Subgroups — C₂×C₁₃×#2241 #15720034

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2241	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₁₃×#358	C₂	1	4	yes	maximal
5	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	—	2	1	no	—
7	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
8	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
9	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
10	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
11	C₁₃×#500	—	2	2	no	—
12	C₁₃×#500	C₂²	1	4	yes	—
13	C₁₃×#494	—	2	2	no	—
14	C₁₃×#494	C₂²	1	4	yes	—
15	C₂×C₁₃×#107	—	2	1	no	—
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#358	C₂²	1	16	yes	—
19	C₄×C₁₃×C₁₆	C₂²	1	4	yes	—
20	C₂²×Q₈×C₁₃	—	2	2	no	—
21	C₂²×Q₈×C₁₃	—	4	1	no	—
22	C₂×C₁₃×Q₁₆	—	2	2	no	—
23	C₂×C₁₃×Q₁₆	—	2	4	no	—
24	C₂×C₁₃×Q₁₆	—	2	8	no	—
25	C₂×C₁₃×Q₁₆	—	4	4	no	—
26	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
27	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
29	C₁₃×C₄⋊Q₈	—	2	4	no	—
30	C₁₃×C₄⋊Q₈	—	2	4	no	—
31	C₁₃×C₄⋊Q₈	—	4	2	no	—
32	C₁₃×C₄⋊Q₈	—	4	2	no	—
33	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
35	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
36	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
37	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
38	C₂×C₁₃×C₁₆	—	2	4	no	—
39	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
40	C₁₃×#107	—	2	4	no	—
41	C₁₃×#107	—	2	2	no	—
42	C₁₃×#107	C₂³	1	4	yes	—
43	C₄×C₈×C₁₃	D₄	1	2	yes	—
44	C₄×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂×#2241	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×Q₈×C₁₃	—	2	4	no	—
47	C₂×Q₈×C₁₃	—	4	4	no	—
48	C₂×Q₈×C₁₃	—	4	2	no	—
49	C₂×Q₈×C₁₃	—	4	4	no	—
50	C₂×Q₈×C₁₃	—	4	4	no	—
51	C₂×Q₈×C₁₃	—	8	4	no	—
52	C₂²×C₄×C₁₃	—	4	2	no	—
53	C₂²×C₄×C₁₃	—	4	2	no	—
54	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₁₃×Q₁₆	—	2	8	no	—
58	C₁₃×Q₁₆	—	4	4	no	—
59	C₁₃×Q₁₆	—	4	8	no	—
60	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
61	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₁₃	#41	1	4	yes	—
64	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
65	C₁₃×C₄⋊C₄	—	2	4	no	—
66	C₁₃×C₄⋊C₄	—	4	2	no	—
67	C₁₃×C₄⋊C₄	—	4	4	no	—
68	C₁₃×C₄⋊C₄	—	4	4	no	—
69	C₁₃×C₄⋊C₄	—	4	4	no	—
70	C₄²×C₁₃	D₈	1	2	yes	—
71	C₄²×C₁₃	C₂×D₄	1	2	yes	—
72	C₁₃×C₁₆	—	2	4	no	—
73	C₂×#500	C₂×C₁₃	1	1	yes	characteristic
74	C₂×#494	C₂×C₁₃	1	1	yes	characteristic
75	#2241	C₂×C₁₃	1	8	yes	direct product factor
76	C₂×#358	C₂×C₁₃	1	4	yes	—
77	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
78	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
79	Q₈×C₁₃	—	4	4	no	—
80	Q₈×C₁₃	—	4	4	no	—
81	Q₈×C₁₃	—	8	4	no	—
82	Q₈×C₁₃	—	8	8	no	—
83	C₂×C₄×C₁₃	—	4	4	no	—
84	C₂×C₄×C₁₃	—	4	4	no	—
85	C₂×C₄×C₁₃	—	8	4	no	—
86	C₂×C₄×C₁₃	—	8	4	no	—
87	C₂×C₄×C₁₃	SD₃₂	1	4	yes	—
88	C₂×C₄×C₁₃	Q₃₂	1	4	yes	—
89	C₂×C₄×C₁₃	#124	1	2	yes	—
90	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
92	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
93	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
94	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
95	C₈×C₁₃	#124	1	2	yes	—
96	C₈×C₁₃	C₂×SD₁₆	1	4	yes	—
97	C₈×C₁₃	C₂×#41	1	2	yes	—
98	C₂²×Q₁₆	—	2	1	no	—
99	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
100	C₂×C₄⋊Q₈	—	2	1	no	—
101	C₂×C₄⋊Q₈	—	2	1	no	—
102	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
103	#500	—	2	2	no	—
104	#500	C₂²×C₁₃	1	4	yes	—
105	#494	—	2	2	no	—
106	#494	C₂²×C₁₃	1	4	yes	—
107	C₂×#107	—	2	1	no	—
108	C₂×#107	C₂²×C₁₃	1	2	yes	—
109	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
110	#358	C₂²×C₁₃	1	16	yes	—
111	C₄×C₁₆	C₂²×C₁₃	1	4	yes	—
112	C₂²×C₁₃	#486	1	2	yes	—
113	C₂²×C₁₃	C₂×SD₃₂	1	2	yes	—
114	C₂²×C₁₃	C₂×Q₃₂	1	2	yes	—
115	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
116	C₄×C₁₃	—	8	4	no	—
