Subgroups — C₁₃×#20510 #15706849

Order 3328.

1006 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2943	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₃×#131	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1778	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1773	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1765	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1764	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1759	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	2	yes	—
14	C₂×C₁₃×#131	C₂²	1	2	yes	—
15	C₄×C₁₃×#41	C₂²	1	2	yes	—
16	C₁₃×#444	C₄	1	8	yes	complemented
17	C₁₃×#443	C₄	1	8	yes	complemented
18	C₁₃×#442	C₄	1	2	yes	complemented
19	C₁₃×#441	C₄	1	2	yes	complemented
20	C₁₃×#440	C₄	1	4	yes	complemented
21	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
23	C₁₃×#427	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#104	C₂²	1	2	yes	—
25	C₂×C₁₃×#104	C₂²	1	2	yes	—
26	C₁₃×#416	C₂²	1	2	yes	—
27	C₁₃×#405	—	2	2	no	—
28	C₁₃×#405	—	2	2	no	—
29	C₁₃×#405	C₂²	1	2	yes	—
30	C₁₃×#405	C₂²	1	2	yes	—
31	C₄×C₁₃×M₁₆	—	2	2	no	—
32	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃	—	2	2	no	—
37	C₂×C₄×C₈×C₁₃	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×#376	C₂²	1	1	yes	characteristic
41	C₁₃×#341	C₂²	1	2	yes	—
42	C₁₃×#339	C₂²	1	2	yes	—
43	C₁₃×#339	C₂²	1	2	yes	—
44	C₂×C₁₃×#41	C₂³	1	2	yes	—
45	C₁₃×#135	C₂×C₄	1	4	yes	—
46	C₁₃×#135	C₂×C₄	1	4	yes	—
47	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
50	C₁₃×#131	—	2	4	no	—
51	C₁₃×#131	—	2	4	no	—
52	C₁₃×#131	C₂×C₄	1	8	yes	complemented
53	C₁₃×#131	C₂×C₄	1	8	yes	complemented
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₂²×C₈×C₁₃	—	2	2	no	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
65	C₄×D₄×C₁₃	—	2	4	no	—
66	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
67	C₁₃×#117	—	2	2	no	—
68	C₁₃×#117	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃	—	2	2	no	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#108	C₂×C₄	1	4	yes	complemented
74	C₁₃×#108	C₂×C₄	1	4	yes	complemented
75	C₁₃×#107	C₂×C₄	1	2	yes	—
76	C₁₃×#106	C₂×C₄	1	2	yes	—
77	C₁₃×#104	C₂×C₄	1	8	yes	complemented
78	C₁₃×#104	C₂×C₄	1	8	yes	complemented
79	C₁₃×#103	C₂×C₄	1	4	yes	—
80	C₁₃×#102	C₂×C₄	1	4	yes	—
81	C₁₃×#97	—	2	2	no	—
82	C₁₃×#97	—	2	2	no	—
83	C₁₃×#97	—	2	2	no	—
84	C₁₃×#97	—	2	2	no	—
85	C₁₃×#97	C₂×C₄	1	2	yes	—
86	C₁₃×#97	C₂×C₄	1	2	yes	—
87	C₁₃×#97	C₂×C₄	1	4	yes	complemented
88	C₄×C₈×C₁₃	—	2	2	no	—
89	C₄×C₈×C₁₃	—	2	2	no	—
90	C₄×C₈×C₁₃	—	2	2	no	—
91	C₄×C₈×C₁₃	—	2	2	no	—
92	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
93	C₄×C₈×C₁₃	D₄	1	2	yes	—
94	C₄×C₈×C₁₃	D₄	1	2	yes	—
95	C₁₃×#95	—	2	2	no	—
96	#20510	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₁₃×#41	—	2	2	no	—
98	C₁₃×#41	—	2	2	no	—
99	C₁₃×#41	C₂²×C₄	1	4	yes	—
100	C₁₃×#41	C₂²×C₄	1	4	yes	—
101	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	#41	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₁₃×Q₁₆	C₄²	1	4	yes	—
111	C₁₃×SD₁₆	C₄²	1	8	yes	—
112	C₁₃×D₈	C₄²	1	4	yes	—
113	C₁₃×M₁₆	—	2	2	no	—
114	C₁₃×M₁₆	—	2	2	no	—
115	C₁₃×M₁₆	—	2	8	no	—
116	C₁₃×M₁₆	—	2	8	no	—
117	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
118	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	8	no	—
124	C₂×C₈×C₁₃	—	2	8	no	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃	#41	1	2	yes	—
136	C₂×C₈×C₁₃	#41	1	2	yes	—
137	C₁₃×C₄⋊C₄	—	2	4	no	—
138	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
139	C₁₃×C₂²⋊C₄	—	2	2	no	—
140	C₁₃×C₂²⋊C₄	—	2	4	no	—
141	C₄²×C₁₃	—	2	4	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
146	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
147	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
148	C₄²×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×#444	C₂×C₁₃	1	1	yes	characteristic
150	C₂×#443	C₂×C₁₃	1	1	yes	characteristic
151	#2943	C₂×C₁₃	1	1	yes	characteristic
152	C₄×#131	C₂×C₁₃	1	2	yes	complemented
153	#1778	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1773	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1772	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#1765	C₂×C₁₃	1	2	yes	complemented
