Subgroups — C₅×#70128 #14313670

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5816	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#101	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#836	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4478	C₂	1	2	yes	maximal, complemented
5	C₅×#4477	C₂	1	2	yes	maximal, complemented
6	C₅×#2133	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₅×#235	C₄	1	1	yes	characteristic
9	C₂×C₃×C₅×M₁₆	—	2	1	no	—
10	C₅×#947	C₄	1	1	yes	characteristic
11	C₅×#947	C₂²	1	1	yes	characteristic
12	C₅×#946	—	2	1	no	—
13	C₅×#946	—	2	1	no	—
14	C₅×#944	C₄	1	1	yes	characteristic
15	C₅×#944	C₂²	1	1	yes	characteristic
16	C₅×#929	—	2	1	no	—
17	C₅×#929	—	2	1	no	—
18	C₅×#926	C₄	1	1	yes	characteristic
19	C₂×C₅×#208	—	2	1	no	—
20	C₃×C₅×#101	—	2	1	no	—
21	C₃×C₅×#101	C₂²	1	2	yes	—
22	C₅×#836	—	2	1	no	—
23	C₅×#836	C₂²	1	2	yes	—
24	#70128	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₅×#536	—	3	1	no	—
26	C₂×C₅×#101	—	3	1	no	—
27	C₂×C₅×#101	D₃	1	1	yes	characteristic, complemented
28	C₅×#356	—	3	2	no	—
29	C₅×#355	—	3	2	no	—
30	C₂×C₃×C₅×Q₈	—	4	1	no	—
31	C₂×C₃×C₅×Q₈	—	4	1	no	—
32	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
34	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
35	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂×C₅×#67	—	2	1	no	—
40	C₅×#235	—	4	1	no	—
41	C₅×#235	—	4	1	no	—
42	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	—	2	1	no	—
44	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×M₁₆	—	2	2	no	—
46	C₃×C₅×M₁₆	—	4	1	no	—
47	C₂×C₃×C₅×C₈	—	4	1	no	—
48	C₅×#217	—	2	1	no	—
49	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
50	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
51	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
52	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
53	C₅×C₄⋊Dic₃	—	2	1	no	—
54	C₅×Dic₃⋊C₄	—	2	1	no	—
55	C₅×Dic₃⋊C₄	—	2	1	no	—
56	C₅×Dic₃⋊C₄	—	2	1	no	—
57	C₅×Dic₃⋊C₄	—	2	1	no	—
58	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
59	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
60	C₅×#208	—	2	2	no	—
61	C₅×#208	—	4	1	no	—
62	C₂×C₅×C₃⋊C₈	—	4	1	no	—
63	#5816	C₂×C₅	1	1	yes	characteristic
64	C₂×C₃×#101	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×#836	C₂×C₅	1	1	yes	characteristic, complemented
66	#4478	C₂×C₅	1	2	yes	complemented
67	#4477	C₂×C₅	1	2	yes	complemented
68	C₂×C₅×#41	—	3	1	no	—
69	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
70	C₂×C₅×M₁₆	—	2	1	no	—
71	C₂×C₅×M₁₆	—	6	1	no	—
72	C₅×C₄⋊Q₈	—	3	1	no	—
73	C₅×C₄⋊Q₈	—	3	1	no	—
74	C₅×#124	—	3	1	no	—
75	C₅×#124	—	3	1	no	—
76	C₅×#123	—	6	1	no	—
77	C₅×#123	—	6	1	no	—
78	C₅×C₂²⋊Q₈	—	6	1	no	—
79	C₅×C₂²⋊Q₈	—	6	1	no	—
80	C₅×#117	—	3	1	no	—
81	C₅×#101	—	2	1	no	—
82	C₅×#101	—	3	2	no	—
83	C₅×#101	—	6	1	no	—
84	C₅×#101	C₂×D₃	1	2	yes	—
85	#2133	—	3	1	no	Sylow
86	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₅×D₃	—	2	1	no	—
88	C₃×C₅×Q₈	—	4	1	no	—
89	C₃×C₅×Q₈	—	4	1	no	—
90	C₃×C₅×Q₈	—	4	1	no	—
91	C₃×C₅×Q₈	—	4	1	no	—
