Subgroups — C₁₃×#22458 #15708797

Order 3328.

1338 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#576	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2957	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2888	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1978	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1903	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1813	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1795	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1757	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
10	C₁₃×#576	—	2	4	no	—
11	C₁₃×#576	—	2	4	no	—
12	C₂×C₁₃×AGL(1,ℤ/8)	C₄	1	4	yes	complemented
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
14	C₂×C₁₃×#135	C₄	1	2	yes	complemented
15	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×D₈	C₄	1	2	yes	complemented
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₁₃×#568	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
20	C₁₃×#444	—	2	4	no	—
21	C₁₃×#443	—	2	4	no	—
22	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
23	C₁₃×#421	C₂²	1	4	yes	complemented
24	C₁₃×#418	C₂²	1	4	yes	complemented
25	C₁₃×#413	—	2	4	no	—
26	C₁₃×#413	C₂²	1	2	yes	—
27	C₁₃×#413	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#100	—	2	4	no	—
29	C₂×C₁₃×#100	C₂²	1	4	yes	complemented
30	C₁₃×#410	C₂²	1	1	yes	characteristic
31	C₁₃×#405	C₂²	1	2	yes	complemented
32	C₁₃×#344	C₂²	1	2	yes	complemented
33	C₁₃×#338	C₂²	1	2	yes	complemented
34	C₁₃×H(5,𝔽₂)	—	2	8	no	—
35	C₁₃×H(5,𝔽₂)	—	4	4	no	—
36	C₂×C₁₃×#41	—	2	2	no	—
37	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
38	C₂×C₁₃×#41	C₂³	1	2	yes	—
39	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	—	2	2	no	—
41	C₂²×D₄×C₁₃	—	2	4	no	—
42	C₂²×D₄×C₁₃	C₂×C₄	1	4	yes	—
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
45	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
46	C₁₃×#135	—	2	4	no	—
47	C₁₃×#135	—	2	4	no	—
48	C₁₃×#135	D₄	1	4	yes	—
49	C₁₃×#135	D₄	1	4	yes	—
50	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
52	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×D₈	—	2	4	no	—
54	C₂×C₁₃×D₈	—	2	4	no	—
55	C₂×C₁₃×D₈	—	2	2	no	—
56	C₂×C₁₃×D₈	—	2	2	no	—
57	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
58	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	—
59	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
60	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
61	C₁₃×#131	—	2	2	no	—
62	C₁₃×#131	—	2	2	no	—
63	C₁₃×#131	—	2	8	no	—
64	C₁₃×#131	—	4	4	no	—
65	C₂×C₁₃×M₁₆	—	2	8	no	—
66	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
69	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×#117	C₂³	1	2	yes	—
73	C₁₃×#108	—	2	2	no	—
74	C₁₃×#108	—	2	2	no	—
75	C₁₃×#104	—	2	8	no	—
76	C₁₃×#102	—	4	4	no	—
77	C₁₃×#101	—	2	2	no	—
78	C₁₃×#101	D₄	1	2	yes	—
79	C₁₃×#100	—	2	2	no	—
80	C₁₃×#100	—	2	8	no	—
81	C₁₃×#100	D₄	1	2	yes	—
82	C₁₃×#99	—	2	2	no	—
83	C₁₃×#97	—	2	2	no	—
84	C₄×C₈×C₁₃	—	2	2	no	—
85	#22458	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	—	2	4	no	—
87	C₂⁴×C₁₃	—	2	2	no	—
88	C₁₃×#41	—	2	2	no	—
89	C₁₃×#41	—	2	4	no	—
90	C₁₃×#41	—	2	2	no	—
91	C₁₃×#41	—	2	8	no	—
92	C₁₃×#41	—	4	4	no	—
93	C₁₃×#41	—	4	8	no	—
94	C₁₃×#41	C₂×D₄	1	8	yes	—
95	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
