Subgroups — C₁₃×#20512 #15706851

Order 3328.

1014 conjugacy classes of subgroups.

The subgroup lattice has 406 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	C₁₃×#2875	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	C₄×C₁₃×#104	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#97	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	—	2	2	no	—
34	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#97	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	C₄³×C₁₃	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	—	2	2	no	—
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#108	C₂×C₄	1	4	yes	complemented
75	C₁₃×#108	C₂×C₄	1	4	yes	complemented
76	C₁₃×#107	C₂×C₄	1	2	yes	—
77	C₁₃×#106	C₂×C₄	1	2	yes	—
78	C₁₃×#104	C₂×C₄	1	8	yes	complemented
79	C₁₃×#104	C₂×C₄	1	8	yes	complemented
80	C₁₃×#103	C₂×C₄	1	4	yes	—
81	C₁₃×#102	C₂×C₄	1	4	yes	—
82	C₁₃×#97	—	2	2	no	—
83	C₁₃×#97	—	2	2	no	—
84	C₁₃×#97	—	2	2	no	—
85	C₁₃×#97	—	2	2	no	—
86	C₁₃×#97	C₂×C₄	1	2	yes	—
87	C₁₃×#97	C₂×C₄	1	2	yes	—
88	C₁₃×#97	C₂×C₄	1	4	yes	complemented
89	C₁₃×#97	D₄	1	2	yes	—
90	C₁₃×#97	D₄	1	2	yes	—
91	C₄×C₈×C₁₃	—	2	2	no	—
92	C₄×C₈×C₁₃	—	2	2	no	—
93	C₄×C₈×C₁₃	—	2	2	no	—
94	C₄×C₈×C₁₃	—	2	2	no	—
95	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
96	#20512	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	1	no	—
105	C₂²×C₄×C₁₃	—	2	2	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	complemented
111	C₁₃×SD₁₆	C₄²	1	8	yes	complemented
112	C₁₃×D₈	C₄²	1	4	yes	complemented
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	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
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	—	4	4	no	—
146	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
147	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
148	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
149	C₄²×C₁₃	C₂×D₄	1	2	yes	—
150	C₂×#444	C₂×C₁₃	1	1	yes	characteristic
151	C₂×#443	C₂×C₁₃	1	1	yes	characteristic
152	#2943	C₂×C₁₃	1	1	yes	characteristic
153	#2875	C₂×C₁₃	1	2	yes	complemented
154	#1778	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1773	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#1772	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#1765	C₂×C₁₃	1	2	yes	complemented
158	#1764	C₂×C₁₃	1	2	yes	complemented
159	C₄×#104	C₂×C₁₃	1	2	yes	complemented
160	C₄×#97	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂³×C₁₃	—	2	2	no	—
162	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
163	Q₈×C₁₃	—	2	2	no	—
164	Q₈×C₁₃	C₂×C₄²	1	4	yes	—
165	D₄×C₁₃	—	2	4	no	—
166	D₄×C₁₃	—	2	4	no	—
167	D₄×C₁₃	—	2	2	no	—
168	D₄×C₁₃	C₂×C₄²	1	4	yes	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	8	4	no	—
179	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
180	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₈×C₁₃	—	2	4	no	—
187	C₈×C₁₃	—	2	4	no	—
188	C₈×C₁₃	—	2	2	no	—
189	C₈×C₁₃	C₂×C₄²	1	2	yes	—
190	C₈×C₁₃	C₂×C₄²	1	2	yes	—
191	C₈×C₁₃	C₄×D₄	1	2	yes	—
192	C₈×C₁₃	C₄×D₄	1	4	yes	—
193	C₈×C₁₃	C₄×D₄	1	2	yes	—
194	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×#131	C₂²×C₁₃	1	2	yes	—
196	C₂×#131	C₂²×C₁₃	1	2	yes	—
197	C₄×#41	C₂²×C₁₃	1	2	yes	—
198	#444	C₄×C₁₃	1	8	yes	complemented
199	#443	C₄×C₁₃	1	8	yes	complemented
200	#442	C₄×C₁₃	1	2	yes	complemented
201	#441	C₄×C₁₃	1	2	yes	complemented
202	#440	C₄×C₁₃	1	4	yes	complemented
203	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
205	#427	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×#104	C₂²×C₁₃	1	2	yes	—
