Subgroups — C₁₃×#24505 #15710844

Order 3328.

996 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#452	—	2	4	no	—
23	C₁₃×#431	—	2	4	no	—
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#391	C₂²	1	1	yes	characteristic
41	C₁₃×#391	C₂²	1	1	yes	characteristic
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#391	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#390	C₂²	1	1	yes	characteristic
46	C₁₃×#389	C₂²	1	1	yes	characteristic
47	C₁₃×#389	C₂²	1	1	yes	characteristic
48	C₁₃×#387	—	2	1	no	—
49	C₁₃×#387	—	2	1	no	—
50	C₁₃×#386	—	2	1	no	—
51	C₁₃×#386	—	2	1	no	—
52	C₁₃×#385	—	2	1	no	—
53	C₁₃×#381	—	2	1	no	—
54	C₁₃×#380	C₂²	1	1	yes	characteristic
55	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
56	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#41	—	2	2	no	—
62	C₂×C₁₃×#41	—	2	2	no	—
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	—	4	1	no	—
66	C₂×C₁₃×#41	—	4	1	no	—
67	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	—	2	1	no	—
72	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×Q₁₆	—	2	2	no	—
76	C₂×C₁₃×Q₁₆	—	2	2	no	—
77	C₂×C₁₃×Q₁₆	—	4	1	no	—
78	C₂×C₁₃×SD₁₆	—	2	2	no	—
79	C₂×C₁₃×SD₁₆	—	2	2	no	—
80	C₂×C₁₃×SD₁₆	—	4	1	no	—
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×#117	—	4	1	no	—
88	C₁₃×#117	—	4	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₄²×C₁₃	—	2	2	no	—
105	C₂×C₄²×C₁₃	—	2	2	no	—
106	C₂×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₁₃×#107	—	4	1	no	—
112	C₁₃×#106	—	4	1	no	—
113	C₁₃×C₄⋊C₈	—	2	2	no	—
114	C₁₃×C₄⋊C₈	—	2	2	no	—
115	C₁₃×#103	—	2	2	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	4	1	no	—
118	C₁₃×#103	—	4	1	no	—
119	C₁₃×#103	—	4	1	no	—
120	C₁₃×#102	—	2	2	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	4	1	no	—
123	C₁₃×C₂²⋊C₈	—	2	2	no	—
124	C₁₃×C₂²⋊C₈	D₄	1	4	yes	—
125	C₄×C₈×C₁₃	—	2	2	no	—
126	C₄×C₈×C₁₃	—	2	2	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	—	2	1	no	—
131	C₁₃×#95	—	2	1	no	—
132	C₁₃×#95	—	2	1	no	—
133	C₁₃×#95	—	2	1	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	—	2	1	no	—
136	C₁₃×#95	—	2	1	no	—
137	C₁₃×#95	—	2	1	no	—
138	#24505	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂⁴×C₁₃	—	2	1	no	—
140	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₁₃×#41	—	4	4	no	—
142	C₁₃×#41	—	4	4	no	—
143	C₁₃×#41	—	4	4	no	—
144	C₁₃×#41	—	4	4	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	#41	1	2	yes	—
157	C₂×D₄×C₁₃	—	2	4	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	1	no	—
163	C₂×D₄×C₁₃	—	4	2	no	—
164	C₂×D₄×C₁₃	—	4	2	no	—
165	C₂×D₄×C₁₃	#41	1	2	yes	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	—	2	2	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	2	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	4	1	no	—
184	C₂²×C₄×C₁₃	—	4	2	no	—
185	C₂²×C₄×C₁₃	—	4	2	no	—
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	#41	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₁₃×Q₁₆	—	4	4	no	—
195	C₁₃×SD₁₆	—	4	4	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	—	2	1	no	—
204	C₂×C₈×C₁₃	—	2	1	no	—
205	C₂×C₈×C₁₃	—	2	1	no	—
206	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
207	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	4	2	no	—
219	C₁₃×C₄⋊C₄	—	4	2	no	—
220	C₁₃×C₄⋊C₄	—	4	2	no	—
221	C₁₃×C₂²⋊C₄	—	4	2	no	—
222	C₁₃×C₂²⋊C₄	—	4	2	no	—
223	C₁₃×C₂²⋊C₄	—	4	2	no	—
224	C₁₃×C₂²⋊C₄	—	4	2	no	—
