Subgroups — C₅×#78697 #14412155

Order 1920.

1512 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1004	C₂	1	1	yes	maximal, characteristic
2	C₅×#5745	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#833	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5132	C₂	1	2	yes	maximal, complemented
6	C₅×#4745	C₂	1	4	yes	maximal, complemented
7	C₅×D₃×#100	C₂	1	4	yes	maximal, complemented
8	C₅×#2888	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₅×#67	C₄	1	4	yes	—
11	C₅×#1004	—	2	4	no	—
12	C₅×#1004	—	2	4	no	—
13	C₂×C₅×#237	C₄	1	2	yes	—
14	C₂×C₅×#237	C₂²	1	2	yes	—
15	C₂×C₅×D₃×D₄	C₄	1	2	yes	—
16	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
17	C₂×C₅×#235	C₂²	1	1	yes	characteristic
18	C₂×C₅×#235	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
20	C₂×C₅×#208	C₂²	1	2	yes	complemented
21	C₅×#907	—	2	4	no	—
22	C₅×D₃×M₁₆	C₂²	1	8	yes	complemented
23	C₅×#901	—	2	4	no	—
24	C₃×C₅×#100	C₂²	1	4	yes	complemented
25	C₅×#833	C₂²	1	4	yes	complemented
26	C₅×#824	C₂²	1	4	yes	complemented
27	C₅×#823	C₂²	1	4	yes	complemented
28	#78697	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×H(5,𝔽₂)	—	3	1	no	—
30	C₅×#568	—	3	2	no	—
31	C₅×#413	—	3	4	no	—
32	C₅×#413	—	3	2	no	—
33	C₂×C₅×#100	—	3	4	no	—
34	C₂×C₅×#100	—	3	1	no	—
35	C₂×C₅×#100	D₃	1	1	yes	characteristic, complemented
36	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
37	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
38	C₂×C₃×C₅×D₄	—	2	2	no	—
39	C₂×C₃×C₅×D₄	—	2	2	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
41	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂×C₅×#67	—	2	8	no	—
44	C₂×C₅×#67	—	2	8	no	—
45	C₂×C₅×#67	C₂×C₄	1	2	yes	—
46	C₂×C₅×#67	C₂×C₄	1	4	yes	—
47	C₂×C₅×#67	C₂×C₄	1	4	yes	—
48	C₂×C₅×#67	C₂×C₄	1	2	yes	—
49	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
50	C₅×#237	—	2	8	no	—
51	C₅×#237	—	2	8	no	—
52	C₅×D₃×D₄	—	2	8	no	—
53	C₅×D₃×D₄	—	2	8	no	—
54	C₅×#235	—	2	2	no	—
55	C₅×#235	—	2	2	no	—
56	C₅×#235	D₄	1	4	yes	—
57	C₅×#235	D₄	1	4	yes	—
58	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
59	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
61	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
62	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
63	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
64	C₃×C₅×M₁₆	—	2	2	no	—
65	C₃×C₅×M₁₆	C₂³	1	4	yes	—
66	C₂×C₃×C₅×C₈	—	2	2	no	—
67	C₅×#208	—	2	2	no	—
68	C₅×#208	C₂³	1	4	yes	—
69	C₂×C₅×C₃⋊C₈	—	2	2	no	—
70	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
71	C₅×D₃×C₈	—	2	8	no	—
72	C₂×#1004	C₂×C₅	1	1	yes	characteristic
73	#5745	C₂×C₅	1	2	yes	complemented
74	C₂×C₃×#100	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#833	C₂×C₅	1	1	yes	characteristic, complemented
