Subgroups — C₁₃×#34398 #15720737

Order 3328.

2538 conjugacy classes of subgroups.

The subgroup lattice has 500 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×#2379	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2361	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2357	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2349	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2339	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2331	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2328	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2325	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2318	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₁₃×#532	C₄	1	16	yes	complemented
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#124	C₂²	1	2	yes	—
18	C₂×C₁₃×#121	C₂²	1	2	yes	—
19	C₂×C₁₃×#121	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#391	C₂²	1	8	yes	—
27	C₁₃×#390	C₂²	1	4	yes	—
28	C₁₃×#389	C₂²	1	4	yes	—
29	C₁₃×#388	C₂²	1	8	yes	—
30	C₁₃×#388	C₂²	1	8	yes	—
31	C₁₃×#387	C₂²	1	8	yes	—
32	C₁₃×#386	C₂²	1	8	yes	—
33	C₁₃×#386	C₂²	1	8	yes	—
34	C₁₃×#386	C₂²	1	8	yes	—
35	C₁₃×#385	C₂²	1	8	yes	—
36	C₁₃×#385	C₂²	1	8	yes	—
37	C₁₃×#383	C₂²	1	2	yes	—
38	C₁₃×#382	C₂²	1	2	yes	—
39	C₁₃×#382	C₂²	1	2	yes	—
40	C₁₃×#382	C₂²	1	2	yes	—
41	C₁₃×#382	C₂²	1	2	yes	—
42	C₁₃×#382	C₂²	1	2	yes	—
43	C₁₃×#381	C₂²	1	2	yes	—
44	C₁₃×#381	C₂²	1	4	yes	—
45	C₁₃×#380	C₂²	1	2	yes	—
46	C₁₃×#380	C₂²	1	4	yes	—
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
50	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
51	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
52	C₁₃×#376	C₂²	1	2	yes	—
53	C₂×C₁₃×#95	C₂²	1	2	yes	—
54	C₂×C₁₃×#95	C₂²	1	2	yes	—
55	C₂×C₁₃×#95	C₂²	1	4	yes	—
56	C₂×C₁₃×#41	—	4	8	no	—
57	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
58	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
70	C₁₃×#127	C₂×C₄	1	8	yes	complemented
71	C₁₃×#124	C₂×C₄	1	16	yes	complemented
72	C₁₃×#121	C₂×C₄	1	16	yes	complemented
73	C₁₃×#121	C₂×C₄	1	16	yes	complemented
74	C₄×D₄×C₁₃	—	4	8	no	—
75	C₄×D₄×C₁₃	—	4	16	no	—
76	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
77	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
78	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
93	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
95	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#95	C₂³	1	2	yes	—
101	C₁₃×#95	C₂³	1	4	yes	—
102	C₁₃×#95	C₂³	1	4	yes	—
103	C₁₃×#95	C₂³	1	2	yes	—
104	C₁₃×#95	C₂³	1	8	yes	—
105	C₁₃×#95	C₂³	1	4	yes	—
106	C₁₃×#95	C₂³	1	4	yes	—
107	C₁₃×#95	C₂³	1	4	yes	—
108	C₁₃×#95	C₂³	1	4	yes	—
109	C₁₃×#95	C₂³	1	4	yes	—
110	C₁₃×#95	C₂³	1	8	yes	—
111	#34398	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
113	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₁₃×#41	—	4	32	no	—
115	C₂×Q₈×C₁₃	—	4	4	no	—
116	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
117	C₂×D₄×C₁₃	—	2	16	no	—
118	C₂×D₄×C₁₃	—	2	4	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	4	4	no	—
121	C₂×D₄×C₁₃	—	4	4	no	—
122	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
123	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
124	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
125	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	8	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	—	4	8	no	—
132	C₂²×C₄×C₁₃	—	4	4	no	—
133	C₂²×C₄×C₁₃	—	4	8	no	—
134	C₂²×C₄×C₁₃	—	4	8	no	—
135	C₂²×C₄×C₁₃	—	4	4	no	—
136	C₂²×C₄×C₁₃	—	4	8	no	—
137	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
139	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	4	4	no	—
153	C₁₃×C₄⋊C₄	—	4	2	no	—
154	C₁₃×C₄⋊C₄	—	4	2	no	—
155	C₁₃×C₄⋊C₄	—	4	8	no	—
156	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
157	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	4	8	no	—
160	C₁₃×C₂²⋊C₄	—	4	8	no	—
161	C₁₃×C₂²⋊C₄	—	4	8	no	—
