Subgroups — C₂×#11751167 #14429921

Order 1920.

896 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	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₆₀	C₂	1	1	yes	maximal, characteristic
3	#11751167	C₂	1	8	yes	maximal, direct product factor
4	C₂×#91093	C₂	1	1	yes	maximal, characteristic
5	C₂×#91093	C₂	1	1	yes	maximal, characteristic
6	C₂×#91092	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#91091	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65355	—	3	1	no	maximal, Hall
10	C₂²×D₆₀	C₂²	1	1	yes	characteristic
11	C₂²×C₄×D₁₅	—	2	1	no	—
12	C₃×C₅×#125	—	2	2	no	—
13	C₃×C₅×#125	C₂²	1	4	yes	complemented
14	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
15	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×#6714	—	2	1	no	—
20	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
21	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
22	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
23	C₄×D₆₀	—	2	2	no	—
24	C₄×D₆₀	C₂²	1	4	yes	—
25	#91093	C₂²	1	4	yes	—
26	#91093	C₂²	1	4	yes	—
27	#91092	C₂²	1	4	yes	complemented
28	#91091	C₂²	1	4	yes	complemented
29	C₄⋊(C₃⋊#168)	C₂²	1	4	yes	complemented
30	C₂×#5066	—	5	1	no	maximal, Hall
31	C₂×C₅×#125	D₃	1	1	yes	characteristic, complemented
32	C₂×C₄×D₂₀	—	3	1	no	—
33	#65355	—	3	8	no	—
34	C₂×#3941	—	3	1	no	—
35	C₂×#3941	—	3	1	no	—
36	C₂×#3940	—	3	1	no	—
37	C₂×#3939	—	3	1	no	—
38	C₂×C₄⋊#168	—	3	1	no	—
39	C₂³×D₁₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×Dic₁₅	—	2	1	no	—
46	C₂×D₆₀	—	2	1	no	—
47	C₂×D₆₀	—	2	2	no	—
48	C₂×D₆₀	Q₈	1	4	yes	—
49	C₂×D₆₀	C₂³	1	2	yes	—
50	C₂×C₄×D₁₅	—	2	4	no	—
51	C₂×C₄×D₁₅	—	4	4	no	—
52	C₃×C₅×C₄⋊C₄	—	2	4	no	—
53	C₃×C₅×C₄⋊C₄	—	2	4	no	—
54	C₃×C₅×C₄⋊C₄	—	2	1	no	—
55	C₃×C₅×C₄⋊C₄	—	2	1	no	—
56	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₃×C₄²×C₅	D₄	1	2	yes	—
59	C₃×C₄²×C₅	C₂³	1	2	yes	—
60	#6714	—	2	4	no	—
61	C₄⋊Dic₁₅	—	2	1	no	—
62	C₄⋊Dic₁₅	C₂³	1	2	yes	—
63	C₂×C₃⋊#168	—	2	2	no	—
64	C₂×C₃⋊#168	—	2	2	no	—
65	C₂×C₃⋊#168	C₂³	1	2	yes	—
66	C₂×C₃⋊#168	C₂³	1	2	yes	—
67	C₂×C₃×#125	D₅	1	1	yes	characteristic, complemented
68	C₂×C₄×D₁₂	—	5	1	no	—
69	#5066	—	5	8	no	—
70	C₂×#809	—	5	1	no	—
71	C₂×#809	—	5	1	no	—
72	C₂×#808	—	5	1	no	—
73	C₂×#807	—	5	1	no	—
74	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
75	C₂²×D₂₀	—	3	1	no	—
76	C₂²×C₄×D₅	—	6	1	no	—
77	C₅×#125	—	2	2	no	—
78	C₅×#125	C₂×D₃	1	4	yes	complemented
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
84	C₂×#685	—	6	1	no	—
85	C₂×C₄⋊Dic₅	—	3	1	no	—
86	C₂²×#168	—	3	1	no	—
87	C₂²×#168	—	3	1	no	—
88	C₄×D₂₀	—	3	4	no	—
89	C₄×D₂₀	—	6	2	no	—
90	#3941	—	3	4	no	—
91	#3941	—	3	4	no	—
92	#3940	—	3	4	no	—
93	#3939	—	3	4	no	—
94	C₄⋊#168	—	3	4	no	—
95	C₂×#478	—	15	1	no	Sylow
96	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂²×D₁₅	—	2	4	no	—
98	C₂²×D₁₅	—	2	2	no	—
99	C₂²×D₁₅	—	4	2	no	—
100	C₂²×D₁₅	—	4	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	4	2	no	—
106	C₂×C₃×C₄×C₅	—	4	2	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
111	C₂×C₃×C₄×C₅	#41	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
113	C₂×Dic₁₅	—	2	2	no	—
114	C₂×Dic₁₅	—	4	2	no	—
115	D₆₀	—	2	4	no	—