76	#5132	C₂×C₅	1	2	yes	complemented
77	#4745	C₂×C₅	1	4	yes	complemented
78	D₃×#100	C₂×C₅	1	4	yes	complemented
79	C₅×H(5,𝔽₂)	—	6	4	no	—
80	C₅×H(5,𝔽₂)	—	6	4	no	—
81	C₂×C₅×#41	—	3	2	no	—
82	C₂×C₅×#41	—	3	2	no	—
83	C₂×C₅×#41	—	3	1	no	—
84	C₂×C₅×#41	—	3	1	no	—
85	C₂²×C₅×D₄	—	3	4	no	—
86	C₂²×C₅×D₄	—	3	2	no	—
87	C₂²×C₅×D₄	—	3	2	no	—
88	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
89	C₅×#131	—	6	4	no	—
90	C₅×#131	—	6	4	no	—
91	C₂×C₅×M₁₆	—	3	2	no	—
92	C₂×C₅×M₁₆	—	3	8	no	—
93	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	complemented
94	C₅×#101	—	3	4	no	—
95	C₅×#100	—	3	4	no	—
96	C₅×#100	—	3	4	no	—
97	C₅×#100	C₂×D₃	1	4	yes	complemented
98	#2888	—	3	1	no	Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	—	8	2	no	—
102	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
103	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₅×D₃	—	2	8	no	—
105	C₂²×C₅×D₃	—	8	4	no	—
106	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
108	C₃×C₅×D₄	—	2	4	no	—
109	C₃×C₅×D₄	—	2	4	no	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
114	C₅×#67	—	2	2	no	—
115	C₅×#67	—	2	2	no	—
116	C₅×#67	—	2	8	no	—
117	C₅×#67	—	2	8	no	—
118	C₅×#67	C₂²⋊C₄	1	4	yes	—
119	C₅×#67	C₂²⋊C₄	1	4	yes	—
120	C₂×C₅×Dic₃	—	2	8	no	—
121	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
122	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
123	C₅×D₁₂	—	2	2	no	—
124	C₅×D₁₂	C₂²⋊C₄	1	4	yes	—
125	C₄×C₅×D₃	—	2	4	no	—
126	C₄×C₅×D₃	C₂×D₄	1	8	yes	—
127	C₅×Dic₆	—	2	2	no	—
128	C₅×Dic₆	C₂²⋊C₄	1	4	yes	—
129	C₃×C₅×C₈	—	2	4	no	—
130	C₅×C₃⋊C₈	—	2	4	no	—
131	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
132	C₂²×#67	C₄×C₅	1	4	yes	—
133	#1004	—	2	4	no	—
134	#1004	—	2	4	no	—
135	C₂×#237	C₄×C₅	1	2	yes	—
136	C₂×#237	C₂²×C₅	1	2	yes	—
137	C₂×D₃×D₄	C₄×C₅	1	2	yes	—
138	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
139	C₂×#235	C₂²×C₅	1	1	yes	characteristic
140	C₂×#235	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
142	C₂×#208	C₂²×C₅	1	2	yes	complemented
143	#907	—	2	4	no	—
144	D₃×M₁₆	C₂²×C₅	1	8	yes	complemented
145	#901	—	2	4	no	—
146	C₃×#100	C₂²×C₅	1	4	yes	complemented
147	#833	C₂²×C₅	1	4	yes	complemented
148	#824	C₂²×C₅	1	4	yes	complemented
149	#823	C₂²×C₅	1	4	yes	complemented
150	C₂⁴×C₅	—	3	4	no	—
151	C₂⁴×C₅	C₄×D₃	1	2	yes	—
152	C₅×#41	—	3	4	no	—
153	C₅×#41	—	3	4	no	—
154	C₅×#41	—	6	8	no	—
155	C₅×#41	—	6	8	no	—
156	C₅×#41	—	6	2	no	—
157	C₅×#41	—	6	2	no	—
158	C₂×C₅×Q₈	—	3	1	no	—
159	C₂×C₅×Q₈	—	3	1	no	—
160	C₂×C₅×D₄	—	2	2	no	—
161	C₂×C₅×D₄	—	2	2	no	—
162	C₂×C₅×D₄	—	3	2	no	—
163	C₂×C₅×D₄	—	3	4	no	—
164	C₂×C₅×D₄	—	3	4	no	—
165	C₂×C₅×D₄	—	3	2	no	—
166	C₂×C₅×D₄	—	3	1	no	—
167	C₂×C₅×D₄	—	3	1	no	—
168	C₂×C₅×D₄	—	6	8	no	—
169	C₂×C₅×D₄	—	6	8	no	—
