Subgroups — C₂×Q₈×C₁₃×Q₁₆ #15747694

Order 3328.

1830 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₁₃	C₂	1	2	yes	maximal
2	Q₈×C₁₃×Q₁₆	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#500	C₂	1	3	yes	maximal
4	C₂×C₁₃×#477	C₂	1	6	yes	maximal
5	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₁₃×Q₁₆	C₂	1	3	yes	maximal
7	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
8	Q₈²×C₁₃	—	2	8	no	—
9	Q₈²×C₁₃	C₂²	1	16	yes	—
10	C₂×C₁₃×C₄⋊Q₈	—	2	6	no	—
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	6	yes	—
12	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
13	C₂×C₄×Q₈×C₁₃	C₂²	1	6	yes	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#500	C₂²	1	24	yes	—
16	C₁₃×#477	C₂²	1	48	yes	—
17	C₈×Q₈×C₁₃	C₂²	1	8	yes	—
18	C₄×C₁₃×Q₁₆	C₂²	1	24	yes	—
19	C₂×C₁₃×#107	C₂²	1	6	yes	—
20	C₂×C₁₃×#107	C₂²	1	3	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	3	yes	—
22	C₂×C₁₃×#103	C₂²	1	6	yes	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
24	C₂²×Q₈×C₁₃	—	2	6	no	—
25	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
26	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
27	C₂×C₁₃×Q₁₆	Q₈	1	8	yes	direct product factor
28	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
29	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
30	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
31	C₁₃×C₄⋊Q₈	—	2	48	no	—
32	C₁₃×C₄⋊Q₈	—	2	12	no	—
33	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	—
34	C₄×Q₈×C₁₃	—	2	16	no	—
35	C₄×Q₈×C₁₃	—	2	12	no	—
36	C₄×Q₈×C₁₃	D₄	1	4	yes	—
37	C₄×Q₈×C₁₃	C₂³	1	24	yes	—
38	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
39	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
40	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
41	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
42	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
43	C₂×C₄²×C₁₃	—	2	6	no	—
44	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
45	C₁₃×#107	C₂³	1	12	yes	—
46	C₁₃×#107	C₂³	1	24	yes	—
47	C₁₃×C₄⋊C₈	C₂³	1	12	yes	—
48	C₁₃×#103	C₂³	1	24	yes	—
49	C₄×C₈×C₁₃	C₂³	1	12	yes	—
50	C₂×Q₈×Q₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂×Q₈×C₁₃	—	2	2	no	—
52	C₂×Q₈×C₁₃	—	2	24	no	—
53	C₂×Q₈×C₁₃	—	2	4	no	—
54	C₂×Q₈×C₁₃	—	8	12	no	—
55	C₂×Q₈×C₁₃	Q₁₆	1	8	yes	direct product factor
56	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
57	C₂×Q₈×C₁₃	C₂×Q₈	1	8	yes	—
58	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
59	C₂²×C₄×C₁₃	—	2	2	no	—
60	C₂²×C₄×C₁₃	—	2	6	no	—
61	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
62	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
63	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
64	C₁₃×Q₁₆	C₂×Q₈	1	16	yes	direct product factor
65	C₂×C₈×C₁₃	—	2	6	no	—
66	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
67	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
68	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
69	C₁₃×C₄⋊C₄	—	2	24	no	—
70	C₁₃×C₄⋊C₄	—	2	24	no	—
71	C₁₃×C₄⋊C₄	—	2	6	no	—
72	C₁₃×C₄⋊C₄	C₂×D₄	1	12	yes	—
73	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
74	C₄²×C₁₃	—	2	24	no	—
75	C₄²×C₁₃	C₂×D₄	1	6	yes	—
76	C₄²×C₁₃	C₂⁴	1	6	yes	—
