Subgroups — C₁₃×#61289 #15747628

Order 3328.

1774 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3512	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3351	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3339	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3336	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3099	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3080	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3061	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2913	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	2	yes	—
14	C₁₃×#553	—	2	8	no	—
15	C₁₃×#553	C₂²	1	8	yes	—
16	C₁₃×#552	C₂²	1	8	yes	—
17	C₁₃×#541	—	2	2	no	—
18	C₁₃×#540	—	2	2	no	—
19	C₁₃×#537	C₂²	1	4	yes	—
20	C₁₃×#532	C₂²	1	1	yes	characteristic
21	C₁₃×#529	—	2	4	no	—
22	C₂×C₁₃×#125	C₂²	1	2	yes	—
23	C₁₃×#520	C₂²	1	4	yes	—
24	C₄×C₁₃×#41	C₂²	1	2	yes	—
25	C₁₃×#499	C₂²	1	4	yes	—
26	C₁₃×#499	C₂²	1	4	yes	—
27	C₁₃×#485	C₂²	1	8	yes	—
28	C₁₃×#483	C₂²	1	8	yes	—
29	C₁₃×#482	C₂²	1	8	yes	—
30	C₁₃×#481	C₂²	1	8	yes	—
31	C₁₃×#479	C₂²	1	8	yes	—
32	C₁₃×#478	C₂²	1	8	yes	—
33	C₁₃×#468	C₂²	1	8	yes	—
34	C₁₃×#467	C₂²	1	4	yes	—
35	C₁₃×#466	C₂²	1	4	yes	—
36	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
37	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
38	C₄×C₁₃×D₈	C₂²	1	2	yes	—
39	C₁₃×#436	C₂²	1	4	yes	—
40	C₈×D₄×C₁₃	C₂²	1	4	yes	—
41	C₁₃×#428	C₂²	1	4	yes	—
42	C₁₃×#428	C₂²	1	8	yes	—
43	C₁₃×#427	C₂²	1	4	yes	—
44	C₁₃×#427	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#107	C₂²	1	2	yes	—
46	C₂×C₁₃×#107	C₂²	1	4	yes	—
47	C₂×C₁₃×#106	C₂²	1	2	yes	—
48	C₁₃×#423	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	4	yes	—
50	C₁₃×#416	C₂²	1	2	yes	—
51	C₁₃×#408	C₂²	1	2	yes	—
52	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#41	C₂³	1	2	yes	—
54	C₂×C₁₃×#41	C₂³	1	2	yes	—
55	C₁₃×#135	—	2	4	no	—
56	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
58	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
59	C₁₃×#131	—	2	8	no	—
60	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
61	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₃×#127	D₄	1	1	yes	characteristic
67	C₁₃×#126	—	2	8	no	—
68	C₁₃×#126	—	2	8	no	—
69	C₁₃×#125	—	2	8	no	—
70	C₁₃×#125	—	2	2	no	—
71	C₁₃×#125	—	2	2	no	—
72	C₁₃×#125	C₂³	1	8	yes	—
73	C₁₃×#124	D₄	1	2	yes	—
74	C₁₃×#123	—	2	8	no	—
75	C₁₃×#123	—	2	8	no	—
76	C₁₃×C₂²⋊Q₈	—	2	4	no	—
77	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
78	C₁₃×#121	—	2	4	no	—
79	C₁₃×#121	—	2	8	no	—
80	C₁₃×#121	—	2	8	no	—
81	C₁₃×#121	D₄	1	4	yes	—
82	C₁₃×#121	C₂³	1	8	yes	—
83	C₄×Q₈×C₁₃	—	2	4	no	—
84	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
85	C₄×D₄×C₁₃	—	2	4	no	—
86	C₄×D₄×C₁₃	—	2	8	no	—
87	C₄×D₄×C₁₃	—	2	4	no	—
88	C₄×D₄×C₁₃	—	2	8	no	—
89	C₄×D₄×C₁₃	C₂³	1	4	yes	—
90	C₄×D₄×C₁₃	C₂³	1	4	yes	—
91	C₁₃×#117	—	2	8	no	—
92	C₁₃×#117	—	2	2	no	—
93	C₁₃×#117	C₂³	1	2	yes	—
94	C₁₃×#117	C₂³	1	8	yes	—
95	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
98	C₂×C₄²×C₁₃	—	2	2	no	—
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#107	C₂³	1	2	yes	—
101	C₁₃×#107	C₂³	1	4	yes	—
102	C₁₃×#107	C₂³	1	4	yes	—
103	C₁₃×#107	C₂³	1	8	yes	—
104	C₁₃×#106	C₂³	1	8	yes	—
105	C₁₃×#106	C₂³	1	2	yes	—
106	C₁₃×#106	C₂³	1	8	yes	—
107	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
108	C₁₃×#103	C₂³	1	4	yes	—
109	C₁₃×#103	C₂³	1	8	yes	—
110	C₁₃×#102	C₂³	1	4	yes	—
111	C₁₃×#102	C₂³	1	8	yes	—
112	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
