Subgroups — C₁₃×#34191 #15720530

Order 3328.

2470 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2355	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2352	C₂	1	4	yes	maximal, complemented
4	D₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2346	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2343	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2339	C₂	1	2	yes	maximal
8	C₁₃×#2320	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2318	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2283	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#382	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2275	C₂	1	2	yes	maximal, complemented
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×#41	C₄	1	16	yes	complemented
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
24	C₂×C₁₃×#117	C₂²	1	2	yes	—
25	C₂×C₁₃×#117	C₂²	1	2	yes	—
26	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
28	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#391	C₂²	1	4	yes	—
31	C₁₃×#389	C₂²	1	4	yes	—
32	C₁₃×#388	C₂²	1	8	yes	—
33	C₁₃×#387	C₂²	1	8	yes	—
34	C₁₃×#387	C₂²	1	8	yes	—
35	C₁₃×#386	C₂²	1	8	yes	—
36	C₁₃×#385	C₂²	1	8	yes	—
37	C₁₃×#384	C₂²	1	2	yes	—
38	C₁₃×#383	C₂²	1	4	yes	—
39	C₁₃×#383	C₂²	1	2	yes	—
40	C₁₃×#382	C₂²	1	1	yes	characteristic
41	C₁₃×#382	C₂²	1	2	yes	—
42	C₁₃×#382	C₂²	1	4	yes	—
43	C₁₃×#382	C₂²	1	4	yes	—
44	C₁₃×#382	C₂²	1	4	yes	—
45	C₁₃×#382	C₂²	1	1	yes	characteristic
46	C₁₃×#381	C₂²	1	2	yes	—
47	C₁₃×#381	C₂²	1	4	yes	—
48	C₁₃×#380	C₂²	1	4	yes	—
49	C₁₃×#380	C₂²	1	2	yes	—
50	C₁₃×#380	C₂²	1	2	yes	—
51	C₁₃×#380	C₂²	1	2	yes	—
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
53	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
54	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
55	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
57	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
58	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
59	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
60	C₁₃×#376	C₂²	1	2	yes	—
61	C₁₃×#376	C₂²	1	4	yes	—
62	C₂×C₁₃×#95	C₂²	1	4	yes	—
63	C₂×C₁₃×#95	C₂²	1	4	yes	—
64	C₂×C₁₃×#41	—	2	8	no	—
65	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
77	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
78	C₄×D₄×C₁₃	—	2	16	no	—
79	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
80	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
81	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
82	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
83	C₁₃×#117	—	4	4	no	—
84	C₁₃×#117	C₂×C₄	1	16	yes	complemented
85	C₁₃×#117	C₂×C₄	1	8	yes	complemented
86	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
103	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
104	C₂×C₄²×C₁₃	C₂×C₄	1	16	yes	complemented
105	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
106	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
107	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
108	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
115	C₁₃×#95	C₂³	1	4	yes	—
116	C₁₃×#95	C₂³	1	2	yes	—
117	C₁₃×#95	C₂³	1	4	yes	—
118	C₁₃×#95	C₂³	1	8	yes	—
119	C₁₃×#95	C₂³	1	2	yes	—
120	C₁₃×#95	C₂³	1	2	yes	—
121	C₁₃×#95	C₂³	1	4	yes	—
122	C₁₃×#95	C₂³	1	4	yes	—
123	C₁₃×#95	C₂³	1	8	yes	—
124	C₁₃×#95	C₂³	1	8	yes	—
125	C₁₃×#95	C₂³	1	2	yes	—
126	C₁₃×#95	C₂³	1	8	yes	—
127	#34191	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
130	C₁₃×#41	—	2	32	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
133	C₂×D₄×C₁₃	—	2	8	no	—
134	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
135	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
136	C₂×D₄×C₁₃	#41	1	8	yes	—
137	C₂²×C₄×C₁₃	—	2	8	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	16	no	—
144	C₂²×C₄×C₁₃	—	4	4	no	—
145	C₂²×C₄×C₁₃	—	4	2	no	—
146	C₂²×C₄×C₁₃	—	4	8	no	—
147	C₂²×C₄×C₁₃	—	4	8	no	—
148	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
149	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
151	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
153	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₁₃×C₄⋊C₄	—	2	8	no	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	8	no	—
169	C₁₃×C₄⋊C₄	—	2	4	no	—
170	C₁₃×C₄⋊C₄	—	4	8	no	—
171	C₁₃×C₄⋊C₄	—	4	4	no	—
172	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
173	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
174	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
175	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