162	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
163	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
164	C₄²×C₁₃	—	2	4	no	—
165	C₄²×C₁₃	—	2	4	no	—
166	C₄²×C₁₃	—	4	8	no	—
167	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
168	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
169	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
170	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
171	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
172	#2379	C₂×C₁₃	1	4	yes	complemented
173	#2361	C₂×C₁₃	1	4	yes	complemented
174	#2357	C₂×C₁₃	1	2	yes	complemented
175	#2349	C₂×C₁₃	1	2	yes	complemented
176	#2339	C₂×C₁₃	1	4	yes	complemented
177	#2331	C₂×C₁₃	1	2	yes	complemented
178	#2328	C₂×C₁₃	1	2	yes	complemented
179	#2325	C₂×C₁₃	1	4	yes	complemented
180	#2318	C₂×C₁₃	1	4	yes	complemented
181	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
182	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
183	C₂³×C₁₃	—	2	1	no	—
184	C₂³×C₁₃	—	2	1	no	—
185	C₂³×C₁₃	—	2	2	no	—
186	C₂³×C₁₃	—	2	4	no	—
187	C₂³×C₁₃	—	2	8	no	—
188	C₂³×C₁₃	—	2	4	no	—
189	C₂³×C₁₃	—	2	8	no	—
190	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
191	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
192	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
193	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
194	Q₈×C₁₃	—	4	8	no	—
195	D₄×C₁₃	—	2	32	no	—
196	D₄×C₁₃	—	2	16	no	—
197	D₄×C₁₃	—	4	8	no	—
198	D₄×C₁₃	—	4	8	no	—
199	C₂×C₄×C₁₃	—	2	8	no	—
200	C₂×C₄×C₁₃	—	2	8	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	8	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	8	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	8	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	4	4	no	—
218	C₂×C₄×C₁₃	—	4	16	no	—
219	C₂×C₄×C₁₃	—	8	8	no	—
220	C₂×C₄×C₁₃	—	8	16	no	—
221	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
223	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
225	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
226	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
227	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
228	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
229	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
230	C₂²×#41	C₂²×C₁₃	1	2	yes	—
231	#532	C₄×C₁₃	1	16	yes	complemented
232	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#124	C₂²×C₁₃	1	2	yes	—
235	C₂×#121	C₂²×C₁₃	1	2	yes	—
236	C₂×#121	C₂²×C₁₃	1	2	yes	—
237	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
238	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
239	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
240	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
241	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
242	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
243	#391	C₂²×C₁₃	1	8	yes	—
244	#390	C₂²×C₁₃	1	4	yes	—
245	#389	C₂²×C₁₃	1	4	yes	—
246	#388	C₂²×C₁₃	1	8	yes	—
247	#388	C₂²×C₁₃	1	8	yes	—
248	#387	C₂²×C₁₃	1	8	yes	—
249	#386	C₂²×C₁₃	1	8	yes	—
250	#386	C₂²×C₁₃	1	8	yes	—
251	#386	C₂²×C₁₃	1	8	yes	—
252	#385	C₂²×C₁₃	1	8	yes	—
253	#385	C₂²×C₁₃	1	8	yes	—
254	#383	C₂²×C₁₃	1	2	yes	—
255	#382	C₂²×C₁₃	1	2	yes	—
256	#382	C₂²×C₁₃	1	2	yes	—
257	#382	C₂²×C₁₃	1	2	yes	—
258	#382	C₂²×C₁₃	1	2	yes	—
259	#382	C₂²×C₁₃	1	2	yes	—
260	#381	C₂²×C₁₃	1	4	yes	—
261	#381	C₂²×C₁₃	1	2	yes	—
262	#380	C₂²×C₁₃	1	4	yes	—
263	#380	C₂²×C₁₃	1	2	yes	—
264	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
265	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
266	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
267	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
268	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
269	#376	C₂²×C₁₃	1	2	yes	—
270	C₂×#95	C₂²×C₁₃	1	4	yes	—
271	C₂×#95	C₂²×C₁₃	1	2	yes	—
272	C₂×#95	C₂²×C₁₃	1	2	yes	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	4	no	—
276	C₂²×C₁₃	—	2	4	no	—
277	C₂²×C₁₃	—	2	8	no	—
