Subgroups — C₁₃×#22686 #15709025

Order 3328.

858 conjugacy classes of subgroups.

The subgroup lattice has 392 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	2	yes	maximal
2	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2906	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1946	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1866	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1848	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1806	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#131	C₂²	1	4	yes	—
11	C₄×C₁₃×#41	C₂²	1	2	yes	—
12	C₁₃×#444	—	2	8	no	—
13	C₄×C₁₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
14	C₄×C₁₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
15	C₄×C₁₃×SD₁₆	C₄	1	2	yes	complemented
16	C₄×C₁₃×SD₁₆	C₄	1	2	yes	complemented
17	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic, complemented
18	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic, complemented
19	C₂×C₁₃×#108	C₂²	1	2	yes	—
20	C₂×C₁₃×#108	C₂²	1	2	yes	—
21	C₁₃×#427	C₂²	1	1	yes	characteristic
22	C₁₃×#424	—	2	4	no	—
23	C₁₃×#424	C₂²	1	4	yes	—
24	C₁₃×#423	—	2	2	no	—
25	C₁₃×#423	C₂²	1	2	yes	—
26	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#104	C₂²	1	4	yes	—
29	C₁₃×#416	C₂²	1	2	yes	—
30	C₂×C₁₃×#97	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₁₃×#339	C₂²	1	4	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂×C₁₃×#41	C₂³	1	2	yes	—
36	C₁₃×#135	D₄	1	4	yes	—
37	C₁₃×#135	Q₈	1	4	yes	—
38	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
40	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
41	C₁₃×#131	—	2	8	no	—
42	C₁₃×#131	—	4	4	no	—
43	C₂×C₁₃×M₁₆	—	2	4	no	—
44	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
45	C₂²×C₈×C₁₃	—	2	4	no	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
50	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
51	C₄×D₄×C₁₃	—	2	2	no	—
52	C₄×D₄×C₁₃	—	2	2	no	—
53	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
54	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
55	C₁₃×#117	—	2	2	no	—
56	C₁₃×#117	C₂³	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₄²×C₁₃	—	2	2	no	—
59	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×#108	—	2	4	no	—
62	C₁₃×#108	—	4	2	no	—
63	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
64	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
65	C₁₃×#106	C₂×C₄	1	2	yes	—
66	C₁₃×C₄⋊C₈	—	2	4	no	—
67	C₁₃×C₄⋊C₈	—	2	4	no	—
68	C₁₃×C₄⋊C₈	—	2	2	no	—
69	C₁₃×C₄⋊C₈	—	2	2	no	—
70	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
71	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
72	C₁₃×#104	—	2	8	no	—
73	C₁₃×#103	C₂×C₄	1	2	yes	—
74	C₁₃×#103	C₂×C₄	1	2	yes	—
75	C₁₃×#102	C₂×C₄	1	2	yes	—
76	C₁₃×#102	C₂×C₄	1	2	yes	—
77	C₁₃×#97	—	2	4	no	—
78	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₁₃×#95	—	2	1	no	—
83	#22686	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₁₃×#41	—	2	2	no	—
85	C₁₃×#41	—	2	2	no	—
86	C₁₃×#41	C₂×D₄	1	4	yes	—
87	C₁₃×#41	C₂×Q₈	1	4	yes	—
88	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₁₃×Q₁₆	C₄⋊C₄	1	4	yes	complemented
99	C₁₃×SD₁₆	C₄⋊C₄	1	8	yes	complemented
100	C₁₃×D₈	C₄⋊C₄	1	4	yes	complemented
101	C₁₃×M₁₆	—	2	4	no	—
102	C₁₃×M₁₆	—	2	4	no	—
103	C₁₃×M₁₆	—	4	8	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	4	no	—
109	C₂×C₈×C₁₃	—	4	8	no	—
110	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
115	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	4	2	no	—
120	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
121	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
122	C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₁₃×C₂²⋊C₄	—	2	2	no	—
124	C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	—	2	2	no	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄²×C₁₃	—	2	2	no	—
130	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×#444	C₂×C₁₃	1	2	yes	—
135	C₄×#135	C₂×C₁₃	1	1	yes	characteristic
