Subgroups — C₁₃×#15202 #15701541

Order 3328.

1738 conjugacy classes of subgroups.

The subgroup lattice has 246 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×#389	C₂	1	3	yes	maximal
3	C₁₃×#1446	C₂	1	2	yes	maximal
4	C₁₃×#1444	C₂	1	6	yes	maximal
5	C₁₃×C₄⋊#95	C₂	1	3	yes	maximal
6	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₃	—	2	12	no	—
8	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
10	C₂²×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
11	C₂²×C₁₃×C₄⋊C₄	C₂²	1	6	yes	—
12	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
13	C₁₃×#389	—	2	12	no	—
14	C₂×C₁₃×#95	C₂²	1	6	yes	—
15	C₂×C₁₃×#95	C₂²	1	6	yes	—
16	C₂×C₁₃×#95	C₂²	1	6	yes	—
17	C₂²×Q₈×C₁₃	—	2	6	no	—
18	C₂²×Q₈×C₁₃	—	2	6	no	—
19	C₂²×Q₈×C₁₃	Q₈	1	4	yes	—
20	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
21	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
22	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
23	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
24	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₄×Q₈×C₁₃	—	2	32	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	12	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	12	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
32	C₂×C₁₃×C₄⋊C₄	—	4	12	no	—
33	C₂×C₁₃×C₄⋊C₄	Q₈	1	12	yes	complemented
34	C₂×C₄²×C₁₃	—	2	12	no	—
35	C₂×C₄²×C₁₃	D₄	1	12	yes	—
36	C₁₃×#95	—	2	12	no	—
37	C₁₃×#95	—	2	12	no	—
38	C₁₃×#95	—	4	6	no	—
39	#15202	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
41	C₂×Q₈×C₁₃	—	2	8	no	—
42	C₂×Q₈×C₁₃	—	2	24	no	—
43	C₂×Q₈×C₁₃	—	2	24	no	—
44	C₂²×C₄×C₁₃	—	2	6	no	—
45	C₂²×C₄×C₁₃	—	2	6	no	—
46	C₂²×C₄×C₁₃	—	2	6	no	—
47	C₂²×C₄×C₁₃	—	2	6	no	—
48	C₂²×C₄×C₁₃	—	2	12	no	—
49	C₂²×C₄×C₁₃	—	2	6	no	—
50	C₂²×C₄×C₁₃	—	2	3	no	—
51	C₂²×C₄×C₁₃	—	2	12	no	—
52	C₂²×C₄×C₁₃	—	2	6	no	—
53	C₂²×C₄×C₁₃	—	2	3	no	—
54	C₂²×C₄×C₁₃	—	2	6	no	—
55	C₂²×C₄×C₁₃	—	2	6	no	—
56	C₂²×C₄×C₁₃	—	2	2	no	—
57	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
58	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
59	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
60	C₂²×C₄×C₁₃	C₂×Q₈	1	12	yes	—
61	C₂²×C₄×C₁₃	C₂×Q₈	1	6	yes	—
62	C₂²×C₄×C₁₃	C₂×Q₈	1	6	yes	—
63	C₂²×C₄×C₁₃	#41	1	6	yes	—
64	C₂²×C₄×C₁₃	#41	1	2	yes	—
65	C₁₃×C₄⋊C₄	—	2	24	no	—
66	C₁₃×C₄⋊C₄	—	2	24	no	—
67	C₁₃×C₄⋊C₄	—	4	24	no	—
68	C₁₃×C₄⋊C₄	—	4	4	no	—
69	C₄²×C₁₃	—	2	24	no	—
70	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
71	C₂×#389	C₂×C₁₃	1	3	yes	—
72	#1446	C₂×C₁₃	1	2	yes	—
73	#1444	C₂×C₁₃	1	6	yes	—
74	C₄⋊#95	C₂×C₁₃	1	3	yes	—
75	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
76	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
77	C₂³×C₁₃	C₂²×Q₈	1	3	yes	—
78	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
79	C₂³×C₁₃	C₂×#41	1	3	yes	—
80	C₂³×C₁₃	H(5,𝔽₂)	1	3	yes	—