117	C₄×C₁₃	—	8	4	no	—
118	C₄×C₁₃	#486	1	2	yes	—
119	C₄×C₁₃	C₂×SD₃₂	1	4	yes	—
120	C₄×C₁₃	C₂×Q₃₂	1	4	yes	—
121	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
122	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
123	C₂²×Q₈	—	2	2	no	—
124	C₂²×Q₈	—	4	1	no	—
125	C₂×Q₁₆	—	2	4	no	—
126	C₂×Q₁₆	—	2	2	no	—
127	C₂×Q₁₆	—	2	8	no	—
128	C₂×Q₁₆	—	4	4	no	—
129	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
130	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
131	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
132	C₄⋊Q₈	—	2	4	no	—
133	C₄⋊Q₈	—	2	4	no	—
134	C₄⋊Q₈	—	4	2	no	—
135	C₄⋊Q₈	—	4	2	no	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	—	4	1	no	—
138	C₂×C₄⋊C₄	—	4	1	no	—
139	C₂×C₄⋊C₄	—	4	1	no	—
140	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
141	C₂×C₁₆	—	2	4	no	—
142	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
143	#107	—	2	4	no	—
144	#107	—	2	2	no	—
145	#107	C₂³×C₁₃	1	4	yes	—
146	C₄×C₈	D₄×C₁₃	1	2	yes	—
147	C₄×C₈	C₂³×C₁₃	1	2	yes	—
148	C₂×C₁₃	#2241	1	4	yes	direct product factor
149	C₂×C₁₃	C₂×#486	1	1	yes	characteristic
150	C₂×C₁₃	C₂²×SD₃₂	1	1	yes	characteristic
151	C₂×C₁₃	C₂²×Q₃₂	1	1	yes	characteristic
152	C₂×Q₈	—	2	4	no	—
153	C₂×Q₈	—	4	4	no	—
154	C₂×Q₈	—	4	2	no	—
155	C₂×Q₈	—	4	4	no	—
156	C₂×Q₈	—	4	4	no	—
157	C₂×Q₈	—	8	4	no	—
158	C₂²×C₄	—	4	2	no	—
159	C₂²×C₄	—	4	2	no	—
160	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
161	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
162	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
163	Q₁₆	—	2	8	no	—
164	Q₁₆	—	4	4	no	—
165	Q₁₆	—	4	8	no	—
166	C₂×C₈	C₁₃×SD₁₆	1	4	yes	—
167	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
168	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
169	C₂×C₈	C₁₃×#41	1	4	yes	—
170	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
171	C₄⋊C₄	—	2	4	no	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	4	4	no	—
174	C₄⋊C₄	—	4	4	no	—
175	C₄⋊C₄	—	4	4	no	—
176	C₄²	C₁₃×D₈	1	2	yes	—
177	C₄²	C₂×D₄×C₁₃	1	2	yes	—
178	C₁₆	—	2	4	no	—
179	C₁₃	C₂×#2241	1	1	yes	characteristic, direct product factor, Sylow
180	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
181	Q₈	—	4	4	no	—
182	Q₈	—	4	4	no	—
183	Q₈	—	8	4	no	—
184	Q₈	—	8	8	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	—	4	4	no	—
187	C₂×C₄	—	8	4	no	—
188	C₂×C₄	—	8	4	no	—
189	C₂×C₄	C₁₃×SD₃₂	1	4	yes	—
190	C₂×C₄	C₁₃×Q₃₂	1	4	yes	—
191	C₂×C₄	C₁₃×#124	1	2	yes	—
192	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
193	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
194	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
195	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
196	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
197	C₈	C₁₃×#124	1	2	yes	—
198	C₈	C₂×C₁₃×SD₁₆	1	4	yes	—
199	C₈	C₂×C₁₃×#41	1	2	yes	—
200	C₂²	C₁₃×#486	1	2	yes	—
201	C₂²	C₂×C₁₃×SD₃₂	1	2	yes	—
202	C₂²	C₂×C₁₃×Q₃₂	1	2	yes	—
203	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
204	C₄	—	8	4	no	—
205	C₄	—	8	4	no	—
206	C₄	C₁₃×#486	1	2	yes	—
207	C₄	C₂×C₁₃×SD₃₂	1	4	yes	—
208	C₄	C₂×C₁₃×Q₃₂	1	4	yes	—
209	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
210	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
211	C₂	C₁₃×#2241	1	4	yes	direct product factor
212	C₂	C₂×C₁₃×#486	1	1	yes	characteristic
213	C₂	C₂²×C₁₃×SD₃₂	1	1	yes	characteristic
214	C₂	C₂²×C₁₃×Q₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2241	C₂	direct (N × H)
45. C₂×#2241	C₁₃	direct (N × H)
75. #2241	C₂×C₁₃	direct (N × H)
148. C₂×C₁₃	#2241	direct (N × H)
179. C₁₃	C₂×#2241	direct (N × H)
211. C₂	C₁₃×#2241	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×C₁₃×#500	2
C₂×C₁₃×#494	2
C₁₃×#2241	2
C₂×C₁₃×#358	2
C₂×C₄×C₁₃×C₁₆	2
C₂×#2241	13

Subgroups — C2×C13×#2241 #15720034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2241 #15720034