Subgroups — C₁₃×#61409 #15747748

Order 3328.

2078 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3399	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3396	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3391	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3155	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3041	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3038	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2948	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
15	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
16	C₁₃×#559	C₂²	1	8	yes	complemented
17	C₁₃×#550	C₂²	1	8	yes	complemented
18	C₁₃×#546	—	2	8	no	—
19	C₁₃×#540	—	2	4	no	—
20	C₁₃×#535	C₂²	1	4	yes	—
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₁₃×#532	—	2	4	no	—
23	C₂×C₁₃×#127	C₂²	1	2	yes	—
24	C₁₃×#518	C₂²	1	4	yes	—
25	C₄×C₁₃×#41	C₂²	1	2	yes	—
26	C₁₃×#496	C₂²	1	8	yes	complemented
27	C₁₃×#495	C₂²	1	4	yes	complemented
28	C₁₃×#493	C₂²	1	4	yes	—
29	C₁₃×#493	C₂²	1	4	yes	—
30	C₁₃×#493	C₂²	1	4	yes	complemented
31	C₁₃×#463	C₂²	1	16	yes	complemented
32	C₁₃×#460	C₂²	1	8	yes	complemented
33	C₁₃×#459	C₂²	1	8	yes	complemented
34	C₁₃×#459	C₂²	1	16	yes	complemented
35	C₁₃×#446	C₂²	1	4	yes	complemented
36	C₈×Q₈×C₁₃	C₂²	1	4	yes	complemented
37	C₁₃×#442	C₂²	1	8	yes	complemented
38	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
39	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
40	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
41	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
42	C₁₃×#427	C₂²	1	1	yes	characteristic
43	C₁₃×#424	C₂²	1	2	yes	—
44	C₁₃×#423	C₂²	1	1	yes	characteristic
45	C₁₃×#418	C₂²	1	4	yes	—
46	C₁₃×#416	C₂²	1	2	yes	—
47	C₁₃×#405	C₂²	1	2	yes	—
48	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#41	—	2	8	no	—
50	C₂×C₁₃×#41	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₃	—	2	4	no	—
52	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
53	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
54	C₁₃×#135	—	2	4	no	—
55	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
58	C₂×C₁₃×D₈	—	2	8	no	—
59	C₂×C₁₃×D₈	—	4	4	no	—
60	C₂×C₁₃×D₈	C₂³	1	4	yes	—
61	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×D₈	C₂³	1	4	yes	—
63	C₂×C₁₃×D₈	C₂³	1	8	yes	—
64	C₂×C₁₃×D₈	C₂³	1	8	yes	—
65	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
69	C₁₃×#127	—	2	2	no	—
70	C₁₃×#127	—	2	2	no	—
71	C₁₃×#127	C₂³	1	8	yes	—
72	C₁₃×#127	C₂³	1	8	yes	—
73	C₁₃×#125	D₄	1	2	yes	—
74	C₁₃×#124	—	2	8	no	—
75	C₁₃×#124	C₂³	1	8	yes	—
76	C₁₃×#123	—	2	16	no	—
77	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
78	C₁₃×#121	—	2	8	no	—
79	C₁₃×#121	—	2	8	no	—
80	C₁₃×#121	—	2	16	no	—
81	C₁₃×#120	—	2	8	no	—
82	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
83	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
84	C₄×D₄×C₁₃	—	2	4	no	—
85	C₄×D₄×C₁₃	—	2	8	no	—
86	C₄×D₄×C₁₃	—	2	8	no	—
87	C₄×D₄×C₁₃	C₂³	1	4	yes	—
88	C₄×D₄×C₁₃	C₂³	1	16	yes	—
89	C₁₃×#117	—	2	2	no	—
90	C₁₃×#117	C₂³	1	2	yes	—
91	C₁₃×#117	C₂³	1	2	yes	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
93	C₂×C₄²×C₁₃	—	2	2	no	—
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×#107	C₂³	1	2	yes	—
96	C₁₃×#106	C₂³	1	2	yes	—
97	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
98	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
99	C₁₃×#103	C₂³	1	4	yes	—
100	C₁₃×#102	C₂³	1	4	yes	—
101	C₁₃×#102	C₂³	1	16	yes	—
102	C₁₃×#97	C₂³	1	4	yes	—
103	C₄×C₈×C₁₃	C₂³	1	2	yes	—
104	C₄×C₈×C₁₃	C₂³	1	2	yes	—
105	C₄×C₈×C₁₃	C₂³	1	4	yes	—
106	#61409	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	—	2	4	no	—
108	C₁₃×#41	—	2	4	no	—
109	C₁₃×#41	—	2	4	no	—
110	C₁₃×#41	—	8	16	no	—
111	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
112	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	4	no	—
115	C₂×D₄×C₁₃	—	2	8	no	—
