Subgroups — C₁₃×#34236 #15720575

Order 3328.

2750 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2369	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2366	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2361	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2357	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2349	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2339	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2337	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2319	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×#121	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2275	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₁₃×#41	C₂²	1	2	yes	—
15	C₁₃×#532	C₄	1	16	yes	complemented
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	C₂²	1	2	yes	—
19	C₂×C₁₃×#121	C₂²	1	2	yes	—
20	C₂×C₁₃×#121	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
28	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#391	C₂²	1	8	yes	—
30	C₁₃×#390	C₂²	1	4	yes	—
31	C₁₃×#390	C₂²	1	4	yes	—
32	C₁₃×#389	C₂²	1	4	yes	—
33	C₁₃×#389	C₂²	1	4	yes	—
34	C₁₃×#388	C₂²	1	8	yes	—
35	C₁₃×#388	C₂²	1	8	yes	—
36	C₁₃×#386	C₂²	1	8	yes	—
37	C₁₃×#386	C₂²	1	8	yes	—
38	C₁₃×#385	C₂²	1	8	yes	—
39	C₁₃×#383	C₂²	1	2	yes	—
40	C₁₃×#382	C₂²	1	1	yes	characteristic
41	C₁₃×#382	C₂²	1	1	yes	characteristic
42	C₁₃×#381	C₂²	1	2	yes	—
43	C₁₃×#381	C₂²	1	4	yes	—
44	C₁₃×#380	C₂²	1	2	yes	—
45	C₁₃×#380	C₂²	1	4	yes	—
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
50	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
53	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
54	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
55	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
56	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
57	C₁₃×#376	C₂²	1	2	yes	—
58	C₂×C₁₃×#95	C₂²	1	2	yes	—
59	C₂×C₁₃×#95	C₂²	1	4	yes	—
60	C₂×C₁₃×#41	—	4	8	no	—
61	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
62	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
73	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
74	C₁₃×#127	C₂×C₄	1	8	yes	complemented
75	C₁₃×#124	C₂×C₄	1	16	yes	complemented
76	C₁₃×#121	C₂×C₄	1	16	yes	complemented
77	C₁₃×#121	C₂×C₄	1	16	yes	complemented
78	C₄×D₄×C₁₃	—	2	16	no	—
79	C₄×D₄×C₁₃	—	4	8	no	—
80	C₄×D₄×C₁₃	—	4	16	no	—
81	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
82	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
83	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₄²×C₁₃	—	4	4	no	—
99	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
100	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
101	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
103	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
104	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#95	C₂³	1	2	yes	—
110	C₁₃×#95	C₂³	1	4	yes	—
111	C₁₃×#95	C₂³	1	2	yes	—
112	C₁₃×#95	C₂³	1	8	yes	—
113	C₁₃×#95	C₂³	1	2	yes	—
114	C₁₃×#95	C₂³	1	2	yes	—
115	C₁₃×#95	C₂³	1	2	yes	—
116	C₁₃×#95	C₂³	1	4	yes	—
117	C₁₃×#95	C₂³	1	4	yes	—
118	C₁₃×#95	C₂³	1	8	yes	—
119	C₁₃×#95	C₂³	1	2	yes	—
120	#34236	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
122	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₁₃×#41	—	4	32	no	—
124	C₂×Q₈×C₁₃	—	4	4	no	—
125	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
126	C₂×D₄×C₁₃	—	2	16	no	—
127	C₂×D₄×C₁₃	—	2	8	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	4	no	—
130	C₂×D₄×C₁₃	—	4	4	no	—
131	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
132	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
133	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
134	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	8	no	—
140	C₂²×C₄×C₁₃	—	2	8	no	—
141	C₂²×C₄×C₁₃	—	2	16	no	—
142	C₂²×C₄×C₁₃	—	4	4	no	—
143	C₂²×C₄×C₁₃	—	4	8	no	—
144	C₂²×C₄×C₁₃	—	4	8	no	—
145	C₂²×C₄×C₁₃	—	4	8	no	—
146	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₁₃×C₄⋊C₄	—	2	8	no	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	—	2	4	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	4	8	no	—
166	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
167	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
168	C₁₃×C₄⋊C₄	#41	1	8	yes	complemented
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	—	2	16	no	—
171	C₁₃×C₂²⋊C₄	—	4	8	no	—
172	C₁₃×C₂²⋊C₄	—	4	8	no	—
173	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
