	C₂²	1	1	yes	characteristic
42	C₅×#341	C₂²	1	1	yes	characteristic
43	#23717	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	C₂³	1	1	yes	characteristic
45	C₂²×C₅×Q₈	C₂³	1	2	yes	—
46	C₅×#137	—	2	4	no	—
47	C₅×#137	—	2	4	no	—
48	C₂×C₅×Q₁₆	—	2	2	no	—
49	C₂×C₅×Q₁₆	—	2	4	no	—
50	C₂×C₅×Q₁₆	—	2	2	no	—
51	C₂×C₅×SD₁₆	—	2	2	no	—
52	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₅×M₁₆	C₂³	1	2	yes	—
55	C₂×C₅×M₁₆	C₂³	1	2	yes	—
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₄×C₅×Q₈	—	2	2	no	—
59	C₄×C₅×Q₈	—	2	2	no	—
60	C₄×C₅×Q₈	—	2	2	no	—
61	C₄×C₅×Q₈	—	2	2	no	—
62	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
63	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
64	C₄×C₅×D₄	—	2	1	no	—
65	C₄×C₅×D₄	—	2	1	no	—
66	C₄×C₅×D₄	D₄	1	1	yes	characteristic
67	C₄×C₅×D₄	D₄	1	1	yes	characteristic
68	C₅×#117	—	2	1	no	—
69	C₅×#117	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	—	2	2	no	—
71	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	2	no	—
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#108	—	2	4	no	—
76	C₅×#107	—	2	2	no	—
77	C₅×#107	—	2	2	no	—
78	C₅×#106	—	2	2	no	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×#103	—	2	2	no	—
82	C₅×#103	—	2	4	no	—
83	C₅×#103	—	2	2	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#102	—	2	2	no	—
86	C₅×#101	—	2	4	no	—
87	C₅×#101	—	2	4	no	—
88	C₅×C₂²⋊C₈	—	2	2	no	—
89	C₅×C₂²⋊C₈	—	2	2	no	—
90	C₅×#97	—	2	1	no	—
91	C₅×#97	—	2	2	no	—
92	C₄×C₅×C₈	—	2	1	no	—
93	C₄×C₅×C₈	—	2	2	no	—
94	C₄×C₅×C₈	D₄	1	2	yes	—
95	C₄×C₅×C₈	D₄	1	2	yes	—
96	C₄×#137	C₂×C₅	1	2	yes	—
97	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
98	#2922	C₂×C₅	1	1	yes	characteristic
99	#2089	C₂×C₅	1	1	yes	characteristic, complemented
100	#2078	C₂×C₅	1	1	yes	characteristic
101	#2064	C₂×C₅	1	2	yes	complemented
102	#2052	C₂×C₅	1	2	yes	—
103	#2047	C₂×C₅	1	1	yes	characteristic, complemented
104	#2020	C₂×C₅	1	1	yes	characteristic
105	C₄×#108	C₂×C₅	1	1	yes	characteristic, complemented
106	C₄×#101	C₂×C₅	1	2	yes	complemented
107	C₅×#41	—	2	2	no	—
108	C₅×#41	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	—	2	2	no	—
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
115	C₂×C₅×Q₈	#41	1	4	yes	—
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	#41	1	1	yes	characteristic
124	C₂²×C₄×C₅	#41	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₅×Q₁₆	—	2	8	no	—
127	C₅×Q₁₆	—	2	8	no	—
128	C₅×SD₁₆	—	2	8	no	—
129	C₅×M₁₆	—	2	2	no	—
130	C₅×M₁₆	—	2	2	no	—
131	C₅×M₁₆	—	2	2	no	—
132	C₅×M₁₆	—	2	2	no	—
133	C₅×M₁₆	—	2	2	no	—
134	C₅×M₁₆	#41	1	4	yes	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
142	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	4	2	no	—
148	C₅×C₄⋊C₄	—	4	2	no	—
149	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
150	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
151	C₅×C₂²⋊C₄	—	2	1	no	—
152	C₅×C₂²⋊C₄	—	2	1	no	—
153	C₅×C₂²⋊C₄	—	2	1	no	—
154	C₄²×C₅	—	2	1	no	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	—	4	2	no	—
158	C₄²×C₅	—	4	2	no	—
159	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×#137	C₂²×C₅	1	2	yes	—
164	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