113	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
114	C₄×C₈×C₁₃	C₂³	1	2	yes	—
115	C₄×C₈×C₁₃	C₂³	1	2	yes	—
116	#61289	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₁₃×#41	—	2	4	no	—
118	C₁₃×#41	—	2	4	no	—
119	C₁₃×#41	—	2	4	no	—
120	C₁₃×#41	—	2	4	no	—
121	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
122	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	8	no	—
125	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
126	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
128	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	8	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₁₃×Q₁₆	—	2	2	no	—
137	C₁₃×SD₁₆	—	2	4	no	—
138	C₁₃×D₈	—	2	2	no	—
139	C₁₃×M₁₆	—	2	4	no	—
140	C₁₃×M₁₆	—	2	8	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	8	no	—
143	C₂×C₈×C₁₃	#41	1	4	yes	—
144	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
145	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
146	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	—	2	8	no	—
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	8	no	—
154	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
155	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
156	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₁₃×C₂²⋊C₄	—	2	2	no	—
159	C₁₃×C₂²⋊C₄	—	2	8	no	—
160	C₁₃×C₂²⋊C₄	—	2	4	no	—
161	C₁₃×C₂²⋊C₄	—	2	8	no	—
162	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
163	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
164	C₄²×C₁₃	—	2	4	no	—
165	C₄²×C₁₃	—	2	2	no	—
166	C₄²×C₁₃	—	2	8	no	—
167	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂⁴	1	2	yes	—
170	#3512	C₂×C₁₃	1	2	yes	complemented
171	#3351	C₂×C₁₃	1	8	yes	complemented
172	#3339	C₂×C₁₃	1	4	yes	complemented
173	#3336	C₂×C₁₃	1	4	yes	complemented
174	C₂×#499	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#3099	C₂×C₁₃	1	4	yes	complemented
176	#3080	C₂×C₁₃	1	2	yes	complemented
177	#3061	C₂×C₁₃	1	2	yes	complemented
178	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#2913	C₂×C₁₃	1	2	yes	complemented
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
183	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₁₃	—	2	4	no	—
185	Q₈×C₁₃	—	2	2	no	—
186	Q₈×C₁₃	—	2	2	no	—
187	D₄×C₁₃	—	2	8	no	—
188	D₄×C₁₃	—	2	4	no	—
189	D₄×C₁₃	—	2	2	no	—
190	D₄×C₁₃	—	2	2	no	—
191	D₄×C₁₃	—	4	4	no	—
192	D₄×C₁₃	—	4	4	no	—
193	D₄×C₁₃	—	8	8	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	8	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	4	no	—
201	C₂×C₄×C₁₃	—	8	4	no	—
202	C₂×C₄×C₁₃	—	8	8	no	—
203	C₂×C₄×C₁₃	—	8	4	no	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
209	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
210	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
211	C₈×C₁₃	—	2	4	no	—
212	C₈×C₁₃	—	2	2	no	—
213	C₈×C₁₃	C₂×#41	1	2	yes	—
214	C₈×C₁₃	C₂×#41	1	2	yes	—
215	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#131	C₂²×C₁₃	1	2	yes	—
217	#553	—	2	8	no	—
218	#553	C₂²×C₁₃	1	8	yes	—
219	#552	C₂²×C₁₃	1	8	yes	—
220	#541	—	2	2	no	—
221	#540	—	2	2	no	—
222	#537	C₂²×C₁₃	1	4	yes	—
223	#532	C₂²×C₁₃	1	1	yes	characteristic
224	#529	—	2	4	no	—
225	C₂×#125	C₂²×C₁₃	1	2	yes	—
226	#520	C₂²×C₁₃	1	4	yes	—
227	C₄×#41	C₂²×C₁₃	1	2	yes	—
228	#499	C₂²×C₁₃	1	4	yes	—
229	#499	C₂²×C₁₃	1	4	yes	—
230	#485	C₂²×C₁₃	1	8	yes	—
231	#483	C₂²×C₁₃	1	8	yes	—
232	#482	C₂²×C₁₃	1	8	yes	—
233	#481	C₂²×C₁₃	1	8	yes	—
234	#479	C₂²×C₁₃	1	8	yes	—
