Subgroups — C₁₃×#60622 #15746961

Order 3328.

2178 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3141	C₂	1	3	yes	maximal, complemented
4	C₁₃×#3138	C₂	1	3	yes	maximal, complemented
5	C₁₃×#3136	C₂	1	12	yes	maximal, complemented
6	C₁₃×#3131	C₂	1	3	yes	maximal, complemented
7	C₂×C₁₃×#486	C₂	1	3	yes	maximal, complemented
8	C₁₃×#2897	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
11	C₂×C₁₃×#131	C₂²	1	2	yes	—
12	Q₈²×C₁₃	—	2	1	no	—
13	C₁₃×#557	—	2	1	no	—
14	C₁₃×#554	—	2	3	no	—
15	C₁₃×#550	—	2	1	no	—
16	C₁₃×#550	—	2	1	no	—
17	D₄×Q₈×C₁₃	—	2	3	no	—
18	D₄²×C₁₃	—	2	3	no	—
19	D₄²×C₁₃	—	2	3	no	—
20	C₁₃×#544	C₂²	1	6	yes	complemented
21	C₁₃×#535	C₂²	1	6	yes	—
22	C₁₃×#533	C₂²	1	3	yes	complemented
23	C₁₃×#532	C₂²	1	3	yes	—
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
25	C₂×C₁₃×#127	C₂²	1	3	yes	—
26	C₁₃×#520	C₂²	1	2	yes	—
27	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
28	C₁₃×#490	C₂²	1	12	yes	complemented
29	C₁₃×#489	C₂²	1	12	yes	complemented
30	C₁₃×#488	C₂²	1	12	yes	complemented
31	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#487	C₂²	1	3	yes	complemented
33	C₁₃×#486	C₂²	1	3	yes	complemented
34	C₁₃×#486	C₂²	1	12	yes	complemented
35	C₁₃×#486	C₂²	1	6	yes	complemented
36	C₁₃×#486	C₂²	1	3	yes	complemented
37	C₁₃×#418	C₂²	1	12	yes	complemented
38	C₁₃×#417	C₂²	1	12	yes	complemented
39	C₁₃×#416	C₂²	1	12	yes	complemented
40	C₂×C₁₃×#102	C₂²	1	12	yes	complemented
41	C₁₃×#405	C₂²	1	6	yes	complemented
42	C₄×C₁₃×M₁₆	C₂²	1	3	yes	complemented
43	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	complemented
44	C₁₃×H(5,𝔽₂)	—	2	16	no	—
45	C₂×C₁₃×#41	—	2	2	no	—
46	C₂×C₁₃×#41	C₂³	1	6	yes	—
47	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	—	2	3	no	—
49	C₂²×D₄×C₁₃	—	2	6	no	—
50	C₂²×D₄×C₁₃	—	2	3	no	—
51	C₂²×D₄×C₁₃	—	2	3	no	—
52	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
53	C₁₃×#131	—	2	8	no	—
54	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
56	C₁₃×C₄⋊Q₈	—	2	6	no	—
57	C₁₃×C₄⋊Q₈	—	2	3	no	—
58	C₁₃×C₄⋊Q₈	—	2	3	no	—
59	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
61	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
63	C₁₃×#127	—	2	3	no	—
64	C₁₃×#127	—	2	3	no	—
65	C₁₃×#127	C₂³	1	3	yes	—
66	C₁₃×#127	C₂³	1	6	yes	—
67	C₁₃×#125	—	2	6	no	—
68	C₁₃×#125	C₂³	1	6	yes	—
69	C₁₃×#124	C₂³	1	6	yes	—
70	C₁₃×C₂²⋊Q₈	—	2	3	no	—
71	C₁₃×C₂²⋊Q₈	—	2	3	no	—
72	C₁₃×C₂²⋊Q₈	—	2	12	no	—
73	C₁₃×#121	—	2	3	no	—
74	C₁₃×#121	—	2	3	no	—
75	C₁₃×#121	—	2	6	no	—
76	C₁₃×#121	—	2	6	no	—
77	C₁₃×#120	—	2	12	no	—
78	C₄×Q₈×C₁₃	—	2	2	no	—
79	C₄×Q₈×C₁₃	—	2	3	no	—
80	C₄×Q₈×C₁₃	—	2	3	no	—
81	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
82	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
83	C₄×D₄×C₁₃	—	2	6	no	—
84	C₄×D₄×C₁₃	—	2	3	no	—
85	C₄×D₄×C₁₃	—	2	3	no	—
86	C₄×D₄×C₁₃	D₄	1	3	yes	—
87	C₄×D₄×C₁₃	D₄	1	3	yes	—