170	C₂×C₅×D₄	—	6	8	no	—
171	C₂×C₅×D₄	—	6	8	no	—
172	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
173	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
174	C₂²×C₄×C₅	—	3	2	no	—
175	C₂²×C₄×C₅	—	3	4	no	—
176	C₂²×C₄×C₅	—	3	2	no	—
177	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
178	C₅×M₁₆	—	2	2	no	—
179	C₅×M₁₆	—	3	4	no	—
180	C₅×M₁₆	—	6	8	no	—
181	C₅×M₁₆	—	6	2	no	—
182	C₅×M₁₆	C₂²×D₃	1	4	yes	—
183	C₂×C₅×C₈	—	2	2	no	—
184	C₂×C₅×C₈	—	6	8	no	—
185	C₂×C₅×C₈	—	6	2	no	—
186	C₂×H(5,𝔽₂)	—	3	1	no	—
187	#568	—	3	2	no	—
188	#413	—	3	2	no	—
189	#413	—	3	4	no	—
190	C₂×#100	—	3	1	no	—
191	C₂×#100	—	3	4	no	—
192	C₂×#100	C₅×D₃	1	1	yes	characteristic, complemented
193	C₂²×C₃×C₅	—	2	4	no	—
194	C₂²×C₃×C₅	—	4	1	no	—
195	C₂²×C₃×C₅	—	4	4	no	—
196	C₂²×C₃×C₅	—	8	2	no	—
197	C₂²×C₃×C₅	—	8	2	no	—
198	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₅×D₃	—	2	2	no	—
202	C₂×C₅×D₃	—	4	2	no	—
203	C₂×C₅×D₃	—	4	2	no	—
204	C₂×C₅×D₃	—	8	8	no	—
205	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	4	yes	—
206	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
207	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
208	C₅×Dic₃	—	2	2	no	—
209	C₅×Dic₃	C₂×C₂²⋊C₄	1	4	yes	—
210	C₂⁴×C₃	C₂×C₄×C₅	1	2	yes	—
211	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
212	C₂×C₃×D₄	—	2	2	no	—
213	C₂×C₃×D₄	—	2	2	no	—
214	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
215	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
216	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
217	C₂×#67	—	2	8	no	—
218	C₂×#67	—	2	8	no	—
219	C₂×#67	C₂×C₄×C₅	1	2	yes	—
220	C₂×#67	C₂×C₄×C₅	1	4	yes	—
221	C₂×#67	C₂×C₄×C₅	1	4	yes	—
222	C₂×#67	C₂×C₄×C₅	1	2	yes	—
223	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
224	#237	—	2	8	no	—
225	#237	—	2	8	no	—
226	D₃×D₄	—	2	8	no	—
227	D₃×D₄	—	2	8	no	—
228	#235	—	2	2	no	—
229	#235	—	2	2	no	—
230	#235	C₅×D₄	1	4	yes	—
231	#235	C₅×D₄	1	4	yes	—
232	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
234	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
235	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
236	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
237	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
238	C₃×M₁₆	—	2	2	no	—
239	C₃×M₁₆	C₂³×C₅	1	4	yes	—
240	C₂×C₃×C₈	—	2	2	no	—
241	#208	—	2	2	no	—
242	#208	C₂³×C₅	1	4	yes	—
243	C₂×C₃⋊C₈	—	2	2	no	—
244	ΓL(1,𝔽₂₅)	—	2	8	no	—
245	D₃×C₈	—	2	8	no	—
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	—	2	2	no	—
248	C₂³×C₅	—	3	2	no	—
249	C₂³×C₅	—	3	2	no	—
250	C₂³×C₅	—	6	8	no	—
251	C₂³×C₅	—	8	2	no	—
252	C₂³×C₅	—	24	4	no	—
253	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
254	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
255	C₅×Q₈	—	3	4	no	—