278	C₂²×C₁₃	—	2	8	no	—
279	C₂²×C₁₃	—	2	8	no	—
280	C₂²×C₁₃	—	4	8	no	—
281	C₂²×C₁₃	—	4	8	no	—
282	C₂²×C₁₃	#518	1	4	yes	—
283	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
284	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
285	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
286	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
287	C₂²×C₁₃	#585	1	2	yes	—
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	2	2	no	—
290	C₄×C₁₃	—	2	8	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	4	4	no	—
295	C₄×C₁₃	—	4	8	no	—
296	C₄×C₁₃	—	4	4	no	—
297	C₄×C₁₃	#520	1	4	yes	—
298	C₂×#41	—	4	8	no	—
299	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
300	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
301	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
302	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
303	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
304	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
305	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
308	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
309	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
310	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
312	#127	C₂×C₄×C₁₃	1	8	yes	complemented
313	#124	C₂×C₄×C₁₃	1	16	yes	complemented
314	#121	C₂×C₄×C₁₃	1	16	yes	complemented
315	#121	C₂×C₄×C₁₃	1	16	yes	complemented
316	C₄×D₄	—	4	8	no	—
317	C₄×D₄	—	4	16	no	—
318	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
319	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
320	C₂×C₄⋊C₄	—	4	4	no	—
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
334	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
335	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
336	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
337	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
338	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
342	#95	C₂³×C₁₃	1	4	yes	—
343	#95	C₂³×C₁₃	1	2	yes	—
344	#95	C₂³×C₁₃	1	4	yes	—
345	#95	C₂³×C₁₃	1	4	yes	—
346	#95	C₂³×C₁₃	1	4	yes	—
347	#95	C₂³×C₁₃	1	8	yes	—
348	#95	C₂³×C₁₃	1	4	yes	—
349	#95	C₂³×C₁₃	1	4	yes	—
350	#95	C₂³×C₁₃	1	2	yes	—
351	#95	C₂³×C₁₃	1	4	yes	—
352	#95	C₂³×C₁₃	1	8	yes	—
353	C₂×C₁₃	—	2	4	no	—
354	C₂×C₁₃	—	4	8	no	—
355	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
356	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
357	C₂×C₁₃	#3428	1	1	yes	characteristic
358	C₂×C₁₃	#3558	1	2	yes	—
359	C₂×C₁₃	#3559	1	2	yes	—
360	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
361	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
362	#41	—	4	32	no	—
363	C₂×Q₈	—	4	4	no	—
364	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
365	C₂×D₄	—	2	16	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
371	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
372	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
373	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	4	8	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	—	4	8	no	—
382	C₂²×C₄	—	4	8	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	8	no	—
385	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
386	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
387	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
388	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
389	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
390	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
391	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
392	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	4	4	no	—
401	C₄⋊C₄	—	4	8	no	—
402	C₄⋊C₄	—	4	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
405	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	4	8	no	—
408	C₂²⋊C₄	—	4	8	no	—
409	C₂²⋊C₄	—	4	8	no	—
410	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
411	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