174	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
175	C₄²×C₁₃	—	2	8	no	—
176	C₄²×C₁₃	—	2	8	no	—
177	C₄²×C₁₃	—	4	2	no	—
178	C₄²×C₁₃	—	4	2	no	—
179	C₄²×C₁₃	—	4	8	no	—
180	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
181	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
182	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
183	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
184	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
185	#2369	C₂×C₁₃	1	2	yes	complemented
186	#2366	C₂×C₁₃	1	2	yes	complemented
187	#2361	C₂×C₁₃	1	4	yes	complemented
188	#2357	C₂×C₁₃	1	2	yes	complemented
189	#2349	C₂×C₁₃	1	2	yes	complemented
190	#2339	C₂×C₁₃	1	4	yes	complemented
191	#2337	C₂×C₁₃	1	4	yes	complemented
192	#2319	C₂×C₁₃	1	2	yes	complemented
193	C₄×#121	C₂×C₁₃	1	4	yes	complemented
194	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#2275	C₂×C₁₃	1	2	yes	complemented
196	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	2	1	no	—
199	C₂³×C₁₃	—	2	1	no	—
200	C₂³×C₁₃	—	2	8	no	—
201	C₂³×C₁₃	—	2	4	no	—
202	C₂³×C₁₃	—	2	8	no	—
203	C₂³×C₁₃	—	2	4	no	—
204	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
205	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
206	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
207	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
208	Q₈×C₁₃	—	4	8	no	—
209	D₄×C₁₃	—	2	32	no	—
210	D₄×C₁₃	—	2	16	no	—
211	D₄×C₁₃	—	2	16	no	—
212	D₄×C₁₃	—	4	8	no	—
213	C₂×C₄×C₁₃	—	2	8	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	8	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	8	no	—
223	C₂×C₄×C₁₃	—	2	8	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	4	16	no	—
234	C₂×C₄×C₁₃	—	4	16	no	—
235	C₂×C₄×C₁₃	—	8	16	no	—
236	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
237	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
238	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
239	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
240	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
241	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
242	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
243	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
244	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
245	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
246	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
247	C₂²×#41	C₂²×C₁₃	1	2	yes	—
248	#532	C₄×C₁₃	1	16	yes	complemented
249	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×#124	C₂²×C₁₃	1	2	yes	—
252	C₂×#121	C₂²×C₁₃	1	2	yes	—
253	C₂×#121	C₂²×C₁₃	1	2	yes	—
254	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
255	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
256	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
257	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
258	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
259	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
260	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
261	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
262	#391	C₂²×C₁₃	1	8	yes	—
263	#390	C₂²×C₁₃	1	4	yes	—
264	#390	C₂²×C₁₃	1	4	yes	—
265	#389	C₂²×C₁₃	1	4	yes	—
266	#389	C₂²×C₁₃	1	4	yes	—
267	#388	C₂²×C₁₃	1	8	yes	—
268	#388	C₂²×C₁₃	1	8	yes	—
269	#386	C₂²×C₁₃	1	8	yes	—
270	#386	C₂²×C₁₃	1	8	yes	—
271	#385	C₂²×C₁₃	1	8	yes	—
272	#383	C₂²×C₁₃	1	2	yes	—
273	#382	C₂²×C₁₃	1	1	yes	characteristic
274	#382	C₂²×C₁₃	1	1	yes	characteristic
275	#381	C₂²×C₁₃	1	4	yes	—
276	#381	C₂²×C₁₃	1	2	yes	—
277	#380	C₂²×C₁₃	1	4	yes	—
278	#380	C₂²×C₁₃	1	2	yes	—
279	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
280	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
281	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
282	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
283	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
284	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
285	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
286	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
287	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
288	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
289	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
290	#376	C₂²×C₁₃	1	2	yes	—
291	C₂×#95	C₂²×C₁₃	1	2	yes	—
292	C₂×#95	C₂²×C₁₃	1	4	yes	—
293	C₂²×C₁₃	—	2	2	no	—
294	C₂²×C₁₃	—	2	2	no	—
295	C₂²×C₁₃	—	2	4	no	—
296	C₂²×C₁₃	—	2	4	no	—
297	C₂²×C₁₃	—	2	8	no	—
