Subgroups — C₅×#83843 #14417425

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×#5812	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5798	C₂	1	1	yes	maximal, characteristic
4	C₅×#5225	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5215	C₂	1	1	yes	maximal, characteristic
6	C₅×#5164	C₂	1	4	yes	maximal, complemented
7	C₅×Dic₃×SD₁₆	C₂	1	4	yes	maximal, complemented
8	C₅×#5106	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5101	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2949	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×SD₁₆	C₄	1	8	yes	complemented
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#217	—	2	2	no	—
18	C₅×Q₈×Dic₃	—	2	2	no	—
19	C₅×Q₈×Dic₃	C₂²	1	4	yes	complemented
20	C₅×D₄×Dic₃	—	2	2	no	—
21	C₅×D₄×Dic₃	C₂²	1	4	yes	—
22	C₅×#926	—	2	2	no	—
23	C₅×#926	C₂²	1	1	yes	characteristic
24	C₅×#926	C₂²	1	1	yes	characteristic
25	C₅×#926	C₂²	1	1	yes	characteristic
26	C₂×C₅×#208	C₂²	1	1	yes	characteristic
27	C₅×#835	C₂²	1	4	yes	complemented
28	C₅×#832	C₂²	1	4	yes	—
29	C₅×#818	C₂²	1	2	yes	complemented
30	C₅×#817	C₂²	1	2	yes	complemented
31	C₅×#815	C₂²	1	2	yes	complemented
32	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
33	#83843	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂²×C₅×SD₁₆	D₃	1	1	yes	characteristic
35	C₅×#519	—	3	1	no	—
36	C₅×#518	—	3	1	no	—
37	C₅×#440	—	3	4	no	—
38	C₄×C₅×SD₁₆	—	3	4	no	—
39	C₅×#427	—	3	1	no	—
40	C₅×#419	—	3	1	no	—
41	C₅×#418	—	3	1	no	—
42	C₅×#405	—	3	1	no	—
43	C₂⁴×C₃×C₅	—	2	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	1	no	—
45	C₂×C₃×C₅×Q₈	—	2	2	no	—
46	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
47	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
48	C₂×C₃×C₅×D₄	—	2	1	no	—
49	C₂×C₃×C₅×D₄	—	2	2	no	—
50	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
51	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	—	2	1	no	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₅×Dic₃	—	2	4	no	—
55	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
56	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
57	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
58	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₅×#217	—	2	1	no	—
61	C₅×#217	—	2	1	no	—
62	C₅×#217	—	2	4	no	—
63	C₅×#217	D₄	1	2	yes	—
64	C₅×C₄⋊Dic₃	—	2	4	no	—
65	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
66	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
67	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
68	C₄×C₅×Dic₃	—	2	1	no	—
69	C₄×C₅×Dic₃	—	2	1	no	—
70	C₄×C₅×Dic₃	—	2	4	no	—
71	C₄×C₅×Dic₃	C₂³	1	2	yes	—
72	C₅×#208	—	2	2	no	—
73	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
74	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic
75	#5812	C₂×C₅	1	1	yes	characteristic, complemented
76	#5798	C₂×C₅	1	1	yes	characteristic
77	#5225	C₂×C₅	1	1	yes	characteristic, complemented
78	#5215	C₂×C₅	1	1	yes	characteristic
79	#5164	C₂×C₅	1	4	yes	complemented
80	Dic₃×SD₁₆	C₂×C₅	1	4	yes	complemented
81	#5106	C₂×C₅	1	1	yes	characteristic, complemented
82	#5101	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
84	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