225	C₁₃×C₂²⋊C₄	—	4	2	no	—
226	C₁₃×C₂²⋊C₄	—	4	2	no	—
227	C₁₃×C₂²⋊C₄	—	4	2	no	—
228	C₄²×C₁₃	—	2	2	no	—
229	C₄²×C₁₃	—	2	2	no	—
230	C₄²×C₁₃	—	2	1	no	—
231	C₄²×C₁₃	—	2	1	no	—
232	C₄²×C₁₃	—	2	1	no	—
233	C₄²×C₁₃	—	2	1	no	—
234	C₄²×C₁₃	—	4	2	no	—
235	C₂×#452	C₂×C₁₃	1	1	yes	characteristic
236	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2855	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#2297	C₂×C₁₃	1	1	yes	characteristic
239	#2067	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2056	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1969	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1968	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#1934	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#1933	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1873	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1788	C₂×C₁₃	1	1	yes	characteristic
250	C₂³×C₁₃	—	2	1	no	—
251	C₂³×C₁₃	—	2	1	no	—
252	C₂³×C₁₃	—	2	1	no	—
253	C₂³×C₁₃	—	2	1	no	—
254	C₂³×C₁₃	—	2	1	no	—
255	C₂³×C₁₃	—	2	1	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	4	1	no	—
258	C₂³×C₁₃	—	4	1	no	—
259	C₂³×C₁₃	—	4	1	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	—	4	1	no	—
263	C₂³×C₁₃	#121	1	2	yes	—
264	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	Q₈×C₁₃	—	2	2	no	—
266	Q₈×C₁₃	—	2	2	no	—
267	Q₈×C₁₃	—	4	1	no	—
268	Q₈×C₁₃	—	4	1	no	—
269	Q₈×C₁₃	—	4	1	no	—
270	Q₈×C₁₃	—	4	1	no	—
271	Q₈×C₁₃	—	4	1	no	—
272	Q₈×C₁₃	—	4	1	no	—
273	D₄×C₁₃	—	2	2	no	—
274	D₄×C₁₃	—	2	2	no	—
275	D₄×C₁₃	—	4	8	no	—
276	D₄×C₁₃	—	4	1	no	—
277	D₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	2	8	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	1	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	2	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	4	4	no	—
296	C₂×C₄×C₁₃	—	4	8	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	1	no	—
317	C₂×C₄×C₁₃	#121	1	2	yes	—
318	C₂×C₄×C₁₃	#135	1	2	yes	—
319	C₂×C₄×C₁₃	#135	1	2	yes	—
320	C₂×C₄×C₁₃	#137	1	2	yes	—
321	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
327	C₈×C₁₃	—	2	2	no	—
328	C₈×C₁₃	—	2	2	no	—
329	C₈×C₁₃	—	4	1	no	—
330	C₈×C₁₃	—	4	1	no	—
331	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
332	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
333	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
336	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
337	#452	—	2	4	no	—
338	#431	—	2	4	no	—
339	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
355	#391	C₂²×C₁₃	1	1	yes	characteristic
356	#391	C₂²×C₁₃	1	1	yes	characteristic
357	#391	C₂²×C₁₃	1	1	yes	characteristic
358	#391	C₂²×C₁₃	1	1	yes	characteristic
359	#390	C₂²×C₁₃	1	1	yes	characteristic
360	#390	C₂²×C₁₃	1	1	yes	characteristic
361	#389	C₂²×C₁₃	1	1	yes	characteristic
362	#389	C₂²×C₁₃	1	1	yes	characteristic
363	#387	—	2	1	no	—
364	#387	—	2	1	no	—
365	#386	—	2	1	no	—
366	#386	—	2	1	no	—
367	#385	—	2	1	no	—
368	#381	—	2	1	no	—
369	#380	C₂²×C₁₃	1	1	yes	characteristic
370	C₄×C₂²⋊C₄	—	2	1	no	—
371	C₄×C₂²⋊C₄	—	2	1	no	—
372	#340	C₂²×C₁₃	1	1	yes	characteristic
373	#340	C₂²×C₁₃	1	1	yes	characteristic
374	#340	C₂²×C₁₃	1	1	yes	characteristic
375	#340	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×C₁₃	—	2	2	no	—
377	C₂²×C₁₃	—	2	2	no	—
378	C₂²×C₁₃	—	2	2	no	—
379	C₂²×C₁₃	—	4	1	no	—
380	C₂²×C₁₃	—	4	1	no	—
381	C₂²×C₁₃	—	4	1	no	—