136	#2906	C₂×C₁₃	1	2	yes	complemented
137	#1946	C₂×C₁₃	1	2	yes	complemented
138	#1866	C₂×C₁₃	1	4	yes	complemented
139	#1848	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1806	C₂×C₁₃	1	2	yes	complemented
141	#1770	C₂×C₁₃	1	1	yes	characteristic, complemented
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
144	Q₈×C₁₃	—	2	2	no	—
145	Q₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
146	D₄×C₁₃	—	2	4	no	—
147	D₄×C₁₃	—	2	4	no	—
148	D₄×C₁₃	—	2	2	no	—
149	D₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	4	no	—
152	C₂×C₄×C₁₃	—	2	4	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	4	1	no	—
157	C₂×C₄×C₁₃	—	4	4	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	8	2	no	—
162	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
172	C₈×C₁₃	—	2	1	no	—
173	C₈×C₁₃	—	2	1	no	—
174	C₈×C₁₃	—	2	4	no	—
175	C₈×C₁₃	—	4	4	no	—
176	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
177	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×#131	C₂²×C₁₃	1	4	yes	—
180	C₄×#41	C₂²×C₁₃	1	2	yes	—
181	#444	—	2	8	no	—
182	C₄×Q₁₆	C₄×C₁₃	1	1	yes	characteristic, complemented
183	C₄×Q₁₆	C₄×C₁₃	1	1	yes	characteristic, complemented
184	C₄×SD₁₆	C₄×C₁₃	1	2	yes	complemented
185	C₄×SD₁₆	C₄×C₁₃	1	2	yes	complemented
186	C₄×D₈	C₄×C₁₃	1	1	yes	characteristic, complemented
187	C₄×D₈	C₄×C₁₃	1	1	yes	characteristic, complemented
188	C₂×#108	C₂²×C₁₃	1	2	yes	—
189	C₂×#108	C₂²×C₁₃	1	2	yes	—
190	#427	C₂²×C₁₃	1	1	yes	characteristic
191	#424	—	2	4	no	—
192	#424	C₂²×C₁₃	1	4	yes	—
193	#423	—	2	2	no	—
194	#423	C₂²×C₁₃	1	2	yes	—
195	C₂×C₄⋊C₈	—	2	2	no	—
196	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#104	C₂²×C₁₃	1	4	yes	—
198	#416	C₂²×C₁₃	1	2	yes	—
199	C₂×#97	C₂²×C₁₃	1	2	yes	—
200	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
201	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
202	#339	C₂²×C₁₃	1	4	yes	—
203	#336	C₂²×C₁₃	1	2	yes	—
204	C₂²×C₁₃	—	2	1	no	—
205	C₂²×C₁₃	—	2	1	no	—
206	C₂²×C₁₃	—	2	4	no	—
207	C₂²×C₁₃	—	4	2	no	—
208	C₂²×C₁₃	—	4	2	no	—
209	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
210	C₂²×C₁₃	#547	1	1	yes	characteristic
211	C₂²×C₁₃	#554	1	1	yes	characteristic
212	C₄×C₁₃	—	2	4	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	4	2	no	—
217	C₄×C₁₃	—	4	2	no	—
218	C₄×C₁₃	—	8	2	no	—
219	C₄×C₁₃	#444	1	2	yes	complemented
220	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
221	C₄×C₁₃	#520	1	1	yes	characteristic
222	C₄×C₁₃	D₄²	1	1	yes	characteristic
223	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
224	C₂×#41	C₂³×C₁₃	1	2	yes	—
225	#135	D₄×C₁₃	1	4	yes	—
226	#135	Q₈×C₁₃	1	4	yes	—
227	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
228	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
229	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
230	#131	—	2	8	no	—
231	#131	—	4	4	no	—
232	C₂×M₁₆	—	2	4	no	—
233	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
237	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
238	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
239	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
243	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
244	#117	—	2	2	no	—
245	#117	C₂³×C₁₃	1	2	yes	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
249	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
250	#108	—	2	4	no	—
251	#108	—	4	2	no	—
252	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
253	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
254	#106	C₂×C₄×C₁₃	1	2	yes	—
255	C₄⋊C₈	—	2	4	no	—
256	C₄⋊C₈	—	2	4	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
260	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
261	#104	—	2	8	no	—
262	#103	C₂×C₄×C₁₃	1	2	yes	—
263	#103	C₂×C₄×C₁₃	1	2	yes	—
264	#102	C₂×C₄×C₁₃	1	2	yes	—
265	#102	C₂×C₄×C₁₃	1	2	yes	—
266	#97	—	2	4	no	—
267	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
268	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
