Subgroups — C₂×C₄×#6716 #14416048

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 444 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	C₂²×#6716	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Dic₃₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91116	C₂	1	1	yes	maximal, characteristic
5	C₄×#6716	C₂	1	8	yes	maximal, direct product factor
6	C₂×#91094	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#91092	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×#687	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	—	2	1	no	—
12	C₂²×Dic₃₀	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₅×D₄	—	2	2	no	—
14	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×#6716	C₄	1	8	yes	direct product factor
19	C₂×#6716	C₂²	1	4	yes	—
20	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
21	C₂×#6712	—	2	1	no	—
22	C₂×C₄×Dic₁₅	—	2	1	no	—
23	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
24	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
25	C₄×Dic₃₀	—	2	2	no	—
26	C₄×Dic₃₀	C₂²	1	4	yes	complemented
27	#91116	C₂²	1	4	yes	—
28	#91094	C₂²	1	4	yes	complemented
29	#91092	C₂²	1	4	yes	complemented
30	C₄×C₃⋊#168	C₂²	1	4	yes	complemented
31	C₂×C₄×#214	—	5	1	no	maximal, Hall
32	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic
33	C₂²×#687	—	3	1	no	—
34	C₂×C₄×Dic₁₀	—	3	1	no	—
35	C₂×#3964	—	3	1	no	—
36	C₄×#687	—	3	8	no	—
37	C₂×#3942	—	3	1	no	—
38	C₂×#3940	—	3	1	no	—
39	C₂×C₄×#168	—	3	1	no	—
40	C₂⁴×C₃×C₅	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
44	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	—	2	4	no	—
47	C₂²×C₃×C₄×C₅	—	4	4	no	—
48	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×Dic₁₅	—	2	1	no	—
52	C₂²×Dic₁₅	—	2	1	no	—
53	C₂×Dic₃₀	—	2	1	no	—
54	C₂×Dic₃₀	—	2	2	no	—
55	C₂×Dic₃₀	C₂×C₄	1	4	yes	complemented
56	C₂×Dic₃₀	C₂³	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	—	2	1	no	—
58	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
60	C₃×C₄²×C₅	D₄	1	2	yes	—
61	C₃×C₄²×C₅	C₂³	1	2	yes	—
62	#6716	C₂×C₄	1	16	yes	direct product factor
63	C₄⋊Dic₁₅	—	2	1	no	—
64	C₄⋊Dic₁₅	C₂³	1	2	yes	—
65	#6712	—	2	4	no	—
66	C₄×Dic₁₅	—	2	4	no	—
67	C₂×C₃⋊#168	—	2	2	no	—
68	C₂×C₃⋊#168	C₂×C₄	1	4	yes	complemented
69	C₂×C₃⋊#168	C₂³	1	2	yes	—
70	C₂×C₃⋊#168	C₂³	1	2	yes	—
71	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic
72	C₂²×#214	—	5	1	no	—
73	C₂×C₄×Dic₆	—	5	1	no	—
74	C₂×#832	—	5	1	no	—
75	C₄×#214	—	5	8	no	—
76	C₂×#810	—	5	1	no	—
77	C₂×#808	—	5	1	no	—
78	C₂×C₄×C₃⋊C₈	—	5	1	no	—
79	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
80	C₂³×C₄×C₅	—	2	1	no	—
81	C₂²×Dic₁₀	—	3	1	no	—
82	C₄×C₅×D₄	—	2	2	no	—
83	C₄×C₅×D₄	C₂×D₃	1	4	yes	—
84	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
85	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
87	C₂×#687	—	3	8	no	—
88	C₂×#687	—	3	4	no	—
89	C₂×C₄⋊Dic₅	—	3	1	no	—
90	C₂×#683	—	6	1	no	—
91	C₂×C₄×Dic₅	—	6	1	no	—
