Subgroups — C₁₃×#34945 #15721284

Order 3328.

1812 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2573	C₂	1	4	yes	maximal, complemented
2	C₁₃×#2571	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2547	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2514	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2494	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2447	C₂	1	2	yes	maximal
9	C₁₃×#2421	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2401	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#124	C₂	1	2	yes	maximal
13	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2295	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2283	C₂	1	2	yes	maximal, complemented
16	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#401	C₂²	1	4	yes	—
30	C₁₃×#400	C₂²	1	4	yes	—
31	C₁₃×#400	C₂²	1	4	yes	—
32	C₁₃×#400	C₂²	1	4	yes	—
33	C₁₃×#397	C₂²	1	4	yes	—
34	C₁₃×#397	C₂²	1	4	yes	—
35	C₁₃×#397	C₂²	1	4	yes	—
36	C₁₃×#396	C₂²	1	4	yes	—
37	C₁₃×#391	C₂²	1	2	yes	—
38	C₁₃×#391	C₂²	1	2	yes	—
39	C₁₃×#391	C₂²	1	2	yes	—
40	C₁₃×#391	C₂²	1	2	yes	—
41	C₁₃×#391	C₂²	1	2	yes	—
42	C₁₃×#390	C₂²	1	2	yes	—
43	C₁₃×#389	C₂²	1	2	yes	—
44	C₁₃×#389	C₂²	1	2	yes	—
45	C₁₃×#389	C₂²	1	2	yes	—
46	C₁₃×#389	C₂²	1	2	yes	—
47	C₁₃×#389	C₂²	1	2	yes	—
48	C₁₃×#388	C₂²	1	4	yes	—
49	C₁₃×#388	C₂²	1	4	yes	—
50	C₁₃×#387	C₂²	1	4	yes	—
51	C₁₃×#387	C₂²	1	4	yes	—
52	C₁₃×#387	C₂²	1	4	yes	—
53	C₁₃×#385	C₂²	1	4	yes	—
54	C₁₃×#384	C₂²	1	1	yes	characteristic
55	C₁₃×#383	C₂²	1	4	yes	—
56	C₁₃×#382	C₂²	1	2	yes	—
57	C₁₃×#382	C₂²	1	2	yes	—
58	C₁₃×#382	C₂²	1	2	yes	—
59	C₁₃×#381	C₂²	1	4	yes	—
60	C₁₃×#380	C₂²	1	2	yes	—
61	C₁₃×#380	C₂²	1	2	yes	—
62	C₁₃×#380	C₂²	1	2	yes	—
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
71	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
73	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
74	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
77	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
78	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₁₃×#376	C₂²	1	4	yes	—
81	C₄³×C₁₃	C₂²	1	1	yes	characteristic
82	C₄³×C₁₃	C₂²	1	2	yes	—
83	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
84	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
89	C₁₃×C₄⋊Q₈	—	2	4	no	—
90	C₁₃×#124	—	2	8	no	—
91	C₁₃×C₂²⋊Q₈	—	2	8	no	—
92	C₄×Q₈×C₁₃	—	2	4	no	—
93	C₄×Q₈×C₁₃	—	2	4	no	—
94	C₄×Q₈×C₁₃	—	2	8	no	—
95	C₄×Q₈×C₁₃	—	2	4	no	—
96	C₄×D₄×C₁₃	—	2	4	no	—
97	C₄×D₄×C₁₃	—	2	4	no	—
98	C₄×D₄×C₁₃	—	2	4	no	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₄²×C₁₃	—	2	8	no	—
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
141	C₁₃×#95	C₂³	1	2	yes	—
142	C₁₃×#95	C₂³	1	2	yes	—
143	C₁₃×#95	C₂³	1	2	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	C₁₃×#95	C₂³	1	4	yes	—
146	C₁₃×#95	C₂³	1	4	yes	—
147	C₁₃×#95	C₂³	1	4	yes	—
148	C₁₃×#95	C₂³	1	2	yes	—
149	C₁₃×#95	C₂³	1	2	yes	—
150	C₁₃×#95	C₂³	1	2	yes	—
151	C₁₃×#95	C₂³	1	4	yes	—
152	C₁₃×#95	C₂³	1	4	yes	—
153	C₁₃×#95	C₂³	1	4	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	C₁₃×#95	C₂³	1	4	yes	—
157	C₁₃×#95	C₂³	1	4	yes	—
158	C₁₃×#95	C₂³	1	4	yes	—
159	#34945	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
161	C₂×Q₈×C₁₃	—	2	2	no	—
162	C₂×Q₈×C₁₃	—	2	2	no	—
163	C₂×Q₈×C₁₃	—	2	4	no	—
164	C₂×Q₈×C₁₃	—	2	4	no	—
165	C₂×Q₈×C₁₃	—	2	4	no	—
166	C₂×Q₈×C₁₃	#41	1	4	yes	—
167	C₂×D₄×C₁₃	—	2	2	no	—
168	C₂×D₄×C₁₃	—	2	2	no	—