81	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
82	Q₈×C₁₃	—	2	32	no	—
83	C₂×C₄×C₁₃	—	2	6	no	—
84	C₂×C₄×C₁₃	—	2	12	no	—
85	C₂×C₄×C₁₃	—	2	6	no	—
86	C₂×C₄×C₁₃	—	2	12	no	—
87	C₂×C₄×C₁₃	—	2	6	no	—
88	C₂×C₄×C₁₃	—	2	12	no	—
89	C₂×C₄×C₁₃	—	2	6	no	—
90	C₂×C₄×C₁₃	—	2	6	no	—
91	C₂×C₄×C₁₃	—	2	24	no	—
92	C₂×C₄×C₁₃	—	4	6	no	—
93	C₂×C₄×C₁₃	—	4	6	no	—
94	C₂×C₄×C₁₃	—	4	6	no	—
95	C₂×C₄×C₁₃	—	4	6	no	—
96	C₂×C₄×C₁₃	—	4	12	no	—
97	C₂×C₄×C₁₃	—	4	2	no	—
98	C₂×C₄×C₁₃	—	4	6	no	—
99	C₂×C₄×C₁₃	—	4	6	no	—
100	C₂×C₄×C₁₃	#120	1	4	yes	—
101	C₂×C₄×C₁₃	C₂²⋊Q₈	1	12	yes	—
102	C₂×C₄×C₁₃	C₂²⋊Q₈	1	12	yes	—
103	C₂×C₄×C₁₃	C₄⋊Q₈	1	12	yes	—
104	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
105	C₂×C₄×Q₈	—	2	12	no	—
106	C₂²×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
107	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
108	C₂²×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
109	C₂²×C₄⋊C₄	C₂²×C₁₃	1	6	yes	—
110	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
111	#389	—	2	12	no	—
112	C₂×#95	C₂²×C₁₃	1	6	yes	—
113	C₂×#95	C₂²×C₁₃	1	6	yes	—
114	C₂×#95	C₂²×C₁₃	1	6	yes	—
115	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
116	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	3	yes	—
117	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	3	yes	—
118	C₂²×C₁₃	#525	1	3	yes	—
119	C₂²×C₁₃	C₂×C₄⋊Q₈	1	3	yes	—
120	C₂²×C₁₃	#535	1	3	yes	—
121	C₂²×C₁₃	#537	1	3	yes	—
122	C₂²×C₁₃	#554	1	6	yes	—
123	C₂²×C₁₃	#557	1	1	yes	characteristic
124	C₂²×C₁₃	#557	1	3	yes	—
125	C₂²×C₁₃	Q₈²	1	3	yes	—
126	C₂²×C₁₃	#559	1	3	yes	—
127	C₄×C₁₃	—	2	12	no	—
128	C₄×C₁₃	—	4	12	no	—
129	C₄×C₁₃	—	4	6	no	—
130	C₄×C₁₃	—	8	2	no	—
131	C₄×C₁₃	#395	1	8	yes	—
132	C₂²×Q₈	—	2	6	no	—
133	C₂²×Q₈	—	2	6	no	—
134	C₂²×Q₈	Q₈×C₁₃	1	4	yes	—
135	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
136	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
137	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
138	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
139	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
140	C₄×Q₈	—	2	32	no	—
141	C₂×C₄⋊C₄	—	2	12	no	—
142	C₂×C₄⋊C₄	—	2	6	no	—
143	C₂×C₄⋊C₄	—	2	6	no	—
144	C₂×C₄⋊C₄	—	2	6	no	—
145	C₂×C₄⋊C₄	—	2	12	no	—
146	C₂×C₄⋊C₄	—	2	6	no	—
147	C₂×C₄⋊C₄	—	4	12	no	—
148	C₂×C₄⋊C₄	Q₈×C₁₃	1	12	yes	complemented
149	C₂×C₄²	—	2	12	no	—
150	C₂×C₄²	D₄×C₁₃	1	12	yes	—
151	#95	—	2	12	no	—
152	#95	—	2	12	no	—
153	#95	—	4	6	no	—
154	C₂×C₁₃	C₂×#395	1	1	yes	characteristic
155	C₂×C₁₃	#2567	1	3	yes	—
156	C₂×C₁₃	#2580	1	3	yes	—
157	C₂×C₁₃	#2582	1	3	yes	—
158	C₂×C₁₃	#2584	1	3	yes	—
159	C₂×C₁₃	#2615	1	1	yes	characteristic
160	C₂×C₁₃	#2848	1	1	yes	characteristic
161	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
162	C₂×Q₈	—	2	8	no	—
163	C₂×Q₈	—	2	24	no	—
164	C₂×Q₈	—	2	24	no	—
165	C₂²×C₄	—	2	6	no	—