116	D₆₀	—	2	2	no	—
117	D₆₀	C₂×Q₈	1	4	yes	—
118	C₄×D₁₅	—	4	8	no	—
119	C₃⋊#168	—	2	2	no	—
120	C₃⋊#168	—	2	2	no	—
121	C₂²×D₁₂	—	5	1	no	—
122	C₂²×C₄×D₃	—	10	1	no	—
123	C₃×#125	—	2	2	no	—
124	C₃×#125	C₂×D₅	1	4	yes	complemented
125	C₂×C₃×C₄⋊C₄	—	2	1	no	—
126	C₂×C₃×C₄⋊C₄	—	2	1	no	—
127	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
129	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
130	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
131	C₂×C₄⋊Dic₃	—	5	1	no	—
132	C₂²×C₃⋊C₈	—	5	1	no	—
133	C₂²×C₃⋊C₈	—	5	1	no	—
134	C₄×D₁₂	—	5	4	no	—
135	C₄×D₁₂	—	10	2	no	—
136	#809	—	5	4	no	—
137	#809	—	5	4	no	—
138	#808	—	5	4	no	—
139	#807	—	5	4	no	—
140	C₄⋊(C₃⋊C₈)	—	5	4	no	—
141	C₂³×D₅	—	6	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	#67	1	1	yes	characteristic
145	C₂²×C₄×C₅	#67	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₂²×Dic₅	—	6	1	no	—
148	C₂×D₂₀	—	3	4	no	—
149	C₂×D₂₀	—	3	2	no	—
150	C₂×D₂₀	—	6	2	no	—
151	C₂×D₂₀	—	6	1	no	—
152	C₂×C₄×D₅	—	6	4	no	—
153	C₂×C₄×D₅	—	12	4	no	—
154	C₅×C₄⋊C₄	—	2	4	no	—
155	C₅×C₄⋊C₄	—	2	4	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
159	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
160	C₄²×C₅	#67	1	2	yes	—
161	C₄²×C₅	C₂²×D₃	1	2	yes	—
162	#685	—	6	4	no	—
163	C₄⋊Dic₅	—	3	2	no	—
164	C₄⋊Dic₅	—	6	1	no	—
165	C₂×#168	—	3	2	no	—
166	C₂×#168	—	3	2	no	—
167	C₂×#168	—	6	2	no	—
168	C₂×#168	—	6	2	no	—
169	C₂×#125	D₁₅	1	1	yes	characteristic, complemented
170	C₂×C₄×D₄	—	15	1	no	—
171	#478	—	15	8	no	—
172	C₂×#107	—	15	1	no	—
173	C₂×#106	—	15	1	no	—
174	C₂×C₄⋊C₈	—	15	1	no	—
175	C₂×#102	—	15	1	no	—
176	C₂×#102	—	15	1	no	—
177	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
178	C₂²×C₃×C₅	#135	1	2	yes	—
179	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
180	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
181	C₂×D₁₅	—	2	4	no	—
182	C₂×D₁₅	—	4	2	no	—
183	C₂×D₁₅	—	4	2	no	—
184	C₂×D₁₅	—	4	8	no	—
185	C₃×C₄×C₅	—	2	2	no	—
186	C₃×C₄×C₅	—	2	2	no	—
187	C₃×C₄×C₅	—	4	2	no	—
188	C₃×C₄×C₅	—	4	2	no	—
189	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
190	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
191	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
192	Dic₁₅	—	4	2	no	—
193	C₂³×D₃	—	10	1	no	—
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	—	2	1	no	—
196	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
197	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
199	C₂²×Dic₃	—	10	1	no	—
200	C₂×D₁₂	—	5	4	no	—
201	C₂×D₁₂	—	5	2	no	—
202	C₂×D₁₂	—	10	2	no	—
203	C₂×D₁₂	—	10	1	no	—
204	C₂×C₄×D₃	—	10	4	no	—
205	C₂×C₄×D₃	—	20	4	no	—
206	C₃×C₄⋊C₄	—	2	4	no	—
207	C₃×C₄⋊C₄	—	2	4	no	—
208	C₃×C₄⋊C₄	—	2	1	no	—
209	C₃×C₄⋊C₄	—	2	1	no	—
210	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
211	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
212	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
213	C₃×C₄²	C₂²×D₅	1	2	yes	—
214	(C₂×D₃)⋊C₄	—	10	4	no	—
215	C₄⋊Dic₃	—	5	2	no	—
216	C₄⋊Dic₃	—	10	1	no	—
217	C₂×C₃⋊C₈	—	5	2	no	—
218	C₂×C₃⋊C₈	—	5	2	no	—
219	C₂×C₃⋊C₈	—	10	2	no	—
220	C₂×C₃⋊C₈	—	10	2	no	—
221	C₂³×C₅	C₂×#67	1	1	yes	characteristic