169	C₂×D₄×C₁₃	#41	1	4	yes	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	2	4	no	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	2	4	no	—
176	C₂²×C₄×C₁₃	—	2	4	no	—
177	C₂²×C₄×C₁₃	—	2	4	no	—
178	C₂²×C₄×C₁₃	—	4	2	no	—
179	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₁₃×C₄⋊C₄	—	2	2	no	—
203	C₁₃×C₄⋊C₄	—	2	2	no	—
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	—	2	8	no	—
206	C₁₃×C₄⋊C₄	—	2	4	no	—
207	C₁₃×C₄⋊C₄	—	2	8	no	—
208	C₁₃×C₄⋊C₄	—	2	4	no	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	4	2	no	—
211	C₁₃×C₄⋊C₄	—	4	4	no	—
212	C₁₃×C₂²⋊C₄	—	2	4	no	—
213	C₁₃×C₂²⋊C₄	—	2	8	no	—
214	C₁₃×C₂²⋊C₄	—	2	8	no	—
215	C₁₃×C₂²⋊C₄	—	2	4	no	—
216	C₁₃×C₂²⋊C₄	—	2	4	no	—
217	C₁₃×C₂²⋊C₄	—	2	8	no	—
218	C₁₃×C₂²⋊C₄	—	4	4	no	—
219	C₄²×C₁₃	—	2	4	no	—
220	C₄²×C₁₃	—	2	4	no	—
221	C₄²×C₁₃	—	2	4	no	—
222	C₄²×C₁₃	—	2	2	no	—
223	C₄²×C₁₃	—	2	4	no	—
224	C₄²×C₁₃	—	2	2	no	—
225	C₄²×C₁₃	—	2	4	no	—
226	C₄²×C₁₃	—	2	4	no	—
227	C₄²×C₁₃	—	2	8	no	—
228	C₄²×C₁₃	—	2	4	no	—
229	C₄²×C₁₃	—	2	2	no	—
230	C₄²×C₁₃	—	2	4	no	—
231	C₄²×C₁₃	—	4	1	no	—
232	C₄²×C₁₃	—	4	2	no	—
233	C₄²×C₁₃	#41	1	4	yes	—
234	C₄²×C₁₃	#41	1	4	yes	—
235	C₄²×C₁₃	#41	1	4	yes	—
236	#2573	C₂×C₁₃	1	4	yes	complemented
237	#2571	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#2568	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2547	C₂×C₁₃	1	1	yes	characteristic
240	#2538	C₂×C₁₃	1	1	yes	characteristic
241	#2514	C₂×C₁₃	1	2	yes	complemented
242	#2494	C₂×C₁₃	1	2	yes	complemented
243	#2447	C₂×C₁₃	1	2	yes	—
244	#2421	C₂×C₁₃	1	2	yes	complemented
245	#2401	C₂×C₁₃	1	4	yes	complemented
246	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
247	C₄×#124	C₂×C₁₃	1	2	yes	—
248	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
249	#2295	C₂×C₁₃	1	2	yes	complemented
250	#2283	C₂×C₁₃	1	2	yes	complemented
251	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
252	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic
253	C₂³×C₁₃	—	2	2	no	—
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	C₂×#41	1	4	yes	—
260	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
261	Q₈×C₁₃	—	2	8	no	—
262	Q₈×C₁₃	—	4	8	no	—
263	D₄×C₁₃	—	2	8	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	4	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	4	no	—
284	C₂×C₄×C₁₃	—	2	4	no	—
285	C₂×C₄×C₁₃	—	2	4	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	4	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	1	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	4	8	no	—
300	C₂×C₄×C₁₃	—	4	8	no	—
301	C₂×C₄×C₁₃	—	4	8	no	—
302	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
303	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
304	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
305	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
306	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
307	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
308	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
309	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
310	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
311	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
312	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
313	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
314	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
315	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#124	C₂²×C₁₃	1	2	yes	—