176	C₁₃×C₂²⋊C₄	—	2	16	no	—
177	C₁₃×C₂²⋊C₄	—	4	4	no	—
178	C₁₃×C₂²⋊C₄	—	4	4	no	—
179	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
180	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
181	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
182	C₄²×C₁₃	—	2	8	no	—
183	C₄²×C₁₃	—	4	8	no	—
184	C₄²×C₁₃	—	4	4	no	—
185	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
186	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
187	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
188	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
189	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
190	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
191	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
192	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic
193	#2355	C₂×C₁₃	1	2	yes	complemented
194	#2352	C₂×C₁₃	1	4	yes	complemented
195	D₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
196	#2346	C₂×C₁₃	1	2	yes	complemented
197	#2343	C₂×C₁₃	1	4	yes	complemented
198	#2339	C₂×C₁₃	1	2	yes	—
199	#2320	C₂×C₁₃	1	2	yes	complemented
200	#2318	C₂×C₁₃	1	4	yes	complemented
201	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#2283	C₂×C₁₃	1	2	yes	complemented
204	C₂×#382	C₂×C₁₃	1	2	yes	complemented
205	#2275	C₂×C₁₃	1	2	yes	complemented
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	2	1	no	—
211	C₂³×C₁₃	—	2	1	no	—
212	C₂³×C₁₃	—	2	2	no	—
213	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
214	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
215	C₂³×C₁₃	C₂×#41	1	8	yes	—
216	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
217	Q₈×C₁₃	—	2	8	no	—
218	D₄×C₁₃	—	2	16	no	—
219	D₄×C₁₃	#117	1	16	yes	complemented
220	C₂×C₄×C₁₃	—	2	16	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	8	no	—
231	C₂×C₄×C₁₃	—	2	16	no	—
232	C₂×C₄×C₁₃	—	2	8	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	2	8	no	—
236	C₂×C₄×C₁₃	—	2	8	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	8	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	4	8	no	—
243	C₂×C₄×C₁₃	—	4	4	no	—
244	C₂×C₄×C₁₃	—	8	16	no	—
245	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
246	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
247	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
248	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
249	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
250	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
251	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
252	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
253	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
254	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
255	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
256	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
257	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
258	C₄×#41	C₄×C₁₃	1	16	yes	complemented
259	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
262	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
265	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
266	C₂×#117	C₂²×C₁₃	1	2	yes	—
267	C₂×#117	C₂²×C₁₃	1	2	yes	—
268	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
270	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
271	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
272	#391	C₂²×C₁₃	1	4	yes	—
273	#389	C₂²×C₁₃	1	4	yes	—
274	#388	C₂²×C₁₃	1	8	yes	—
275	#387	C₂²×C₁₃	1	8	yes	—
276	#387	C₂²×C₁₃	1	8	yes	—
277	#386	C₂²×C₁₃	1	8	yes	—
278	#385	C₂²×C₁₃	1	8	yes	—
279	#384	C₂²×C₁₃	1	2	yes	—
280	#383	C₂²×C₁₃	1	4	yes	—
281	#383	C₂²×C₁₃	1	2	yes	—
282	#382	C₂²×C₁₃	1	4	yes	—
283	#382	C₂²×C₁₃	1	4	yes	—
284	#382	C₂²×C₁₃	1	4	yes	—
285	#382	C₂²×C₁₃	1	1	yes	characteristic
286	#382	C₂²×C₁₃	1	2	yes	—
287	#382	C₂²×C₁₃	1	1	yes	characteristic
288	#381	C₂²×C₁₃	1	2	yes	—
289	#381	C₂²×C₁₃	1	4	yes	—
290	#380	C₂²×C₁₃	1	2	yes	—
291	#380	C₂²×C₁₃	1	2	yes	—
292	#380	C₂²×C₁₃	1	4	yes	—
293	#380	C₂²×C₁₃	1	2	yes	—
294	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
295	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
296	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
297	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
298	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
299	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
300	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
301	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