269	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
270	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
271	#95	—	2	1	no	—
272	C₂×C₁₃	—	2	1	no	—
273	C₂×C₁₃	—	2	1	no	—
274	C₂×C₁₃	—	4	4	no	—
275	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
276	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
277	C₂×C₁₃	#2957	1	1	yes	characteristic
278	#41	—	2	2	no	—
279	#41	—	2	2	no	—
280	#41	C₂×D₄×C₁₃	1	4	yes	—
281	#41	C₂×Q₈×C₁₃	1	4	yes	—
282	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
290	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
291	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
292	Q₁₆	C₁₃×C₄⋊C₄	1	4	yes	complemented
293	SD₁₆	C₁₃×C₄⋊C₄	1	8	yes	complemented
294	D₈	C₁₃×C₄⋊C₄	1	4	yes	complemented
295	M₁₆	—	2	4	no	—
296	M₁₆	—	2	4	no	—
297	M₁₆	—	4	8	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	4	8	no	—
304	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
305	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
306	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
307	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
309	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
310	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
315	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
325	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
327	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
328	C₁₃	#22686	1	1	yes	characteristic, direct product factor, Sylow
329	C₂³	—	2	2	no	—
330	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
331	Q₈	—	2	2	no	—
332	Q₈	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
333	D₄	—	2	4	no	—
334	D₄	—	2	4	no	—
335	D₄	—	2	2	no	—
336	D₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
350	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
351	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
357	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	4	no	—
362	C₈	—	4	4	no	—
363	C₈	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
364	C₈	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
371	C₂²	C₁₃×#547	1	1	yes	characteristic
372	C₂²	C₁₃×#554	1	1	yes	characteristic
373	C₄	—	2	4	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	8	2	no	—
380	C₄	C₁₃×#444	1	2	yes	complemented
381	C₄	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
382	C₄	C₁₃×#520	1	1	yes	characteristic
383	C₄	D₄²×C₁₃	1	1	yes	characteristic
384	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	4	4	no	—
388	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
389	C₂	C₂×C₁₃×#444	1	1	yes	characteristic
390	C₂	C₁₃×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2906	C₂	semidirect
4. C₁₃×#1946	C₂	semidirect
5. C₁₃×#1866	C₂	semidirect
6. C₁₃×#1848	C₂	semidirect
7. C₁₃×#1806	C₂	semidirect
8. C₁₃×#1770	C₂	semidirect
13. C₄×C₁₃×Q₁₆	C₄	semidirect
14. C₄×C₁₃×Q₁₆	C₄	semidirect
15. C₄×C₁₃×SD₁₆	C₄	semidirect
16. C₄×C₁₃×SD₁₆	C₄	semidirect
17. C₄×C₁₃×D₈	C₄	semidirect
18. C₄×C₁₃×D₈	C₄	semidirect
83. #22686	C₁₃	direct (N × H)
98. C₁₃×Q₁₆	C₄⋊C₄	semidirect
99. C₁₃×SD₁₆	C₄⋊C₄	semidirect
100. C₁₃×D₈	C₄⋊C₄	semidirect
136. #2906	C₂×C₁₃	semidirect
137. #1946	C₂×C₁₃	semidirect
138. #1866	C₂×C₁₃	semidirect
139. #1848	C₂×C₁₃	semidirect
140. #1806	C₂×C₁₃	semidirect
141. #1770	C₂×C₁₃	semidirect
182. C₄×Q₁₆	C₄×C₁₃	semidirect
183. C₄×Q₁₆	C₄×C₁₃	semidirect
184. C₄×SD₁₆	C₄×C₁₃	semidirect
185. C₄×SD₁₆	C₄×C₁₃	semidirect
186. C₄×D₈	C₄×C₁₃	semidirect
187. C₄×D₈	C₄×C₁₃	semidirect
219. C₄×C₁₃	#444	semidirect
292. Q₁₆	C₁₃×C₄⋊C₄	semidirect
293. SD₁₆	C₁₃×C₄⋊C₄	semidirect
294. D₈	C₁₃×C₄⋊C₄	semidirect
328. C₁₃	#22686	direct (N × H)
380. C₄	C₁₃×#444	semidirect

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
C₄×C₁₃×#135	2
C₁₃×#2906	2
C₁₃×#1946	2
C₁₃×#1866	2
C₁₃×#1848	2
C₁₃×#1806	2
C₁₃×#1770	2
#22686	13

Subgroups — C13×#22686 #15709025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22686 #15709025