Subgroups — C₂×#11751110 #14429930

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×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#91759	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91116	C₂	1	1	yes	maximal, characteristic
4	C₂×#91116	C₂	1	1	yes	maximal, characteristic
5	#11751110	C₂	1	8	yes	maximal, direct product factor
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×#65298	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	—	2	1	no	—
12	C₃×C₄×C₅×D₄	—	2	2	no	—
13	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
19	C₂×#6712	—	2	1	no	—
20	C₂×#6712	—	2	1	no	—
21	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
22	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
23	#91759	—	2	2	no	—
24	#91759	C₂²	1	4	yes	complemented
25	#91116	C₂²	1	4	yes	—
26	#91116	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×#5009	—	5	1	no	maximal, Hall
31	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic
32	C₂×#4016	—	3	1	no	—
33	C₂×#3964	—	3	1	no	—
34	C₂×#3964	—	3	1	no	—
35	#65298	—	3	8	no	—
36	C₂×#3940	—	3	1	no	—
37	C₂×#3939	—	3	1	no	—
38	C₂×C₄⋊#168	—	3	1	no	—
39	C₂⁴×C₃×C₅	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	2	no	—
42	C₂×C₃×C₅×D₄	Q₈	1	4	yes	—
43	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	—	4	4	no	—
47	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×Dic₁₅	—	2	1	no	—
51	C₂²×Dic₁₅	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
54	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
55	C₃×C₄²×C₅	D₄	1	2	yes	—
56	C₃×C₄²×C₅	C₂³	1	2	yes	—
57	C₄⋊Dic₁₅	—	2	1	no	—
58	C₄⋊Dic₁₅	—	2	1	no	—
59	C₄⋊Dic₁₅	C₂³	1	2	yes	—
60	C₄⋊Dic₁₅	C₂³	1	2	yes	—
61	#6712	—	2	4	no	—
62	#6712	—	2	4	no	—
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×C₄×D₄	D₅	1	1	yes	characteristic
68	C₂×#870	—	5	1	no	—
69	C₂×#832	—	5	1	no	—
70	C₂×#832	—	5	1	no	—
71	#5009	—	5	8	no	—
72	C₂×#808	—	5	1	no	—
73	C₂×#807	—	5	1	no	—
74	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
75	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
76	C₂³×C₄×C₅	—	2	1	no	—
77	C₄×C₅×D₄	—	2	2	no	—
78	C₄×C₅×D₄	C₂×D₃	1	4	yes	—
79	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
80	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
82	C₂×C₄⋊Dic₅	—	3	1	no	—
83	C₂×C₄⋊Dic₅	—	3	1	no	—
84	C₂×#683	—	6	1	no	—
85	C₂×#683	—	6	1	no	—
86	C₂²×#168	—	3	1	no	—
87	C₂²×#168	—	3	1	no	—
88	#4016	—	3	4	no	—
89	#4016	—	6	2	no	—
90	#3964	—	3	4	no	—
91	#3964	—	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	—	2	4	no	—
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	—	4	2	no	—
99	C₂³×C₃×C₅	—	4	2	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
101	C₃×C₅×D₄	—	2	4	no	—
102	C₃×C₅×D₄	—	2	2	no	—
103	C₃×C₅×D₄	C₂×Q₈	1	4	yes	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	4	8	no	—
108	C₂×C₃×C₄×C₅	—	4	2	no	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
113	C₂×C₃×C₄×C₅	#41	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₂×Dic₁₅	—	2	2	no	—
116	C₂×Dic₁₅	—	2	2	no	—
117	C₂×Dic₁₅	—	4	2	no	—
118	C₂×Dic₁₅	—	4	2	no	—
119	C₃⋊#168	—	2	2	no	—
120	C₃⋊#168	—	2	2	no	—
121	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
122	C₂³×C₃×C₄	—	2	1	no	—
123	C₃×C₄×D₄	—	2	2	no	—
124	C₃×C₄×D₄	C₂×D₅	1	4	yes	—
125	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
126	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
128	C₂×C₄⋊Dic₃	—	5	1	no	—
129	C₂×C₄⋊Dic₃	—	5	1	no	—
130	C₂×Dic₃⋊C₄	—	10	1	no	—
131	C₂×Dic₃⋊C₄	—	10	1	no	—
132	C₂²×C₃⋊C₈	—	5	1	no	—
133	C₂²×C₃⋊C₈	—	5	1	no	—
134	#870	—	5	4	no	—
135	#870	—	10	2	no	—
136	#832	—	5	4	no	—
137	#832	—	5	4	no	—
138	#808	—	5	4	no	—
139	#807	—	5	4	no	—
140	C₄⋊(C₃⋊C₈)	—	5	4	no	—
141	C₂⁴×C₅	—	2	1	no	—
142	C₂×C₅×D₄	—	2	2	no	—
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	Dic₆	1	4	yes	—
145	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	4	no	—
