Subgroups — C₁₃×#61891 #15748230

Order 3328.

2034 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3399	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3373	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3213	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3205	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3109	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3103	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
11	C₁₃×#559	—	2	4	no	—
12	C₁₃×#559	C₂²	1	8	yes	—
13	C₁₃×#550	C₂²	1	4	yes	complemented
14	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
15	C₁₃×#548	—	2	4	no	—
16	C₁₃×#537	—	2	1	no	—
17	C₁₃×#537	—	2	2	no	—
18	C₁₃×#532	C₂²	1	2	yes	—
19	C₁₃×#532	C₂²	1	4	yes	—
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#124	—	2	1	no	—
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×#123	—	2	2	no	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	—	2	1	no	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#496	C₂²	1	8	yes	complemented
29	C₁₃×#493	C₂²	1	4	yes	—
30	C₁₃×#489	C₂²	1	8	yes	complemented
31	C₁₃×#486	C₂²	1	4	yes	—
32	C₁₃×#481	C₂²	1	4	yes	—
33	C₁₃×#476	C₂²	1	8	yes	complemented
34	C₁₃×#475	C₂²	1	4	yes	complemented
35	C₁₃×#463	C₂²	1	16	yes	complemented
36	C₁₃×#460	C₂²	1	4	yes	complemented
37	C₁₃×#459	C₂²	1	8	yes	—
38	C₁₃×#459	C₂²	1	8	yes	complemented
39	C₁₃×#448	C₂²	1	4	yes	—
40	C₁₃×#447	C₂²	1	8	yes	—
41	C₁₃×#446	C₂²	1	8	yes	complemented
42	C₁₃×#442	C₂²	1	16	yes	complemented
43	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
44	C₁₃×#432	C₂²	1	4	yes	—
45	C₁₃×#431	C₂²	1	2	yes	—
46	C₁₃×2₋¹⁺⁴	—	4	8	no	—
47	C₂×C₁₃×#41	—	2	4	no	—
48	C₂×C₁₃×#41	—	2	4	no	—
49	C₂×C₁₃×#41	—	2	2	no	—
50	C₂²×Q₈×C₁₃	—	2	4	no	—
51	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	—	2	1	no	—
55	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	—	2	2	no	—
57	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
58	C₂×C₁₃×D₈	C₂³	1	16	yes	—
59	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
61	C₁₃×#127	—	2	2	no	—
62	C₁₃×#127	C₂³	1	4	yes	—
63	C₁₃×#127	C₂³	1	4	yes	—
64	C₁₃×#127	C₂³	1	2	yes	—
65	C₁₃×#124	—	2	8	no	—
66	C₁₃×#124	—	2	4	no	—
67	C₁₃×#124	—	2	4	no	—
68	C₁₃×#124	—	2	2	no	—
69	C₁₃×#124	C₂³	1	8	yes	—
70	C₁₃×#123	—	2	16	no	—
71	C₁₃×C₂²⋊Q₈	—	2	4	no	—
72	C₁₃×C₂²⋊Q₈	—	2	8	no	—
73	C₁₃×#121	—	2	4	no	—
74	C₁₃×#121	—	2	2	no	—
75	C₁₃×#121	—	2	4	no	—
76	C₁₃×#121	—	2	8	no	—
77	C₁₃×#121	C₂³	1	4	yes	—
78	C₄×Q₈×C₁₃	—	2	2	no	—
79	C₄×Q₈×C₁₃	D₄	1	4	yes	—
80	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
81	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
82	C₄×D₄×C₁₃	—	2	8	no	—
83	C₄×D₄×C₁₃	—	2	4	no	—
84	C₄×D₄×C₁₃	—	2	4	no	—
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	C₂³	1	4	yes	—
87	C₄×D₄×C₁₃	C₂³	1	8	yes	—
88	C₄×D₄×C₁₃	C₂³	1	8	yes	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₄²×C₁₃	—	2	1	no	—
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
99	C₁₃×#106	C₂³	1	8	yes	—
100	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
101	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
102	C₁₃×#103	C₂³	1	8	yes	—
103	C₁₃×#102	C₂³	1	8	yes	—
104	C₁₃×#102	C₂³	1	16	yes	—
105	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
106	C₁₃×#97	C₂³	1	8	yes	—
107	C₄×C₈×C₁₃	C₂³	1	4	yes	—
108	#61891	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	2	no	—
110	C₁₃×#41	—	4	16	no	—