92	C₂²×#168	—	3	1	no	—
93	C₂²×#168	—	3	1	no	—
94	C₄×Dic₁₀	—	3	4	no	—
95	C₄×Dic₁₀	—	6	2	no	—
96	#3964	—	3	4	no	—
97	#3942	—	3	4	no	—
98	#3940	—	3	4	no	—
99	C₄×#168	—	3	4	no	—
100	C₂×C₄×SD₁₆	—	15	1	no	Sylow
101	C₂³×C₃×C₅	—	2	4	no	—
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	4	2	no	—
104	C₂³×C₃×C₅	—	4	2	no	—
105	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
106	C₃×C₅×D₄	—	2	4	no	—
107	C₃×C₅×D₄	—	2	2	no	—
108	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	4	2	no	—
112	C₂×C₃×C₄×C₅	—	4	8	no	—
113	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	#41	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₂×Dic₁₅	—	2	4	no	—
121	C₂×Dic₁₅	—	2	2	no	—
122	C₂×Dic₁₅	—	2	2	no	—
123	C₂×Dic₁₅	—	4	2	no	—
124	Dic₃₀	—	2	4	no	—
125	Dic₃₀	—	2	2	no	—
126	Dic₃₀	C₂²×C₄	1	4	yes	complemented
127	C₃⋊#168	—	2	2	no	—
128	C₃⋊#168	C₂²×C₄	1	4	yes	complemented
129	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
130	C₂³×C₃×C₄	—	2	1	no	—
131	C₂²×Dic₆	—	5	1	no	—
132	C₃×C₄×D₄	—	2	2	no	—
133	C₃×C₄×D₄	C₂×D₅	1	4	yes	—
134	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
135	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
136	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
137	C₂×#214	—	5	8	no	—
138	C₂×#214	—	5	4	no	—
139	C₂×C₄⋊Dic₃	—	5	1	no	—
140	C₂×Dic₃⋊C₄	—	10	1	no	—
141	C₂×C₄×Dic₃	—	10	1	no	—
142	C₂²×C₃⋊C₈	—	5	1	no	—
143	C₂²×C₃⋊C₈	—	5	1	no	—
144	C₄×Dic₆	—	5	4	no	—
145	C₄×Dic₆	—	10	2	no	—
146	#832	—	5	4	no	—
147	#810	—	5	4	no	—
148	#808	—	5	4	no	—
149	C₄×C₃⋊C₈	—	5	4	no	—
150	C₂⁴×C₅	—	2	1	no	—
151	C₂×C₅×D₄	—	2	2	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂×C₅×D₄	C₄×D₃	1	4	yes	—
154	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	4	no	—
157	C₂²×C₄×C₅	—	4	4	no	—
158	C₂²×C₄×C₅	#67	1	1	yes	characteristic
159	C₂²×C₄×C₅	#67	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
161	C₂²×Dic₅	—	6	1	no	—
162	C₂²×Dic₅	—	6	1	no	—
163	C₂×Dic₁₀	—	3	4	no	—
164	C₂×Dic₁₀	—	3	2	no	—
165	C₂×Dic₁₀	—	6	2	no	—
166	C₂×Dic₁₀	—	6	1	no	—
167	C₅×C₄⋊C₄	—	2	1	no	—
168	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
169	C₅×C₂²⋊C₄	—	2	4	no	—
170	C₄²×C₅	#67	1	2	yes	—
171	C₄²×C₅	C₂²×D₃	1	2	yes	—
172	#687	—	3	16	no	—
173	C₄⋊Dic₅	—	3	2	no	—
174	C₄⋊Dic₅	—	6	1	no	—
175	#683	—	6	4	no	—
176	C₄×Dic₅	—	6	4	no	—
177	C₂×#168	—	3	4	no	—
178	C₂×#168	—	3	2	no	—
179	C₂×#168	—	3	2	no	—
180	C₂×#168	—	6	2	no	—
181	C₂²×SD₁₆	—	15	1	no	—
182	C₂×C₄×Q₈	—	15	1	no	—
183	C₂×C₄×D₄	D₁₅	1	1	yes	characteristic
184	C₄×SD₁₆	—	15	8	no	—
185	C₂×#106	—	15	1	no	—
186	C₂×#103	—	15	1	no	—
187	C₂×#102	—	15	1	no	—
188	C₂×C₄×C₈	—	15	1	no	—
189	C₂²×C₃×C₅	—	2	4	no	—
190	C₂²×C₃×C₅	—	4	2	no	—
191	C₂²×C₃×C₅	—	4	2	no	—
192	C₂²×C₃×C₅	—	4	8	no	—
193	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
194	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
195	C₂²×C₃×C₅	#135	1	2	yes	—
196	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	—	4	2	no	—
