Subgroups — C₁₃×#61290 #15747629

Order 3328.

1774 conjugacy classes of subgroups.

The subgroup lattice has 448 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×#3355	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3352	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3337	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3098	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3080	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3060	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×#2912	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×#484	C₂²	1	8	yes	—
29	C₁₃×#482	C₂²	1	8	yes	—
30	C₁₃×#480	C₂²	1	8	yes	—
31	C₁₃×#479	C₂²	1	8	yes	—
32	C₁₃×#478	C₂²	1	8	yes	—
33	C₁₃×#470	C₂²	1	4	yes	—
34	C₁₃×#469	C₂²	1	4	yes	—
35	C₁₃×#465	C₂²	1	8	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×#106	C₂²	1	2	yes	—
47	C₂×C₁₃×#106	C₂²	1	4	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	4	yes	—
101	C₁₃×#107	C₂³	1	4	yes	—
102	C₁₃×#107	C₂³	1	2	yes	—
103	C₁₃×#107	C₂³	1	8	yes	—
104	C₁₃×#106	C₂³	1	2	yes	—
105	C₁₃×#106	C₂³	1	4	yes	—
106	C₁₃×#106	C₂³	1	4	yes	—
107	C₁₃×#106	C₂³	1	8	yes	—
108	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
109	C₁₃×#103	C₂³	1	4	yes	—
110	C₁₃×#103	C₂³	1	8	yes	—
111	C₁₃×#102	C₂³	1	4	yes	—
112	C₁₃×#102	C₂³	1	8	yes	—
113	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
114	C₄×C₈×C₁₃	C₂³	1	2	yes	—
115	C₄×C₈×C₁₃	C₂³	1	2	yes	—
116	#61290	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	8	yes	—
163	C₄²×C₁₃	—	2	4	no	—
164	C₄²×C₁₃	—	2	2	no	—
165	C₄²×C₁₃	—	2	8	no	—
166	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂⁴	1	2	yes	—
169	#3512	C₂×C₁₃	1	2	yes	complemented
170	#3355	C₂×C₁₃	1	4	yes	complemented
171	#3352	C₂×C₁₃	1	4	yes	complemented
172	#3337	C₂×C₁₃	1	8	yes	complemented
173	C₂×#499	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#3098	C₂×C₁₃	1	4	yes	complemented
175	#3080	C₂×C₁₃	1	2	yes	complemented
176	#3060	C₂×C₁₃	1	2	yes	complemented
177	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#2912	C₂×C₁₃	1	2	yes	complemented
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
182	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₁₃	—	2	4	no	—
184	Q₈×C₁₃	—	2	2	no	—
185	Q₈×C₁₃	—	2	2	no	—
186	D₄×C₁₃	—	2	8	no	—
187	D₄×C₁₃	—	2	4	no	—
188	D₄×C₁₃	—	2	2	no	—
189	D₄×C₁₃	—	2	2	no	—
190	D₄×C₁₃	—	4	4	no	—
191	D₄×C₁₃	—	4	4	no	—
192	D₄×C₁₃	—	8	8	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	8	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	4	no	—
200	C₂×C₄×C₁₃	—	8	4	no	—
201	C₂×C₄×C₁₃	—	8	8	no	—
202	C₂×C₄×C₁₃	—	8	4	no	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
208	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
209	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
210	C₈×C₁₃	—	2	4	no	—
211	C₈×C₁₃	—	2	2	no	—
212	C₈×C₁₃	C₂×#41	1	2	yes	—
213	C₈×C₁₃	C₂×#41	1	2	yes	—
214	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#131	C₂²×C₁₃	1	2	yes	—
216	#553	—	2	8	no	—
217	#553	C₂²×C₁₃	1	8	yes	—
218	#552	C₂²×C₁₃	1	8	yes	—
219	#541	—	2	2	no	—
220	#540	—	2	2	no	—
221	#537	C₂²×C₁₃	1	4	yes	—
222	#532	C₂²×C₁₃	1	1	yes	characteristic
223	#529	—	2	4	no	—
224	C₂×#125	C₂²×C₁₃	1	2	yes	—
225	#520	C₂²×C₁₃	1	4	yes	—
226	C₄×#41	C₂²×C₁₃	1	2	yes	—
227	#499	C₂²×C₁₃	1	4	yes	—
228	#499	C₂²×C₁₃	1	4	yes	—