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₅×#67	—	4	1	no	—
105	C₅×#67	—	4	1	no	—
106	C₂×C₅×Dic₃	—	2	1	no	—
107	C₂×C₅×Dic₃	—	2	1	no	—
108	C₂×C₅×Dic₃	—	2	1	no	—
109	C₅×D₁₂	—	4	1	no	—
110	C₄×C₅×D₃	—	4	2	no	—
111	C₅×Dic₆	—	4	1	no	—
112	C₃×C₅×C₈	—	4	2	no	—
113	C₅×C₃⋊C₈	—	4	2	no	—
114	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
115	C₂×#235	C₄×C₅	1	1	yes	characteristic
116	C₂×C₃×M₁₆	—	2	1	no	—
117	#947	C₄×C₅	1	1	yes	characteristic
118	#947	C₂²×C₅	1	1	yes	characteristic
119	#946	—	2	1	no	—
120	#946	—	2	1	no	—
121	#944	C₄×C₅	1	1	yes	characteristic
122	#944	C₂²×C₅	1	1	yes	characteristic
123	#929	—	2	1	no	—
124	#929	—	2	1	no	—
125	#926	C₄×C₅	1	1	yes	characteristic
126	C₂×#208	—	2	1	no	—
127	C₃×#101	—	2	1	no	—
128	C₃×#101	C₂²×C₅	1	2	yes	—
129	#836	—	2	1	no	—
130	#836	C₂²×C₅	1	2	yes	—
131	C₅×#41	—	12	1	no	—
132	C₅×#41	—	12	1	no	—
133	C₂×C₅×Q₈	—	3	1	no	—
134	C₂×C₅×Q₈	—	4	1	no	—
135	C₂×C₅×Q₈	—	4	1	no	—
136	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
137	C₂×C₅×Q₈	D₁₂	1	1	yes	characteristic
138	C₂×C₅×Q₈	#67	1	1	yes	characteristic
139	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
140	C₂×C₅×D₄	—	3	1	no	—
141	C₂×C₅×D₄	—	6	1	no	—
142	C₂²×C₄×C₅	—	6	1	no	—
143	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
144	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
145	C₂²×C₄×C₅	#67	1	1	yes	characteristic
146	C₅×M₁₆	—	2	2	no	—
147	C₅×M₁₆	—	4	1	no	—
148	C₅×M₁₆	—	6	2	no	—
149	C₅×M₁₆	—	12	1	no	—
150	C₂×C₅×C₈	—	4	1	no	—
151	C₂×C₅×C₈	—	12	1	no	—
152	C₅×C₄⋊C₄	—	6	1	no	—
153	C₅×C₄⋊C₄	—	6	1	no	—
154	C₅×C₄⋊C₄	—	6	1	no	—
155	C₅×C₄⋊C₄	—	6	1	no	—
156	C₅×C₄⋊C₄	—	6	1	no	—
157	C₅×C₂²⋊C₄	—	6	1	no	—
158	C₅×C₂²⋊C₄	—	6	1	no	—
159	C₅×C₂²⋊C₄	—	6	1	no	—
160	C₅×C₂²⋊C₄	—	6	1	no	—
161	C₅×C₂²⋊C₄	—	6	1	no	—
162	C₄²×C₅	—	3	1	no	—
163	C₄²×C₅	—	3	1	no	—
164	#536	—	3	1	no	—
165	C₂×#101	—	3	1	no	—
166	C₂×#101	C₅×D₃	1	1	yes	characteristic, complemented
167	#356	—	3	2	no	—
168	#355	—	3	2	no	—
169	C₂²×C₃×C₅	—	4	1	no	—
170	C₂²×C₃×C₅	#99	1	1	yes	characteristic
171	C₂²×C₃×C₅	#99	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₅×D₃	—	4	2	no	—
174	C₂×C₅×D₃	—	4	1	no	—
175	C₃×C₄×C₅	—	2	1	no	—
176	C₃×C₄×C₅	—	2	1	no	—
177	C₃×C₄×C₅	—	2	1	no	—
178	C₃×C₄×C₅	—	2	1	no	—
179	C₃×C₄×C₅	—	2	1	no	—
180	C₃×C₄×C₅	—	2	1	no	—
181	C₅×Dic₃	—	4	1	no	—
182	C₅×Dic₃	—	4	1	no	—
183	C₅×Dic₃	—	4	1	no	—
184	C₂×C₃×Q₈	—	4	1	no	—
185	C₂×C₃×Q₈	—	4	1	no	—
186	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
187	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
188	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
189	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
193	C₂×#67	—	2	1	no	—
194	#235	—	4	1	no	—
195	#235	—	4	1	no	—
196	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
197	C₂×C₄×D₃	—	2	1	no	—
198	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
199	C₃×M₁₆	—	2	2	no	—
200	C₃×M₁₆	—	4	1	no	—
201	C₂×C₃×C₈	—	4	1	no	—
202	#217	—	2	1	no	—
203	(C₂×D₃)⋊C₄	—	2	1	no	—
204	(C₂×D₃)⋊C₄	—	2	1	no	—
205	(C₂×D₃)⋊C₄	—	2	1	no	—