302	#376	C₂²×C₁₃	1	2	yes	—
303	#376	C₂²×C₁₃	1	4	yes	—
304	C₂×#95	C₂²×C₁₃	1	4	yes	—
305	C₂×#95	C₂²×C₁₃	1	4	yes	—
306	C₂²×C₁₃	—	2	4	no	—
307	C₂²×C₁₃	—	2	4	no	—
308	C₂²×C₁₃	—	2	8	no	—
309	C₂²×C₁₃	—	2	8	no	—
310	C₂²×C₁₃	—	2	2	no	—
311	C₂²×C₁₃	—	2	2	no	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	4	2	no	—
314	C₂²×C₁₃	—	4	2	no	—
315	C₂²×C₁₃	C₂×#117	1	8	yes	—
316	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
317	C₂²×C₁₃	C₂²×#41	1	2	yes	—
318	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
319	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
320	C₂²×C₁₃	#585	1	2	yes	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	2	4	no	—
323	C₄×C₁₃	—	2	2	no	—
324	C₄×C₁₃	—	2	4	no	—
325	C₄×C₁₃	—	2	2	no	—
326	C₄×C₁₃	—	2	4	no	—
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	4	8	no	—
329	C₄×C₁₃	—	4	4	no	—
330	C₄×C₁₃	—	4	4	no	—
331	C₄×C₁₃	C₂×#117	1	4	yes	—
332	C₄×C₁₃	#520	1	4	yes	—
333	C₂×#41	—	2	8	no	—
334	C₂×#41	C₂×C₄×C₁₃	1	8	yes	—
335	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
336	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
337	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
339	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
341	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
343	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
346	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
347	C₄×D₄	—	2	16	no	—
348	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
349	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
350	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
351	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
352	#117	—	4	4	no	—
353	#117	C₂×C₄×C₁₃	1	16	yes	complemented
354	#117	C₂×C₄×C₁₃	1	8	yes	complemented
355	C₂×C₄⋊C₄	—	4	8	no	—
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
372	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
373	C₂×C₄²	C₂×C₄×C₁₃	1	16	yes	complemented
374	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
375	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
376	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
377	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
378	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
381	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
383	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
384	#95	C₂³×C₁₃	1	2	yes	—
385	#95	C₂³×C₁₃	1	2	yes	—
386	#95	C₂³×C₁₃	1	4	yes	—
387	#95	C₂³×C₁₃	1	4	yes	—
388	#95	C₂³×C₁₃	1	8	yes	—
389	#95	C₂³×C₁₃	1	8	yes	—
390	#95	C₂³×C₁₃	1	2	yes	—
391	#95	C₂³×C₁₃	1	4	yes	—
392	#95	C₂³×C₁₃	1	2	yes	—
393	#95	C₂³×C₁₃	1	8	yes	—
394	#95	C₂³×C₁₃	1	4	yes	—
395	#95	C₂³×C₁₃	1	8	yes	—
396	C₂×C₁₃	—	2	8	no	—
397	C₂×C₁₃	—	4	2	no	—
398	C₂×C₁₃	C₂²×#117	1	1	yes	characteristic
399	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
400	C₂×C₁₃	#3428	1	1	yes	characteristic
401	C₂×C₁₃	#3514	1	2	yes	—
402	C₂×C₁₃	#3515	1	2	yes	—
403	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
404	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
405	#41	—	2	32	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
410	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
411	C₂×D₄	C₁₃×#41	1	8	yes	—
412	C₂²×C₄	—	2	8	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	16	no	—
419	C₂²×C₄	—	4	4	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	8	no	—
422	C₂²×C₄	—	4	8	no	—
423	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
424	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
425	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
426	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
427	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
428	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
430	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
432	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	8	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	4	8	no	—
446	C₄⋊C₄	—	4	4	no	—
447	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
448	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
449	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
450	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
451	C₂²⋊C₄	—	2	16	no	—
452	C₂²⋊C₄	—	4	4	no	—
453	C₂²⋊C₄	—	4	4	no	—
454	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
455	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
456	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
457	C₄²	—	2	8	no	—
458	C₄²	—	4	4	no	—