116	C₂×D₄×C₁₃	—	2	16	no	—
117	C₂×D₄×C₁₃	—	2	8	no	—
118	C₂×D₄×C₁₃	—	2	8	no	—
119	C₂×D₄×C₁₃	—	2	8	no	—
120	C₂×D₄×C₁₃	—	8	8	no	—
121	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
122	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	16	no	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₁₃×Q₁₆	—	2	2	no	—
129	C₁₃×SD₁₆	—	2	4	no	—
130	C₁₃×SD₁₆	—	4	8	no	—
131	C₁₃×D₈	—	2	8	no	—
132	C₁₃×D₈	—	2	8	no	—
133	C₁₃×D₈	—	2	2	no	—
134	C₁₃×D₈	—	4	8	no	—
135	C₁₃×D₈	—	4	8	no	—
136	C₁₃×M₁₆	—	2	4	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	#41	1	4	yes	complemented
139	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
140	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
141	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×C₄⋊C₄	—	2	4	no	—
144	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
145	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
146	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
147	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
148	C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₁₃×C₂²⋊C₄	—	2	16	no	—
150	C₁₃×C₂²⋊C₄	—	2	4	no	—
151	C₁₃×C₂²⋊C₄	—	2	16	no	—
152	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	—	2	4	no	—
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₃	C₂⁴	1	2	yes	—
158	C₄²×C₁₃	C₂⁴	1	4	yes	—
159	#3508	C₂×C₁₃	1	2	yes	complemented
160	#3399	C₂×C₁₃	1	8	yes	complemented
161	#3396	C₂×C₁₃	1	4	yes	complemented
162	#3391	C₂×C₁₃	1	4	yes	complemented
163	#3155	C₂×C₁₃	1	2	yes	complemented
164	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#3041	C₂×C₁₃	1	4	yes	complemented
166	#3038	C₂×C₁₃	1	2	yes	complemented
167	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#2948	C₂×C₁₃	1	2	yes	complemented
169	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂³×C₁₃	—	2	8	no	—
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	4	8	no	—
173	C₂³×C₁₃	—	8	8	no	—
174	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₃	—	2	8	no	—
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	2	8	no	—
179	D₄×C₁₃	—	2	2	no	—
180	D₄×C₁₃	—	2	2	no	—
181	D₄×C₁₃	—	2	8	no	—
182	D₄×C₁₃	—	4	4	no	—
183	D₄×C₁₃	—	4	8	no	—
184	D₄×C₁₃	—	4	16	no	—
185	D₄×C₁₃	—	8	8	no	—
186	D₄×C₁₃	—	8	16	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	4	4	no	—
191	C₂×C₄×C₁₃	—	4	8	no	—
192	C₂×C₄×C₁₃	—	8	16	no	—
193	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
195	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
198	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
199	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
200	C₈×C₁₃	—	2	2	no	—
201	C₈×C₁₃	—	2	4	no	—
202	C₈×C₁₃	C₂×#41	1	2	yes	—
203	C₈×C₁₃	C₂×#41	1	2	yes	—
204	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
205	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
206	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
207	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
208	#559	C₂²×C₁₃	1	8	yes	complemented
209	#550	C₂²×C₁₃	1	8	yes	complemented
210	#546	—	2	8	no	—
211	#540	—	2	4	no	—
212	#535	C₂²×C₁₃	1	4	yes	—
213	#533	C₂²×C₁₃	1	1	yes	characteristic
214	#532	—	2	4	no	—
215	C₂×#127	C₂²×C₁₃	1	2	yes	—
216	#518	C₂²×C₁₃	1	4	yes	—
217	C₄×#41	C₂²×C₁₃	1	2	yes	—
218	#496	C₂²×C₁₃	1	8	yes	complemented
219	#495	C₂²×C₁₃	1	4	yes	complemented
220	#493	C₂²×C₁₃	1	4	yes	—
221	#493	C₂²×C₁₃	1	4	yes	—
222	#493	C₂²×C₁₃	1	4	yes	complemented
223	#463	C₂²×C₁₃	1	16	yes	complemented
224	#460	C₂²×C₁₃	1	8	yes	complemented
225	#459	C₂²×C₁₃	1	8	yes	complemented
226	#459	C₂²×C₁₃	1	16	yes	complemented
227	#446	C₂²×C₁₃	1	4	yes	complemented
228	C₈×Q₈	C₂²×C₁₃	1	4	yes	complemented
229	#442	C₂²×C₁₃	1	8	yes	complemented
230	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
231	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
232	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