235	#478	C₂²×C₁₃	1	8	yes	—
236	#468	C₂²×C₁₃	1	8	yes	—
237	#467	C₂²×C₁₃	1	4	yes	—
238	#466	C₂²×C₁₃	1	4	yes	—
239	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
240	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
241	C₄×D₈	C₂²×C₁₃	1	2	yes	—
242	#436	C₂²×C₁₃	1	4	yes	—
243	C₈×D₄	C₂²×C₁₃	1	4	yes	—
244	#428	C₂²×C₁₃	1	4	yes	—
245	#428	C₂²×C₁₃	1	8	yes	—
246	#427	C₂²×C₁₃	1	4	yes	—
247	#427	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×#107	C₂²×C₁₃	1	4	yes	—
249	C₂×#107	C₂²×C₁₃	1	2	yes	—
250	C₂×#106	C₂²×C₁₃	1	2	yes	—
251	#423	C₂²×C₁₃	1	1	yes	characteristic
252	#417	C₂²×C₁₃	1	4	yes	—
253	#416	C₂²×C₁₃	1	2	yes	—
254	#408	C₂²×C₁₃	1	2	yes	—
255	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
256	C₂²×C₁₃	—	2	2	no	—
257	C₂²×C₁₃	—	2	4	no	—
258	C₂²×C₁₃	—	2	4	no	—
259	C₂²×C₁₃	—	2	4	no	—
260	C₂²×C₁₃	—	4	4	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	#547	1	2	yes	—
263	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	2	2	no	—
266	C₄×C₁₃	—	2	4	no	—
267	C₄×C₁₃	—	4	4	no	—
268	C₄×C₁₃	—	4	8	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	#547	1	2	yes	—
271	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
272	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
273	C₂×#41	C₂³×C₁₃	1	2	yes	—
274	C₂×#41	C₂³×C₁₃	1	2	yes	—
275	#135	—	2	4	no	—
276	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
278	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
279	#131	—	2	8	no	—
280	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
281	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
282	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
283	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
286	#127	D₄×C₁₃	1	1	yes	characteristic
287	#126	—	2	8	no	—
288	#126	—	2	8	no	—
289	#125	—	2	8	no	—
290	#125	—	2	2	no	—
291	#125	—	2	2	no	—
292	#125	C₂³×C₁₃	1	8	yes	—
293	#124	D₄×C₁₃	1	2	yes	—
294	#123	—	2	8	no	—
295	#123	—	2	8	no	—
296	C₂²⋊Q₈	—	2	4	no	—
297	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
298	#121	—	2	4	no	—
299	#121	—	2	8	no	—
300	#121	—	2	8	no	—
301	#121	D₄×C₁₃	1	4	yes	—
302	#121	C₂³×C₁₃	1	8	yes	—
303	C₄×Q₈	—	2	4	no	—
304	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	8	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	2	8	no	—
309	C₄×D₄	C₂³×C₁₃	1	4	yes	—
310	C₄×D₄	C₂³×C₁₃	1	4	yes	—
311	#117	—	2	8	no	—
312	#117	—	2	2	no	—
313	#117	C₂³×C₁₃	1	2	yes	—
314	#117	C₂³×C₁₃	1	8	yes	—
315	C₂×C₄⋊C₄	—	2	4	no	—
316	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
320	#107	C₂³×C₁₃	1	2	yes	—
321	#107	C₂³×C₁₃	1	4	yes	—
322	#107	C₂³×C₁₃	1	4	yes	—
323	#107	C₂³×C₁₃	1	8	yes	—
324	#106	C₂³×C₁₃	1	8	yes	—
325	#106	C₂³×C₁₃	1	2	yes	—
326	#106	C₂³×C₁₃	1	8	yes	—
327	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
328	#103	C₂³×C₁₃	1	4	yes	—
329	#103	C₂³×C₁₃	1	8	yes	—
330	#102	C₂³×C₁₃	1	4	yes	—
331	#102	C₂³×C₁₃	1	8	yes	—
332	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
333	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
334	C₄×C₈	C₂³×C₁₃	1	2	yes	—
335	C₄×C₈	C₂³×C₁₃	1	2	yes	—
336	C₂×C₁₃	—	2	2	no	—
337	C₂×C₁₃	—	4	4	no	—
338	C₂×C₁₃	—	8	2	no	—
339	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
340	C₂×C₁₃	#3584	1	2	yes	—
341	#41	—	2	4	no	—
342	#41	—	2	4	no	—
343	#41	—	2	4	no	—
344	#41	—	2	4	no	—
345	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
346	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
350	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