298	C₂²×C₁₃	—	2	8	no	—
299	C₂²×C₁₃	—	2	8	no	—
300	C₂²×C₁₃	—	4	8	no	—
301	C₂²×C₁₃	—	4	8	no	—
302	C₂²×C₁₃	#518	1	4	yes	—
303	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
304	C₂²×C₁₃	C₂²×#41	1	2	yes	—
305	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
306	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
307	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	2	2	no	—
311	C₄×C₁₃	—	2	8	no	—
312	C₄×C₁₃	—	2	2	no	—
313	C₄×C₁₃	—	2	8	no	—
314	C₄×C₁₃	—	4	4	no	—
315	C₄×C₁₃	—	4	4	no	—
316	C₄×C₁₃	—	4	4	no	—
317	C₄×C₁₃	C₄×#41	1	4	yes	—
318	C₄×C₁₃	#520	1	4	yes	—
319	C₂×#41	—	4	8	no	—
320	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
321	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
322	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
323	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
324	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
325	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
326	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
327	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
331	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
332	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
333	#127	C₂×C₄×C₁₃	1	8	yes	complemented
334	#124	C₂×C₄×C₁₃	1	16	yes	complemented
335	#121	C₂×C₄×C₁₃	1	16	yes	complemented
336	#121	C₂×C₄×C₁₃	1	16	yes	complemented
337	C₄×D₄	—	2	16	no	—
338	C₄×D₄	—	4	8	no	—
339	C₄×D₄	—	4	16	no	—
340	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
341	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
342	C₂×C₄⋊C₄	—	2	8	no	—
343	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
357	C₂×C₄²	—	4	4	no	—
358	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
359	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
360	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
361	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
362	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
363	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
364	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
368	#95	C₂³×C₁₃	1	2	yes	—
369	#95	C₂³×C₁₃	1	2	yes	—
370	#95	C₂³×C₁₃	1	8	yes	—
371	#95	C₂³×C₁₃	1	2	yes	—
372	#95	C₂³×C₁₃	1	4	yes	—
373	#95	C₂³×C₁₃	1	4	yes	—
374	#95	C₂³×C₁₃	1	2	yes	—
375	#95	C₂³×C₁₃	1	2	yes	—
376	#95	C₂³×C₁₃	1	2	yes	—
377	#95	C₂³×C₁₃	1	4	yes	—
378	#95	C₂³×C₁₃	1	8	yes	—
379	C₂×C₁₃	—	2	4	no	—
380	C₂×C₁₃	—	4	8	no	—
381	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
382	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
383	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
384	C₂×C₁₃	#3519	1	2	yes	—
385	C₂×C₁₃	#3522	1	2	yes	—
386	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
387	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
388	#41	—	4	32	no	—
389	C₂×Q₈	—	4	4	no	—
390	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
391	C₂×D₄	—	2	16	no	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	4	4	no	—
396	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
397	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
398	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
399	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	2	8	no	—
406	C₂²×C₄	—	2	16	no	—
407	C₂²×C₄	—	4	4	no	—
408	C₂²×C₄	—	4	8	no	—
409	C₂²×C₄	—	4	8	no	—
410	C₂²×C₄	—	4	8	no	—
411	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
412	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
413	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
414	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
415	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
419	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
423	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
424	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
426	C₄⋊C₄	—	2	8	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	4	8	no	—
431	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
432	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
433	C₄⋊C₄	C₁₃×#41	1	8	yes	complemented
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	16	no	—
436	C₂²⋊C₄	—	4	8	no	—
437	C₂²⋊C₄	—	4	8	no	—
438	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
439	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
440	C₄²	—	2	8	no	—
441	C₄²	—	2	8	no	—
442	C₄²	—	4	2	no	—
443	C₄²	—	4	2	no	—
444	C₄²	—	4	8	no	—
445	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