206	(C₂×D₃)⋊C₄	—	2	1	no	—
207	C₄⋊Dic₃	—	2	1	no	—
208	Dic₃⋊C₄	—	2	1	no	—
209	Dic₃⋊C₄	—	2	1	no	—
210	Dic₃⋊C₄	—	2	1	no	—
211	Dic₃⋊C₄	—	2	1	no	—
212	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
213	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
214	#208	—	2	2	no	—
215	#208	—	4	1	no	—
216	C₂×C₃⋊C₈	—	4	1	no	—
217	C₂³×C₅	—	6	1	no	—
218	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
219	C₅×Q₈	—	4	1	no	—
220	C₅×Q₈	—	4	1	no	—
221	C₅×Q₈	—	4	1	no	—
222	C₅×Q₈	—	4	1	no	—
223	C₅×Q₈	—	12	1	no	—
224	C₅×D₄	—	12	1	no	—
225	C₅×D₄	—	12	1	no	—
226	C₅×D₄	—	12	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	6	1	no	—
234	C₂×C₄×C₅	—	6	1	no	—
235	C₂×C₄×C₅	—	6	1	no	—
236	C₂×C₄×C₅	—	12	2	no	—
237	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
243	C₅×C₈	—	4	2	no	—
244	C₅×C₈	—	12	2	no	—
245	C₂×#41	—	3	1	no	—
246	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	6	1	no	—
249	C₄⋊Q₈	—	3	1	no	—
250	C₄⋊Q₈	—	3	1	no	—
251	#124	—	3	1	no	—
252	#124	—	3	1	no	—
253	#123	—	6	1	no	—
254	#123	—	6	1	no	—
255	C₂²⋊Q₈	—	6	1	no	—
256	C₂²⋊Q₈	—	6	1	no	—
257	#117	—	3	1	no	—
258	#101	—	2	1	no	—
259	#101	—	3	2	no	—
260	#101	—	6	1	no	—
261	#101	C₂×C₅×D₃	1	2	yes	—
262	C₂×C₃×C₅	—	2	1	no	—
263	C₂×C₃×C₅	—	2	1	no	—
264	C₂×C₃×C₅	—	2	1	no	—
265	C₂×C₃×C₅	C₂×#99	1	1	yes	characteristic
266	C₅×D₃	—	8	1	no	—
267	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×D₃	—	2	1	no	—
269	C₃×Q₈	—	4	1	no	—
270	C₃×Q₈	—	4	1	no	—
271	C₃×Q₈	—	4	1	no	—
272	C₃×Q₈	—	4	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
285	#67	—	4	1	no	—
286	#67	—	4	1	no	—
287	C₂×Dic₃	—	2	1	no	—
288	C₂×Dic₃	—	2	1	no	—
289	C₂×Dic₃	—	2	1	no	—
290	D₁₂	—	4	1	no	—
291	C₄×D₃	—	4	2	no	—
292	Dic₆	—	4	1	no	—
293	C₃×C₈	—	4	2	no	—
294	C₃⋊C₈	—	4	2	no	—
295	C₂²×C₅	—	4	1	no	—
296	C₂²×C₅	—	12	2	no	—
297	C₂²×C₅	—	12	1	no	—
298	C₂²×C₅	#806	1	1	yes	characteristic
299	C₂²×C₅	#806	1	1	yes	characteristic
300	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
301	C₄×C₅	—	2	1	no	—
302	C₄×C₅	—	2	1	no	—
303	C₄×C₅	—	2	1	no	—
304	C₄×C₅	—	2	1	no	—
305	C₄×C₅	—	2	1	no	—
306	C₄×C₅	—	2	1	no	—
307	C₄×C₅	—	12	1	no	—
308	C₄×C₅	—	12	1	no	—
309	C₄×C₅	—	12	1	no	—
310	#41	—	12	1	no	—
311	#41	—	12	1	no	—
312	C₂×Q₈	—	3	1	no	—
313	C₂×Q₈	—	4	1	no	—
314	C₂×Q₈	—	4	1	no	—
315	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
316	C₂×Q₈	C₅×D₁₂	1	1	yes	characteristic
317	C₂×Q₈	C₅×#67	1	1	yes	characteristic
318	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
319	C₂×D₄	—	3	1	no	—
320	C₂×D₄	—	6	1	no	—
321	C₂²×C₄	—	6	1	no	—
322	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
323	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
324	C₂²×C₄	C₅×#67	1	1	yes	characteristic
325	M₁₆	—	2	2	no	—
326	M₁₆	—	4	1	no	—
327	M₁₆	—	6	2	no	—
328	M₁₆	—	12	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	12	1	no	—
331	C₄⋊C₄	—	6	1	no	—
332	C₄⋊C₄	—	6	1	no	—
333	C₄⋊C₄	—	6	1	no	—
334	C₄⋊C₄	—	6	1	no	—
335	C₄⋊C₄	—	6	1	no	—
336	C₂²⋊C₄	—	6	1	no	—
337	C₂²⋊C₄	—	6	1	no	—
338	C₂²⋊C₄	—	6	1	no	—
339	C₂²⋊C₄	—	6	1	no	—