351	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
352	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
359	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
360	Q₁₆	—	2	2	no	—
361	SD₁₆	—	2	4	no	—
362	D₈	—	2	2	no	—
363	M₁₆	—	2	4	no	—
364	M₁₆	—	2	8	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	8	no	—
367	C₂×C₈	C₁₃×#41	1	4	yes	—
368	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
369	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
370	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
371	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
379	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
380	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
387	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
388	C₄²	—	2	4	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	8	no	—
391	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₄²	C₂⁴×C₁₃	1	2	yes	—
394	C₁₃	#61289	1	1	yes	characteristic, direct product factor, Sylow
395	C₂³	—	2	2	no	—
396	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
397	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
398	Q₈	—	2	4	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	2	2	no	—
401	D₄	—	2	8	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	4	4	no	—
406	D₄	—	4	4	no	—
407	D₄	—	8	8	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	8	4	no	—
416	C₂×C₄	—	8	8	no	—
417	C₂×C₄	—	8	4	no	—
418	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
419	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
420	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
421	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
423	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
424	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
425	C₈	—	2	4	no	—
426	C₈	—	2	2	no	—
427	C₈	C₂×C₁₃×#41	1	2	yes	—
428	C₈	C₂×C₁₃×#41	1	2	yes	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	2	no	—
435	C₂²	C₁₃×#547	1	2	yes	—
436	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	4	no	—
440	C₄	—	4	4	no	—
441	C₄	—	4	8	no	—
442	C₄	—	4	2	no	—
443	C₄	C₁₃×#547	1	2	yes	—
444	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
445	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
446	C₂	—	2	2	no	—
447	C₂	—	4	4	no	—
448	C₂	—	8	2	no	—
449	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
450	C₂	C₁₃×#3584	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3512	C₂	semidirect
2. C₁₃×#3351	C₂	semidirect
3. C₁₃×#3339	C₂	semidirect
4. C₁₃×#3336	C₂	semidirect
5. C₂×C₁₃×#499	C₂	semidirect
6. C₁₃×#3099	C₂	semidirect
7. C₁₃×#3080	C₂	semidirect
8. C₁₃×#3061	C₂	semidirect
9. C₄×C₁₃×#135	C₂	semidirect
10. C₁₃×#2931	C₂	semidirect
11. C₁₃×#2913	C₂	semidirect
116. #61289	C₁₃	direct (N × H)
170. #3512	C₂×C₁₃	semidirect
171. #3351	C₂×C₁₃	semidirect
172. #3339	C₂×C₁₃	semidirect
173. #3336	C₂×C₁₃	semidirect
174. C₂×#499	C₂×C₁₃	semidirect
175. #3099	C₂×C₁₃	semidirect
176. #3080	C₂×C₁₃	semidirect
177. #3061	C₂×C₁₃	semidirect
178. C₄×#135	C₂×C₁₃	semidirect
179. #2931	C₂×C₁₃	semidirect
180. #2913	C₂×C₁₃	semidirect
394. C₁₃	#61289	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×#3512	2
C₁₃×#3351	2
C₁₃×#3339	2
C₁₃×#3336	2
C₂×C₁₃×#499	2
C₁₃×#3099	2
C₁₃×#3080	2
C₁₃×#3061	2
C₄×C₁₃×#135	2
C₁₃×#2931	2
C₁₃×#2913	2
#61289	13

Subgroups — C13×#61289 #15747628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61289 #15747628