222	C₂²×D₅	—	6	4	no	—
223	C₂²×D₅	—	6	2	no	—
224	C₂²×D₅	—	12	2	no	—
225	C₂²×D₅	—	12	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	4	2	no	—
231	C₂×C₄×C₅	—	4	2	no	—
232	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
233	C₂×C₄×C₅	#239	1	2	yes	—
234	C₂×C₄×C₅	C₂×#67	1	2	yes	—
235	C₂×C₄×C₅	C₂×#67	1	2	yes	—
236	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
238	C₂×Dic₅	—	6	2	no	—
239	C₂×Dic₅	—	12	2	no	—
240	D₂₀	—	3	4	no	—
241	D₂₀	—	6	4	no	—
242	D₂₀	—	6	2	no	—
243	C₄×D₅	—	12	8	no	—
244	#168	—	6	2	no	—
245	#168	—	6	2	no	—
246	C₂²×D₄	—	15	1	no	—
247	C₂³×C₄	—	30	1	no	—
248	C₂²×C₈	—	15	1	no	—
249	C₂²×C₈	—	15	1	no	—
250	#125	—	2	2	no	—
251	#125	C₂×D₁₅	1	4	yes	complemented
252	C₄×D₄	—	15	4	no	—
253	C₄×D₄	—	30	2	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	15	1	no	—
257	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	30	1	no	—
260	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
261	#107	—	15	4	no	—
262	#106	—	15	4	no	—
263	C₄⋊C₈	—	15	4	no	—
264	#102	—	15	4	no	—
265	#102	—	15	4	no	—
266	C₂×C₃×C₅	#478	1	4	yes	complemented
267	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
269	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
270	D₁₅	—	4	4	no	—
271	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
272	C₂²×D₃	—	10	2	no	—
273	C₂²×D₃	—	10	4	no	—
274	C₂²×D₃	—	20	2	no	—
275	C₂²×D₃	—	20	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	4	2	no	—
281	C₂×C₃×C₄	—	4	2	no	—
282	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
283	C₂×C₃×C₄	#713	1	2	yes	—
284	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
285	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
286	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
288	C₂×Dic₃	—	10	2	no	—
289	C₂×Dic₃	—	20	2	no	—
290	D₁₂	—	5	4	no	—
291	D₁₂	—	10	2	no	—
292	D₁₂	—	10	4	no	—
293	C₄×D₃	—	20	8	no	—
294	C₃⋊C₈	—	10	2	no	—
295	C₃⋊C₈	—	10	2	no	—
296	C₂²×C₅	#946	1	2	yes	—
297	C₂²×C₅	#949	1	2	yes	—
298	C₂²×C₅	#950	1	2	yes	—
299	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
300	C₂×D₅	—	6	4	no	—
301	C₂×D₅	—	12	2	no	—
302	C₂×D₅	—	12	2	no	—
303	C₂×D₅	—	12	8	no	—
304	C₄×C₅	—	2	2	no	—
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	—	4	2	no	—
308	C₄×C₅	#946	1	2	yes	—
309	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
310	C₄×C₅	C₂×#239	1	1	yes	characteristic
311	Dic₅	—	12	2	no	—
312	C₂⁴	—	30	1	no	—
313	C₂×D₄	—	15	4	no	—
314	C₂×D₄	—	15	2	no	—
315	C₂×D₄	—	30	2	no	—
316	C₂×D₄	—	30	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	30	1	no	—
320	C₂²×C₄	—	30	4	no	—
321	C₂²×C₄	—	60	4	no	—
322	C₂²×C₄	#1220	1	1	yes	characteristic
323	C₂²×C₄	#1220	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
325	C₂×C₈	—	15	2	no	—
326	C₂×C₈	—	15	2	no	—
327	C₂×C₈	—	30	2	no	—
328	C₂×C₈	—	30	2	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	15	2	no	—
334	C₄⋊C₄	—	30	1	no	—
335	C₄⋊C₄	C₂²×D₁₅	1	2	yes	—
336	C₄⋊C₄	C₂²×D₁₅	1	2	yes	—
337	C₂²⋊C₄	—	30	4	no	—
338	C₄²	#1220	1	2	yes	—
339	C₄²	C₂²×D₁₅	1	2	yes	—
340	C₃×C₅	C₂×#478	1	1	yes	characteristic, complemented, Hall
341	C₂²×C₃	#4092	1	2	yes	—
342	C₂²×C₃	#4095	1	2	yes	—
343	C₂²×C₃	#4096	1	2	yes	—