165	C₄×#41	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
167	#441	—	2	2	no	—
168	#440	—	2	2	no	—
169	C₄×Q₁₆	—	2	2	no	—
170	C₄×Q₁₆	—	2	2	no	—
171	C₄×Q₁₆	—	2	2	no	—
172	C₄×SD₁₆	—	2	2	no	—
173	#433	—	2	2	no	—
174	#431	—	2	2	no	—
175	C₂×#108	C₂²×C₅	1	2	yes	—
176	#428	C₂²×C₅	1	2	yes	—
177	C₂×#107	C₂²×C₅	1	1	yes	characteristic
178	#424	C₂²×C₅	1	1	yes	characteristic
179	#424	C₂²×C₅	1	1	yes	characteristic
180	#419	C₂²×C₅	1	2	yes	—
181	#417	C₂²×C₅	1	2	yes	—
182	C₂×#103	C₂²×C₅	1	2	yes	—
183	C₂×#101	C₂²×C₅	1	2	yes	—
184	C₂×#101	C₂²×C₅	1	2	yes	—
185	#408	C₂²×C₅	1	1	yes	characteristic
186	#408	C₂²×C₅	1	1	yes	characteristic
187	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
188	C₄×M₁₆	C₂²×C₅	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
190	#343	C₂²×C₅	1	2	yes	—
191	#343	C₂²×C₅	1	2	yes	—
192	#341	C₂²×C₅	1	1	yes	characteristic
193	#341	C₂²×C₅	1	1	yes	characteristic
194	C₂³×C₅	—	2	1	no	—
195	C₂³×C₅	C₂×#41	1	1	yes	characteristic
196	C₅×Q₈	—	2	4	no	—
197	C₅×Q₈	—	2	4	no	—
198	C₅×Q₈	—	2	2	no	—
199	C₅×Q₈	—	4	2	no	—
200	C₅×Q₈	—	4	2	no	—
201	C₅×D₄	—	2	2	no	—
202	C₅×D₄	—	4	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	2	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	8	2	no	—
217	C₂×C₄×C₅	#121	1	1	yes	characteristic
218	C₂×C₄×C₅	#121	1	1	yes	characteristic
219	C₂×C₄×C₅	#121	1	1	yes	characteristic
220	C₂×C₄×C₅	#121	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×#41	1	2	yes	—
224	C₂×C₄×C₅	C₂×#41	1	2	yes	—
225	C₅×C₈	—	2	2	no	—
226	C₅×C₈	—	2	4	no	—
227	C₅×C₈	—	2	2	no	—
228	C₅×C₈	—	4	1	no	—
229	C₅×C₈	—	4	2	no	—
230	C₅×C₈	—	4	1	no	—
231	C₂×#41	C₂³×C₅	1	1	yes	characteristic
232	C₂²×Q₈	C₂³×C₅	1	2	yes	—
233	#137	—	2	4	no	—
234	#137	—	2	4	no	—
235	C₂×Q₁₆	—	2	2	no	—
236	C₂×Q₁₆	—	2	4	no	—
237	C₂×Q₁₆	—	2	2	no	—
238	C₂×SD₁₆	—	2	2	no	—
239	C₂×M₁₆	C₂³×C₅	1	2	yes	—
240	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
241	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
242	C₂×M₁₆	C₂³×C₅	1	2	yes	—
243	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
245	C₄×Q₈	—	2	2	no	—
246	C₄×Q₈	—	2	2	no	—
247	C₄×Q₈	—	2	2	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
250	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	C₅×D₄	1	1	yes	characteristic
254	C₄×D₄	C₅×D₄	1	1	yes	characteristic
255	#117	—	2	1	no	—
256	#117	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
259	C₂×C₄²	—	2	1	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
262	#108	—	2	4	no	—
263	#107	—	2	2	no	—
264	#107	—	2	2	no	—
265	#106	—	2	2	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	#103	—	2	2	no	—
269	#103	—	2	4	no	—
270	#103	—	2	2	no	—
271	#103	—	2	2	no	—
272	#102	—	2	2	no	—
273	#101	—	2	4	no	—
274	#101	—	2	4	no	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₂²⋊C₈	—	2	2	no	—
277	#97	—	2	1	no	—
278	#97	—	2	2	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	C₅×D₄	1	2	yes	—
282	C₄×C₈	C₅×D₄	1	2	yes	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	4	1	no	—
286	C₂²×C₅	—	4	1	no	—
287	C₂²×C₅	—	4	1	no	—
288	C₂²×C₅	C₂×#121	1	1	yes	characteristic
289	C₂²×C₅	#529	1	2	yes	—
290	C₄×C₅	—	2	1	no	—
291	C₄×C₅	—	2	1	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	—	4	1	no	—