317	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
318	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
319	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
325	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
326	#401	C₂²×C₁₃	1	4	yes	—
327	#400	C₂²×C₁₃	1	4	yes	—
328	#400	C₂²×C₁₃	1	4	yes	—
329	#400	C₂²×C₁₃	1	4	yes	—
330	#397	C₂²×C₁₃	1	4	yes	—
331	#397	C₂²×C₁₃	1	4	yes	—
332	#397	C₂²×C₁₃	1	4	yes	—
333	#396	C₂²×C₁₃	1	4	yes	—
334	#391	C₂²×C₁₃	1	2	yes	—
335	#391	C₂²×C₁₃	1	2	yes	—
336	#391	C₂²×C₁₃	1	2	yes	—
337	#391	C₂²×C₁₃	1	2	yes	—
338	#391	C₂²×C₁₃	1	2	yes	—
339	#390	C₂²×C₁₃	1	2	yes	—
340	#389	C₂²×C₁₃	1	2	yes	—
341	#389	C₂²×C₁₃	1	2	yes	—
342	#389	C₂²×C₁₃	1	2	yes	—
343	#389	C₂²×C₁₃	1	2	yes	—
344	#389	C₂²×C₁₃	1	2	yes	—
345	#388	C₂²×C₁₃	1	4	yes	—
346	#388	C₂²×C₁₃	1	4	yes	—
347	#387	C₂²×C₁₃	1	4	yes	—
348	#387	C₂²×C₁₃	1	4	yes	—
349	#387	C₂²×C₁₃	1	4	yes	—
350	#385	C₂²×C₁₃	1	4	yes	—
351	#384	C₂²×C₁₃	1	1	yes	characteristic
352	#383	C₂²×C₁₃	1	4	yes	—
353	#382	C₂²×C₁₃	1	2	yes	—
354	#382	C₂²×C₁₃	1	2	yes	—
355	#382	C₂²×C₁₃	1	2	yes	—
356	#381	C₂²×C₁₃	1	4	yes	—
357	#380	C₂²×C₁₃	1	2	yes	—
358	#380	C₂²×C₁₃	1	2	yes	—
359	#380	C₂²×C₁₃	1	2	yes	—
360	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
361	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
362	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
363	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
364	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
365	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
366	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
367	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
368	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
369	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
370	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
371	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
372	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
373	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
374	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
375	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
376	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
377	#376	C₂²×C₁₃	1	4	yes	—
378	C₄³	C₂²×C₁₃	1	1	yes	characteristic
379	C₄³	C₂²×C₁₃	1	2	yes	—
380	C₂²×C₁₃	—	2	4	no	—
381	C₂²×C₁₃	—	2	4	no	—
382	C₂²×C₁₃	—	2	4	no	—
383	C₂²×C₁₃	—	4	2	no	—
384	C₂²×C₁₃	—	4	2	no	—
385	C₂²×C₁₃	—	4	2	no	—
386	C₂²×C₁₃	—	4	2	no	—
387	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
388	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
389	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
390	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
391	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
392	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
393	C₂²×C₁₃	#585	1	1	yes	characteristic
394	C₄×C₁₃	—	2	4	no	—
395	C₄×C₁₃	—	2	2	no	—
396	C₄×C₁₃	—	2	2	no	—
397	C₄×C₁₃	—	2	2	no	—
398	C₄×C₁₃	—	4	2	no	—
399	C₄×C₁₃	—	4	4	no	—
400	C₄×C₁₃	—	4	2	no	—
401	C₄×C₁₃	—	4	2	no	—
402	C₄×C₁₃	—	4	2	no	—
403	C₄×C₁₃	—	4	2	no	—
404	C₄×C₁₃	—	4	4	no	—
405	C₄×C₁₃	—	4	1	no	—
406	C₄×C₁₃	—	4	2	no	—
407	C₄×C₁₃	#529	1	4	yes	—
408	C₄×C₁₃	#529	1	4	yes	—
409	C₄×C₁₃	#556	1	4	yes	—
410	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
411	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
