Subgroups — C₁₃×#13910 #15700249

Order 3328.

1774 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#389	C₂	1	4	yes	maximal
2	C₂×C₁₃×#384	C₂	1	2	yes	maximal
3	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1444	C₂	1	4	yes	maximal
7	C₁₃×C₄⋊#95	C₂	1	2	yes	maximal
8	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
11	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#389	—	2	16	no	—
19	C₁₃×#384	—	2	8	no	—
20	C₁₃×#384	—	2	4	no	—
21	C₄×C₁₃×C₄⋊C₄	—	2	4	no	—
22	C₄×C₁₃×C₄⋊C₄	C₄	1	8	yes	complemented
23	C₂×C₁₃×#95	C₂²	1	2	yes	—
24	C₂×C₁₃×#95	C₂²	1	8	yes	—
25	C₂×C₁₃×#95	C₂²	1	2	yes	—
26	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
27	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
28	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
29	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
30	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
35	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
36	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
37	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
38	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
39	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
40	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
41	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
42	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
45	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
46	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
48	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
49	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
50	C₂×C₁₃×C₄⋊C₄	Q₈	1	4	yes	—
51	C₂×C₁₃×C₄⋊C₄	Q₈	1	8	yes	—
52	C₂×C₄²×C₁₃	—	2	4	no	—
53	C₂×C₄²×C₁₃	—	2	4	no	—
54	C₂×C₄²×C₁₃	—	2	4	no	—
55	C₂×C₄²×C₁₃	—	2	8	no	—
56	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
57	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
58	C₂×C₄²×C₁₃	D₄	1	4	yes	—
59	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
60	C₁₃×#95	—	2	4	no	—
61	C₁₃×#95	—	2	16	no	—
62	C₁₃×#95	C₂×C₄	1	8	yes	—
63	#13910	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	—	2	4	no	—
66	C₂²×C₄×C₁₃	—	2	4	no	—
67	C₂²×C₄×C₁₃	—	2	2	no	—
68	C₂²×C₄×C₁₃	—	2	4	no	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	—	2	4	no	—
71	C₂²×C₄×C₁₃	—	2	4	no	—
72	C₂²×C₄×C₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	4	no	—
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	4	no	—
78	C₂²×C₄×C₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₃	—	2	8	no	—
80	C₂²×C₄×C₁₃	—	2	4	no	—
81	C₂²×C₄×C₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₃	—	2	8	no	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
98	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
101	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₁₃	#41	1	2	yes	—
103	C₂²×C₄×C₁₃	#41	1	2	yes	—
104	C₁₃×C₄⋊C₄	—	2	8	no	—
105	C₁₃×C₄⋊C₄	—	2	8	no	—
106	C₁₃×C₄⋊C₄	—	4	32	no	—
107	C₁₃×C₄⋊C₄	—	4	8	no	—
108	C₁₃×C₄⋊C₄	—	4	8	no	—
109	C₁₃×C₄⋊C₄	—	4	8	no	—
110	C₁₃×C₄⋊C₄	C₄⋊C₄	1	32	yes	complemented
111	C₄²×C₁₃	—	2	16	no	—
112	C₄²×C₁₃	—	4	8	no	—
113	C₄²×C₁₃	C₄⋊C₄	1	16	yes	complemented
114	C₂×#389	C₂×C₁₃	1	4	yes	—
115	C₂×#384	C₂×C₁₃	1	1	yes	characteristic
116	C₂×#384	C₂×C₁₃	1	2	yes	—
117	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
118	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
119	#1444	C₂×C₁₃	1	4	yes	—
120	C₄⋊#95	C₂×C₁₃	1	2	yes	—
121	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
122	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
123	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
124	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
125	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
126	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
127	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
128	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
129	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
130	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
131	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
132	C₂×C₄×C₁₃	—	2	8	no	—
133	C₂×C₄×C₁₃	—	2	4	no	—
134	C₂×C₄×C₁₃	—	2	8	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	4	no	—
138	C₂×C₄×C₁₃	—	2	8	no	—
139	C₂×C₄×C₁₃	—	2	8	no	—
140	C₂×C₄×C₁₃	—	2	8	no	—
141	C₂×C₄×C₁₃	—	2	8	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	—	2	8	no	—
145	C₂×C₄×C₁₃	—	2	8	no	—
146	C₂×C₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	—	4	2	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	4	no	—
151	C₂×C₄×C₁₃	—	4	4	no	—