294	C₄×C₅	—	4	4	no	—
295	C₄×C₅	—	4	1	no	—
296	C₄×C₅	—	4	1	no	—
297	C₄×C₅	—	8	2	no	—
298	C₄×C₅	#473	1	2	yes	—
299	C₄×C₅	#525	1	1	yes	characteristic
300	C₄×C₅	#525	1	2	yes	—
301	C₄×C₅	#532	1	1	yes	characteristic
302	#41	—	2	2	no	—
303	#41	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂×Q₈	C₅×#41	1	4	yes	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	C₅×#41	1	1	yes	characteristic
319	C₂²×C₄	C₅×#41	1	1	yes	characteristic
320	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
321	Q₁₆	—	2	8	no	—
322	Q₁₆	—	2	8	no	—
323	SD₁₆	—	2	8	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	2	2	no	—
329	M₁₆	C₅×#41	1	4	yes	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
337	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
345	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	4	2	no	—
353	C₄²	—	4	2	no	—
354	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
355	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
356	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
357	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂×C₅	—	2	2	no	—
359	C₂×C₅	—	8	1	no	—
360	C₂×C₅	#2392	1	1	yes	characteristic
361	C₂×C₅	C₂×#473	1	1	yes	characteristic
362	C₂×C₅	#3067	1	1	yes	characteristic
363	C₂³	—	2	1	no	—
364	C₂³	C₂×C₅×#41	1	1	yes	characteristic
365	Q₈	—	2	4	no	—
366	Q₈	—	2	4	no	—
367	Q₈	—	2	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	D₄	—	2	2	no	—
371	D₄	—	4	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	C₅×#121	1	1	yes	characteristic
387	C₂×C₄	C₅×#121	1	1	yes	characteristic
388	C₂×C₄	C₅×#121	1	1	yes	characteristic
389	C₂×C₄	C₅×#121	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
392	C₂×C₄	C₂×C₅×#41	1	2	yes	—
393	C₂×C₄	C₂×C₅×#41	1	2	yes	—
394	C₈	—	2	2	no	—
395	C₈	—	2	4	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	2	no	—
399	C₈	—	4	1	no	—
400	C₅	#23717	1	1	yes	characteristic, direct product factor, Sylow
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	C₂×C₅×#121	1	1	yes	characteristic
407	C₂²	C₅×#529	1	2	yes	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	4	no	—
415	C₄	—	8	2	no	—
416	C₄	C₅×#473	1	2	yes	—
417	C₄	C₅×#525	1	1	yes	characteristic
418	C₄	C₅×#525	1	2	yes	—
419	C₄	C₅×#532	1	1	yes	characteristic
420	C₂	—	2	2	no	—
421	C₂	—	8	1	no	—
422	C₂	C₅×#2392	1	1	yes	characteristic
423	C₂	C₂×C₅×#473	1	1	yes	characteristic
424	C₂	C₅×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×#121
prime radical	C₂×C₅×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×Q₁₆	C₂	semidirect
4. C₅×#2089	C₂	semidirect
6. C₅×#2064	C₂	semidirect
8. C₅×#2047	C₂	semidirect
10. C₄×C₅×#108	C₂	semidirect
11. C₄×C₅×#101	C₂	semidirect
43. #23717	C₅	direct (N × H)
97. C₂×C₄×Q₁₆	C₂×C₅	semidirect
99. #2089	C₂×C₅	semidirect
101. #2064	C₂×C₅	semidirect
103. #2047	C₂×C₅	semidirect
105. C₄×#108	C₂×C₅	semidirect
106. C₄×#101	C₂×C₅	semidirect
400. C₅	#23717	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×#137	2
C₂×C₄×C₅×Q₁₆	2
C₅×#2922	2
C₅×#2089	2
C₅×#2078	2
C₅×#2064	2
C₅×#2052	2
C₅×#2047	2
C₅×#2020	2
C₄×C₅×#108	2
C₄×C₅×#101	2
#23717	5

Subgroups — C5×#23717 #11946437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23717 #11946437