199	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
200	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	complemented
201	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
202	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
203	Dic₁₅	—	2	4	no	—
204	Dic₁₅	—	4	2	no	—
205	C₂⁴×C₃	—	2	1	no	—
206	C₂×C₃×D₄	—	2	2	no	—
207	C₂×C₃×D₄	—	2	1	no	—
208	C₂×C₃×D₄	C₄×D₅	1	4	yes	—
209	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
210	C₂²×C₃×C₄	—	2	1	no	—
211	C₂²×C₃×C₄	—	2	4	no	—
212	C₂²×C₃×C₄	—	4	4	no	—
213	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
216	C₂²×Dic₃	—	10	1	no	—
217	C₂²×Dic₃	—	10	1	no	—
218	C₂×Dic₆	—	5	4	no	—
219	C₂×Dic₆	—	5	2	no	—
220	C₂×Dic₆	—	10	2	no	—
221	C₂×Dic₆	—	10	1	no	—
222	C₃×C₄⋊C₄	—	2	1	no	—
223	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
224	C₃×C₂²⋊C₄	—	2	4	no	—
225	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
226	C₃×C₄²	C₂²×D₅	1	2	yes	—
227	#214	—	5	16	no	—
228	C₄⋊Dic₃	—	5	2	no	—
229	C₄⋊Dic₃	—	10	1	no	—
230	Dic₃⋊C₄	—	10	4	no	—
231	C₄×Dic₃	—	10	4	no	—
232	C₂×C₃⋊C₈	—	5	4	no	—
233	C₂×C₃⋊C₈	—	5	2	no	—
234	C₂×C₃⋊C₈	—	5	2	no	—
235	C₂×C₃⋊C₈	—	10	2	no	—
236	C₂³×C₅	—	2	4	no	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	—	4	2	no	—
239	C₂³×C₅	—	4	2	no	—
240	C₂³×C₅	C₂×#67	1	1	yes	characteristic
241	C₅×D₄	—	2	4	no	—
242	C₅×D₄	—	2	2	no	—
243	C₅×D₄	C₂×C₄×D₃	1	4	yes	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	4	8	no	—
248	C₂×C₄×C₅	#214	1	4	yes	complemented
249	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
250	C₂×C₄×C₅	#235	1	2	yes	—
251	C₂×C₄×C₅	C₂×#67	1	2	yes	—
252	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂×#67	1	2	yes	—
254	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
255	C₂×Dic₅	—	6	4	no	—
256	C₂×Dic₅	—	6	2	no	—
257	C₂×Dic₅	—	6	2	no	—
258	C₂×Dic₅	—	12	2	no	—
259	Dic₁₀	—	3	4	no	—
260	Dic₁₀	—	6	4	no	—
261	Dic₁₀	—	6	2	no	—
262	#168	—	3	4	no	—
263	#168	—	6	2	no	—
264	C₂²×Q₈	—	15	1	no	—
265	C₂²×D₄	C₂×D₁₅	1	1	yes	characteristic
266	C₂³×C₄	—	2	1	no	—
267	C₂×SD₁₆	—	15	8	no	—
268	C₂×SD₁₆	—	15	4	no	—
269	C₂²×C₈	—	15	1	no	—
270	C₂²×C₈	—	15	1	no	—
271	C₄×Q₈	—	15	4	no	—
272	C₄×Q₈	—	30	2	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	C₂×D₁₅	1	4	yes	—
275	C₂×C₄⋊C₄	—	15	1	no	—
276	C₂×C₄⋊C₄	—	30	1	no	—
277	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₄²	—	30	1	no	—
280	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
281	#106	—	15	4	no	—
282	#103	—	15	4	no	—
283	#102	—	15	4	no	—
284	C₄×C₈	—	15	4	no	—
285	C₂×C₃×C₅	—	4	4	no	—
286	C₂×C₃×C₅	C₄×SD₁₆	1	4	yes	complemented
287	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
290	C₂³×C₃	—	2	2	no	—
291	C₂³×C₃	—	2	4	no	—
292	C₂³×C₃	—	4	2	no	—
293	C₂³×C₃	—	4	2	no	—
294	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
295	C₃×D₄	—	2	2	no	—
296	C₃×D₄	—	2	4	no	—
297	C₃×D₄	C₂×C₄×D₅	1	4	yes	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	4	2	no	—