152	C₂×C₄×C₁₃	—	4	4	no	—
153	C₂×C₄×C₁₃	—	4	4	no	—
154	C₂×C₄×C₁₃	—	4	4	no	—
155	C₂×C₄×C₁₃	—	4	8	no	—
156	C₂×C₄×C₁₃	—	4	8	no	—
157	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
158	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	16	yes	—
159	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
160	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
161	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
164	C₂×C₄×C₁₃	#121	1	4	yes	—
165	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
166	C₂×C₄×C₁₃	#125	1	4	yes	—
167	C₂×C₄×C₁₃	#127	1	4	yes	—
168	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
169	C₂×C₄×C₁₃	C₄⋊Q₈	1	8	yes	—
170	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
171	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
172	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
173	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
174	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
175	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
176	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
177	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
178	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
179	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
180	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
181	#389	—	2	16	no	—
182	#384	—	2	8	no	—
183	#384	—	2	4	no	—
184	C₄×C₄⋊C₄	—	2	4	no	—
185	C₄×C₄⋊C₄	C₄×C₁₃	1	8	yes	complemented
186	C₂×#95	C₂²×C₁₃	1	8	yes	—
187	C₂×#95	C₂²×C₁₃	1	2	yes	—
188	C₂×#95	C₂²×C₁₃	1	2	yes	—
189	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
190	C₂²×C₁₃	C₂²×C₄⋊C₄	1	2	yes	—
191	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
193	C₂²×C₁₃	#520	1	2	yes	—
194	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
195	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
196	C₂²×C₁₃	C₂×#125	1	1	yes	characteristic
197	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
198	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
199	C₂²×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
200	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
201	C₂²×C₁₃	#535	1	1	yes	characteristic
202	C₂²×C₁₃	#536	1	1	yes	characteristic
203	C₂²×C₁₃	#544	1	2	yes	—
204	C₂²×C₁₃	D₄²	1	2	yes	—
205	C₂²×C₁₃	#547	1	2	yes	—
206	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
207	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
208	C₂²×C₁₃	#550	1	2	yes	—
209	C₂²×C₁₃	#554	1	2	yes	—
210	C₂²×C₁₃	#557	1	2	yes	—
211	C₂²×C₁₃	Q₈²	1	2	yes	—
212	C₄×C₁₃	—	2	4	no	—
213	C₄×C₁₃	—	2	16	no	—
214	C₄×C₁₃	—	4	4	no	—
215	C₄×C₁₃	—	4	4	no	—
216	C₄×C₁₃	—	8	4	no	—
217	C₄×C₁₃	#384	1	8	yes	complemented
218	C₄×C₁₃	#389	1	8	yes	complemented
219	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
220	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
221	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
222	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
223	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
224	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
225	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	16	no	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	4	no	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	—	2	16	no	—
236	C₂×C₄⋊C₄	—	2	8	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	4	8	no	—
239	C₂×C₄⋊C₄	—	4	4	no	—
240	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
241	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
242	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
243	C₂×C₄⋊C₄	Q₈×C₁₃	1	4	yes	—
244	C₂×C₄⋊C₄	Q₈×C₁₃	1	8	yes	—
245	C₂×C₄²	—	2	4	no	—
246	C₂×C₄²	—	2	4	no	—
247	C₂×C₄²	—	2	4	no	—
248	C₂×C₄²	—	2	8	no	—
249	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	—
250	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
251	C₂×C₄²	D₄×C₁₃	1	4	yes	—
252	C₂×C₄²	Q₈×C₁₃	1	4	yes	—
253	#95	—	2	4	no	—
254	#95	—	2	16	no	—
255	#95	C₂×C₄×C₁₃	1	8	yes	—
256	C₂×C₁₃	C₂×#384	1	1	yes	characteristic
257	C₂×C₁₃	C₂×#389	1	1	yes	characteristic
258	C₂×C₁₃	#2317	1	1	yes	characteristic
259	C₂×C₁₃	D₄×C₄⋊C₄	1	2	yes	—
260	C₂×C₁₃	Q₈×C₄⋊C₄	1	2	yes	—
261	C₂×C₁₃	#2541	1	1	yes	characteristic
262	C₂×C₁₃	#2542	1	1	yes	characteristic
263	C₂×C₁₃	#2546	1	1	yes	characteristic
264	C₂×C₁₃	#2551	1	2	yes	—
265	C₂×C₁₃	#2552	1	2	yes	—
266	C₂×C₁₃	#2567	1	1	yes	characteristic
267	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	8	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	8	no	—
287	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