85	C₂×C₅×SD₁₆	Dic₃	1	8	yes	complemented
86	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
87	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
88	C₂×C₅×M₁₆	—	3	1	no	—
89	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
90	C₄×C₅×Q₈	—	3	4	no	—
91	C₄×C₅×Q₈	—	6	2	no	—
92	C₄×C₅×D₄	—	3	4	no	—
93	C₄×C₅×D₄	—	6	2	no	—
94	C₅×#117	—	3	1	no	—
95	C₅×#117	—	3	1	no	—
96	C₅×#117	—	3	1	no	—
97	C₅×#117	—	6	2	no	—
98	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
99	C₅×#107	—	3	2	no	—
100	C₅×#106	—	3	2	no	—
101	C₅×#103	—	3	4	no	—
102	C₅×#102	—	3	4	no	—
103	C₅×#97	—	3	2	no	—
104	C₄×C₅×C₈	—	3	2	no	—
105	#2949	—	3	1	no	Sylow
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	2	4	no	—
108	C₂³×C₃×C₅	—	8	2	no	—
109	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
110	C₃×C₅×Q₈	—	2	4	no	—
111	C₃×C₅×Q₈	—	2	2	no	—
112	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
113	C₃×C₅×D₄	—	2	4	no	—
114	C₃×C₅×D₄	—	2	2	no	—
115	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
116	C₂×C₃×C₄×C₅	—	2	4	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	#41	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
122	C₂×C₅×Dic₃	—	2	2	no	—
123	C₂×C₅×Dic₃	—	2	2	no	—
124	C₂×C₅×Dic₃	—	8	4	no	—
125	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
126	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
127	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
128	C₅×C₃⋊C₈	—	2	2	no	—
129	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×SD₁₆	C₄×C₅	1	8	yes	complemented
132	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
133	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
134	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
135	C₂×#217	—	2	2	no	—
136	Q₈×Dic₃	—	2	2	no	—
137	Q₈×Dic₃	C₂²×C₅	1	4	yes	complemented
138	D₄×Dic₃	—	2	2	no	—
139	D₄×Dic₃	C₂²×C₅	1	4	yes	—
140	#926	—	2	2	no	—
141	#926	C₂²×C₅	1	1	yes	characteristic
142	#926	C₂²×C₅	1	1	yes	characteristic
143	#926	C₂²×C₅	1	1	yes	characteristic
144	C₂×#208	C₂²×C₅	1	1	yes	characteristic
145	#835	C₂²×C₅	1	4	yes	complemented
146	#832	C₂²×C₅	1	4	yes	—
147	#818	C₂²×C₅	1	2	yes	complemented
148	#817	C₂²×C₅	1	2	yes	complemented
149	#815	C₂²×C₅	1	2	yes	complemented
150	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
151	C₂⁴×C₅	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	—	2	2	no	—
154	C₂×C₅×Q₈	C₂×Dic₃	1	4	yes	complemented
155	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
156	C₂×C₅×D₄	—	2	1	no	—
157	C₂×C₅×D₄	—	2	2	no	—
158	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	—
159	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	6	4	no	—
162	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₅×SD₁₆	C₂×Dic₃	1	8	yes	complemented
164	C₅×SD₁₆	C₂×Dic₃	1	8	yes	complemented
165	C₅×M₁₆	—	6	2	no	—
166	C₂×C₅×C₈	—	3	2	no	—
167	C₂×C₅×C₈	C₂×Dic₃	1	4	yes	complemented
168	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
169	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
170	C₅×C₄⋊C₄	—	3	2	no	—
171	C₅×C₄⋊C₄	—	3	2	no	—
172	C₅×C₄⋊C₄	—	3	2	no	—
173	C₅×C₄⋊C₄	—	6	4	no	—
174	C₅×C₂²⋊C₄	—	3	2	no	—
175	C₅×C₂²⋊C₄	—	6	4	no	—