157	#1764	C₂×C₁₃	1	2	yes	complemented
158	#1759	C₂×C₁₃	1	2	yes	complemented
159	#1726	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	2	no	—
163	Q₈×C₁₃	C₂×C₄²	1	4	yes	—
164	D₄×C₁₃	—	2	4	no	—
165	D₄×C₁₃	—	2	4	no	—
166	D₄×C₁₃	—	2	2	no	—
167	D₄×C₁₃	C₂×C₄²	1	4	yes	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	8	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
179	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
185	C₈×C₁₃	—	2	4	no	—
186	C₈×C₁₃	—	2	4	no	—
187	C₈×C₁₃	—	2	2	no	—
188	C₈×C₁₃	C₂×C₄²	1	2	yes	—
189	C₈×C₁₃	C₂×C₄²	1	2	yes	—
190	C₈×C₁₃	C₄×D₄	1	2	yes	—
191	C₈×C₁₃	C₄×D₄	1	4	yes	—
192	C₈×C₁₃	C₄×D₄	1	2	yes	—
193	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×#131	C₂²×C₁₃	1	2	yes	—
195	C₂×#131	C₂²×C₁₃	1	2	yes	—
196	C₄×#41	C₂²×C₁₃	1	2	yes	—
197	#444	C₄×C₁₃	1	8	yes	complemented
198	#443	C₄×C₁₃	1	8	yes	complemented
199	#442	C₄×C₁₃	1	2	yes	complemented
200	#441	C₄×C₁₃	1	2	yes	complemented
201	#440	C₄×C₁₃	1	4	yes	complemented
202	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
204	#427	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#104	C₂²×C₁₃	1	2	yes	—
206	C₂×#104	C₂²×C₁₃	1	2	yes	—
207	#416	C₂²×C₁₃	1	2	yes	—
208	#405	—	2	2	no	—
209	#405	—	2	2	no	—
210	#405	C₂²×C₁₃	1	2	yes	—
211	#405	C₂²×C₁₃	1	2	yes	—
212	C₄×M₁₆	—	2	2	no	—
213	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
214	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₄×C₈	—	2	2	no	—
218	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
221	#376	C₂²×C₁₃	1	1	yes	characteristic
222	#341	C₂²×C₁₃	1	2	yes	—
223	#339	C₂²×C₁₃	1	2	yes	—
224	#339	C₂²×C₁₃	1	2	yes	—
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	—	2	4	no	—
227	C₂²×C₁₃	—	4	4	no	—
228	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
229	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
230	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
231	C₄×C₁₃	—	2	4	no	—
232	C₄×C₁₃	—	2	4	no	—
233	C₄×C₁₃	—	4	2	no	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	—	4	4	no	—
236	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
237	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
238	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
240	C₂×#41	C₂³×C₁₃	1	2	yes	—
241	#135	C₂×C₄×C₁₃	1	4	yes	—
242	#135	C₂×C₄×C₁₃	1	4	yes	—
243	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
244	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
245	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
246	#131	—	2	4	no	—
247	#131	—	2	4	no	—
248	#131	C₂×C₄×C₁₃	1	8	yes	complemented
249	#131	C₂×C₄×C₁₃	1	8	yes	complemented
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
253	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
260	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
263	#117	—	2	2	no	—
264	#117	C₂³×C₁₃	1	2	yes	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
269	#108	C₂×C₄×C₁₃	1	4	yes	complemented
270	#108	C₂×C₄×C₁₃	1	4	yes	complemented
271	#107	C₂×C₄×C₁₃	1	2	yes	—
272	#106	C₂×C₄×C₁₃	1	2	yes	—
273	#104	C₂×C₄×C₁₃	1	8	yes	complemented
274	#104	C₂×C₄×C₁₃	1	8	yes	complemented
275	#103	C₂×C₄×C₁₃	1	4	yes	—
276	#102	C₂×C₄×C₁₃	1	4	yes	—
277	#97	—	2	2	no	—
278	#97	—	2	2	no	—
279	#97	—	2	2	no	—
280	#97	—	2	2	no	—
281	#97	C₂×C₄×C₁₃	1	2	yes	—
282	#97	C₂×C₄×C₁₃	1	2	yes	—
283	#97	C₂×C₄×C₁₃	1	4	yes	complemented
284	C₄×C₈	—	2	2	no	—
285	C₄×C₈	—	2	2	no	—
286	C₄×C₈	—	2	2	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
289	C₄×C₈	D₄×C₁₃	1	2	yes	—
290	C₄×C₈	D₄×C₁₃	1	2	yes	—
291	#95	—	2	2	no	—
292	C₂×C₁₃	—	2	1	no	—
293	C₂×C₁₃	—	2	1	no	—
294	C₂×C₁₃	—	4	4	no	—
295	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
296	C₂×C₁₃	#2955	1	2	yes	—
297	#41	—	2	2	no	—
298	#41	—	2	2	no	—
299	#41	C₂²×C₄×C₁₃	1	4	yes	—
300	#41	C₂²×C₄×C₁₃	1	4	yes	—
301	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	C₁₃×#41	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
310	Q₁₆	C₄²×C₁₃	1	4	yes	—
311	SD₁₆	C₄²×C₁₃	1	8	yes	—