229	#485	C₂²×C₁₃	1	8	yes	—
230	#484	C₂²×C₁₃	1	8	yes	—
231	#482	C₂²×C₁₃	1	8	yes	—
232	#480	C₂²×C₁₃	1	8	yes	—
233	#479	C₂²×C₁₃	1	8	yes	—
234	#478	C₂²×C₁₃	1	8	yes	—
235	#470	C₂²×C₁₃	1	4	yes	—
236	#469	C₂²×C₁₃	1	4	yes	—
237	#465	C₂²×C₁₃	1	8	yes	—
238	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
239	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
240	C₄×D₈	C₂²×C₁₃	1	2	yes	—
241	#436	C₂²×C₁₃	1	4	yes	—
242	C₈×D₄	C₂²×C₁₃	1	4	yes	—
243	#428	C₂²×C₁₃	1	4	yes	—
244	#428	C₂²×C₁₃	1	8	yes	—
245	#427	C₂²×C₁₃	1	4	yes	—
246	#427	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×#107	C₂²×C₁₃	1	2	yes	—
248	C₂×#106	C₂²×C₁₃	1	4	yes	—
249	C₂×#106	C₂²×C₁₃	1	2	yes	—
250	#423	C₂²×C₁₃	1	1	yes	characteristic
251	#417	C₂²×C₁₃	1	4	yes	—
252	#416	C₂²×C₁₃	1	2	yes	—
253	#408	C₂²×C₁₃	1	2	yes	—
254	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂²×C₁₃	—	2	2	no	—
256	C₂²×C₁₃	—	2	8	no	—
257	C₂²×C₁₃	—	2	4	no	—
258	C₂²×C₁₃	—	4	4	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	#547	1	2	yes	—
261	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
262	C₄×C₁₃	—	2	2	no	—
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	4	no	—
265	C₄×C₁₃	—	4	4	no	—
266	C₄×C₁₃	—	4	8	no	—
267	C₄×C₁₃	—	4	2	no	—
268	C₄×C₁₃	#547	1	2	yes	—
269	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
270	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
271	C₂×#41	C₂³×C₁₃	1	2	yes	—
272	C₂×#41	C₂³×C₁₃	1	2	yes	—
273	#135	—	2	4	no	—
274	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
276	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
277	#131	—	2	8	no	—
278	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
279	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
280	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
281	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
284	#127	D₄×C₁₃	1	1	yes	characteristic
285	#126	—	2	8	no	—
286	#126	—	2	8	no	—
287	#125	—	2	8	no	—
288	#125	—	2	2	no	—
289	#125	—	2	2	no	—
290	#125	C₂³×C₁₃	1	8	yes	—
291	#124	D₄×C₁₃	1	2	yes	—
292	#123	—	2	8	no	—
293	#123	—	2	8	no	—
294	C₂²⋊Q₈	—	2	4	no	—
295	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
296	#121	—	2	4	no	—
297	#121	—	2	8	no	—
298	#121	—	2	8	no	—
299	#121	D₄×C₁₃	1	4	yes	—
300	#121	C₂³×C₁₃	1	8	yes	—
301	C₄×Q₈	—	2	4	no	—
302	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	—	2	8	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	8	no	—
307	C₄×D₄	C₂³×C₁₃	1	4	yes	—
308	C₄×D₄	C₂³×C₁₃	1	4	yes	—
309	#117	—	2	8	no	—
310	#117	—	2	2	no	—
311	#117	C₂³×C₁₃	1	2	yes	—
312	#117	C₂³×C₁₃	1	8	yes	—
313	C₂×C₄⋊C₄	—	2	4	no	—
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
318	#107	C₂³×C₁₃	1	4	yes	—
319	#107	C₂³×C₁₃	1	4	yes	—
320	#107	C₂³×C₁₃	1	2	yes	—
321	#107	C₂³×C₁₃	1	8	yes	—
322	#106	C₂³×C₁₃	1	2	yes	—
323	#106	C₂³×C₁₃	1	4	yes	—
324	#106	C₂³×C₁₃	1	4	yes	—
325	#106	C₂³×C₁₃	1	8	yes	—
326	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
327	#103	C₂³×C₁₃	1	4	yes	—
328	#103	C₂³×C₁₃	1	8	yes	—
329	#102	C₂³×C₁₃	1	4	yes	—
330	#102	C₂³×C₁₃	1	8	yes	—
331	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
332	C₄×C₈	C₂³×C₁₃	1	2	yes	—
333	C₄×C₈	C₂³×C₁₃	1	2	yes	—
334	C₂×C₁₃	—	2	2	no	—
335	C₂×C₁₃	—	4	4	no	—
336	C₂×C₁₃	—	8	2	no	—
337	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