148	C₂²×C₄×C₅	—	4	4	no	—
149	C₂²×C₄×C₅	#67	1	1	yes	characteristic
150	C₂²×C₄×C₅	#67	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
152	C₂²×Dic₅	—	6	1	no	—
153	C₂²×Dic₅	—	6	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
156	C₅×C₂²⋊C₄	—	2	4	no	—
157	C₄²×C₅	#67	1	2	yes	—
158	C₄²×C₅	C₂²×D₃	1	2	yes	—
159	C₄⋊Dic₅	—	3	2	no	—
160	C₄⋊Dic₅	—	3	2	no	—
161	C₄⋊Dic₅	—	6	1	no	—
162	C₄⋊Dic₅	—	6	1	no	—
163	#683	—	6	4	no	—
164	#683	—	6	4	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	—	15	1	no	—
170	C₂×C₄×D₄	D₁₅	1	1	yes	characteristic
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	—	2	4	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	4	8	no	—
181	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
182	C₂²×C₃×C₅	#135	1	2	yes	—
183	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
184	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
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	C₂²⋊Q₈	1	2	yes	—
189	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
190	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
191	Dic₁₅	—	4	2	no	—
192	Dic₁₅	—	4	2	no	—
193	C₂⁴×C₃	—	2	1	no	—
194	C₂×C₃×D₄	—	2	2	no	—
195	C₂×C₃×D₄	—	2	1	no	—
196	C₂×C₃×D₄	Dic₁₀	1	4	yes	—
197	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
198	C₂²×C₃×C₄	—	2	1	no	—
199	C₂²×C₃×C₄	—	2	4	no	—
200	C₂²×C₃×C₄	—	4	4	no	—
201	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
203	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
204	C₂²×Dic₃	—	10	1	no	—
205	C₂²×Dic₃	—	10	1	no	—
206	C₃×C₄⋊C₄	—	2	1	no	—
207	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
208	C₃×C₂²⋊C₄	—	2	4	no	—
209	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
210	C₃×C₄²	C₂²×D₅	1	2	yes	—
211	C₄⋊Dic₃	—	5	2	no	—
212	C₄⋊Dic₃	—	5	2	no	—
213	C₄⋊Dic₃	—	10	1	no	—
214	C₄⋊Dic₃	—	10	1	no	—
215	Dic₃⋊C₄	—	10	4	no	—
216	Dic₃⋊C₄	—	10	4	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	—	2	4	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	4	2	no	—
224	C₂³×C₅	—	4	2	no	—
225	C₂³×C₅	C₂×#67	1	1	yes	characteristic
226	C₅×D₄	—	2	4	no	—
227	C₅×D₄	—	2	2	no	—
228	C₅×D₄	C₂×Dic₆	1	4	yes	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	4	8	no	—
233	C₂×C₄×C₅	—	4	2	no	—
234	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
235	C₂×C₄×C₅	#235	1	2	yes	—
236	C₂×C₄×C₅	C₂×#67	1	2	yes	—
237	C₂×C₄×C₅	C₂×#67	1	2	yes	—
238	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
240	C₂×Dic₅	—	6	2	no	—
241	C₂×Dic₅	—	6	2	no	—
242	C₂×Dic₅	—	12	2	no	—
243	C₂×Dic₅	—	12	2	no	—
244	#168	—	6	2	no	—
245	#168	—	6	2	no	—
246	C₂²×D₄	C₂×D₁₅	1	1	yes	characteristic
247	C₂³×C₄	—	2	1	no	—
248	C₂²×C₈	—	15	1	no	—
249	C₂²×C₈	—	15	1	no	—
250	#125	—	15	4	no	—
251	#125	—	30	2	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	C₂×D₁₅	1	4	yes	—
254	C₂×C₄⋊C₄	—	15	1	no	—
255	C₂×C₄⋊C₄	—	15	1	no	—
256	C₂×C₄⋊C₄	—	30	1	no	—
257	C₂×C₄⋊C₄	—	30	1	no	—
258	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	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	—	4	4	no	—
267	C₂×C₃×C₅	#478	1	4	yes	complemented
268	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
269	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
270	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
271	C₂³×C₃	—	2	2	no	—
272	C₂³×C₃	—	2	4	no	—
273	C₂³×C₃	—	4	2	no	—
274	C₂³×C₃	—	4	2	no	—
275	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
276	C₃×D₄	—	2	2	no	—
277	C₃×D₄	—	2	4	no	—
278	C₃×D₄	C₂×Dic₁₀	1	4	yes	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	4	8	no	—
283	C₂×C₃×C₄	—	4	2	no	—
284	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
285	C₂×C₃×C₄	#709	1	2	yes	—
286	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
287	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
288	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
