Subgroups — C₁₃×#24697 #15711036

Order 3328.

780 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2357	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2073	C₂	1	2	yes	maximal
6	C₁₃×#2055	C₂	1	2	yes	maximal
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1949	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1927	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#476	—	2	4	no	—
17	C₁₃×#440	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
27	C₁₃×#400	—	2	1	no	—
28	C₁₃×#400	—	2	1	no	—
29	C₁₃×#391	—	2	2	no	—
30	C₁₃×#391	C₂²	1	2	yes	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#388	—	2	2	no	—
33	C₁₃×#382	C₂²	1	1	yes	characteristic
34	C₁₃×#382	C₂²	1	2	yes	—
35	C₁₃×#381	—	2	1	no	—
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂×C₁₃×SD₁₆	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×SD₁₆	—	2	2	no	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₄×Q₈×C₁₃	—	2	2	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×D₄×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	D₄	1	4	yes	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₄²×C₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₃	—	2	2	no	—
71	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#107	—	2	2	no	—
74	C₁₃×#106	—	2	4	no	—
75	C₁₃×C₄⋊C₈	—	2	4	no	—
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×#103	—	2	4	no	—
78	C₁₃×#103	—	2	2	no	—
79	C₁₃×#102	—	2	2	no	—
80	C₁₃×#102	—	2	4	no	—
81	C₁₃×#97	—	2	2	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	D₄	1	1	yes	characteristic
90	C₁₃×#95	D₄	1	1	yes	characteristic
91	#24697	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	4	4	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×Q₈×C₁₃	#41	1	2	yes	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	8	2	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×SD₁₆	—	2	8	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	#41	1	2	yes	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	—	4	2	no	—
139	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
140	C₁₃×C₂²⋊C₄	—	2	4	no	—
141	C₁₃×C₂²⋊C₄	—	4	4	no	—
142	C₁₃×C₂²⋊C₄	—	8	2	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₄²×C₁₃	—	4	2	no	—
146	C₄²×C₁₃	—	8	2	no	—
147	C₄²×C₁₃	C₂×D₄	1	2	yes	—
148	C₄²×C₁₃	#41	1	2	yes	—
149	C₂×#476	C₂×C₁₃	1	1	yes	characteristic
150	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
151	#2568	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#2357	C₂×C₁₃	1	1	yes	characteristic
153	#2073	C₂×C₁₃	1	2	yes	—
154	#2055	C₂×C₁₃	1	2	yes	—
155	#1993	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#1949	C₂×C₁₃	1	2	yes	complemented
157	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#1927	C₂×C₁₃	1	2	yes	complemented
159	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₁₃	—	2	2	no	—
167	Q₈×C₁₃	—	2	2	no	—
168	Q₈×C₁₃	—	4	1	no	—
169	Q₈×C₁₃	—	4	1	no	—
170	Q₈×C₁₃	—	8	4	no	—
171	D₄×C₁₃	—	2	2	no	—
172	D₄×C₁₃	—	2	2	no	—
173	D₄×C₁₃	—	4	1	no	—
174	D₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	8	4	no	—
196	C₂×C₄×C₁₃	#121	1	2	yes	—
197	C₂×C₄×C₁₃	#121	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
204	C₈×C₁₃	—	2	2	no	—
205	C₈×C₁₃	—	4	2	no	—
206	C₈×C₁₃	—	4	1	no	—
207	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
211	#476	—	2	4	no	—
212	#440	—	2	4	no	—
213	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#106	C₂²×C₁₃	1	2	yes	—
215	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
216	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#103	C₂²×C₁₃	1	2	yes	—
218	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#102	C₂²×C₁₃	1	2	yes	—
220	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
222	#400	—	2	1	no	—
223	#400	—	2	1	no	—
224	#391	—	2	2	no	—
225	#391	C₂²×C₁₃	1	2	yes	—
226	#390	C₂²×C₁₃	1	2	yes	—
227	#388	—	2	2	no	—
228	#382	C₂²×C₁₃	1	2	yes	—
229	#382	C₂²×C₁₃	1	1	yes	characteristic
230	#381	—	2	1	no	—
231	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
232	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₄×C₂²⋊C₄	—	2	1	no	—
234	#340	C₂²×C₁₃	1	2	yes	—
235	#340	C₂²×C₁₃	1	2	yes	—
236	#340	C₂²×C₁₃	1	2	yes	—