414	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
415	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
416	C₄⋊Q₈	—	2	4	no	—
417	#124	—	2	8	no	—
418	C₂²⋊Q₈	—	2	8	no	—
419	C₄×Q₈	—	2	4	no	—
420	C₄×Q₈	—	2	4	no	—
421	C₄×Q₈	—	2	8	no	—
422	C₄×Q₈	—	2	4	no	—
423	C₄×D₄	—	2	4	no	—
424	C₄×D₄	—	2	4	no	—
425	C₄×D₄	—	2	4	no	—
426	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
450	C₂×C₄²	—	2	8	no	—
451	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
453	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
455	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
456	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
457	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
458	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
459	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
461	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
462	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
463	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
465	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
468	#95	C₂³×C₁₃	1	4	yes	—
469	#95	C₂³×C₁₃	1	4	yes	—
470	#95	C₂³×C₁₃	1	4	yes	—
471	#95	C₂³×C₁₃	1	4	yes	—
472	#95	C₂³×C₁₃	1	2	yes	—
473	#95	C₂³×C₁₃	1	2	yes	—
474	#95	C₂³×C₁₃	1	2	yes	—
475	#95	C₂³×C₁₃	1	4	yes	—
476	#95	C₂³×C₁₃	1	4	yes	—
477	#95	C₂³×C₁₃	1	4	yes	—
478	#95	C₂³×C₁₃	1	4	yes	—
479	#95	C₂³×C₁₃	1	2	yes	—
480	#95	C₂³×C₁₃	1	2	yes	—
481	#95	C₂³×C₁₃	1	2	yes	—
482	#95	C₂³×C₁₃	1	4	yes	—
483	#95	C₂³×C₁₃	1	4	yes	—
484	#95	C₂³×C₁₃	1	4	yes	—
485	#95	C₂³×C₁₃	1	4	yes	—
486	C₂×C₁₃	—	4	4	no	—
487	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
488	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
489	C₂×C₁₃	#3461	1	1	yes	characteristic
490	C₂×C₁₃	C₂×#556	1	1	yes	characteristic
491	C₂×C₁₃	#3475	1	1	yes	characteristic
492	C₂×C₁₃	#3480	1	1	yes	characteristic
493	C₂×C₁₃	#3482	1	1	yes	characteristic
494	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
495	C₂×Q₈	—	2	2	no	—
496	C₂×Q₈	—	2	2	no	—
497	C₂×Q₈	—	2	4	no	—
498	C₂×Q₈	—	2	4	no	—
499	C₂×Q₈	—	2	4	no	—
500	C₂×Q₈	C₁₃×#41	1	4	yes	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	C₁₃×#41	1	4	yes	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
514	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
515	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
516	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
517	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
518	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
520	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	8	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	8	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	4	no	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	2	8	no	—
548	C₂²⋊C₄	—	2	8	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	8	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₄²	—	2	4	no	—
554	C₄²	—	2	4	no	—
555	C₄²	—	2	4	no	—
556	C₄²	—	2	2	no	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	2	no	—
559	C₄²	—	2	4	no	—
560	C₄²	—	2	4	no	—
561	C₄²	—	2	8	no	—
562	C₄²	—	2	4	no	—
563	C₄²	—	2	2	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	4	1	no	—
566	C₄²	—	4	2	no	—
567	C₄²	C₁₃×#41	1	4	yes	—
568	C₄²	C₁₃×#41	1	4	yes	—
569	C₄²	C₁₃×#41	1	4	yes	—
570	C₁₃	#34945	1	1	yes	characteristic, direct product factor, Sylow
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	C₂×C₁₃×#41	1	4	yes	—