77	C₂×Q₈²	C₂×C₁₃	1	2	yes	—
78	Q₈×Q₁₆	C₂×C₁₃	1	16	yes	direct product factor
79	C₂×#500	C₂×C₁₃	1	3	yes	—
80	C₂×#477	C₂×C₁₃	1	6	yes	—
81	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic
82	C₂×C₄×Q₁₆	C₂×C₁₃	1	3	yes	—
83	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
84	Q₈×C₁₃	—	2	8	no	—
85	Q₈×C₁₃	—	2	4	no	—
86	Q₈×C₁₃	—	8	24	no	—
87	Q₈×C₁₃	C₂×Q₁₆	1	16	yes	direct product factor
88	Q₈×C₁₃	C₂²×Q₈	1	8	yes	—
89	C₂×C₄×C₁₃	—	2	8	no	—
90	C₂×C₄×C₁₃	—	2	6	no	—
91	C₂×C₄×C₁₃	—	2	4	no	—
92	C₂×C₄×C₁₃	—	2	12	no	—
93	C₂×C₄×C₁₃	—	4	12	no	—
94	C₂×C₄×C₁₃	C₂×Q₁₆	1	12	yes	—
95	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
96	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
98	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
99	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
100	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
101	C₈×C₁₃	—	2	6	no	—
102	C₈×C₁₃	C₂²×Q₈	1	4	yes	—
103	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
104	Q₈²	—	2	8	no	—
105	Q₈²	C₂²×C₁₃	1	16	yes	—
106	C₂×C₄⋊Q₈	—	2	6	no	—
107	C₂×C₄⋊Q₈	C₂²×C₁₃	1	6	yes	—
108	C₂×C₄×Q₈	—	2	2	no	—
109	C₂×C₄×Q₈	C₂²×C₁₃	1	6	yes	—
110	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
111	#500	C₂²×C₁₃	1	24	yes	—
112	#477	C₂²×C₁₃	1	48	yes	—
113	C₈×Q₈	C₂²×C₁₃	1	8	yes	—
114	C₄×Q₁₆	C₂²×C₁₃	1	24	yes	—
115	C₂×#107	C₂²×C₁₃	1	6	yes	—
116	C₂×#107	C₂²×C₁₃	1	3	yes	—
117	C₂×C₄⋊C₈	C₂²×C₁₃	1	3	yes	—
118	C₂×#103	C₂²×C₁₃	1	6	yes	—
119	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
120	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
121	C₂²×C₁₃	C₂²×Q₁₆	1	2	yes	—
122	C₂²×C₁₃	#576	1	2	yes	—
123	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
124	C₄×C₁₃	—	2	8	no	—
125	C₄×C₁₃	—	2	6	no	—
126	C₄×C₁₃	—	4	12	no	—
127	C₄×C₁₃	D₄×Q₈	1	2	yes	—
128	C₄×C₁₃	C₂²×Q₁₆	1	12	yes	—
129	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
130	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
131	C₂²×Q₈	—	2	6	no	—
132	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
133	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
134	C₂×Q₁₆	Q₈×C₁₃	1	8	yes	direct product factor
135	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
136	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
137	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
138	C₄⋊Q₈	—	2	48	no	—
139	C₄⋊Q₈	—	2	12	no	—
140	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	—
141	C₄×Q₈	—	2	16	no	—
142	C₄×Q₈	—	2	12	no	—
143	C₄×Q₈	D₄×C₁₃	1	4	yes	—
144	C₄×Q₈	C₂³×C₁₃	1	24	yes	—
145	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
146	C₂×C₄⋊C₄	—	2	6	no	—
147	C₂×C₄⋊C₄	—	2	6	no	—
148	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
149	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
150	C₂×C₄²	—	2	6	no	—
151	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
152	#107	C₂³×C₁₃	1	12	yes	—
153	#107	C₂³×C₁₃	1	24	yes	—
154	C₄⋊C₈	C₂³×C₁₃	1	12	yes	—
155	#103	C₂³×C₁₃	1	24	yes	—
156	C₄×C₈	C₂³×C₁₃	1	12	yes	—
157	C₂×C₁₃	Q₈×Q₁₆	1	4	yes	direct product factor
158	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
159	C₂×C₁₃	C₂³×Q₁₆	1	1	yes	characteristic