290	C₂×Dic₃	—	10	2	no	—
291	C₂×Dic₃	—	10	2	no	—
292	C₂×Dic₃	—	20	2	no	—
293	C₂×Dic₃	—	20	2	no	—
294	C₃⋊C₈	—	10	2	no	—
295	C₃⋊C₈	—	10	2	no	—
296	C₂²×C₅	—	2	4	no	—
297	C₂²×C₅	—	4	8	no	—
298	C₂²×C₅	—	4	2	no	—
299	C₂²×C₅	—	4	2	no	—
300	C₂²×C₅	#924	1	2	yes	—
301	C₂²×C₅	#932	1	2	yes	—
302	C₂²×C₅	#950	1	2	yes	—
303	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
304	C₄×C₅	—	2	2	no	—
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	#924	1	2	yes	—
308	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
309	C₄×C₅	C₂×#235	1	1	yes	characteristic
310	Dic₅	—	12	2	no	—
311	Dic₅	—	12	2	no	—
312	C₂⁴	—	2	1	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	Dic₃₀	1	4	yes	—
316	C₂×D₄	C₂²×D₁₅	1	2	yes	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	30	1	no	—
321	C₂²×C₄	—	30	1	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	1	no	—
330	C₄⋊C₄	—	15	2	no	—
331	C₄⋊C₄	—	15	2	no	—
332	C₄⋊C₄	—	30	1	no	—
333	C₄⋊C₄	—	30	1	no	—
334	C₄⋊C₄	—	30	4	no	—
335	C₄⋊C₄	—	30	4	no	—
336	C₄⋊C₄	C₂²×D₁₅	1	2	yes	—
337	C₂²⋊C₄	—	2	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	—	2	4	no	—
342	C₂²×C₃	—	4	8	no	—
343	C₂²×C₃	—	4	2	no	—
344	C₂²×C₃	—	4	2	no	—
345	C₂²×C₃	#4070	1	2	yes	—
346	C₂²×C₃	#4078	1	2	yes	—
347	C₂²×C₃	#4096	1	2	yes	—
348	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	4	2	no	—
352	C₃×C₄	#4070	1	2	yes	—
353	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
354	C₃×C₄	C₂×#709	1	1	yes	characteristic
355	Dic₃	—	20	2	no	—
356	Dic₃	—	20	2	no	—
357	C₂×C₅	—	4	4	no	—
358	C₂×C₅	#5009	1	4	yes	complemented
359	C₂×C₅	C₂×#924	1	1	yes	characteristic
360	C₂×C₅	C₂×#932	1	1	yes	characteristic
361	C₂×C₅	C₂×#950	1	1	yes	characteristic
362	C₂³	—	2	4	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	C₂×#1220	1	1	yes	characteristic
367	D₄	—	2	4	no	—
368	D₄	—	2	2	no	—
369	D₄	C₂×Dic₃₀	1	4	yes	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	8	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	30	2	no	—
376	C₂×C₄	—	30	2	no	—
377	C₂×C₄	—	60	2	no	—
378	C₂×C₄	—	60	2	no	—
379	C₂×C₄	C₂×Dic₃₀	1	2	yes	—
380	C₂×C₄	#6817	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	—	4	4	no	—
388	C₂×C₃	#65298	1	4	yes	complemented
389	C₂×C₃	C₂×#4070	1	1	yes	characteristic
390	C₂×C₃	C₂×#4078	1	1	yes	characteristic
391	C₂×C₃	C₂×#4096	1	1	yes	characteristic
392	C₅	C₂×#5009	1	1	yes	characteristic, complemented, Sylow
393	C₂²	—	2	4	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	8	no	—
397	C₂²	#91813	1	2	yes	—
398	C₂²	#91821	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	—	60	2	no	—
405	C₄	—	60	2	no	—
406	C₄	#91813	1	2	yes	—
407	C₄	C₂²×Dic₃₀	1	1	yes	characteristic
408	C₄	C₂×#6817	1	1	yes	characteristic
409	C₃	C₂×#65298	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	4	4	no	—
411	C₂	#11751110	1	4	yes	direct product factor
412	C₂	C₂×#91813	1	1	yes	characteristic
413	C₂	C₂×#91821	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×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₂×C₄×D₄	D₁₅
hypocenter	C₃×C₅	C₂×#478
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#91759	C₂	semidirect
5. #11751110	C₂	direct (N × H)
6. C₂×#91092	C₂	semidirect
7. C₂×#91091	C₂	semidirect
8. C₂×C₄⋊(C₃⋊#168)	C₂	semidirect
24. #91759	C₂²	semidirect
27. #91092	C₂²	semidirect
28. #91091	C₂²	semidirect
29. C₄⋊(C₃⋊#168)	C₂²	semidirect
267. C₂×C₃×C₅	#478	semidirect
340. C₃×C₅	C₂×#478	semidirect
358. C₂×C₅	#5009	semidirect
388. C₂×C₃	#65298	semidirect
392. C₅	C₂×#5009	semidirect
409. C₃	C₂×#65298	semidirect
411. C₂	#11751110	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×C₄×C₅×D₄	2
C₂×#91759	2
C₂×#91116	2
#11751110	2
C₂×#91092	2
C₂×#91091	2
C₂×C₄⋊(C₃⋊#168)	2
C₂×#65298	3
C₂×#5009	5

Subgroups — C2×#11751110 #14429930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11751110 #14429930