382	C₂²×C₁₃	—	4	1	no	—
383	C₂²×C₁₃	—	4	2	no	—
384	C₂²×C₁₃	—	4	2	no	—
385	C₂²×C₁₃	—	4	2	no	—
386	C₂²×C₁₃	—	8	1	no	—
387	C₂²×C₁₃	—	8	1	no	—
388	C₂²×C₁₃	—	8	1	no	—
389	C₂²×C₁₃	—	8	1	no	—
390	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
391	C₂²×C₁₃	#525	1	1	yes	characteristic
392	C₂²×C₁₃	#535	1	1	yes	characteristic
393	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
394	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
395	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
396	C₂²×C₁₃	#575	1	1	yes	characteristic
397	C₄×C₁₃	—	2	2	no	—
398	C₄×C₁₃	—	2	2	no	—
399	C₄×C₁₃	—	2	2	no	—
400	C₄×C₁₃	—	2	2	no	—
401	C₄×C₁₃	—	4	2	no	—
402	C₄×C₁₃	—	4	1	no	—
403	C₄×C₁₃	—	8	1	no	—
404	C₄×C₁₃	—	8	1	no	—
405	C₄×C₁₃	—	8	1	no	—
406	C₄×C₁₃	—	8	1	no	—
407	C₄×C₁₃	—	8	1	no	—
408	C₄×C₁₃	—	8	1	no	—
409	C₄×C₁₃	#546	1	1	yes	characteristic
410	C₄×C₁₃	#546	1	1	yes	characteristic
411	C₄×C₁₃	#551	1	1	yes	characteristic
412	C₄×C₁₃	#551	1	1	yes	characteristic
413	C₂×#41	—	2	2	no	—
414	C₂×#41	—	2	2	no	—
415	C₂×#41	—	2	2	no	—
416	C₂×#41	—	2	2	no	—
417	C₂×#41	—	4	1	no	—
418	C₂×#41	—	4	1	no	—
419	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
420	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
421	C₂²×D₄	—	2	1	no	—
422	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂³×C₄	—	2	1	no	—
424	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
425	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×Q₁₆	—	2	2	no	—
428	C₂×Q₁₆	—	2	2	no	—
429	C₂×Q₁₆	—	4	1	no	—
430	C₂×SD₁₆	—	2	2	no	—
431	C₂×SD₁₆	—	2	2	no	—
432	C₂×SD₁₆	—	4	1	no	—
433	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
434	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
437	C₂²⋊Q₈	—	2	2	no	—
438	C₂²⋊Q₈	—	2	2	no	—
439	#117	—	4	1	no	—
440	#117	—	4	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₄²	—	2	2	no	—
457	C₂×C₄²	—	2	2	no	—
458	C₂×C₄²	—	2	1	no	—
459	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
460	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
463	#107	—	4	1	no	—
464	#106	—	4	1	no	—
465	C₄⋊C₈	—	2	2	no	—
466	C₄⋊C₈	—	2	2	no	—
467	#103	—	2	2	no	—
468	#103	—	2	2	no	—
469	#103	—	4	1	no	—
470	#103	—	4	1	no	—
471	#103	—	4	1	no	—
472	#102	—	2	2	no	—
473	#102	—	2	2	no	—
474	#102	—	4	1	no	—
475	C₂²⋊C₈	—	2	2	no	—
476	C₂²⋊C₈	D₄×C₁₃	1	4	yes	—
477	C₄×C₈	—	2	2	no	—
478	C₄×C₈	—	2	2	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	C₂×C₁₃	—	4	2	no	—
491	C₂×C₁₃	—	8	2	no	—
492	C₂×C₁₃	#2411	1	1	yes	characteristic
493	C₂×C₁₃	#3050	1	1	yes	characteristic
494	C₂×C₁₃	#3056	1	1	yes	characteristic
495	C₂×C₁₃	#3102	1	1	yes	characteristic
496	C₂×C₁₃	#3107	1	1	yes	characteristic
497	C₂×C₁₃	#3210	1	1	yes	characteristic
498	C₂×C₁₃	#3212	1	1	yes	characteristic
499	C₂⁴	—	2	1	no	—
500	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
501	#41	—	4	4	no	—
502	#41	—	4	4	no	—
503	#41	—	4	4	no	—
504	#41	—	4	4	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	C₁₃×#41	1	2	yes	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	4	2	no	—
524	C₂×D₄	—	4	2	no	—
525	C₂×D₄	C₁₃×#41	1	2	yes	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	4	1	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
549	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₂²×C₄	C₁₃×#41	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
554	Q₁₆	—	4	4	no	—