88	C₁₃×#117	C₂³	1	6	yes	—
89	C₁₃×#117	C₂³	1	3	yes	—
90	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
93	C₁₃×#103	C₂³	1	4	yes	—
94	C₁₃×#103	C₂³	1	12	yes	—
95	C₁₃×#102	C₂³	1	12	yes	—
96	C₁₃×#102	C₂³	1	24	yes	—
97	C₁₃×#102	C₂³	1	12	yes	—
98	C₁₃×#97	C₂³	1	6	yes	—
99	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₃	C₂³	1	3	yes	—
101	C₄×C₈×C₁₃	C₂³	1	6	yes	—
102	#60622	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	—	2	6	no	—
104	C₁₃×#41	—	2	24	no	—
105	C₁₃×#41	—	4	8	no	—
106	C₁₃×#41	#41	1	8	yes	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	—	2	3	no	—
109	C₂×Q₈×C₁₃	—	2	6	no	—
110	C₂×Q₈×C₁₃	—	8	6	no	—
111	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
113	C₂×D₄×C₁₃	—	2	6	no	—
114	C₂×D₄×C₁₃	—	2	3	no	—
115	C₂×D₄×C₁₃	—	2	3	no	—
116	C₂×D₄×C₁₃	—	2	6	no	—
117	C₂×D₄×C₁₃	—	2	6	no	—
118	C₂×D₄×C₁₃	—	2	6	no	—
119	C₂×D₄×C₁₃	—	2	24	no	—
120	C₂×D₄×C₁₃	—	4	24	no	—
121	C₂×D₄×C₁₃	—	8	6	no	—
122	C₂×D₄×C₁₃	—	8	6	no	—
123	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
124	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
125	C₂²×C₄×C₁₃	—	2	6	no	—
126	C₂²×C₄×C₁₃	—	2	6	no	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
130	C₁₃×M₁₆	—	2	12	no	—
131	C₂×C₈×C₁₃	—	2	12	no	—
132	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
133	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
134	C₁₃×C₄⋊C₄	—	2	3	no	—
135	C₁₃×C₄⋊C₄	—	2	6	no	—
136	C₁₃×C₄⋊C₄	—	2	6	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	6	no	—
141	C₁₃×C₄⋊C₄	—	2	6	no	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
143	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
144	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
145	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
146	C₁₃×C₂²⋊C₄	—	2	6	no	—
147	C₁₃×C₂²⋊C₄	—	2	6	no	—
148	C₁₃×C₂²⋊C₄	—	2	6	no	—
149	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
150	C₄²×C₁₃	—	2	6	no	—
151	C₄²×C₁₃	C₂×D₄	1	3	yes	—
152	C₄²×C₁₃	C₂×D₄	1	3	yes	—
153	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₄²×C₁₃	C₂⁴	1	3	yes	—
155	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#3498	C₂×C₁₃	1	1	yes	characteristic
157	#3141	C₂×C₁₃	1	3	yes	complemented
158	#3138	C₂×C₁₃	1	3	yes	complemented
159	#3136	C₂×C₁₃	1	12	yes	complemented
160	#3131	C₂×C₁₃	1	3	yes	complemented
161	C₂×#486	C₂×C₁₃	1	3	yes	complemented
162	#2897	C₂×C₁₃	1	4	yes	complemented
163	C₄×#131	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	—	2	6	no	—
165	C₂³×C₁₃	—	4	12	no	—
166	C₂³×C₁₃	—	8	6	no	—
167	C₂³×C₁₃	—	8	6	no	—
168	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
169	Q₈×C₁₃	—	2	4	no	—
170	Q₈×C₁₃	—	4	6	no	—
171	Q₈×C₁₃	—	4	2	no	—
172	Q₈×C₁₃	—	8	6	no	—
173	Q₈×C₁₃	#124	1	4	yes	—
174	D₄×C₁₃	—	2	12	no	—
175	D₄×C₁₃	—	4	12	no	—
176	D₄×C₁₃	—	4	12	no	—
177	D₄×C₁₃	—	4	6	no	—
