Subgroups — C₁₃×#21822 #15708161

Order 3328.

1242 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#432	C₂	1	2	yes	maximal
3	C₁₃×#1985	C₂	1	8	yes	maximal, complemented
4	C₁₃×#1817	C₂	1	4	yes	maximal
5	C₂³×Q₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
7	C₂×C₄×Q₈×C₁₃	C₄	1	4	yes	—
8	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
9	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
10	C₂²×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
11	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
12	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#432	—	2	8	no	—
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
15	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
16	C₂×C₁₃×#97	C₂²	1	4	yes	—
17	C₁₃×#336	C₂²	1	16	yes	—
18	C₂²×Q₈×C₁₃	—	2	4	no	—
19	C₂²×Q₈×C₁₃	—	2	8	no	—
20	C₂²×Q₈×C₁₃	C₂×C₄	1	4	yes	—
21	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
23	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
27	C₄×Q₈×C₁₃	—	2	16	no	—
28	C₄×Q₈×C₁₃	—	2	8	no	—
29	C₄×Q₈×C₁₃	—	2	8	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
32	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
33	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
34	C₂×C₄²×C₁₃	—	2	8	no	—
35	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
36	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₁₃	D₄	1	8	yes	—
38	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
39	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
40	C₁₃×C₄⋊C₈	—	2	8	no	—
41	C₁₃×C₂²⋊C₈	—	2	8	no	—
42	C₁₃×#97	—	2	8	no	—
43	#21822	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×Q₈×C₁₃	—	2	32	no	—
46	C₂×Q₈×C₁₃	—	2	8	no	—
47	C₂×Q₈×C₁₃	—	2	16	no	—
48	C₂²×C₄×C₁₃	—	2	4	no	—
49	C₂²×C₄×C₁₃	—	2	4	no	—
50	C₂²×C₄×C₁₃	—	2	4	no	—
51	C₂²×C₄×C₁₃	—	2	4	no	—
52	C₂²×C₄×C₁₃	—	2	4	no	—
53	C₂²×C₄×C₁₃	—	4	2	no	—
54	C₂²×C₄×C₁₃	—	4	4	no	—
55	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
56	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
57	C₂²×C₄×C₁₃	M₁₆	1	8	yes	—
58	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
59	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
61	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
62	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
63	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
64	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
65	C₂×C₈×C₁₃	—	2	8	no	—
66	C₂×C₈×C₁₃	—	2	16	no	—
67	C₁₃×C₄⋊C₄	—	2	16	no	—
68	C₁₃×C₄⋊C₄	—	2	8	no	—
69	C₄²×C₁₃	—	2	8	no	—
70	C₄²×C₁₃	—	2	8	no	—
71	C₄²×C₁₃	C₂²⋊C₄	1	8	yes	—
72	C₄²×C₁₃	C₂×D₄	1	4	yes	—
73	C₄²×C₁₃	C₂×D₄	1	4	yes	—
74	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
75	C₂×#432	C₂×C₁₃	1	2	yes	—
76	#1985	C₂×C₁₃	1	8	yes	complemented
77	#1817	C₂×C₁₃	1	4	yes	—
78	C₂³×C₁₃	—	2	2	no	—
79	C₂³×C₁₃	—	2	2	no	—
80	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
81	C₂³×C₁₃	C₂×M₁₆	1	4	yes	—
82	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
83	Q₈×C₁₃	—	2	32	no	—
84	C₂×C₄×C₁₃	—	2	4	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	4	no	—
87	C₂×C₄×C₁₃	—	2	4	no	—
88	C₂×C₄×C₁₃	—	2	4	no	—
89	C₂×C₄×C₁₃	—	2	8	no	—
90	C₂×C₄×C₁₃	—	2	16	no	—
91	C₂×C₄×C₁₃	—	2	8	no	—
92	C₂×C₄×C₁₃	—	2	4	no	—
93	C₂×C₄×C₁₃	—	2	8	no	—
94	C₂×C₄×C₁₃	—	4	4	no	—
95	C₂×C₄×C₁₃	—	4	8	no	—
96	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
97	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
98	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
99	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
100	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
101	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
102	C₈×C₁₃	—	4	8	no	—
103	C₂³×Q₈	C₄×C₁₃	1	1	yes	characteristic
104	C₂×C₄×Q₈	—	2	8	no	—
105	C₂×C₄×Q₈	C₄×C₁₃	1	4	yes	—
106	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
107	C₂²×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
108	C₂²×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
109	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
110	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
111	#432	—	2	8	no	—
112	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
113	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
114	C₂×#97	C₂²×C₁₃	1	4	yes	—
115	#336	C₂²×C₁₃	1	16	yes	—
116	C₂²×C₁₃	—	2	2	no	—