555	SD₁₆	—	4	4	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
567	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	4	2	no	—
579	C₄⋊C₄	—	4	2	no	—
580	C₄⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	4	2	no	—
595	C₁₃	#24505	1	1	yes	characteristic, direct product factor, Sylow
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	C₁₃×#121	1	2	yes	—
610	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
611	Q₈	—	2	2	no	—
612	Q₈	—	2	2	no	—
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	Q₈	—	4	1	no	—
618	Q₈	—	4	1	no	—
619	D₄	—	2	2	no	—
620	D₄	—	2	2	no	—
621	D₄	—	4	8	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	C₂×C₄	—	2	8	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	8	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	C₁₃×#121	1	2	yes	—
664	C₂×C₄	C₁₃×#135	1	2	yes	—
665	C₂×C₄	C₁₃×#135	1	2	yes	—
666	C₂×C₄	C₁₃×#137	1	2	yes	—
667	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
668	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
669	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
670	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
671	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
672	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
673	C₈	—	2	2	no	—
674	C₈	—	2	2	no	—
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
692	C₂²	C₁₃×#525	1	1	yes	characteristic
693	C₂²	C₁₃×#535	1	1	yes	characteristic
694	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
695	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
696	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
697	C₂²	C₁₃×#575	1	1	yes	characteristic
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	2	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₄	—	8	1	no	—
709	C₄	—	8	1	no	—
710	C₄	C₁₃×#546	1	1	yes	characteristic
711	C₄	C₁₃×#546	1	1	yes	characteristic
712	C₄	C₁₃×#551	1	1	yes	characteristic
713	C₄	C₁₃×#551	1	1	yes	characteristic
714	C₂	—	4	2	no	—
715	C₂	—	8	2	no	—
716	C₂	C₁₃×#2411	1	1	yes	characteristic
717	C₂	C₁₃×#3050	1	1	yes	characteristic
718	C₂	C₁₃×#3056	1	1	yes	characteristic
719	C₂	C₁₃×#3102	1	1	yes	characteristic
720	C₂	C₁₃×#3107	1	1	yes	characteristic
721	C₂	C₁₃×#3210	1	1	yes	characteristic
722	C₂	C₁₃×#3212	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#431	C₂	semidirect
3. C₁₃×#2855	C₂	semidirect
5. C₁₃×#2067	C₂	semidirect
6. C₁₃×#2066	C₂	semidirect
7. C₁₃×#2056	C₂	semidirect
8. C₁₃×#2055	C₂	semidirect
9. C₁₃×#1969	C₂	semidirect
10. C₁₃×#1968	C₂	semidirect
11. C₁₃×#1934	C₂	semidirect
12. C₁₃×#1933	C₂	semidirect
13. C₁₃×#1873	C₂	semidirect
14. C₁₃×#1854	C₂	semidirect
138. #24505	C₁₃	direct (N × H)
236. C₂×#431	C₂×C₁₃	semidirect
237. #2855	C₂×C₁₃	semidirect
239. #2067	C₂×C₁₃	semidirect
240. #2066	C₂×C₁₃	semidirect
241. #2056	C₂×C₁₃	semidirect
242. #2055	C₂×C₁₃	semidirect
243. #1969	C₂×C₁₃	semidirect
244. #1968	C₂×C₁₃	semidirect
245. #1934	C₂×C₁₃	semidirect
246. #1933	C₂×C₁₃	semidirect
247. #1873	C₂×C₁₃	semidirect
248. #1854	C₂×C₁₃	semidirect
595. C₁₃	#24505	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×#452	2
C₂×C₁₃×#431	2
C₁₃×#2855	2
C₁₃×#2297	2
C₁₃×#2067	2
C₁₃×#2066	2
C₁₃×#2056	2
C₁₃×#2055	2
C₁₃×#1969	2
C₁₃×#1968	2
C₁₃×#1934	2
C₁₃×#1933	2
C₁₃×#1873	2
C₁₃×#1854	2
C₁₃×#1788	2
#24505	13

Subgroups — C13×#24505 #15710844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24505 #15710844