446	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
447	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
448	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
449	C₁₃	#34236	1	1	yes	characteristic, direct product factor, Sylow
450	C₂³	—	2	2	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	8	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	8	no	—
456	C₂³	—	2	4	no	—
457	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
458	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
459	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
460	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
461	Q₈	—	4	8	no	—
462	D₄	—	2	32	no	—
463	D₄	—	2	16	no	—
464	D₄	—	2	16	no	—
465	D₄	—	4	8	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	8	no	—
476	C₂×C₄	—	2	8	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	4	16	no	—
487	C₂×C₄	—	4	16	no	—
488	C₂×C₄	—	8	16	no	—
489	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
490	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
491	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
492	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
493	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
494	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
495	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
496	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
497	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
498	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
499	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
500	C₂²	—	2	4	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	8	no	—
505	C₂²	—	2	8	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	4	8	no	—
508	C₂²	—	4	8	no	—
509	C₂²	C₁₃×#518	1	4	yes	—
510	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
511	C₂²	C₂²×C₁₃×#41	1	2	yes	—
512	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
513	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
514	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
515	C₄	—	2	8	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	8	no	—
520	C₄	—	2	2	no	—
521	C₄	—	4	4	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	4	no	—
524	C₄	C₄×C₁₃×#41	1	4	yes	—
525	C₄	C₁₃×#520	1	4	yes	—
526	C₂	—	2	4	no	—
527	C₂	—	4	8	no	—
528	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
529	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
530	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
531	C₂	C₁₃×#3519	1	2	yes	—
532	C₂	C₁₃×#3522	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2369	C₂	semidirect
3. C₁₃×#2366	C₂	semidirect
4. C₁₃×#2361	C₂	semidirect
5. C₁₃×#2357	C₂	semidirect
6. C₁₃×#2349	C₂	semidirect
7. C₁₃×#2339	C₂	semidirect
8. C₁₃×#2337	C₂	semidirect
9. C₁₃×#2319	C₂	semidirect
10. C₄×C₁₃×#121	C₂	semidirect
11. C₁₃×#2283	C₂	semidirect
12. C₁₃×#2275	C₂	semidirect
13. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
15. C₁₃×#532	C₄	semidirect
61. C₂×C₁₃×#41	C₂×C₄	semidirect
73. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
74. C₁₃×#127	C₂×C₄	semidirect
75. C₁₃×#124	C₂×C₄	semidirect
76. C₁₃×#121	C₂×C₄	semidirect
77. C₁₃×#121	C₂×C₄	semidirect
81. C₄×D₄×C₁₃	C₂×C₄	semidirect
82. C₄×D₄×C₁₃	C₂×C₄	semidirect
99. C₂×C₄²×C₁₃	C₂×C₄	semidirect
120. #34236	C₁₃	direct (N × H)
168. C₁₃×C₄⋊C₄	#41	semidirect
185. #2369	C₂×C₁₃	semidirect
186. #2366	C₂×C₁₃	semidirect
187. #2361	C₂×C₁₃	semidirect
188. #2357	C₂×C₁₃	semidirect
189. #2349	C₂×C₁₃	semidirect
190. #2339	C₂×C₁₃	semidirect
191. #2337	C₂×C₁₃	semidirect
192. #2319	C₂×C₁₃	semidirect
193. C₄×#121	C₂×C₁₃	semidirect
194. #2283	C₂×C₁₃	semidirect
195. #2275	C₂×C₁₃	semidirect
196. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
248. #532	C₄×C₁₃	semidirect
320. C₂×#41	C₂×C₄×C₁₃	semidirect
332. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
333. #127	C₂×C₄×C₁₃	semidirect
334. #124	C₂×C₄×C₁₃	semidirect
335. #121	C₂×C₄×C₁₃	semidirect
336. #121	C₂×C₄×C₁₃	semidirect
340. C₄×D₄	C₂×C₄×C₁₃	semidirect
341. C₄×D₄	C₂×C₄×C₁₃	semidirect
358. C₂×C₄²	C₂×C₄×C₁₃	semidirect
433. C₄⋊C₄	C₁₃×#41	semidirect
449. C₁₃	#34236	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×#532	2
C₁₃×#2369	2
C₁₃×#2366	2
C₁₃×#2361	2
C₁₃×#2357	2
C₁₃×#2349	2
C₁₃×#2339	2
C₁₃×#2337	2
C₁₃×#2319	2
C₄×C₁₃×#121	2
C₁₃×#2283	2
C₁₃×#2275	2
C₂×C₄×C₁₃×C₄⋊C₄	2
#34236	13

Subgroups — C13×#34236 #15720575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34236 #15720575