233	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
234	#427	C₂²×C₁₃	1	1	yes	characteristic
235	#424	C₂²×C₁₃	1	2	yes	—
236	#423	C₂²×C₁₃	1	1	yes	characteristic
237	#418	C₂²×C₁₃	1	4	yes	—
238	#416	C₂²×C₁₃	1	2	yes	—
239	#405	C₂²×C₁₃	1	2	yes	—
240	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	8	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	4	16	no	—
246	C₂²×C₁₃	—	16	8	no	—
247	C₂²×C₁₃	#550	1	2	yes	—
248	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	2	8	no	—
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	—	4	4	no	—
253	C₄×C₁₃	#550	1	2	yes	—
254	C₄×C₁₃	#576	1	4	yes	—
255	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
256	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
257	C₂×#41	—	2	8	no	—
258	C₂×#41	C₂³×C₁₃	1	2	yes	—
259	C₂²×D₄	—	2	4	no	—
260	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
261	AGL(1,ℤ/8)	—	4	8	no	—
262	#135	—	2	4	no	—
263	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
265	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
266	C₂×D₈	—	2	8	no	—
267	C₂×D₈	—	4	4	no	—
268	C₂×D₈	C₂³×C₁₃	1	4	yes	—
269	C₂×D₈	C₂³×C₁₃	1	4	yes	—
270	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×D₈	C₂³×C₁₃	1	8	yes	—
272	C₂×D₈	C₂³×C₁₃	1	8	yes	—
273	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
274	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
277	#127	—	2	2	no	—
278	#127	—	2	2	no	—
279	#127	C₂³×C₁₃	1	8	yes	—
280	#127	C₂³×C₁₃	1	8	yes	—
281	#125	D₄×C₁₃	1	2	yes	—
282	#124	—	2	8	no	—
283	#124	C₂³×C₁₃	1	8	yes	—
284	#123	—	2	16	no	—
285	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
286	#121	—	2	8	no	—
287	#121	—	2	8	no	—
288	#121	—	2	16	no	—
289	#120	—	2	8	no	—
290	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
291	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
292	C₄×D₄	—	2	4	no	—
293	C₄×D₄	—	2	8	no	—
294	C₄×D₄	—	2	8	no	—
295	C₄×D₄	C₂³×C₁₃	1	4	yes	—
296	C₄×D₄	C₂³×C₁₃	1	16	yes	—
297	#117	—	2	2	no	—
298	#117	C₂³×C₁₃	1	2	yes	—
299	#117	C₂³×C₁₃	1	2	yes	—
300	C₂×C₂²⋊C₄	—	2	8	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
303	#107	C₂³×C₁₃	1	2	yes	—
304	#106	C₂³×C₁₃	1	2	yes	—
305	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
306	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
307	#103	C₂³×C₁₃	1	4	yes	—
308	#102	C₂³×C₁₃	1	4	yes	—
309	#102	C₂³×C₁₃	1	16	yes	—
310	#97	C₂³×C₁₃	1	4	yes	—
311	C₄×C₈	C₂³×C₁₃	1	2	yes	—
312	C₄×C₈	C₂³×C₁₃	1	2	yes	—
313	C₄×C₈	C₂³×C₁₃	1	4	yes	—
314	C₂×C₁₃	—	2	2	no	—
315	C₂×C₁₃	—	8	2	no	—
316	C₂×C₁₃	—	8	8	no	—
317	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
318	C₂×C₁₃	C₂×#576	1	2	yes	—
319	C₂⁴	—	2	4	no	—
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	8	16	no	—
323	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
324	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	2	16	no	—
329	C₂×D₄	—	2	8	no	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	8	8	no	—
333	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
334	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	16	no	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
339	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
340	Q₁₆	—	2	2	no	—
341	SD₁₆	—	2	4	no	—
342	SD₁₆	—	4	8	no	—
343	D₈	—	2	8	no	—
344	D₈	—	2	8	no	—
345	D₈	—	2	2	no	—
346	D₈	—	4	8	no	—
347	D₈	—	4	8	no	—
348	M₁₆	—	2	4	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	C₁₃×#41	1	4	yes	complemented
351	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
352	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
353	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
354	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
357	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
358	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
359	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	16	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	16	no	—