578	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
579	Q₈	—	2	8	no	—
580	Q₈	—	4	8	no	—
581	D₄	—	2	8	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	4	8	no	—
618	C₂×C₄	—	4	8	no	—
619	C₂×C₄	—	4	8	no	—
620	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
621	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
622	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
623	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
624	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
625	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
626	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
627	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
628	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
629	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
630	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
631	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
632	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	4	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
641	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
642	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
643	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
644	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
645	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
646	C₂²	C₁₃×#585	1	1	yes	characteristic
647	C₄	—	2	4	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	4	no	—
653	C₄	—	4	2	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	4	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	2	no	—
660	C₄	C₁₃×#529	1	4	yes	—
661	C₄	C₁₃×#529	1	4	yes	—
662	C₄	C₁₃×#556	1	4	yes	—
663	C₂	—	4	4	no	—
664	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
665	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
666	C₂	C₁₃×#3461	1	1	yes	characteristic
667	C₂	C₂×C₁₃×#556	1	1	yes	characteristic
668	C₂	C₁₃×#3475	1	1	yes	characteristic
669	C₂	C₁₃×#3480	1	1	yes	characteristic
670	C₂	C₁₃×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2573	C₂	semidirect
2. C₁₃×#2571	C₂	semidirect
3. C₁₃×#2568	C₂	semidirect
6. C₁₃×#2514	C₂	semidirect
7. C₁₃×#2494	C₂	semidirect
9. C₁₃×#2421	C₂	semidirect
10. C₁₃×#2401	C₂	semidirect
11. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
13. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
14. C₁₃×#2295	C₂	semidirect
15. C₁₃×#2283	C₂	semidirect
16. C₄²×Q₈×C₁₃	C₂	semidirect
159. #34945	C₁₃	direct (N × H)
236. #2573	C₂×C₁₃	semidirect
237. #2571	C₂×C₁₃	semidirect
238. #2568	C₂×C₁₃	semidirect
241. #2514	C₂×C₁₃	semidirect
242. #2494	C₂×C₁₃	semidirect
244. #2421	C₂×C₁₃	semidirect
245. #2401	C₂×C₁₃	semidirect
246. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
248. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
249. #2295	C₂×C₁₃	semidirect
250. #2283	C₂×C₁₃	semidirect
251. C₄²×Q₈	C₂×C₁₃	semidirect
570. C₁₃	#34945	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2573	2
C₁₃×#2571	2
C₁₃×#2568	2
C₁₃×#2547	2
C₁₃×#2538	2
C₁₃×#2514	2
C₁₃×#2494	2
C₁₃×#2447	2
C₁₃×#2421	2
C₁₃×#2401	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#124	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2295	2
C₁₃×#2283	2
C₄²×Q₈×C₁₃	2
C₄²×D₄×C₁₃	2
#34945	13

Subgroups — C13×#34945 #15721284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34945 #15721284