312	D₈	C₄²×C₁₃	1	4	yes	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	8	no	—
316	M₁₆	—	2	8	no	—
317	M₁₆	C₂²×C₄×C₁₃	1	4	yes	—
318	M₁₆	C₂²×C₄×C₁₃	1	4	yes	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	8	no	—
324	C₂×C₈	—	2	8	no	—
325	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
326	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
327	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
328	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
329	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
330	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
331	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
332	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
334	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂×C₈	C₁₃×#41	1	2	yes	—
336	C₂×C₈	C₁₃×#41	1	2	yes	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
346	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
347	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
348	C₄²	C₂×D₄×C₁₃	1	2	yes	—
349	C₁₃	#20510	1	1	yes	characteristic, direct product factor, Sylow
350	C₂³	—	2	2	no	—
351	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
352	Q₈	—	2	2	no	—
353	Q₈	C₂×C₄²×C₁₃	1	4	yes	—
354	D₄	—	2	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	D₄	C₂×C₄²×C₁₃	1	4	yes	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	8	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
369	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
370	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
373	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
374	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	2	4	no	—
377	C₈	—	2	2	no	—
378	C₈	C₂×C₄²×C₁₃	1	2	yes	—
379	C₈	C₂×C₄²×C₁₃	1	2	yes	—
380	C₈	C₄×D₄×C₁₃	1	2	yes	—
381	C₈	C₄×D₄×C₁₃	1	4	yes	—
382	C₈	C₄×D₄×C₁₃	1	2	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
387	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
388	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
389	C₄	—	2	4	no	—
390	C₄	—	2	4	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	4	no	—
394	C₄	C₂²×C₄²×C₁₃	1	1	yes	characteristic
395	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
396	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
397	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	4	4	no	—
401	C₂	C₄²×D₄×C₁₃	1	1	yes	characteristic
402	C₂	C₁₃×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂×D₄
commutator	C₄	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄×C₁₃×#131	C₂	semidirect
5. C₁₃×#1778	C₂	semidirect
6. C₁₃×#1773	C₂	semidirect
7. C₁₃×#1772	C₂	semidirect
8. C₁₃×#1765	C₂	semidirect
9. C₁₃×#1764	C₂	semidirect
10. C₁₃×#1759	C₂	semidirect
11. C₁₃×#1726	C₂	semidirect
16. C₁₃×#444	C₄	semidirect
17. C₁₃×#443	C₄	semidirect
18. C₁₃×#442	C₄	semidirect
19. C₁₃×#441	C₄	semidirect
20. C₁₃×#440	C₄	semidirect
52. C₁₃×#131	C₂×C₄	semidirect
53. C₁₃×#131	C₂×C₄	semidirect
73. C₁₃×#108	C₂×C₄	semidirect
74. C₁₃×#108	C₂×C₄	semidirect
77. C₁₃×#104	C₂×C₄	semidirect
78. C₁₃×#104	C₂×C₄	semidirect
87. C₁₃×#97	C₂×C₄	semidirect
92. C₄×C₈×C₁₃	C₂×C₄	semidirect
96. #20510	C₁₃	direct (N × H)
152. C₄×#131	C₂×C₁₃	semidirect
153. #1778	C₂×C₁₃	semidirect
154. #1773	C₂×C₁₃	semidirect
155. #1772	C₂×C₁₃	semidirect
156. #1765	C₂×C₁₃	semidirect
157. #1764	C₂×C₁₃	semidirect
158. #1759	C₂×C₁₃	semidirect
159. #1726	C₂×C₁₃	semidirect
197. #444	C₄×C₁₃	semidirect
198. #443	C₄×C₁₃	semidirect
199. #442	C₄×C₁₃	semidirect
200. #441	C₄×C₁₃	semidirect
201. #440	C₄×C₁₃	semidirect
248. #131	C₂×C₄×C₁₃	semidirect
249. #131	C₂×C₄×C₁₃	semidirect
269. #108	C₂×C₄×C₁₃	semidirect
270. #108	C₂×C₄×C₁₃	semidirect
273. #104	C₂×C₄×C₁₃	semidirect
274. #104	C₂×C₄×C₁₃	semidirect
283. #97	C₂×C₄×C₁₃	semidirect
288. C₄×C₈	C₂×C₄×C₁₃	semidirect
349. C₁₃	#20510	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×#444	2
C₂×C₁₃×#443	2
C₁₃×#2943	2
C₄×C₁₃×#131	2
C₁₃×#1778	2
C₁₃×#1773	2
C₁₃×#1772	2
C₁₃×#1765	2
C₁₃×#1764	2
C₁₃×#1759	2
C₁₃×#1726	2
#20510	13

Subgroups — C13×#20510 #15706849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20510 #15706849