340	C₂²⋊C₄	—	6	1	no	—
341	C₄²	—	3	1	no	—
342	C₄²	—	3	1	no	—
343	C₃×C₅	#2133	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	4	1	no	—
345	C₂²×C₃	C₅×#99	1	1	yes	characteristic
346	C₂²×C₃	C₅×#99	1	1	yes	characteristic
347	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
348	C₂×D₃	—	4	2	no	—
349	C₂×D₃	—	4	1	no	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	2	1	no	—
356	Dic₃	—	4	1	no	—
357	Dic₃	—	4	1	no	—
358	Dic₃	—	4	1	no	—
359	C₂×C₅	—	2	1	no	—
360	C₂×C₅	—	2	1	no	—
361	C₂×C₅	—	2	1	no	—
362	C₂×C₅	—	24	1	no	—
363	C₂×C₅	C₂×#806	1	1	yes	characteristic
364	C₂³	—	6	1	no	—
365	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
366	Q₈	—	4	1	no	—
367	Q₈	—	4	1	no	—
368	Q₈	—	4	1	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	12	1	no	—
371	D₄	—	12	1	no	—
372	D₄	—	12	1	no	—
373	D₄	—	12	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	6	1	no	—
381	C₂×C₄	—	6	1	no	—
382	C₂×C₄	—	6	1	no	—
383	C₂×C₄	—	12	2	no	—
384	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
385	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
386	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
387	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
388	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
389	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	12	2	no	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	2	1	no	—
394	C₂×C₃	—	2	1	no	—
395	C₂×C₃	C₂×C₅×#99	1	1	yes	characteristic
396	D₃	—	8	1	no	—
397	C₅	#70128	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	—	4	1	no	—
399	C₂²	—	12	2	no	—
400	C₂²	—	12	1	no	—
401	C₂²	C₅×#806	1	1	yes	characteristic
402	C₂²	C₅×#806	1	1	yes	characteristic
403	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	12	1	no	—
411	C₄	—	12	1	no	—
412	C₄	—	12	1	no	—
413	C₃	C₅×#2133	1	1	yes	characteristic, complemented, Sylow
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	—	2	1	no	—
417	C₂	—	24	1	no	—
418	C₂	C₂×C₅×#806	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×#806
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂×Q₈	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#101	C₂
socle	C₂×C₃×C₅	C₂×#99
prime radical	C₂×C₅×#235	C₄
cosocle	C₂×C₃×Q₈	C₂³×C₅
hypercenter	C₂×C₅×#101	D₃
hypocenter	C₃	C₅×#2133
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂³×C₅ ◁ C₂²×C₅×Q₈ ◁ C₂×C₅×#101

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#101	C₂	semidirect
3. C₂×C₅×#836	C₂	semidirect
4. C₅×#4478	C₂	semidirect
5. C₅×#4477	C₂	semidirect
24. #70128	C₅	direct (N × H)
27. C₂×C₅×#101	D₃	semidirect
64. C₂×C₃×#101	C₂×C₅	semidirect
65. C₂×#836	C₂×C₅	semidirect
66. #4478	C₂×C₅	semidirect
67. #4477	C₂×C₅	semidirect
166. C₂×#101	C₅×D₃	semidirect
343. C₃×C₅	#2133	semidirect
397. C₅	#70128	direct (N × H)
413. C₃	C₅×#2133	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5816	2
C₂×C₃×C₅×#101	2
C₂×C₅×#836	2
C₅×#4478	2
C₅×#4477	2
C₅×#2133	3
#70128	5

Subgroups — C5×#70128 #14313670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70128 #14313670