364	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	4	no	—
367	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₄²	C₂⁴×C₁₃	1	2	yes	—
370	C₄²	C₂⁴×C₁₃	1	4	yes	—
371	C₁₃	#61409	1	1	yes	characteristic, direct product factor, Sylow
372	C₂³	—	2	8	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	4	8	no	—
375	C₂³	—	8	8	no	—
376	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
377	Q₈	—	2	8	no	—
378	Q₈	—	2	2	no	—
379	Q₈	—	2	2	no	—
380	D₄	—	2	8	no	—
381	D₄	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	8	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	8	no	—
386	D₄	—	4	16	no	—
387	D₄	—	8	8	no	—
388	D₄	—	8	16	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	8	no	—
394	C₂×C₄	—	8	16	no	—
395	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
396	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
397	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
399	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
400	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
401	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	2	4	no	—
404	C₈	C₂×C₁₃×#41	1	2	yes	—
405	C₈	C₂×C₁₃×#41	1	2	yes	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	16	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	8	no	—
411	C₂²	—	16	8	no	—
412	C₂²	C₁₃×#550	1	2	yes	—
413	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
414	C₄	—	2	2	no	—
415	C₄	—	2	8	no	—
416	C₄	—	4	4	no	—
417	C₄	—	4	2	no	—
418	C₄	C₁₃×#550	1	2	yes	—
419	C₄	C₁₃×#576	1	4	yes	—
420	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
421	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	8	8	no	—
424	C₂	—	8	2	no	—
425	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
426	C₂	C₂×C₁₃×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3508	C₂	semidirect
2. C₁₃×#3399	C₂	semidirect
3. C₁₃×#3396	C₂	semidirect
4. C₁₃×#3391	C₂	semidirect
5. C₁₃×#3155	C₂	semidirect
6. C₂×C₁₃×#493	C₂	semidirect
7. C₁₃×#3041	C₂	semidirect
8. C₁₃×#3038	C₂	semidirect
9. C₁₃×#2960	C₂	semidirect
10. C₁₃×#2948	C₂	semidirect
11. C₄×C₁₃×#135	C₂	semidirect
16. C₁₃×#559	C₂²	semidirect
17. C₁₃×#550	C₂²	semidirect
26. C₁₃×#496	C₂²	semidirect
27. C₁₃×#495	C₂²	semidirect
30. C₁₃×#493	C₂²	semidirect
31. C₁₃×#463	C₂²	semidirect
32. C₁₃×#460	C₂²	semidirect
33. C₁₃×#459	C₂²	semidirect
34. C₁₃×#459	C₂²	semidirect
35. C₁₃×#446	C₂²	semidirect
36. C₈×Q₈×C₁₃	C₂²	semidirect
37. C₁₃×#442	C₂²	semidirect
38. C₄×C₁₃×Q₁₆	C₂²	semidirect
39. C₄×C₁₃×SD₁₆	C₂²	semidirect
40. C₄×C₁₃×D₈	C₂²	semidirect
41. C₄×C₁₃×D₈	C₂²	semidirect
106. #61409	C₁₃	direct (N × H)
138. C₂×C₈×C₁₃	#41	semidirect
159. #3508	C₂×C₁₃	semidirect
160. #3399	C₂×C₁₃	semidirect
161. #3396	C₂×C₁₃	semidirect
162. #3391	C₂×C₁₃	semidirect
163. #3155	C₂×C₁₃	semidirect
164. C₂×#493	C₂×C₁₃	semidirect
165. #3041	C₂×C₁₃	semidirect
166. #3038	C₂×C₁₃	semidirect
167. #2960	C₂×C₁₃	semidirect
168. #2948	C₂×C₁₃	semidirect
169. C₄×#135	C₂×C₁₃	semidirect
208. #559	C₂²×C₁₃	semidirect
209. #550	C₂²×C₁₃	semidirect
218. #496	C₂²×C₁₃	semidirect
219. #495	C₂²×C₁₃	semidirect
222. #493	C₂²×C₁₃	semidirect
223. #463	C₂²×C₁₃	semidirect
224. #460	C₂²×C₁₃	semidirect
225. #459	C₂²×C₁₃	semidirect
226. #459	C₂²×C₁₃	semidirect
227. #446	C₂²×C₁₃	semidirect
228. C₈×Q₈	C₂²×C₁₃	semidirect
229. #442	C₂²×C₁₃	semidirect
230. C₄×Q₁₆	C₂²×C₁₃	semidirect
231. C₄×SD₁₆	C₂²×C₁₃	semidirect
232. C₄×D₈	C₂²×C₁₃	semidirect
233. C₄×D₈	C₂²×C₁₃	semidirect
350. C₂×C₈	C₁₃×#41	semidirect
371. C₁₃	#61409	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3508	2
C₁₃×#3399	2
C₁₃×#3396	2
C₁₃×#3391	2
C₁₃×#3155	2
C₂×C₁₃×#493	2
C₁₃×#3041	2
C₁₃×#3038	2
C₁₃×#2960	2
C₁₃×#2948	2
C₄×C₁₃×#135	2
#61409	13

Subgroups — C13×#61409 #15747748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61409 #15747748