178	D₄×C₁₃	—	4	6	no	—
179	D₄×C₁₃	—	8	6	no	—
180	D₄×C₁₃	—	8	6	no	—
181	D₄×C₁₃	#124	1	12	yes	—
182	C₂×C₄×C₁₃	—	2	6	no	—
183	C₂×C₄×C₁₃	—	2	6	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	6	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	4	12	no	—
188	C₂×C₄×C₁₃	—	8	6	no	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
192	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
195	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
196	C₈×C₁₃	—	2	2	no	—
197	C₈×C₁₃	—	2	6	no	—
198	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
199	C₂×#131	C₂²×C₁₃	1	2	yes	—
200	Q₈²	—	2	1	no	—
201	#557	—	2	1	no	—
202	#554	—	2	3	no	—
203	#550	—	2	1	no	—
204	#550	—	2	1	no	—
205	D₄×Q₈	—	2	3	no	—
206	D₄²	—	2	3	no	—
207	D₄²	—	2	3	no	—
208	#544	C₂²×C₁₃	1	6	yes	complemented
209	#535	C₂²×C₁₃	1	6	yes	—
210	#533	C₂²×C₁₃	1	3	yes	complemented
211	#532	C₂²×C₁₃	1	3	yes	—
212	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
213	C₂×#127	C₂²×C₁₃	1	3	yes	—
214	#520	C₂²×C₁₃	1	2	yes	—
215	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
216	#490	C₂²×C₁₃	1	12	yes	complemented
217	#489	C₂²×C₁₃	1	12	yes	complemented
218	#488	C₂²×C₁₃	1	12	yes	complemented
219	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
220	#487	C₂²×C₁₃	1	3	yes	complemented
221	#486	C₂²×C₁₃	1	3	yes	complemented
222	#486	C₂²×C₁₃	1	12	yes	complemented
223	#486	C₂²×C₁₃	1	6	yes	complemented
224	#486	C₂²×C₁₃	1	3	yes	complemented
225	#418	C₂²×C₁₃	1	12	yes	complemented
226	#417	C₂²×C₁₃	1	12	yes	complemented
227	#416	C₂²×C₁₃	1	12	yes	complemented
228	C₂×#102	C₂²×C₁₃	1	12	yes	complemented
229	#405	C₂²×C₁₃	1	6	yes	complemented
230	C₄×M₁₆	C₂²×C₁₃	1	3	yes	complemented
231	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	complemented
232	C₂²×C₁₃	—	2	3	no	—
233	C₂²×C₁₃	—	2	3	no	—
234	C₂²×C₁₃	—	4	6	no	—
235	C₂²×C₁₃	—	4	6	no	—
236	C₂²×C₁₃	—	4	6	no	—
237	C₂²×C₁₃	—	16	12	no	—
238	C₂²×C₁₃	C₂×#124	1	6	yes	—
239	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
240	C₄×C₁₃	—	2	3	no	—
241	C₄×C₁₃	—	2	3	no	—
242	C₄×C₁₃	—	4	2	no	—
243	C₄×C₁₃	—	4	6	no	—
244	C₄×C₁₃	—	4	2	no	—
245	C₄×C₁₃	C₂×#124	1	6	yes	—
246	C₄×C₁₃	#576	1	2	yes	—
247	C₄×C₁₃	#577	1	2	yes	—
248	C₄×C₁₃	C₂²×#41	1	2	yes	—
249	H(5,𝔽₂)	—	2	16	no	—
250	C₂×#41	—	2	2	no	—
251	C₂×#41	C₂³×C₁₃	1	6	yes	—
252	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
253	C₂²×Q₈	—	2	3	no	—
254	C₂²×D₄	—	2	6	no	—
255	C₂²×D₄	—	2	3	no	—
256	C₂²×D₄	—	2	3	no	—
257	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
258	#131	—	2	8	no	—
259	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
260	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
261	C₄⋊Q₈	—	2	6	no	—
262	C₄⋊Q₈	—	2	3	no	—
263	C₄⋊Q₈	—	2	3	no	—
264	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
265	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