459	C₄²	—	4	8	no	—
460	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
461	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
462	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
463	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
464	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
465	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
466	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
467	C₁₃	#34191	1	1	yes	characteristic, direct product factor, Sylow
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	2	no	—
475	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
476	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
477	C₂³	C₂×C₁₃×#41	1	8	yes	—
478	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
479	Q₈	—	2	8	no	—
480	D₄	—	2	16	no	—
481	D₄	C₁₃×#117	1	16	yes	complemented
482	C₂×C₄	—	2	16	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	16	no	—
494	C₂×C₄	—	2	8	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	8	no	—
498	C₂×C₄	—	2	8	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	8	16	no	—
507	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
508	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
509	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
510	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
511	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
512	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
513	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
514	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
515	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
516	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
517	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
518	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	8	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	C₂×C₁₃×#117	1	8	yes	—
529	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
530	C₂²	C₂²×C₁₃×#41	1	2	yes	—
531	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
533	C₂²	C₁₃×#585	1	2	yes	—
534	C₄	—	2	2	no	—
535	C₄	—	2	4	no	—
536	C₄	—	2	2	no	—
537	C₄	—	2	4	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	4	no	—
540	C₄	—	2	2	no	—
541	C₄	—	4	8	no	—
542	C₄	—	4	4	no	—
543	C₄	—	4	4	no	—
544	C₄	C₂×C₁₃×#117	1	4	yes	—
545	C₄	C₁₃×#520	1	4	yes	—
546	C₂	—	2	8	no	—
547	C₂	—	4	2	no	—
548	C₂	C₂²×C₁₃×#117	1	1	yes	characteristic
549	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
550	C₂	C₁₃×#3428	1	1	yes	characteristic
551	C₂	C₁₃×#3514	1	2	yes	—
552	C₂	C₁₃×#3515	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
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×#2355	C₂	semidirect
3. C₁₃×#2352	C₂	semidirect
4. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
5. C₁₃×#2346	C₂	semidirect
6. C₁₃×#2343	C₂	semidirect
8. C₁₃×#2320	C₂	semidirect
9. C₁₃×#2318	C₂	semidirect
10. C₁₃×#2285	C₂	semidirect
11. C₁₃×#2283	C₂	semidirect
12. C₁₃×#2283	C₂	semidirect
13. C₂×C₁₃×#382	C₂	semidirect
14. C₁₃×#2275	C₂	semidirect
16. C₄×C₁₃×#41	C₄	semidirect
76. C₄×Q₈×C₁₃	C₂×C₄	semidirect
77. C₄×Q₈×C₁₃	C₂×C₄	semidirect
81. C₄×D₄×C₁₃	C₂×C₄	semidirect
82. C₄×D₄×C₁₃	C₂×C₄	semidirect
84. C₁₃×#117	C₂×C₄	semidirect
85. C₁₃×#117	C₂×C₄	semidirect
103. C₂×C₄²×C₁₃	C₂×C₄	semidirect
104. C₂×C₄²×C₁₃	C₂×C₄	semidirect
127. #34191	C₁₃	direct (N × H)
193. #2355	C₂×C₁₃	semidirect
194. #2352	C₂×C₁₃	semidirect
195. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
196. #2346	C₂×C₁₃	semidirect
197. #2343	C₂×C₁₃	semidirect
199. #2320	C₂×C₁₃	semidirect
200. #2318	C₂×C₁₃	semidirect
201. #2285	C₂×C₁₃	semidirect
202. #2283	C₂×C₁₃	semidirect
203. #2283	C₂×C₁₃	semidirect
204. C₂×#382	C₂×C₁₃	semidirect
205. #2275	C₂×C₁₃	semidirect
219. D₄×C₁₃	#117	semidirect
258. C₄×#41	C₄×C₁₃	semidirect
345. C₄×Q₈	C₂×C₄×C₁₃	semidirect
346. C₄×Q₈	C₂×C₄×C₁₃	semidirect
350. C₄×D₄	C₂×C₄×C₁₃	semidirect
351. C₄×D₄	C₂×C₄×C₁₃	semidirect
353. #117	C₂×C₄×C₁₃	semidirect
354. #117	C₂×C₄×C₁₃	semidirect
372. C₂×C₄²	C₂×C₄×C₁₃	semidirect
373. C₂×C₄²	C₂×C₄×C₁₃	semidirect
467. C₁₃	#34191	direct (N × H)
481. D₄	C₁₃×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₃×#41	2
C₁₃×#2355	2
C₁₃×#2352	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2346	2
C₁₃×#2343	2
C₁₃×#2339	2
C₁₃×#2320	2
C₁₃×#2318	2
C₁₃×#2285	2
C₁₃×#2283	2
C₂×C₁₃×#382	2
C₁₃×#2275	2
#34191	13

Subgroups — C13×#34191 #15720530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34191 #15720530