111	C₁₃×#41	—	4	16	no	—
112	C₁₃×#41	—	4	8	no	—
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	2	4	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	4	2	no	—
118	C₂×Q₈×C₁₃	—	4	16	no	—
119	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
120	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
121	C₂×D₄×C₁₃	—	2	4	no	—
122	C₂×D₄×C₁₃	—	2	2	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	2	no	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	4	4	no	—
130	C₂×D₄×C₁₃	—	4	4	no	—
131	C₂×D₄×C₁₃	—	8	2	no	—
132	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
133	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	8	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	8	4	no	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₁₃×SD₁₆	—	4	8	no	—
146	C₁₃×D₈	—	4	16	no	—
147	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
153	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
154	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
155	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
156	C₁₃×C₂²⋊C₄	—	2	8	no	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₁₃×C₂²⋊C₄	—	2	8	no	—
161	C₁₃×C₂²⋊C₄	—	2	4	no	—
162	C₄²×C₁₃	—	2	4	no	—
163	C₄²×C₁₃	C₂×D₄	1	4	yes	—
164	C₄²×C₁₃	C₂×D₄	1	2	yes	—
165	C₄²×C₁₃	C₂⁴	1	2	yes	—
166	C₄²×C₁₃	C₂⁴	1	4	yes	—
167	#3497	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#3399	C₂×C₁₃	1	8	yes	complemented
170	#3373	C₂×C₁₃	1	8	yes	complemented
171	#3213	C₂×C₁₃	1	4	yes	complemented
172	#3205	C₂×C₁₃	1	2	yes	complemented
173	#3109	C₂×C₁₃	1	4	yes	complemented
174	#3103	C₂×C₁₃	1	2	yes	complemented
175	#2983	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂³×C₁₃	—	2	4	no	—
177	C₂³×C₁₃	—	2	4	no	—
178	C₂³×C₁₃	—	4	4	no	—
179	C₂³×C₁₃	—	4	4	no	—
180	C₂³×C₁₃	—	4	4	no	—
181	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₁₃	—	2	8	no	—
183	Q₈×C₁₃	—	2	4	no	—
184	Q₈×C₁₃	—	4	2	no	—
185	Q₈×C₁₃	—	4	8	no	—
186	Q₈×C₁₃	—	4	4	no	—
187	D₄×C₁₃	—	2	8	no	—
188	D₄×C₁₃	—	2	8	no	—
189	D₄×C₁₃	—	4	4	no	—
190	D₄×C₁₃	—	4	8	no	—
191	D₄×C₁₃	—	4	8	no	—
192	D₄×C₁₃	—	4	8	no	—
193	D₄×C₁₃	—	4	4	no	—
194	D₄×C₁₃	—	8	4	no	—
195	D₄×C₁₃	—	8	2	no	—
196	D₄×C₁₃	—	8	4	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	16	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	8	no	—
208	C₂×C₄×C₁₃	—	8	8	no	—
209	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
213	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
216	C₈×C₁₃	—	2	8	no	—
217	C₂×2₋¹⁺⁴	—	2	1	no	—
218	#559	—	2	4	no	—
219	#559	C₂²×C₁₃	1	8	yes	—
220	#550	C₂²×C₁₃	1	4	yes	complemented
221	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
222	#548	—	2	4	no	—
223	#537	—	2	1	no	—
224	#537	—	2	2	no	—
225	#532	C₂²×C₁₃	1	2	yes	—
226	#532	C₂²×C₁₃	1	4	yes	—
227	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#124	—	2	1	no	—
229	C₂×#124	C₂²×C₁₃	1	2	yes	—
230	C₂×#123	—	2	2	no	—
231	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×C₄×D₄	—	2	1	no	—
234	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
235	#496	C₂²×C₁₃	1	8	yes	complemented
236	#493	C₂²×C₁₃	1	4	yes	—
237	#489	C₂²×C₁₃	1	8	yes	complemented
238	#486	C₂²×C₁₃	1	4	yes	—
239	#481	C₂²×C₁₃	1	4	yes	—
240	#476	C₂²×C₁₃	1	8	yes	complemented
241	#475	C₂²×C₁₃	1	4	yes	complemented
242	#463	C₂²×C₁₃	1	16	yes	complemented
243	#460	C₂²×C₁₃	1	4	yes	complemented
244	#459	C₂²×C₁₃	1	8	yes	—
245	#459	C₂²×C₁₃	1	8	yes	complemented