266	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
267	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
268	#127	—	2	3	no	—
269	#127	—	2	3	no	—
270	#127	C₂³×C₁₃	1	3	yes	—
271	#127	C₂³×C₁₃	1	6	yes	—
272	#125	—	2	6	no	—
273	#125	C₂³×C₁₃	1	6	yes	—
274	#124	C₂³×C₁₃	1	6	yes	—
275	C₂²⋊Q₈	—	2	3	no	—
276	C₂²⋊Q₈	—	2	3	no	—
277	C₂²⋊Q₈	—	2	12	no	—
278	#121	—	2	3	no	—
279	#121	—	2	3	no	—
280	#121	—	2	6	no	—
281	#121	—	2	6	no	—
282	#120	—	2	12	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	—	2	3	no	—
285	C₄×Q₈	—	2	3	no	—
286	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
287	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
288	C₄×D₄	—	2	6	no	—
289	C₄×D₄	—	2	3	no	—
290	C₄×D₄	—	2	3	no	—
291	C₄×D₄	D₄×C₁₃	1	3	yes	—
292	C₄×D₄	D₄×C₁₃	1	3	yes	—
293	#117	C₂³×C₁₃	1	6	yes	—
294	#117	C₂³×C₁₃	1	3	yes	—
295	C₂×C₄⋊C₄	—	2	3	no	—
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
297	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
298	#103	C₂³×C₁₃	1	4	yes	—
299	#103	C₂³×C₁₃	1	12	yes	—
300	#102	C₂³×C₁₃	1	12	yes	—
301	#102	C₂³×C₁₃	1	24	yes	—
302	#102	C₂³×C₁₃	1	12	yes	—
303	#97	C₂³×C₁₃	1	6	yes	—
304	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₄×C₈	C₂³×C₁₃	1	3	yes	—
306	C₄×C₈	C₂³×C₁₃	1	6	yes	—
307	C₂×C₁₃	—	2	6	no	—
308	C₂×C₁₃	—	8	6	no	—
309	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
310	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
311	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
312	C₂⁴	—	2	6	no	—
313	#41	—	2	24	no	—
314	#41	—	4	8	no	—
315	#41	C₁₃×#41	1	8	yes	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	3	no	—
318	C₂×Q₈	—	2	6	no	—
319	C₂×Q₈	—	8	6	no	—
320	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
322	C₂×D₄	—	2	6	no	—
323	C₂×D₄	—	2	3	no	—
324	C₂×D₄	—	2	3	no	—
325	C₂×D₄	—	2	6	no	—
326	C₂×D₄	—	2	6	no	—
327	C₂×D₄	—	2	6	no	—
328	C₂×D₄	—	2	24	no	—
329	C₂×D₄	—	4	24	no	—
330	C₂×D₄	—	8	6	no	—
331	C₂×D₄	—	8	6	no	—
332	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
333	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
334	C₂²×C₄	—	2	6	no	—
335	C₂²×C₄	—	2	6	no	—
336	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
337	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
338	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
339	M₁₆	—	2	12	no	—
340	C₂×C₈	—	2	12	no	—
341	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
342	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
343	C₄⋊C₄	—	2	3	no	—
344	C₄⋊C₄	—	2	6	no	—
345	C₄⋊C₄	—	2	6	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	6	no	—
350	C₄⋊C₄	—	2	6	no	—
351	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
352	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
353	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
354	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