96	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	8	no	—
99	C₂×D₄×C₁₃	—	2	4	no	—
100	C₂×D₄×C₁₃	—	2	4	no	—
101	C₂×D₄×C₁₃	—	2	4	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	4	no	—
104	C₂×D₄×C₁₃	—	4	4	no	—
105	C₂×D₄×C₁₃	—	4	8	no	—
106	C₂×D₄×C₁₃	—	4	16	no	—
107	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
108	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×D₄×C₁₃	#41	1	2	yes	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×Q₁₆	C₂²⋊C₄	1	2	yes	—
116	C₁₃×Q₁₆	C₂²⋊C₄	1	2	yes	—
117	C₁₃×SD₁₆	—	2	8	no	—
118	C₁₃×SD₁₆	C₂²⋊C₄	1	8	yes	—
119	C₁₃×D₈	—	2	8	no	—
120	C₁₃×D₈	—	2	2	no	—
121	C₁₃×D₈	—	2	2	no	—
122	C₁₃×D₈	—	2	4	no	—
123	C₁₃×D₈	C₂²⋊C₄	1	2	yes	—
124	C₁₃×D₈	C₂²⋊C₄	1	2	yes	—
125	C₁₃×M₁₆	—	2	2	no	—
126	C₁₃×M₁₆	—	2	2	no	—
127	C₁₃×M₁₆	—	2	4	no	—
128	C₁₃×M₁₆	—	2	4	no	—
129	C₁₃×M₁₆	—	2	4	no	—
130	C₁₃×M₁₆	—	4	8	no	—
131	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	4	no	—
136	C₂×C₈×C₁₃	—	4	8	no	—
137	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₂²⋊C₄	—	2	2	no	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₂×#576	C₂×C₁₃	1	1	yes	characteristic
146	#2957	C₂×C₁₃	1	2	yes	complemented
147	#2888	C₂×C₁₃	1	2	yes	complemented
148	#1978	C₂×C₁₃	1	2	yes	complemented
149	#1903	C₂×C₁₃	1	4	yes	complemented
150	#1813	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1795	C₂×C₁₃	1	2	yes	complemented
152	#1757	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	2	4	no	—
155	C₂³×C₁₃	—	4	8	no	—
156	C₂³×C₁₃	—	4	4	no	—
157	C₂³×C₁₃	—	16	2	no	—
158	C₂³×C₁₃	—	16	4	no	—
159	C₂³×C₁₃	C₄×D₄	1	2	yes	—
160	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
161	Q₈×C₁₃	—	2	2	no	—
162	Q₈×C₁₃	—	2	2	no	—
163	Q₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
164	D₄×C₁₃	—	2	8	no	—
165	D₄×C₁₃	—	2	4	no	—
166	D₄×C₁₃	—	2	4	no	—
167	D₄×C₁₃	—	2	2	no	—
168	D₄×C₁₃	—	2	4	no	—
169	D₄×C₁₃	—	2	2	no	—
170	D₄×C₁₃	—	4	8	no	—
171	D₄×C₁₃	—	4	8	no	—
172	D₄×C₁₃	—	4	4	no	—
173	D₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	4	8	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	—	2	4	no	—
187	C₈×C₁₃	—	4	4	no	—
188	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
192	#576	—	2	4	no	—
193	#576	—	2	4	no	—
194	C₂×AGL(1,ℤ/8)	C₄×C₁₃	1	4	yes	complemented
195	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
196	C₂×#135	C₄×C₁₃	1	2	yes	complemented
197	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
198	C₂²×D₈	C₄×C₁₃	1	2	yes	complemented
199	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
200	#568	C₂²×C₁₃	1	4	yes	complemented
201	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
202	#444	—	2	4	no	—
203	#443	—	2	4	no	—
204	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
205	#421	C₂²×C₁₃	1	4	yes	complemented
206	#418	C₂²×C₁₃	1	4	yes	complemented
207	#413	—	2	4	no	—
208	#413	C₂²×C₁₃	1	2	yes	—
209	#413	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#100	—	2	4	no	—
211	C₂×#100	C₂²×C₁₃	1	4	yes	complemented
212	#410	C₂²×C₁₃	1	1	yes	characteristic
213	#405	C₂²×C₁₃	1	2	yes	complemented
214	#344	C₂²×C₁₃	1	2	yes	complemented
215	#338	C₂²×C₁₃	1	2	yes	complemented
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	2	4	no	—
218	C₂²×C₁₃	—	4	1	no	—
219	C₂²×C₁₃	—	4	2	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	—	8	2	no	—
222	C₂²×C₁₃	—	8	4	no	—