256	C₅×Q₈	—	6	2	no	—
257	C₅×D₄	—	2	4	no	—
258	C₅×D₄	—	2	4	no	—
259	C₅×D₄	—	3	4	no	—
260	C₅×D₄	—	3	4	no	—
261	C₅×D₄	—	3	4	no	—
262	C₅×D₄	—	6	8	no	—
263	C₅×D₄	—	6	8	no	—
264	C₅×D₄	—	6	2	no	—
265	C₅×D₄	—	6	2	no	—
266	C₅×D₄	—	6	2	no	—
267	C₂×C₄×C₅	—	3	2	no	—
268	C₂×C₄×C₅	—	3	8	no	—
269	C₂×C₄×C₅	—	3	2	no	—
270	C₂×C₄×C₅	—	6	8	no	—
271	C₂×C₄×C₅	—	6	4	no	—
272	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
273	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
274	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
275	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
276	C₅×C₈	—	2	4	no	—
277	C₅×C₈	—	6	4	no	—
278	H(5,𝔽₂)	—	6	4	no	—
279	H(5,𝔽₂)	—	6	4	no	—
280	C₂×#41	—	3	2	no	—
281	C₂×#41	—	3	2	no	—
282	C₂×#41	—	3	1	no	—
283	C₂×#41	—	3	1	no	—
284	C₂²×D₄	—	3	4	no	—
285	C₂²×D₄	—	3	2	no	—
286	C₂²×D₄	—	3	2	no	—
287	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
288	#131	—	6	4	no	—
289	#131	—	6	4	no	—
290	C₂×M₁₆	—	3	2	no	—
291	C₂×M₁₆	—	3	8	no	—
292	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	complemented
293	#101	—	3	4	no	—
294	#100	—	3	4	no	—
295	#100	—	3	4	no	—
296	#100	C₂×C₅×D₃	1	4	yes	complemented
297	C₂×C₃×C₅	—	2	1	no	—
298	C₂×C₃×C₅	—	2	1	no	—
299	C₂×C₃×C₅	—	2	1	no	—
300	C₂×C₃×C₅	—	4	4	no	—
301	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
302	C₅×D₃	—	2	4	no	—
303	C₅×D₃	—	4	2	no	—
304	C₂³×C₃	—	2	2	no	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	—	8	2	no	—
307	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
308	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
309	C₂²×D₃	—	2	8	no	—
310	C₂²×D₃	—	8	4	no	—
311	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
312	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
313	C₃×D₄	—	2	4	no	—
314	C₃×D₄	—	2	4	no	—
315	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
317	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
318	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
319	#67	—	2	2	no	—
320	#67	—	2	2	no	—
321	#67	—	2	8	no	—
322	#67	—	2	8	no	—
323	#67	C₅×C₂²⋊C₄	1	4	yes	—
324	#67	C₅×C₂²⋊C₄	1	4	yes	—
325	C₂×Dic₃	—	2	8	no	—
326	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
327	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
328	D₁₂	—	2	2	no	—
329	D₁₂	C₅×C₂²⋊C₄	1	4	yes	—
330	C₄×D₃	—	2	4	no	—
331	C₄×D₃	C₂×C₅×D₄	1	8	yes	—
332	Dic₆	—	2	2	no	—
333	Dic₆	C₅×C₂²⋊C₄	1	4	yes	—
334	C₃×C₈	—	2	4	no	—
335	C₃⋊C₈	—	2	4	no	—
336	C₂²×C₅	—	2	4	no	—
337	C₂²×C₅	—	3	4	no	—
338	C₂²×C₅	—	4	1	no	—
339	C₂²×C₅	—	4	4	no	—
340	C₂²×C₅	—	6	2	no	—
341	C₂²×C₅	—	8	2	no	—
342	C₂²×C₅	—	8	2	no	—
343	C₂²×C₅	—	12	2	no	—
344	C₂²×C₅	—	12	2	no	—
345	C₂²×C₅	—	24	8	no	—
346	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