176	C₅×C₂²⋊C₄	—	6	1	no	—
177	C₅×C₂²⋊C₄	—	6	1	no	—
178	C₄²×C₅	—	3	2	no	—
179	C₄²×C₅	—	6	4	no	—
180	C₄²×C₅	—	6	1	no	—
181	C₄²×C₅	—	6	1	no	—
182	C₂²×SD₁₆	C₅×D₃	1	1	yes	characteristic
183	#519	—	3	1	no	—
184	#518	—	3	1	no	—
185	#440	—	3	4	no	—
186	C₄×SD₁₆	—	3	4	no	—
187	#427	—	3	1	no	—
188	#419	—	3	1	no	—
189	#418	—	3	1	no	—
190	#405	—	3	1	no	—
191	C₂²×C₃×C₅	—	2	2	no	—
192	C₂²×C₃×C₅	—	2	4	no	—
193	C₂²×C₃×C₅	—	4	4	no	—
194	C₂²×C₃×C₅	—	8	4	no	—
195	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
196	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
199	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
201	C₅×Dic₃	—	2	4	no	—
202	C₅×Dic₃	—	4	2	no	—
203	C₅×Dic₃	—	4	2	no	—
204	C₂⁴×C₃	—	2	1	no	—
205	C₂×C₃×Q₈	—	2	1	no	—
206	C₂×C₃×Q₈	—	2	2	no	—
207	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
208	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
209	C₂×C₃×D₄	—	2	1	no	—
210	C₂×C₃×D₄	—	2	2	no	—
211	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
212	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
213	C₂²×C₃×C₄	—	2	1	no	—
214	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
215	C₂²×Dic₃	—	2	4	no	—
216	C₃×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
217	C₃×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
218	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
219	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
220	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
221	#217	—	2	1	no	—
222	#217	—	2	1	no	—
223	#217	—	2	4	no	—
224	#217	C₅×D₄	1	2	yes	—
225	C₄⋊Dic₃	—	2	4	no	—
226	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
227	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
228	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
229	C₄×Dic₃	—	2	1	no	—
230	C₄×Dic₃	—	2	1	no	—
231	C₄×Dic₃	—	2	4	no	—
232	C₄×Dic₃	C₂³×C₅	1	2	yes	—
233	#208	—	2	2	no	—
234	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
235	C₂³×C₅	—	2	2	no	—
236	C₂³×C₅	—	2	4	no	—
237	C₂³×C₅	—	8	2	no	—
238	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
239	C₅×Q₈	—	2	4	no	—
240	C₅×Q₈	—	2	2	no	—
241	C₅×Q₈	C₂²×Dic₃	1	4	yes	—
242	C₅×D₄	—	2	4	no	—
243	C₅×D₄	—	2	2	no	—
244	C₅×D₄	C₂²×Dic₃	1	4	yes	—
245	C₂×C₄×C₅	—	2	4	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	3	4	no	—
248	C₂×C₄×C₅	—	6	2	no	—
249	C₂×C₄×C₅	—	6	2	no	—
250	C₂×C₄×C₅	—	24	4	no	—
251	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅	#237	1	2	yes	—
253	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
254	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
255	C₅×C₈	—	6	2	no	—
256	C₅×C₈	C₂²×Dic₃	1	2	yes	—
257	C₅×C₈	C₂²×Dic₃	1	2	yes	—
258	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
259	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
260	C₂×SD₁₆	C₅×Dic₃	1	8	yes	complemented
261	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
262	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
263	C₂×M₁₆	—	3	1	no	—
264	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
265	C₄×Q₈	—	3	4	no	—
266	C₄×Q₈	—	6	2	no	—
267	C₄×D₄	—	3	4	no	—
268	C₄×D₄	—	6	2	no	—
269	#117	—	3	1	no	—
270	#117	—	3	1	no	—
271	#117	—	3	1	no	—