246	#448	C₂²×C₁₃	1	4	yes	—
247	#447	C₂²×C₁₃	1	8	yes	—
248	#446	C₂²×C₁₃	1	8	yes	complemented
249	#442	C₂²×C₁₃	1	16	yes	complemented
250	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
251	#432	C₂²×C₁₃	1	4	yes	—
252	#431	C₂²×C₁₃	1	2	yes	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	4	4	no	—
257	C₂²×C₁₃	—	4	4	no	—
258	C₂²×C₁₃	—	4	4	no	—
259	C₂²×C₁₃	—	4	4	no	—
260	C₂²×C₁₃	—	4	4	no	—
261	C₂²×C₁₃	—	8	8	no	—
262	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
263	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
264	C₄×C₁₃	—	2	4	no	—
265	C₄×C₁₃	—	2	2	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	2	4	no	—
268	C₄×C₁₃	—	4	2	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	4	4	no	—
271	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
272	C₄×C₁₃	#585	1	2	yes	—
273	2₋¹⁺⁴	—	4	8	no	—
274	C₂×#41	—	2	4	no	—
275	C₂×#41	—	2	4	no	—
276	C₂×#41	—	2	2	no	—
277	C₂²×Q₈	—	2	4	no	—
278	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
279	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
283	C₂³×C₄	—	2	2	no	—
284	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
285	C₂×D₈	C₂³×C₁₃	1	16	yes	—
286	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
287	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
288	#127	—	2	2	no	—
289	#127	C₂³×C₁₃	1	4	yes	—
290	#127	C₂³×C₁₃	1	4	yes	—
291	#127	C₂³×C₁₃	1	2	yes	—
292	#124	—	2	8	no	—
293	#124	—	2	4	no	—
294	#124	—	2	4	no	—
295	#124	—	2	2	no	—
296	#124	C₂³×C₁₃	1	8	yes	—
297	#123	—	2	16	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	—	2	8	no	—
300	#121	—	2	4	no	—
301	#121	—	2	2	no	—
302	#121	—	2	4	no	—
303	#121	—	2	8	no	—
304	#121	C₂³×C₁₃	1	4	yes	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	D₄×C₁₃	1	4	yes	—
307	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
308	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
309	C₄×D₄	—	2	8	no	—
310	C₄×D₄	—	2	4	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	C₂³×C₁₃	1	8	yes	—
314	C₄×D₄	C₂³×C₁₃	1	4	yes	—
315	C₄×D₄	C₂³×C₁₃	1	8	yes	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
325	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
326	#106	C₂³×C₁₃	1	8	yes	—
327	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
328	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
329	#103	C₂³×C₁₃	1	8	yes	—
330	#102	C₂³×C₁₃	1	8	yes	—
331	#102	C₂³×C₁₃	1	16	yes	—
332	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
333	#97	C₂³×C₁₃	1	8	yes	—
334	C₄×C₈	C₂³×C₁₃	1	4	yes	—
335	C₂×C₁₃	—	2	2	no	—
336	C₂×C₁₃	—	8	4	no	—
337	C₂×C₁₃	—	8	4	no	—
338	C₂×C₁₃	#3487	1	1	yes	characteristic
339	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
340	C₂×C₁₃	#3585	1	1	yes	characteristic
341	C₂⁴	—	2	2	no	—
342	#41	—	4	16	no	—
343	#41	—	4	16	no	—
344	#41	—	4	8	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	4	2	no	—
350	C₂×Q₈	—	4	16	no	—
351	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
352	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
365	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	8	4	no	—
372	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
377	SD₁₆	—	4	8	no	—
378	D₈	—	4	16	no	—
379	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
385	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
386	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