347	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
348	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
349	C₄×C₅	—	3	4	no	—
350	C₄×C₅	—	6	2	no	—
351	C₄×C₅	D₃×C₂²⋊C₄	1	2	yes	—
352	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
353	C₂⁴	—	3	4	no	—
354	C₂⁴	C₄×C₅×D₃	1	2	yes	—
355	#41	—	3	4	no	—
356	#41	—	3	4	no	—
357	#41	—	6	8	no	—
358	#41	—	6	8	no	—
359	#41	—	6	2	no	—
360	#41	—	6	2	no	—
361	C₂×Q₈	—	3	1	no	—
362	C₂×Q₈	—	3	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	3	2	no	—
366	C₂×D₄	—	3	4	no	—
367	C₂×D₄	—	3	4	no	—
368	C₂×D₄	—	3	2	no	—
369	C₂×D₄	—	3	1	no	—
370	C₂×D₄	—	3	1	no	—
371	C₂×D₄	—	6	8	no	—
372	C₂×D₄	—	6	8	no	—
373	C₂×D₄	—	6	8	no	—
374	C₂×D₄	—	6	8	no	—
375	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
376	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
377	C₂²×C₄	—	3	2	no	—
378	C₂²×C₄	—	3	4	no	—
379	C₂²×C₄	—	3	2	no	—
380	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
381	M₁₆	—	2	2	no	—
382	M₁₆	—	3	4	no	—
383	M₁₆	—	6	8	no	—
384	M₁₆	—	6	2	no	—
385	M₁₆	C₂²×C₅×D₃	1	4	yes	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	6	8	no	—
388	C₂×C₈	—	6	2	no	—
389	C₃×C₅	#2888	1	1	yes	characteristic, complemented, Hall
390	C₂²×C₃	—	2	4	no	—
391	C₂²×C₃	—	4	1	no	—
392	C₂²×C₃	—	4	4	no	—
393	C₂²×C₃	—	8	2	no	—
394	C₂²×C₃	—	8	2	no	—
395	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
396	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
397	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
398	C₂×D₃	—	2	2	no	—
399	C₂×D₃	—	4	2	no	—
400	C₂×D₃	—	4	2	no	—
401	C₂×D₃	—	8	8	no	—
402	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
403	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
404	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
405	Dic₃	—	2	2	no	—
406	Dic₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
407	C₂×C₅	—	2	1	no	—
408	C₂×C₅	—	2	1	no	—
409	C₂×C₅	—	2	1	no	—
410	C₂×C₅	—	4	4	no	—
411	C₂×C₅	—	6	4	no	—
412	C₂×C₅	—	12	2	no	—
413	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	3	2	no	—
417	C₂³	—	3	2	no	—
418	C₂³	—	6	8	no	—
419	C₂³	—	8	2	no	—
420	C₂³	—	24	4	no	—
421	C₂³	C₂×C₄×C₅×D₃	1	4	yes	—
422	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
423	Q₈	—	3	4	no	—
424	Q₈	—	6	2	no	—
425	D₄	—	2	4	no	—
426	D₄	—	2	4	no	—
427	D₄	—	3	4	no	—
428	D₄	—	3	4	no	—
429	D₄	—	3	4	no	—
430	D₄	—	6	8	no	—
431	D₄	—	6	8	no	—
432	D₄	—	6	2	no	—
433	D₄	—	6	2	no	—
434	D₄	—	6	2	no	—
435	C₂×C₄	—	3	2	no	—
436	C₂×C₄	—	3	8	no	—
437	C₂×C₄	—	3	2	no	—
438	C₂×C₄	—	6	8	no	—
439	C₂×C₄	—	6	4	no	—
440	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
441	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
442	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
443	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