117	C₂²×C₁₃	—	2	2	no	—
118	C₂²×C₁₃	—	2	8	no	—
119	C₂²×C₁₃	#407	1	4	yes	—
120	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₁₃	#519	1	2	yes	—
122	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
123	C₂²×C₁₃	#568	1	2	yes	—
124	C₄×C₁₃	—	2	2	no	—
125	C₄×C₁₃	—	2	4	no	—
126	C₄×C₁₃	—	2	8	no	—
127	C₄×C₁₃	—	2	4	no	—
128	C₄×C₁₃	—	4	4	no	—
129	C₄×C₁₃	#536	1	4	yes	—
130	C₂²×Q₈	—	2	4	no	—
131	C₂²×Q₈	—	2	8	no	—
132	C₂²×Q₈	C₂×C₄×C₁₃	1	4	yes	—
133	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
134	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
135	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
136	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
137	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
138	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
139	C₄×Q₈	—	2	16	no	—
140	C₄×Q₈	—	2	8	no	—
141	C₄×Q₈	—	2	8	no	—
142	C₂×C₄⋊C₄	—	2	8	no	—
143	C₂×C₄⋊C₄	—	2	4	no	—
144	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
145	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
146	C₂×C₄²	—	2	8	no	—
147	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
148	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
149	C₂×C₄²	D₄×C₁₃	1	8	yes	—
150	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
151	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
152	C₄⋊C₈	—	2	8	no	—
153	C₂²⋊C₈	—	2	8	no	—
154	#97	—	2	8	no	—
155	C₂×C₁₃	—	2	4	no	—
156	C₂×C₁₃	#2310	1	1	yes	characteristic
157	C₂×C₁₃	C₂×#407	1	1	yes	characteristic
158	C₂×C₁₃	#2879	1	1	yes	characteristic
159	C₂×C₁₃	#2983	1	4	yes	—
160	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
161	C₂×Q₈	—	2	32	no	—
162	C₂×Q₈	—	2	8	no	—
163	C₂×Q₈	—	2	16	no	—
164	C₂²×C₄	—	2	4	no	—
165	C₂²×C₄	—	2	4	no	—
166	C₂²×C₄	—	2	4	no	—
167	C₂²×C₄	—	2	4	no	—
168	C₂²×C₄	—	2	4	no	—
169	C₂²×C₄	—	4	2	no	—
170	C₂²×C₄	—	4	4	no	—
171	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
172	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
173	C₂²×C₄	C₁₃×M₁₆	1	8	yes	—
174	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
175	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
176	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
177	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
178	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
179	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
180	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
181	C₂×C₈	—	2	8	no	—
182	C₂×C₈	—	2	16	no	—
183	C₄⋊C₄	—	2	16	no	—
184	C₄⋊C₄	—	2	8	no	—
185	C₄²	—	2	8	no	—
186	C₄²	—	2	8	no	—
187	C₄²	C₁₃×C₂²⋊C₄	1	8	yes	—
188	C₄²	C₂×D₄×C₁₃	1	4	yes	—
189	C₄²	C₂×D₄×C₁₃	1	4	yes	—
190	C₁₃	#21822	1	1	yes	characteristic, direct product factor, Sylow
191	C₂³	—	2	2	no	—
192	C₂³	—	2	2	no	—
193	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
194	C₂³	C₂×C₁₃×M₁₆	1	4	yes	—
195	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
196	Q₈	—	2	32	no	—
197	C₂×C₄	—	2	8	no	—
198	C₂×C₄	—	2	16	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	2	8	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	2	8	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	4	8	no	—
209	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
211	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
212	C₂×C₄	C₂×C₁₃×M₁₆	1	8	yes	—
213	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
214	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
215	C₈	—	4	8	no	—
216	C₂²	—	2	2	no	—
217	C₂²	—	2	2	no	—
218	C₂²	—	2	8	no	—
219	C₂²	C₁₃×#407	1	4	yes	—
220	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
221	C₂²	C₁₃×#519	1	2	yes	—
222	C₂²	C₂²×C₁₃×M₁₆	1	2	yes	—
223	C₂²	C₁₃×#568	1	2	yes	—
224	C₄	—	2	2	no	—
225	C₄	—	2	4	no	—
226	C₄	—	2	8	no	—
227	C₄	—	2	4	no	—
228	C₄	—	4	4	no	—
229	C₄	C₁₃×#536	1	4	yes	—
230	C₂	—	2	4	no	—
231	C₂	C₁₃×#2310	1	1	yes	characteristic
232	C₂	C₂×C₁₃×#407	1	1	yes	characteristic
233	C₂	C₁₃×#2879	1	1	yes	characteristic
234	C₂	C₁₃×#2983	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1985	C₂	semidirect
43. #21822	C₁₃	direct (N × H)
76. #1985	C₂×C₁₃	semidirect
190. C₁₃	#21822	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₃	2
C₂×C₁₃×#432	2
C₁₃×#1985	2
C₁₃×#1817	2
#21822	13

Subgroups — C13×#21822 #15708161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21822 #15708161