301	C₂×C₃×C₄	—	4	8	no	—
302	C₂×C₃×C₄	#687	1	4	yes	complemented
303	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
304	C₂×C₃×C₄	#709	1	2	yes	—
305	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
306	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
307	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
308	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
309	C₂×Dic₃	—	10	2	no	—
310	C₂×Dic₃	—	10	4	no	—
311	C₂×Dic₃	—	10	2	no	—
312	C₂×Dic₃	—	20	2	no	—
313	Dic₆	—	5	4	no	—
314	Dic₆	—	10	2	no	—
315	Dic₆	—	10	4	no	—
316	C₃⋊C₈	—	5	4	no	—
317	C₃⋊C₈	—	10	2	no	—
318	C₂²×C₅	—	2	4	no	—
319	C₂²×C₅	—	4	8	no	—
320	C₂²×C₅	—	4	2	no	—
321	C₂²×C₅	—	4	2	no	—
322	C₂²×C₅	C₄×#67	1	2	yes	—
323	C₂²×C₅	C₂×#214	1	2	yes	—
324	C₂²×C₅	#950	1	2	yes	—
325	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
326	C₄×C₅	—	2	2	no	—
327	C₄×C₅	—	4	2	no	—
328	C₄×C₅	C₄×#67	1	2	yes	—
329	C₄×C₅	C₂×#214	1	4	yes	complemented
330	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
331	C₄×C₅	C₂×#235	1	1	yes	characteristic
332	Dic₅	—	6	4	no	—
333	Dic₅	—	12	2	no	—
334	C₂⁴	—	2	1	no	—
335	C₂×Q₈	—	15	4	no	—
336	C₂×Q₈	—	15	2	no	—
337	C₂×Q₈	—	30	2	no	—
338	C₂×Q₈	—	30	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	C₄×D₁₅	1	4	yes	—
342	C₂×D₄	C₂²×D₁₅	1	2	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	30	1	no	—
347	C₂²×C₄	—	30	1	no	—
348	C₂²×C₄	#1220	1	1	yes	characteristic
349	C₂²×C₄	#1220	1	1	yes	characteristic
350	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
351	SD₁₆	—	15	16	no	—
352	C₂×C₈	—	15	4	no	—
353	C₂×C₈	—	15	2	no	—
354	C₂×C₈	—	15	2	no	—
355	C₂×C₈	—	30	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	15	2	no	—
358	C₄⋊C₄	—	30	1	no	—
359	C₄⋊C₄	—	30	4	no	—
360	C₄⋊C₄	C₂²×D₁₅	1	2	yes	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₄²	—	30	4	no	—
363	C₄²	#1220	1	2	yes	—
364	C₄²	C₂²×D₁₅	1	2	yes	—
365	C₃×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	4	8	no	—
368	C₂²×C₃	—	4	2	no	—
369	C₂²×C₃	—	4	2	no	—
370	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
371	C₂²×C₃	C₂×#687	1	2	yes	—
372	C₂²×C₃	#4096	1	2	yes	—
373	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
374	C₃×C₄	—	2	2	no	—
375	C₃×C₄	—	4	2	no	—
376	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
377	C₃×C₄	C₂×#687	1	4	yes	complemented
378	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
379	C₃×C₄	C₂×#709	1	1	yes	characteristic
380	Dic₃	—	10	4	no	—
381	Dic₃	—	20	2	no	—
382	C₂×C₅	—	4	4	no	—
383	C₂×C₅	C₄×#214	1	4	yes	complemented
384	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
385	C₂×C₅	C₂²×#214	1	1	yes	characteristic
386	C₂×C₅	C₂×#950	1	1	yes	characteristic
387	C₂³	—	2	4	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	C₂×#1220	1	1	yes	characteristic
392	Q₈	—	15	4	no	—
393	Q₈	—	30	4	no	—
394	Q₈	—	30	2	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	2	no	—