237	#336	C₂²×C₁₃	1	2	yes	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	8	2	no	—
242	C₂²×C₁₃	—	8	2	no	—
243	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
244	C₂²×C₁₃	#547	1	1	yes	characteristic
245	C₂²×C₁₃	#548	1	1	yes	characteristic
246	C₂²×C₁₃	#575	1	2	yes	—
247	C₂²×C₁₃	#577	1	2	yes	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	—	8	2	no	—
255	C₄×C₁₃	—	8	2	no	—
256	C₄×C₁₃	—	8	1	no	—
257	C₄×C₁₃	#525	1	1	yes	characteristic
258	C₄×C₁₃	#536	1	1	yes	characteristic
259	C₄×C₁₃	#552	1	1	yes	characteristic
260	C₄×C₁₃	#556	1	1	yes	characteristic
261	C₂²×Q₈	—	2	1	no	—
262	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
263	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
264	C₂³×C₄	—	2	1	no	—
265	C₂×SD₁₆	—	2	2	no	—
266	C₂×SD₁₆	—	2	2	no	—
267	C₂×SD₁₆	—	2	2	no	—
268	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
270	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	D₄×C₁₃	1	4	yes	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
291	#107	—	2	2	no	—
292	#106	—	2	4	no	—
293	C₄⋊C₈	—	2	4	no	—
294	C₄⋊C₈	—	2	2	no	—
295	#103	—	2	4	no	—
296	#103	—	2	2	no	—
297	#102	—	2	2	no	—
298	#102	—	2	4	no	—
299	#97	—	2	2	no	—
300	#95	—	2	1	no	—
301	#95	—	2	2	no	—
302	#95	—	2	1	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	D₄×C₁₃	1	1	yes	characteristic
308	#95	D₄×C₁₃	1	1	yes	characteristic
309	C₂×C₁₃	—	8	2	no	—
310	C₂×C₁₃	#2415	1	1	yes	characteristic
311	C₂×C₁₃	#3040	1	1	yes	characteristic
312	C₂×C₁₃	#3042	1	1	yes	characteristic
313	C₂×C₁₃	#3350	1	2	yes	—
314	C₂×C₁₃	#3371	1	2	yes	—
315	C₂⁴	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	4	4	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	C₁₃×#41	1	2	yes	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	8	2	no	—
337	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
342	SD₁₆	—	2	8	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	C₁₃×#41	1	2	yes	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₂²⋊C₄	—	8	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	2	no	—
369	C₄²	—	8	2	no	—
370	C₄²	C₂×D₄×C₁₃	1	2	yes	—
371	C₄²	C₁₃×#41	1	2	yes	—
372	C₁₃	#24697	1	1	yes	characteristic, direct product factor, Sylow
373	C₂³	—	2	2	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	2	2	no	—
381	Q₈	—	4	1	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	8	4	no	—
384	D₄	—	2	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	4	no	—
409	C₂×C₄	C₁₃×#121	1	2	yes	—
410	C₂×C₄	C₁₃×#121	1	2	yes	—
411	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
413	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
414	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
415	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
416	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
426	C₂²	C₁₃×#547	1	1	yes	characteristic
427	C₂²	C₁₃×#548	1	1	yes	characteristic
428	C₂²	C₁₃×#575	1	2	yes	—
429	C₂²	C₁₃×#577	1	2	yes	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	2	no	—
437	C₄	—	8	1	no	—
438	C₄	—	8	2	no	—
439	C₄	C₁₃×#525	1	1	yes	characteristic
440	C₄	C₁₃×#536	1	1	yes	characteristic
441	C₄	C₁₃×#552	1	1	yes	characteristic
442	C₄	C₁₃×#556	1	1	yes	characteristic
443	C₂	—	8	2	no	—
444	C₂	C₁₃×#2415	1	1	yes	characteristic
445	C₂	C₁₃×#3040	1	1	yes	characteristic
446	C₂	C₁₃×#3042	1	1	yes	characteristic
447	C₂	C₁₃×#3350	1	2	yes	—
448	C₂	C₁₃×#3371	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2568	C₂	semidirect
7. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1949	C₂	semidirect
9. C₁₃×#1940	C₂	semidirect
10. C₁₃×#1927	C₂	semidirect
11. C₁₃×#1805	C₂	semidirect
91. #24697	C₁₃	direct (N × H)
151. #2568	C₂×C₁₃	semidirect
155. #1993	C₂×C₁₃	semidirect
156. #1949	C₂×C₁₃	semidirect
157. #1940	C₂×C₁₃	semidirect
158. #1927	C₂×C₁₃	semidirect
159. #1805	C₂×C₁₃	semidirect
372. C₁₃	#24697	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×#476	2
C₂×C₁₃×#440	2
C₁₃×#2568	2
C₁₃×#2357	2
C₁₃×#2073	2
C₁₃×#2055	2
C₁₃×#1993	2
C₁₃×#1949	2
C₁₃×#1940	2
C₁₃×#1927	2
C₁₃×#1805	2
#24697	13

Subgroups — C13×#24697 #15711036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24697 #15711036