166	C₂²×C₄	—	2	6	no	—
167	C₂²×C₄	—	2	6	no	—
168	C₂²×C₄	—	2	6	no	—
169	C₂²×C₄	—	2	12	no	—
170	C₂²×C₄	—	2	6	no	—
171	C₂²×C₄	—	2	3	no	—
172	C₂²×C₄	—	2	12	no	—
173	C₂²×C₄	—	2	6	no	—
174	C₂²×C₄	—	2	3	no	—
175	C₂²×C₄	—	2	6	no	—
176	C₂²×C₄	—	2	6	no	—
177	C₂²×C₄	—	2	2	no	—
178	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
179	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
180	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
181	C₂²×C₄	C₂×Q₈×C₁₃	1	12	yes	—
182	C₂²×C₄	C₂×Q₈×C₁₃	1	6	yes	—
183	C₂²×C₄	C₂×Q₈×C₁₃	1	6	yes	—
184	C₂²×C₄	C₁₃×#41	1	6	yes	—
185	C₂²×C₄	C₁₃×#41	1	2	yes	—
186	C₄⋊C₄	—	2	24	no	—
187	C₄⋊C₄	—	2	24	no	—
188	C₄⋊C₄	—	4	24	no	—
189	C₄⋊C₄	—	4	4	no	—
190	C₄²	—	2	24	no	—
191	C₁₃	#15202	1	1	yes	characteristic, direct product factor, Sylow
192	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
193	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
194	C₂³	C₂²×Q₈×C₁₃	1	3	yes	—
195	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
196	C₂³	C₂×C₁₃×#41	1	3	yes	—
197	C₂³	C₁₃×H(5,𝔽₂)	1	3	yes	—
198	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
199	Q₈	—	2	32	no	—
200	C₂×C₄	—	2	6	no	—
201	C₂×C₄	—	2	12	no	—
202	C₂×C₄	—	2	6	no	—
203	C₂×C₄	—	2	12	no	—
204	C₂×C₄	—	2	6	no	—
205	C₂×C₄	—	2	12	no	—
206	C₂×C₄	—	2	6	no	—
207	C₂×C₄	—	2	6	no	—
208	C₂×C₄	—	2	24	no	—
209	C₂×C₄	—	4	6	no	—
210	C₂×C₄	—	4	6	no	—
211	C₂×C₄	—	4	6	no	—
212	C₂×C₄	—	4	6	no	—
213	C₂×C₄	—	4	12	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	6	no	—
216	C₂×C₄	—	4	6	no	—
217	C₂×C₄	C₁₃×#120	1	4	yes	—
218	C₂×C₄	C₁₃×C₂²⋊Q₈	1	12	yes	—
219	C₂×C₄	C₁₃×C₂²⋊Q₈	1	12	yes	—
220	C₂×C₄	C₁₃×C₄⋊Q₈	1	12	yes	—
221	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
222	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	3	yes	—
223	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	3	yes	—
224	C₂²	C₁₃×#525	1	3	yes	—
225	C₂²	C₂×C₁₃×C₄⋊Q₈	1	3	yes	—
226	C₂²	C₁₃×#535	1	3	yes	—
227	C₂²	C₁₃×#537	1	3	yes	—
228	C₂²	C₁₃×#554	1	6	yes	—
229	C₂²	C₁₃×#557	1	1	yes	characteristic
230	C₂²	C₁₃×#557	1	3	yes	—
231	C₂²	Q₈²×C₁₃	1	3	yes	—
232	C₂²	C₁₃×#559	1	3	yes	—
233	C₄	—	2	12	no	—
234	C₄	—	4	12	no	—
235	C₄	—	4	6	no	—
236	C₄	—	8	2	no	—
237	C₄	C₁₃×#395	1	8	yes	—
238	C₂	C₂×C₁₃×#395	1	1	yes	characteristic
239	C₂	C₁₃×#2567	1	3	yes	—
240	C₂	C₁₃×#2580	1	3	yes	—
241	C₂	C₁₃×#2582	1	3	yes	—
242	C₂	C₁₃×#2584	1	3	yes	—
243	C₂	C₁₃×#2615	1	1	yes	characteristic
244	C₂	C₁₃×#2848	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
33. C₂×C₁₃×C₄⋊C₄	Q₈	semidirect
39. #15202	C₁₃	direct (N × H)
148. C₂×C₄⋊C₄	Q₈×C₁₃	semidirect
191. C₁₃	#15202	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×#389	2
C₁₃×#1446	2
C₁₃×#1444	2
C₁₃×C₄⋊#95	2
#15202	13

Subgroups — C13×#15202 #15701541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#15202 #15701541