444	C₈	—	2	4	no	—
445	C₈	—	6	4	no	—
446	C₂×C₃	—	2	1	no	—
447	C₂×C₃	—	2	1	no	—
448	C₂×C₃	—	2	1	no	—
449	C₂×C₃	—	4	4	no	—
450	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
451	D₃	—	2	4	no	—
452	D₃	—	4	2	no	—
453	C₅	#78697	1	1	yes	characteristic, direct product factor, Sylow
454	C₂²	—	2	4	no	—
455	C₂²	—	3	4	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	6	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	12	2	no	—
462	C₂²	—	12	2	no	—
463	C₂²	—	24	8	no	—
464	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
465	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
466	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
467	C₄	—	3	4	no	—
468	C₄	—	6	2	no	—
469	C₄	C₅×D₃×C₂²⋊C₄	1	2	yes	—
470	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
471	C₃	C₅×#2888	1	1	yes	characteristic, complemented, Sylow
472	C₂	—	2	1	no	—
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	4	4	no	—
476	C₂	—	6	4	no	—
477	C₂	—	12	2	no	—
478	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×D₃×C₂²⋊C₄
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#100	C₂
socle	C₂×C₃×C₅	C₂²×C₂²⋊C₄
prime radical	C₂×C₅×#1004	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#100	D₃
hypocenter	C₃	C₅×#2888
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#100

Complements

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

N	H ≅ G/N	type
2. C₅×#5745	C₂	semidirect
3. C₂×C₃×C₅×#100	C₂	semidirect
4. C₂×C₅×#833	C₂	semidirect
5. C₅×#5132	C₂	semidirect
6. C₅×#4745	C₂	semidirect
7. C₅×D₃×#100	C₂	semidirect
19. C₂×C₃×C₅×M₁₆	C₂²	semidirect
20. C₂×C₅×#208	C₂²	semidirect
22. C₅×D₃×M₁₆	C₂²	semidirect
24. C₃×C₅×#100	C₂²	semidirect
25. C₅×#833	C₂²	semidirect
26. C₅×#824	C₂²	semidirect
27. C₅×#823	C₂²	semidirect
28. #78697	C₅	direct (N × H)
35. C₂×C₅×#100	D₃	semidirect
73. #5745	C₂×C₅	semidirect
74. C₂×C₃×#100	C₂×C₅	semidirect
75. C₂×#833	C₂×C₅	semidirect
76. #5132	C₂×C₅	semidirect
77. #4745	C₂×C₅	semidirect
78. D₃×#100	C₂×C₅	semidirect
93. C₂×C₅×M₁₆	C₂×D₃	semidirect
97. C₅×#100	C₂×D₃	semidirect
141. C₂×C₃×M₁₆	C₂²×C₅	semidirect
142. C₂×#208	C₂²×C₅	semidirect
144. D₃×M₁₆	C₂²×C₅	semidirect
146. C₃×#100	C₂²×C₅	semidirect
147. #833	C₂²×C₅	semidirect
148. #824	C₂²×C₅	semidirect
149. #823	C₂²×C₅	semidirect
192. C₂×#100	C₅×D₃	semidirect
292. C₂×M₁₆	C₂×C₅×D₃	semidirect
296. #100	C₂×C₅×D₃	semidirect
389. C₃×C₅	#2888	semidirect
453. C₅	#78697	direct (N × H)
471. C₃	C₅×#2888	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#1004	2
C₅×#5745	2
C₂×C₃×C₅×#100	2
C₂×C₅×#833	2
C₅×#5132	2
C₅×#4745	2
C₅×D₃×#100	2
C₅×#2888	3
#78697	5

Subgroups — C5×#78697 #14412155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78697 #14412155