344	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
345	C₂×D₃	—	10	4	no	—
346	C₂×D₃	—	20	8	no	—
347	C₂×D₃	—	20	2	no	—
348	C₂×D₃	—	20	2	no	—
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	4	2	no	—
352	C₃×C₄	—	4	2	no	—
353	C₃×C₄	#4092	1	2	yes	—
354	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
355	C₃×C₄	C₂×#713	1	1	yes	characteristic
356	Dic₃	—	20	2	no	—
357	C₂×C₅	#5066	1	4	yes	complemented
358	C₂×C₅	C₂×#946	1	1	yes	characteristic
359	C₂×C₅	C₂×#949	1	1	yes	characteristic
360	C₂×C₅	C₂×#950	1	1	yes	characteristic
361	D₅	—	12	4	no	—
362	C₂³	—	30	4	no	—
363	C₂³	—	30	2	no	—
364	C₂³	—	60	2	no	—
365	C₂³	—	60	2	no	—
366	C₂³	C₂×#1220	1	1	yes	characteristic
367	D₄	—	15	4	no	—
368	D₄	—	30	4	no	—
369	D₄	—	30	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	30	2	no	—
377	C₂×C₄	—	60	8	no	—
378	C₂×C₄	—	60	2	no	—
379	C₂×C₄	Q₈×D₁₅	1	2	yes	—
380	C₂×C₄	#6821	1	2	yes	—
381	C₂×C₄	C₂×#1220	1	2	yes	—
382	C₂×C₄	C₂×#1220	1	2	yes	—
383	C₂×C₄	C₂×#1220	1	1	yes	characteristic
384	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
385	C₈	—	30	2	no	—
386	C₈	—	30	2	no	—
387	C₂×C₃	#65355	1	4	yes	complemented
388	C₂×C₃	C₂×#4092	1	1	yes	characteristic
389	C₂×C₃	C₂×#4095	1	1	yes	characteristic
390	C₂×C₃	C₂×#4096	1	1	yes	characteristic
391	D₃	—	20	4	no	—
392	C₅	C₂×#5066	1	1	yes	characteristic, complemented, Sylow
393	C₂²	—	30	4	no	—
394	C₂²	—	60	2	no	—
395	C₂²	—	60	2	no	—
396	C₂²	—	60	8	no	—
397	C₂²	#91835	1	2	yes	—
398	C₂²	#91838	1	2	yes	—
399	C₂²	#91839	1	2	yes	—
400	C₂²	C₂²×#1220	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	60	2	no	—
406	C₄	#91835	1	2	yes	—
407	C₄	C₂×Q₈×D₁₅	1	1	yes	characteristic
408	C₄	C₂×#6821	1	1	yes	characteristic
409	C₃	C₂×#65355	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	60	4	no	—
411	C₂	#11751167	1	4	yes	direct product factor
412	C₂	C₂×#91835	1	1	yes	characteristic
413	C₂	C₂×#91838	1	1	yes	characteristic
414	C₂	C₂×#91839	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#1220
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₅×#125	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×D₆₀	C₂²
hypercenter	C₂×#125	D₁₅
hypocenter	C₃×C₅	C₂×#478
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#125	C₂	semidirect
3. #11751167	C₂	direct (N × H)
6. C₂×#91092	C₂	semidirect
7. C₂×#91091	C₂	semidirect
8. C₂×C₄⋊(C₃⋊#168)	C₂	semidirect
13. C₃×C₅×#125	C₂²	semidirect
27. #91092	C₂²	semidirect
28. #91091	C₂²	semidirect
29. C₄⋊(C₃⋊#168)	C₂²	semidirect
31. C₂×C₅×#125	D₃	semidirect
67. C₂×C₃×#125	D₅	semidirect
78. C₅×#125	C₂×D₃	semidirect
124. C₃×#125	C₂×D₅	semidirect
169. C₂×#125	D₁₅	semidirect
251. #125	C₂×D₁₅	semidirect
266. C₂×C₃×C₅	#478	semidirect
340. C₃×C₅	C₂×#478	semidirect
357. C₂×C₅	#5066	semidirect
387. C₂×C₃	#65355	semidirect
392. C₅	C₂×#5066	semidirect
409. C₃	C₂×#65355	semidirect
411. C₂	#11751167	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#125	2
C₂×C₄×D₆₀	2
#11751167	2
C₂×#91093	2
C₂×#91092	2
C₂×#91091	2
C₂×C₄⋊(C₃⋊#168)	2
C₂×#65355	3
C₂×#5066	5

Subgroups — C2×#11751167 #14429921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11751167 #14429921