289	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
292	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
297	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
298	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
299	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
300	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
301	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
302	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
303	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
304	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
305	C₂²×C₄	C₁₃×#41	1	2	yes	—
306	C₂²×C₄	C₁₃×#41	1	2	yes	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	4	32	no	—
310	C₄⋊C₄	—	4	8	no	—
311	C₄⋊C₄	—	4	8	no	—
312	C₄⋊C₄	—	4	8	no	—
313	C₄⋊C₄	C₁₃×C₄⋊C₄	1	32	yes	complemented
314	C₄²	—	2	16	no	—
315	C₄²	—	4	8	no	—
316	C₄²	C₁₃×C₄⋊C₄	1	16	yes	complemented
317	C₁₃	#13910	1	1	yes	characteristic, direct product factor, Sylow
318	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
319	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
320	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
321	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
322	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
323	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
324	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
325	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
326	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
327	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
328	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
355	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	16	yes	—
356	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
357	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	8	yes	—
358	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
359	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
360	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
361	C₂×C₄	C₁₃×#121	1	4	yes	—
362	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
363	C₂×C₄	C₁₃×#125	1	4	yes	—
364	C₂×C₄	C₁₃×#127	1	4	yes	—
365	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
366	C₂×C₄	C₁₃×C₄⋊Q₈	1	8	yes	—
367	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
368	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
369	C₂²	C₂²×C₁₃×C₄⋊C₄	1	2	yes	—
370	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
371	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
372	C₂²	C₁₃×#520	1	2	yes	—
373	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
374	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
375	C₂²	C₂×C₁₃×#125	1	1	yes	characteristic
376	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
377	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
378	C₂²	C₂×C₁₃×C₄⋊Q₈	1	2	yes	—
379	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
380	C₂²	C₁₃×#535	1	1	yes	characteristic
381	C₂²	C₁₃×#536	1	1	yes	characteristic
382	C₂²	C₁₃×#544	1	2	yes	—
383	C₂²	D₄²×C₁₃	1	2	yes	—
384	C₂²	C₁₃×#547	1	2	yes	—
385	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
386	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
387	C₂²	C₁₃×#550	1	2	yes	—
388	C₂²	C₁₃×#554	1	2	yes	—
389	C₂²	C₁₃×#557	1	2	yes	—
390	C₂²	Q₈²×C₁₃	1	2	yes	—
391	C₄	—	2	4	no	—
392	C₄	—	2	16	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	4	no	—
395	C₄	—	8	4	no	—
396	C₄	C₁₃×#384	1	8	yes	complemented
397	C₄	C₁₃×#389	1	8	yes	complemented
398	C₂	C₂×C₁₃×#384	1	1	yes	characteristic
399	C₂	C₂×C₁₃×#389	1	1	yes	characteristic
400	C₂	C₁₃×#2317	1	1	yes	characteristic
401	C₂	D₄×C₁₃×C₄⋊C₄	1	2	yes	—
402	C₂	Q₈×C₁₃×C₄⋊C₄	1	2	yes	—
403	C₂	C₁₃×#2541	1	1	yes	characteristic
404	C₂	C₁₃×#2542	1	1	yes	characteristic
405	C₂	C₁₃×#2546	1	1	yes	characteristic
406	C₂	C₁₃×#2551	1	2	yes	—
407	C₂	C₁₃×#2552	1	2	yes	—
408	C₂	C₁₃×#2567	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
22. C₄×C₁₃×C₄⋊C₄	C₄	semidirect
63. #13910	C₁₃	direct (N × H)
110. C₁₃×C₄⋊C₄	C₄⋊C₄	semidirect
113. C₄²×C₁₃	C₄⋊C₄	semidirect
185. C₄×C₄⋊C₄	C₄×C₁₃	semidirect
217. C₄×C₁₃	#384	semidirect
218. C₄×C₁₃	#389	semidirect
313. C₄⋊C₄	C₁₃×C₄⋊C₄	semidirect
316. C₄²	C₁₃×C₄⋊C₄	semidirect
317. C₁₃	#13910	direct (N × H)
396. C₄	C₁₃×#384	semidirect
397. C₄	C₁₃×#389	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#389	2
C₂×C₁₃×#384	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₁₃×#1444	2
C₁₃×C₄⋊#95	2
#13910	13

Subgroups — C13×#13910 #15700249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13910 #15700249