272	#117	—	6	2	no	—
273	C₂×C₂²⋊C₄	—	6	2	no	—
274	#107	—	3	2	no	—
275	#106	—	3	2	no	—
276	#103	—	3	4	no	—
277	#102	—	3	4	no	—
278	#97	—	3	2	no	—
279	C₄×C₈	—	3	2	no	—
280	C₂×C₃×C₅	—	2	2	no	—
281	C₂×C₃×C₅	—	4	4	no	—
282	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
283	C₂×C₃×C₅	#577	1	2	yes	—
284	C₂³×C₃	—	2	2	no	—
285	C₂³×C₃	—	2	4	no	—
286	C₂³×C₃	—	8	2	no	—
287	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
288	C₃×Q₈	—	2	4	no	—
289	C₃×Q₈	—	2	2	no	—
290	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
291	C₃×D₄	—	2	4	no	—
292	C₃×D₄	—	2	2	no	—
293	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
297	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×C₃×C₄	C₅×#41	1	2	yes	—
299	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
300	C₂×Dic₃	—	2	2	no	—
301	C₂×Dic₃	—	2	2	no	—
302	C₂×Dic₃	—	8	4	no	—
303	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
304	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
305	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
306	C₃⋊C₈	—	2	2	no	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	4	4	no	—
310	C₂²×C₅	—	8	4	no	—
311	C₂²×C₅	D₄×Dic₃	1	2	yes	—
312	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
313	C₄×C₅	—	2	4	no	—
314	C₄×C₅	—	6	4	no	—
315	C₄×C₅	—	12	2	no	—
316	C₄×C₅	—	12	2	no	—
317	C₄×C₅	D₄×Dic₃	1	2	yes	—
318	C₄×C₅	C₂×#237	1	1	yes	characteristic
319	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
320	C₂⁴	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂×C₅×Dic₃	1	4	yes	complemented
324	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₂×C₅×Dic₃	1	4	yes	—
328	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	6	4	no	—
331	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
332	SD₁₆	C₂×C₅×Dic₃	1	8	yes	complemented
333	SD₁₆	C₂×C₅×Dic₃	1	8	yes	complemented
334	M₁₆	—	6	2	no	—
335	C₂×C₈	—	3	2	no	—
336	C₂×C₈	C₂×C₅×Dic₃	1	4	yes	complemented
337	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
338	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
339	C₄⋊C₄	—	3	2	no	—
340	C₄⋊C₄	—	3	2	no	—
341	C₄⋊C₄	—	3	2	no	—
342	C₄⋊C₄	—	6	4	no	—
343	C₂²⋊C₄	—	3	2	no	—
344	C₂²⋊C₄	—	6	4	no	—
345	C₂²⋊C₄	—	6	1	no	—
346	C₂²⋊C₄	—	6	1	no	—
347	C₄²	—	3	2	no	—
348	C₄²	—	6	4	no	—
349	C₄²	—	6	1	no	—
350	C₄²	—	6	1	no	—
351	C₃×C₅	#2949	1	1	yes	characteristic, complemented, Hall
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	2	4	no	—
354	C₂²×C₃	—	4	4	no	—
355	C₂²×C₃	—	8	4	no	—
356	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
357	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
360	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
361	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
362	Dic₃	—	2	4	no	—
363	Dic₃	—	4	2	no	—
364	Dic₃	—	4	2	no	—
365	C₂×C₅	—	2	2	no	—
366	C₂×C₅	—	4	4	no	—
367	C₂×C₅	#5762	1	2	yes	—
368	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
369	C₂³	—	2	2	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	8	2	no	—
372	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
373	Q₈	—	2	4	no	—
374	Q₈	—	2	2	no	—
375	Q₈	C₂²×C₅×Dic₃	1	4	yes	—
376	D₄	—	2	4	no	—
377	D₄	—	2	2	no	—