412	C₄²	—	2	4	no	—
413	C₄²	—	2	4	no	—
414	C₄²	—	4	8	no	—
415	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
416	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
417	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
418	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
419	C₁₃	#34398	1	1	yes	characteristic, direct product factor, Sylow
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	8	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	8	no	—
427	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
428	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
429	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
430	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
431	Q₈	—	4	8	no	—
432	D₄	—	2	32	no	—
433	D₄	—	2	16	no	—
434	D₄	—	4	8	no	—
435	D₄	—	4	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	16	no	—
456	C₂×C₄	—	8	8	no	—
457	C₂×C₄	—	8	16	no	—
458	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
459	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
460	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
461	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
462	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
463	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
464	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
465	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
466	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	8	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	4	8	no	—
475	C₂²	—	4	8	no	—
476	C₂²	C₁₃×#518	1	4	yes	—
477	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
478	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
480	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
481	C₂²	C₁₃×#585	1	2	yes	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	8	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	8	no	—
490	C₄	—	4	4	no	—
491	C₄	C₁₃×#520	1	4	yes	—
492	C₂	—	2	4	no	—
493	C₂	—	4	8	no	—
494	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
495	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
496	C₂	C₁₃×#3428	1	1	yes	characteristic
497	C₂	C₁₃×#3558	1	2	yes	—
498	C₂	C₁₃×#3559	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×#2379	C₂	semidirect
3. C₁₃×#2361	C₂	semidirect
4. C₁₃×#2357	C₂	semidirect
5. C₁₃×#2349	C₂	semidirect
6. C₁₃×#2339	C₂	semidirect
7. C₁₃×#2331	C₂	semidirect
8. C₁₃×#2328	C₂	semidirect
9. C₁₃×#2325	C₂	semidirect
10. C₁₃×#2318	C₂	semidirect
11. C₁₃×#2283	C₂	semidirect
12. C₂×C₁₃×#382	C₂	semidirect
14. C₁₃×#532	C₄	semidirect
57. C₂×C₁₃×#41	C₂×C₄	semidirect
69. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
70. C₁₃×#127	C₂×C₄	semidirect
71. C₁₃×#124	C₂×C₄	semidirect
72. C₁₃×#121	C₂×C₄	semidirect
73. C₁₃×#121	C₂×C₄	semidirect
76. C₄×D₄×C₁₃	C₂×C₄	semidirect
77. C₄×D₄×C₁₃	C₂×C₄	semidirect
92. C₂×C₄²×C₁₃	C₂×C₄	semidirect
111. #34398	C₁₃	direct (N × H)
172. #2379	C₂×C₁₃	semidirect
173. #2361	C₂×C₁₃	semidirect
174. #2357	C₂×C₁₃	semidirect
175. #2349	C₂×C₁₃	semidirect
176. #2339	C₂×C₁₃	semidirect
177. #2331	C₂×C₁₃	semidirect
178. #2328	C₂×C₁₃	semidirect
179. #2325	C₂×C₁₃	semidirect
180. #2318	C₂×C₁₃	semidirect
181. #2283	C₂×C₁₃	semidirect
182. C₂×#382	C₂×C₁₃	semidirect
231. #532	C₄×C₁₃	semidirect
299. C₂×#41	C₂×C₄×C₁₃	semidirect
311. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
312. #127	C₂×C₄×C₁₃	semidirect
313. #124	C₂×C₄×C₁₃	semidirect
314. #121	C₂×C₄×C₁₃	semidirect
315. #121	C₂×C₄×C₁₃	semidirect
318. C₄×D₄	C₂×C₄×C₁₃	semidirect
319. C₄×D₄	C₂×C₄×C₁₃	semidirect
334. C₂×C₄²	C₂×C₄×C₁₃	semidirect
419. C₁₃	#34398	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×#2379	2
C₁₃×#2361	2
C₁₃×#2357	2
C₁₃×#2349	2
C₁₃×#2339	2
C₁₃×#2331	2
C₁₃×#2328	2
C₁₃×#2325	2
C₁₃×#2318	2
C₁₃×#2283	2
C₂×C₁₃×#382	2
#34398	13

Subgroups — C13×#34398 #15720737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34398 #15720737