387	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₄²	—	2	4	no	—
395	C₄²	C₂×D₄×C₁₃	1	4	yes	—
396	C₄²	C₂×D₄×C₁₃	1	2	yes	—
397	C₄²	C₂⁴×C₁₃	1	2	yes	—
398	C₄²	C₂⁴×C₁₃	1	4	yes	—
399	C₁₃	#61891	1	1	yes	characteristic, direct product factor, Sylow
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	4	4	no	—
403	C₂³	—	4	4	no	—
404	C₂³	—	4	4	no	—
405	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
406	Q₈	—	2	8	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	8	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	4	no	—
411	D₄	—	2	8	no	—
412	D₄	—	2	8	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	8	no	—
415	D₄	—	4	8	no	—
416	D₄	—	4	8	no	—
417	D₄	—	4	4	no	—
418	D₄	—	8	4	no	—
419	D₄	—	8	4	no	—
420	D₄	—	8	2	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	16	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	—	8	8	no	—
433	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
434	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
436	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
437	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
438	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
439	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
440	C₈	—	2	8	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	8	8	no	—
450	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
451	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
452	C₄	—	2	4	no	—
453	C₄	—	2	4	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	1	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
460	C₄	C₁₃×#585	1	2	yes	—
461	C₂	—	2	2	no	—
462	C₂	—	8	4	no	—
463	C₂	—	8	4	no	—
464	C₂	C₁₃×#3487	1	1	yes	characteristic
465	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
466	C₂	C₁₃×#3585	1	1	yes	characteristic

	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3497	C₂	semidirect
2. C₂×C₁₃×#559	C₂	semidirect
3. C₁₃×#3399	C₂	semidirect
4. C₁₃×#3373	C₂	semidirect
5. C₁₃×#3213	C₂	semidirect
6. C₁₃×#3205	C₂	semidirect
7. C₁₃×#3109	C₂	semidirect
8. C₁₃×#3103	C₂	semidirect
9. C₁₃×#2983	C₂	semidirect
13. C₁₃×#550	C₂²	semidirect
14. D₄×Q₈×C₁₃	C₂²	semidirect
28. C₁₃×#496	C₂²	semidirect
30. C₁₃×#489	C₂²	semidirect
33. C₁₃×#476	C₂²	semidirect
34. C₁₃×#475	C₂²	semidirect
35. C₁₃×#463	C₂²	semidirect
36. C₁₃×#460	C₂²	semidirect
38. C₁₃×#459	C₂²	semidirect
41. C₁₃×#446	C₂²	semidirect
42. C₁₃×#442	C₂²	semidirect
43. C₄×C₁₃×SD₁₆	C₂²	semidirect
108. #61891	C₁₃	direct (N × H)
167. #3497	C₂×C₁₃	semidirect
168. C₂×#559	C₂×C₁₃	semidirect
169. #3399	C₂×C₁₃	semidirect
170. #3373	C₂×C₁₃	semidirect
171. #3213	C₂×C₁₃	semidirect
172. #3205	C₂×C₁₃	semidirect
173. #3109	C₂×C₁₃	semidirect
174. #3103	C₂×C₁₃	semidirect
175. #2983	C₂×C₁₃	semidirect
220. #550	C₂²×C₁₃	semidirect
221. D₄×Q₈	C₂²×C₁₃	semidirect
235. #496	C₂²×C₁₃	semidirect
237. #489	C₂²×C₁₃	semidirect
240. #476	C₂²×C₁₃	semidirect
241. #475	C₂²×C₁₃	semidirect
242. #463	C₂²×C₁₃	semidirect
243. #460	C₂²×C₁₃	semidirect
245. #459	C₂²×C₁₃	semidirect
248. #446	C₂²×C₁₃	semidirect
249. #442	C₂²×C₁₃	semidirect
250. C₄×SD₁₆	C₂²×C₁₃	semidirect
399. C₁₃	#61891	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×#3497	2
C₂×C₁₃×#559	2
C₁₃×#3399	2
C₁₃×#3373	2
C₁₃×#3213	2
C₁₃×#3205	2
C₁₃×#3109	2
C₁₃×#3103	2
C₁₃×#2983	2
#61891	13

Subgroups — C13×#61891 #15748230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61891 #15748230