378	D₄	C₂²×C₅×Dic₃	1	4	yes	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	3	4	no	—
382	C₂×C₄	—	6	2	no	—
383	C₂×C₄	—	6	2	no	—
384	C₂×C₄	—	24	4	no	—
385	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
386	C₂×C₄	C₅×#237	1	2	yes	—
387	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
388	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
389	C₈	—	6	2	no	—
390	C₈	C₂²×C₅×Dic₃	1	2	yes	—
391	C₈	C₂²×C₅×Dic₃	1	2	yes	—
392	C₂×C₃	—	2	2	no	—
393	C₂×C₃	—	4	4	no	—
394	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
395	C₂×C₃	C₅×#577	1	2	yes	—
396	C₅	#83843	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²	—	2	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	8	4	no	—
401	C₂²	C₅×D₄×Dic₃	1	2	yes	—
402	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
403	C₄	—	2	4	no	—
404	C₄	—	6	4	no	—
405	C₄	—	12	2	no	—
406	C₄	—	12	2	no	—
407	C₄	C₅×D₄×Dic₃	1	2	yes	—
408	C₄	C₂×C₅×#237	1	1	yes	characteristic
409	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
410	C₃	C₅×#2949	1	1	yes	characteristic, complemented, Sylow
411	C₂	—	2	2	no	—
412	C₂	—	4	4	no	—
413	C₂	C₅×#5762	1	2	yes	—
414	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×SD₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₅×SD₁₆	D₃
hypocenter	C₃	C₅×#2949
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×#5812	C₂	semidirect
4. C₅×#5225	C₂	semidirect
6. C₅×#5164	C₂	semidirect
7. C₅×Dic₃×SD₁₆	C₂	semidirect
8. C₅×#5106	C₂	semidirect
9. C₅×#5101	C₂	semidirect
13. C₂×C₃×C₅×SD₁₆	C₄	semidirect
19. C₅×Q₈×Dic₃	C₂²	semidirect
27. C₅×#835	C₂²	semidirect
29. C₅×#818	C₂²	semidirect
30. C₅×#817	C₂²	semidirect
31. C₅×#815	C₂²	semidirect
32. C₅×C₈×Dic₃	C₂²	semidirect
33. #83843	C₅	direct (N × H)
46. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
55. C₃×C₅×SD₁₆	C₂×C₄	semidirect
56. C₃×C₅×SD₁₆	C₂×C₄	semidirect
57. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
75. #5812	C₂×C₅	semidirect
77. #5225	C₂×C₅	semidirect
79. #5164	C₂×C₅	semidirect
80. Dic₃×SD₁₆	C₂×C₅	semidirect
81. #5106	C₂×C₅	semidirect
82. #5101	C₂×C₅	semidirect
85. C₂×C₅×SD₁₆	Dic₃	semidirect
131. C₂×C₃×SD₁₆	C₄×C₅	semidirect
137. Q₈×Dic₃	C₂²×C₅	semidirect
145. #835	C₂²×C₅	semidirect
147. #818	C₂²×C₅	semidirect
148. #817	C₂²×C₅	semidirect
149. #815	C₂²×C₅	semidirect
150. C₈×Dic₃	C₂²×C₅	semidirect
154. C₂×C₅×Q₈	C₂×Dic₃	semidirect
163. C₅×SD₁₆	C₂×Dic₃	semidirect
164. C₅×SD₁₆	C₂×Dic₃	semidirect
167. C₂×C₅×C₈	C₂×Dic₃	semidirect
207. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
216. C₃×SD₁₆	C₂×C₄×C₅	semidirect
217. C₃×SD₁₆	C₂×C₄×C₅	semidirect
218. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
260. C₂×SD₁₆	C₅×Dic₃	semidirect
323. C₂×Q₈	C₂×C₅×Dic₃	semidirect
332. SD₁₆	C₂×C₅×Dic₃	semidirect
333. SD₁₆	C₂×C₅×Dic₃	semidirect
336. C₂×C₈	C₂×C₅×Dic₃	semidirect
351. C₃×C₅	#2949	semidirect
396. C₅	#83843	direct (N × H)
410. C₃	C₅×#2949	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×SD₁₆	2
C₅×#5812	2
C₅×#5798	2
C₅×#5225	2
C₅×#5215	2
C₅×#5164	2
C₅×Dic₃×SD₁₆	2
C₅×#5106	2
C₅×#5101	2
C₅×#2949	3
#83843	5

Subgroups — C5×#83843 #14417425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83843 #14417425