223	C₂²×C₁₃	—	16	4	no	—
224	C₂²×C₁₃	—	16	8	no	—
225	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
226	C₂²×C₁₃	#546	1	2	yes	—
227	C₄×C₁₃	—	2	4	no	—
228	C₄×C₁₃	—	2	2	no	—
229	C₄×C₁₃	—	8	2	no	—
230	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
231	C₄×C₁₃	#518	1	1	yes	characteristic
232	C₄×C₁₃	D₄²	1	2	yes	—
233	H(5,𝔽₂)	—	2	8	no	—
234	H(5,𝔽₂)	—	4	4	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	C₂×C₄×C₁₃	1	4	yes	—
237	C₂×#41	C₂³×C₁₃	1	2	yes	—
238	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	—	2	4	no	—
241	C₂²×D₄	C₂×C₄×C₁₃	1	4	yes	—
242	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
243	AGL(1,ℤ/8)	—	2	8	no	—
244	AGL(1,ℤ/8)	—	2	16	no	—
245	#135	—	2	4	no	—
246	#135	—	2	4	no	—
247	#135	D₄×C₁₃	1	4	yes	—
248	#135	D₄×C₁₃	1	4	yes	—
249	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
250	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
251	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
252	C₂×D₈	—	2	4	no	—
253	C₂×D₈	—	2	4	no	—
254	C₂×D₈	—	2	2	no	—
255	C₂×D₈	—	2	2	no	—
256	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
257	C₂×D₈	C₂×C₄×C₁₃	1	4	yes	—
258	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
259	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
260	#131	—	2	2	no	—
261	#131	—	2	2	no	—
262	#131	—	2	8	no	—
263	#131	—	4	4	no	—
264	C₂×M₁₆	—	2	8	no	—
265	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
266	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
267	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
268	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
269	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
270	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	#117	C₂³×C₁₃	1	2	yes	—
272	#108	—	2	2	no	—
273	#108	—	2	2	no	—
274	#104	—	2	8	no	—
275	#102	—	4	4	no	—
276	#101	—	2	2	no	—
277	#101	D₄×C₁₃	1	2	yes	—
278	#100	—	2	2	no	—
279	#100	—	2	8	no	—
280	#100	D₄×C₁₃	1	2	yes	—
281	#99	—	2	2	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	C₂×C₁₃	—	2	2	no	—
285	C₂×C₁₃	—	2	1	no	—
286	C₂×C₁₃	—	4	2	no	—
287	C₂×C₁₃	—	4	4	no	—
288	C₂×C₁₃	—	8	4	no	—
289	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	2	2	no	—
292	#41	—	2	2	no	—
293	#41	—	2	4	no	—
294	#41	—	2	2	no	—
295	#41	—	2	8	no	—
296	#41	—	4	4	no	—
297	#41	—	4	8	no	—
298	#41	C₂×D₄×C₁₃	1	8	yes	—
299	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
300	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	8	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	4	4	no	—
309	C₂×D₄	—	4	8	no	—
310	C₂×D₄	—	4	16	no	—
311	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
312	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
313	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂×D₄	C₁₃×#41	1	2	yes	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
319	Q₁₆	C₁₃×C₂²⋊C₄	1	2	yes	—
320	Q₁₆	C₁₃×C₂²⋊C₄	1	2	yes	—
321	SD₁₆	—	2	8	no	—
322	SD₁₆	C₁₃×C₂²⋊C₄	1	8	yes	—
323	D₈	—	2	8	no	—
324	D₈	—	2	2	no	—
325	D₈	—	2	2	no	—
326	D₈	—	2	4	no	—
327	D₈	C₁₃×C₂²⋊C₄	1	2	yes	—
328	D₈	C₁₃×C₂²⋊C₄	1	2	yes	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	4	no	—
332	M₁₆	—	2	4	no	—
333	M₁₆	—	2	4	no	—
334	M₁₆	—	4	8	no	—
335	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	4	8	no	—
341	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