338	C₂×C₁₃	#3584	1	2	yes	—
339	#41	—	2	4	no	—
340	#41	—	2	4	no	—
341	#41	—	2	4	no	—
342	#41	—	2	4	no	—
343	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
344	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
348	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
349	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
350	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
358	Q₁₆	—	2	2	no	—
359	SD₁₆	—	2	4	no	—
360	D₈	—	2	2	no	—
361	M₁₆	—	2	4	no	—
362	M₁₆	—	2	8	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	8	no	—
365	C₂×C₈	C₁₃×#41	1	4	yes	—
366	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
367	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
368	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
369	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
377	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
378	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	8	no	—
388	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₄²	C₂⁴×C₁₃	1	2	yes	—
391	C₁₃	#61290	1	1	yes	characteristic, direct product factor, Sylow
392	C₂³	—	2	2	no	—
393	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
394	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	2	2	no	—
398	D₄	—	2	8	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	4	4	no	—
403	D₄	—	4	4	no	—
404	D₄	—	8	8	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	8	4	no	—
413	C₂×C₄	—	8	8	no	—
414	C₂×C₄	—	8	4	no	—
415	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
416	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
420	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
421	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
422	C₈	—	2	4	no	—
423	C₈	—	2	2	no	—
424	C₈	C₂×C₁₃×#41	1	2	yes	—
425	C₈	C₂×C₁₃×#41	1	2	yes	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	8	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	2	no	—
431	C₂²	C₁₃×#547	1	2	yes	—
432	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	8	no	—
438	C₄	—	4	2	no	—
439	C₄	C₁₃×#547	1	2	yes	—
440	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
441	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
442	C₂	—	2	2	no	—
443	C₂	—	4	4	no	—
444	C₂	—	8	2	no	—
445	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
446	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×#3355	C₂	semidirect
3. C₁₃×#3352	C₂	semidirect
4. C₁₃×#3337	C₂	semidirect
5. C₂×C₁₃×#499	C₂	semidirect
6. C₁₃×#3098	C₂	semidirect
7. C₁₃×#3080	C₂	semidirect
8. C₁₃×#3060	C₂	semidirect
9. C₄×C₁₃×#135	C₂	semidirect
10. C₁₃×#2931	C₂	semidirect
11. C₁₃×#2912	C₂	semidirect
116. #61290	C₁₃	direct (N × H)
169. #3512	C₂×C₁₃	semidirect
170. #3355	C₂×C₁₃	semidirect
171. #3352	C₂×C₁₃	semidirect
172. #3337	C₂×C₁₃	semidirect
173. C₂×#499	C₂×C₁₃	semidirect
174. #3098	C₂×C₁₃	semidirect
175. #3080	C₂×C₁₃	semidirect
176. #3060	C₂×C₁₃	semidirect
177. C₄×#135	C₂×C₁₃	semidirect
178. #2931	C₂×C₁₃	semidirect
179. #2912	C₂×C₁₃	semidirect
391. C₁₃	#61290	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×#3355	2
C₁₃×#3352	2
C₁₃×#3337	2
C₂×C₁₃×#499	2
C₁₃×#3098	2
C₁₃×#3080	2
C₁₃×#3060	2
C₄×C₁₃×#135	2
C₁₃×#2931	2
C₁₃×#2912	2
#61290	13

Subgroups — C13×#61290 #15747629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61290 #15747629