207	C₂×#104	C₂²×C₁₃	1	2	yes	—
208	#416	C₂²×C₁₃	1	2	yes	—
209	#405	—	2	2	no	—
210	#405	—	2	2	no	—
211	#405	C₂²×C₁₃	1	2	yes	—
212	#405	C₂²×C₁₃	1	2	yes	—
213	C₄×M₁₆	—	2	2	no	—
214	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
215	C₂×#97	—	2	2	no	—
216	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₄³	C₂²×C₁₃	1	1	yes	characteristic
223	#341	C₂²×C₁₃	1	2	yes	—
224	#339	C₂²×C₁₃	1	2	yes	—
225	#339	C₂²×C₁₃	1	2	yes	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	2	4	no	—
228	C₂²×C₁₃	—	4	4	no	—
229	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
230	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
231	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
232	C₄×C₁₃	—	2	4	no	—
233	C₄×C₁₃	—	2	4	no	—
234	C₄×C₁₃	—	2	4	no	—
235	C₄×C₁₃	—	4	2	no	—
236	C₄×C₁₃	—	4	4	no	—
237	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
238	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
241	C₂×#41	C₂³×C₁₃	1	2	yes	—
242	#135	C₂×C₄×C₁₃	1	4	yes	—
243	#135	C₂×C₄×C₁₃	1	4	yes	—
244	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
245	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
246	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
247	#131	—	2	4	no	—
248	#131	—	2	4	no	—
249	#131	C₂×C₄×C₁₃	1	8	yes	complemented
250	#131	C₂×C₄×C₁₃	1	8	yes	complemented
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
254	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	2	2	no	—
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	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
261	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
262	C₄×D₄	—	2	4	no	—
263	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
264	#117	—	2	2	no	—
265	#117	C₂³×C₁₃	1	2	yes	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
271	#108	C₂×C₄×C₁₃	1	4	yes	complemented
272	#108	C₂×C₄×C₁₃	1	4	yes	complemented
273	#107	C₂×C₄×C₁₃	1	2	yes	—
274	#106	C₂×C₄×C₁₃	1	2	yes	—
275	#104	C₂×C₄×C₁₃	1	8	yes	complemented
276	#104	C₂×C₄×C₁₃	1	8	yes	complemented
277	#103	C₂×C₄×C₁₃	1	4	yes	—
278	#102	C₂×C₄×C₁₃	1	4	yes	—
279	#97	—	2	2	no	—
280	#97	—	2	2	no	—
281	#97	—	2	2	no	—
282	#97	—	2	2	no	—
283	#97	C₂×C₄×C₁₃	1	2	yes	—
284	#97	C₂×C₄×C₁₃	1	2	yes	—
285	#97	C₂×C₄×C₁₃	1	4	yes	complemented
286	#97	D₄×C₁₃	1	2	yes	—
287	#97	D₄×C₁₃	1	2	yes	—
288	C₄×C₈	—	2	2	no	—
289	C₄×C₈	—	2	2	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
293	C₂×C₁₃	—	2	1	no	—
294	C₂×C₁₃	—	2	1	no	—
295	C₂×C₁₃	—	4	4	no	—
296	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
297	C₂×C₁₃	#2956	1	2	yes	—
298	#41	—	2	2	no	—
299	#41	—	2	2	no	—
300	#41	C₂²×C₄×C₁₃	1	4	yes	—
301	#41	C₂²×C₄×C₁₃	1	4	yes	—
302	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	C₁₃×#41	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
311	Q₁₆	C₄²×C₁₃	1	4	yes	complemented
312	SD₁₆	C₄²×C₁₃	1	8	yes	complemented
313	D₈	C₄²×C₁₃	1	4	yes	complemented
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	8	no	—
317	M₁₆	—	2	8	no	—
318	M₁₆	C₂²×C₄×C₁₃	1	4	yes	—
319	M₁₆	C₂²×C₄×C₁₃	1	4	yes	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	8	no	—
325	C₂×C₈	—	2	8	no	—
326	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
327	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
328	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
329	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
330	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
331	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