342	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
343	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
344	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
345	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₁₃	#22458	1	1	yes	characteristic, direct product factor, Sylow
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	4	8	no	—
353	C₂³	—	4	4	no	—
354	C₂³	—	16	2	no	—
355	C₂³	—	16	4	no	—
356	C₂³	C₄×D₄×C₁₃	1	2	yes	—
357	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
358	Q₈	—	2	2	no	—
359	Q₈	—	2	2	no	—
360	Q₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
361	D₄	—	2	8	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	2	no	—
365	D₄	—	2	4	no	—
366	D₄	—	2	2	no	—
367	D₄	—	4	8	no	—
368	D₄	—	4	8	no	—
369	D₄	—	4	4	no	—
370	D₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	4	8	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
378	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
380	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
381	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
382	C₈	—	2	2	no	—
383	C₈	—	2	4	no	—
384	C₈	—	4	4	no	—
385	C₈	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
386	C₈	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
387	C₈	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	4	no	—
395	C₂²	—	16	4	no	—
396	C₂²	—	16	8	no	—
397	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
398	C₂²	C₁₃×#546	1	2	yes	—
399	C₄	—	2	4	no	—
400	C₄	—	2	2	no	—
401	C₄	—	8	2	no	—
402	C₄	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
403	C₄	C₁₃×#518	1	1	yes	characteristic
404	C₄	D₄²×C₁₃	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	2	1	no	—
407	C₂	—	4	2	no	—
408	C₂	—	4	4	no	—
409	C₂	—	8	4	no	—
410	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	D₄×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#576	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2957	C₂	semidirect
3. C₁₃×#2888	C₂	semidirect
4. C₁₃×#1978	C₂	semidirect
5. C₁₃×#1903	C₂	semidirect
6. C₁₃×#1813	C₂	semidirect
7. C₁₃×#1795	C₂	semidirect
8. C₁₃×#1757	C₂	semidirect
12. C₂×C₁₃×AGL(1,ℤ/8)	C₄	semidirect
14. C₂×C₁₃×#135	C₄	semidirect
16. C₂²×C₁₃×D₈	C₄	semidirect
18. C₁₃×#568	C₂²	semidirect
22. C₂×C₁₃×#108	C₂²	semidirect
23. C₁₃×#421	C₂²	semidirect
24. C₁₃×#418	C₂²	semidirect
29. C₂×C₁₃×#100	C₂²	semidirect
31. C₁₃×#405	C₂²	semidirect
32. C₁₃×#344	C₂²	semidirect
33. C₁₃×#338	C₂²	semidirect
85. #22458	C₁₃	direct (N × H)
146. #2957	C₂×C₁₃	semidirect
147. #2888	C₂×C₁₃	semidirect
148. #1978	C₂×C₁₃	semidirect
149. #1903	C₂×C₁₃	semidirect
150. #1813	C₂×C₁₃	semidirect
151. #1795	C₂×C₁₃	semidirect
152. #1757	C₂×C₁₃	semidirect
194. C₂×AGL(1,ℤ/8)	C₄×C₁₃	semidirect
196. C₂×#135	C₄×C₁₃	semidirect
198. C₂²×D₈	C₄×C₁₃	semidirect
200. #568	C₂²×C₁₃	semidirect
204. C₂×#108	C₂²×C₁₃	semidirect
205. #421	C₂²×C₁₃	semidirect
206. #418	C₂²×C₁₃	semidirect
211. C₂×#100	C₂²×C₁₃	semidirect
213. #405	C₂²×C₁₃	semidirect
214. #344	C₂²×C₁₃	semidirect
215. #338	C₂²×C₁₃	semidirect
349. C₁₃	#22458	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×#576	2
C₁₃×#2957	2
C₁₃×#2888	2
C₁₃×#1978	2
C₁₃×#1903	2
C₁₃×#1813	2
C₁₃×#1795	2
C₁₃×#1757	2
#22458	13

Subgroups — C13×#22458 #15708797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22458 #15708797