160	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	2	24	no	—
163	C₂×Q₈	—	2	4	no	—
164	C₂×Q₈	—	8	12	no	—
165	C₂×Q₈	C₁₃×Q₁₆	1	8	yes	direct product factor
166	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
167	C₂×Q₈	C₂×Q₈×C₁₃	1	8	yes	—
168	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	6	no	—
171	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
172	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
173	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
174	Q₁₆	C₂×Q₈×C₁₃	1	16	yes	direct product factor
175	C₂×C₈	—	2	6	no	—
176	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
177	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
178	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
179	C₄⋊C₄	—	2	24	no	—
180	C₄⋊C₄	—	2	24	no	—
181	C₄⋊C₄	—	2	6	no	—
182	C₄⋊C₄	C₂×D₄×C₁₃	1	12	yes	—
183	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
184	C₄²	—	2	24	no	—
185	C₄²	C₂×D₄×C₁₃	1	6	yes	—
186	C₄²	C₂⁴×C₁₃	1	6	yes	—
187	C₁₃	C₂×Q₈×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
188	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
189	Q₈	—	2	8	no	—
190	Q₈	—	2	4	no	—
191	Q₈	—	8	24	no	—
192	Q₈	C₂×C₁₃×Q₁₆	1	16	yes	direct product factor
193	Q₈	C₂²×Q₈×C₁₃	1	8	yes	—
194	C₂×C₄	—	2	8	no	—
195	C₂×C₄	—	2	6	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	12	no	—
198	C₂×C₄	—	4	12	no	—
199	C₂×C₄	C₂×C₁₃×Q₁₆	1	12	yes	—
200	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
201	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
202	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
203	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
204	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
205	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
206	C₈	—	2	6	no	—
207	C₈	C₂²×Q₈×C₁₃	1	4	yes	—
208	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
209	C₂²	C₂²×C₁₃×Q₁₆	1	2	yes	—
210	C₂²	C₁₃×#576	1	2	yes	—
211	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
212	C₄	—	2	6	no	—
213	C₄	—	2	8	no	—
214	C₄	—	4	12	no	—
215	C₄	D₄×Q₈×C₁₃	1	2	yes	—
216	C₄	C₂²×C₁₃×Q₁₆	1	12	yes	—
217	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
218	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
219	C₂	Q₈×C₁₃×Q₁₆	1	4	yes	direct product factor
220	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
221	C₂	C₂³×C₁₃×Q₁₆	1	1	yes	characteristic
222	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₃×Q₁₆	C₂	direct (N × H)
27. C₂×C₁₃×Q₁₆	Q₈	direct (N × H)
50. C₂×Q₈×Q₁₆	C₁₃	direct (N × H)
55. C₂×Q₈×C₁₃	Q₁₆	direct (N × H)
64. C₁₃×Q₁₆	C₂×Q₈	direct (N × H)
78. Q₈×Q₁₆	C₂×C₁₃	direct (N × H)
87. Q₈×C₁₃	C₂×Q₁₆	direct (N × H)
134. C₂×Q₁₆	Q₈×C₁₃	direct (N × H)
157. C₂×C₁₃	Q₈×Q₁₆	direct (N × H)
165. C₂×Q₈	C₁₃×Q₁₆	direct (N × H)
174. Q₁₆	C₂×Q₈×C₁₃	direct (N × H)
187. C₁₃	C₂×Q₈×Q₁₆	direct (N × H)
192. Q₈	C₂×C₁₃×Q₁₆	direct (N × H)
219. C₂	Q₈×C₁₃×Q₁₆	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×Q₈²×C₁₃	2
Q₈×C₁₃×Q₁₆	2
C₂×C₁₃×#500	2
C₂×C₁₃×#477	2
C₂×C₈×Q₈×C₁₃	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×Q₈×Q₁₆	13

Subgroups — C2×Q8×C13×Q16 #15747694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×C₁₃×Q₁₆ #15747694