332	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
333	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
335	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂×C₈	C₁₃×#41	1	2	yes	—
337	C₂×C₈	C₁₃×#41	1	2	yes	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	4	4	no	—
347	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
348	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
349	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
350	C₄²	C₂×D₄×C₁₃	1	2	yes	—
351	C₁₃	#20512	1	1	yes	characteristic, direct product factor, Sylow
352	C₂³	—	2	2	no	—
353	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	C₂×C₄²×C₁₃	1	4	yes	—
356	D₄	—	2	4	no	—
357	D₄	—	2	4	no	—
358	D₄	—	2	2	no	—
359	D₄	C₂×C₄²×C₁₃	1	4	yes	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	4	no	—
370	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
371	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
373	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
375	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
376	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	2	4	no	—
379	C₈	—	2	2	no	—
380	C₈	C₂×C₄²×C₁₃	1	2	yes	—
381	C₈	C₂×C₄²×C₁₃	1	2	yes	—
382	C₈	C₄×D₄×C₁₃	1	2	yes	—
383	C₈	C₄×D₄×C₁₃	1	4	yes	—
384	C₈	C₄×D₄×C₁₃	1	2	yes	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
389	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
390	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
391	C₄	—	2	4	no	—
392	C₄	—	2	4	no	—
393	C₄	—	2	4	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	4	no	—
396	C₄	C₂²×C₄²×C₁₃	1	1	yes	characteristic
397	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
398	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
399	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	4	4	no	—
403	C₂	C₄²×D₄×C₁₃	1	1	yes	characteristic
404	C₂	C₁₃×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×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×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#2875	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. C₄×C₁₃×#104	C₂	semidirect
11. C₄×C₁₃×#97	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
74. C₁₃×#108	C₂×C₄	semidirect
75. C₁₃×#108	C₂×C₄	semidirect
78. C₁₃×#104	C₂×C₄	semidirect
79. C₁₃×#104	C₂×C₄	semidirect
88. C₁₃×#97	C₂×C₄	semidirect
95. C₄×C₈×C₁₃	C₂×C₄	semidirect
96. #20512	C₁₃	direct (N × H)
110. C₁₃×Q₁₆	C₄²	semidirect
111. C₁₃×SD₁₆	C₄²	semidirect
112. C₁₃×D₈	C₄²	semidirect
153. #2875	C₂×C₁₃	semidirect
154. #1778	C₂×C₁₃	semidirect
155. #1773	C₂×C₁₃	semidirect
156. #1772	C₂×C₁₃	semidirect
157. #1765	C₂×C₁₃	semidirect
158. #1764	C₂×C₁₃	semidirect
159. C₄×#104	C₂×C₁₃	semidirect
160. C₄×#97	C₂×C₁₃	semidirect
198. #444	C₄×C₁₃	semidirect
199. #443	C₄×C₁₃	semidirect
200. #442	C₄×C₁₃	semidirect
201. #441	C₄×C₁₃	semidirect
202. #440	C₄×C₁₃	semidirect
249. #131	C₂×C₄×C₁₃	semidirect
250. #131	C₂×C₄×C₁₃	semidirect
271. #108	C₂×C₄×C₁₃	semidirect
272. #108	C₂×C₄×C₁₃	semidirect
275. #104	C₂×C₄×C₁₃	semidirect
276. #104	C₂×C₄×C₁₃	semidirect
285. #97	C₂×C₄×C₁₃	semidirect
292. C₄×C₈	C₂×C₄×C₁₃	semidirect
311. Q₁₆	C₄²×C₁₃	semidirect
312. SD₁₆	C₄²×C₁₃	semidirect
313. D₈	C₄²×C₁₃	semidirect
351. C₁₃	#20512	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
C₁₃×#2875	2
C₁₃×#1778	2
C₁₃×#1773	2
C₁₃×#1772	2
C₁₃×#1765	2
C₁₃×#1764	2
C₄×C₁₃×#104	2
C₄×C₁₃×#97	2
#20512	13

Subgroups — C13×#20512 #15706851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20512 #15706851