397	D₄	C₂×C₄×D₁₅	1	4	yes	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	30	4	no	—
403	C₂×C₄	—	30	2	no	—
404	C₂×C₄	—	30	2	no	—
405	C₂×C₄	—	60	2	no	—
406	C₂×C₄	#6716	1	4	yes	direct product factor
407	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
408	C₂×C₄	#6817	1	2	yes	—
409	C₂×C₄	C₂×#1220	1	2	yes	—
410	C₂×C₄	C₂×#1220	1	1	yes	characteristic
411	C₂×C₄	C₂×#1220	1	2	yes	—
412	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
413	C₈	—	15	4	no	—
414	C₈	—	30	2	no	—
415	C₂×C₃	—	4	4	no	—
416	C₂×C₃	C₄×#687	1	4	yes	complemented
417	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
418	C₂×C₃	C₂²×#687	1	1	yes	characteristic
419	C₂×C₃	C₂×#4096	1	1	yes	characteristic
420	C₅	C₂×C₄×#214	1	1	yes	characteristic, complemented, Sylow
421	C₂²	—	2	4	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	8	no	—
425	C₂²	C₄×#1220	1	2	yes	—
426	C₂²	C₂×#6716	1	2	yes	—
427	C₂²	#91839	1	2	yes	—
428	C₂²	C₂²×#1220	1	1	yes	characteristic
429	C₄	—	2	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	30	4	no	—
432	C₄	—	60	2	no	—
433	C₄	C₄×#1220	1	2	yes	—
434	C₄	C₂×#6716	1	4	yes	direct product factor
435	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
436	C₄	C₂×#6817	1	1	yes	characteristic
437	C₃	C₂×C₄×#687	1	1	yes	characteristic, complemented, Sylow
438	C₂	—	4	4	no	—
439	C₂	C₄×#6716	1	4	yes	direct product factor
440	C₂	C₂×C₄×#1220	1	1	yes	characteristic
441	C₂	C₂²×#6716	1	1	yes	characteristic
442	C₂	C₂×#91839	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#1220
commutator	C₃×C₄×C₅	C₂³×C₄
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
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄×D₄	D₁₅
hypocenter	C₃×C₅	C₂×C₄×SD₁₆
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Dic₃₀	C₂	semidirect
5. C₄×#6716	C₂	direct (N × H)
6. C₂×#91094	C₂	semidirect
7. C₂×#91092	C₂	semidirect
8. C₂×C₄×C₃⋊#168	C₂	semidirect
18. C₂×#6716	C₄	direct (N × H)
26. C₄×Dic₃₀	C₂²	semidirect
28. #91094	C₂²	semidirect
29. #91092	C₂²	semidirect
30. C₄×C₃⋊#168	C₂²	semidirect
55. C₂×Dic₃₀	C₂×C₄	semidirect
62. #6716	C₂×C₄	direct (N × H)
68. C₂×C₃⋊#168	C₂×C₄	semidirect
113. C₂×C₃×C₄×C₅	SD₁₆	semidirect
126. Dic₃₀	C₂²×C₄	semidirect
128. C₃⋊#168	C₂²×C₄	semidirect
200. C₃×C₄×C₅	C₂×SD₁₆	semidirect
248. C₂×C₄×C₅	#214	semidirect
286. C₂×C₃×C₅	C₄×SD₁₆	semidirect
302. C₂×C₃×C₄	#687	semidirect
329. C₄×C₅	C₂×#214	semidirect
365. C₃×C₅	C₂×C₄×SD₁₆	semidirect
377. C₃×C₄	C₂×#687	semidirect
383. C₂×C₅	C₄×#214	semidirect
406. C₂×C₄	#6716	direct (N × H)
416. C₂×C₃	C₄×#687	semidirect
420. C₅	C₂×C₄×#214	semidirect
434. C₄	C₂×#6716	direct (N × H)
437. C₃	C₂×C₄×#687	semidirect
439. C₂	C₄×#6716	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
C₂²×#6716	2
C₂×C₄×Dic₃₀	2
C₂×#91116	2
C₄×#6716	2
C₂×#91094	2
C₂×#91092	2
C₂×C₄×C₃⋊#168	2
C₂×C₄×#687	3
C₂×C₄×#214	5

Subgroups — C2×C4×#6716 #14416048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#6716 #14416048