355	C₂²⋊C₄	—	2	6	no	—
356	C₂²⋊C₄	—	2	6	no	—
357	C₂²⋊C₄	—	2	6	no	—
358	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
359	C₄²	—	2	6	no	—
360	C₄²	C₂×D₄×C₁₃	1	3	yes	—
361	C₄²	C₂×D₄×C₁₃	1	3	yes	—
362	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
363	C₄²	C₂⁴×C₁₃	1	3	yes	—
364	C₁₃	#60622	1	1	yes	characteristic, direct product factor, Sylow
365	C₂³	—	2	6	no	—
366	C₂³	—	4	12	no	—
367	C₂³	—	8	6	no	—
368	C₂³	—	8	6	no	—
369	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
370	Q₈	—	2	4	no	—
371	Q₈	—	4	6	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	8	6	no	—
374	Q₈	C₁₃×#124	1	4	yes	—
375	D₄	—	2	12	no	—
376	D₄	—	4	12	no	—
377	D₄	—	4	12	no	—
378	D₄	—	4	6	no	—
379	D₄	—	4	6	no	—
380	D₄	—	8	6	no	—
381	D₄	—	8	6	no	—
382	D₄	C₁₃×#124	1	12	yes	—
383	C₂×C₄	—	2	6	no	—
384	C₂×C₄	—	2	6	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	6	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	12	no	—
389	C₂×C₄	—	8	6	no	—
390	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
391	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
392	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
393	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
396	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	2	6	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	2	3	no	—
401	C₂²	—	4	6	no	—
402	C₂²	—	4	6	no	—
403	C₂²	—	4	6	no	—
404	C₂²	—	16	12	no	—
405	C₂²	C₂×C₁₃×#124	1	6	yes	—
406	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
407	C₄	—	2	3	no	—
408	C₄	—	2	3	no	—
409	C₄	—	4	6	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	C₂×C₁₃×#124	1	6	yes	—
413	C₄	C₁₃×#576	1	2	yes	—
414	C₄	C₁₃×#577	1	2	yes	—
415	C₄	C₂²×C₁₃×#41	1	2	yes	—
416	C₂	—	2	6	no	—
417	C₂	—	8	6	no	—
418	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
419	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
420	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3498	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3141	C₂	semidirect
4. C₁₃×#3138	C₂	semidirect
5. C₁₃×#3136	C₂	semidirect
6. C₁₃×#3131	C₂	semidirect
7. C₂×C₁₃×#486	C₂	semidirect
8. C₁₃×#2897	C₂	semidirect
9. C₄×C₁₃×#131	C₂	semidirect
20. C₁₃×#544	C₂²	semidirect
22. C₁₃×#533	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
28. C₁₃×#490	C₂²	semidirect
29. C₁₃×#489	C₂²	semidirect
30. C₁₃×#488	C₂²	semidirect
31. C₁₃×#487	C₂²	semidirect
32. C₁₃×#487	C₂²	semidirect
33. C₁₃×#486	C₂²	semidirect
34. C₁₃×#486	C₂²	semidirect
35. C₁₃×#486	C₂²	semidirect
36. C₁₃×#486	C₂²	semidirect
37. C₁₃×#418	C₂²	semidirect
38. C₁₃×#417	C₂²	semidirect
39. C₁₃×#416	C₂²	semidirect
40. C₂×C₁₃×#102	C₂²	semidirect
41. C₁₃×#405	C₂²	semidirect
42. C₄×C₁₃×M₁₆	C₂²	semidirect
43. C₂×C₄×C₈×C₁₃	C₂²	semidirect
102. #60622	C₁₃	direct (N × H)
155. #3503	C₂×C₁₃	semidirect
157. #3141	C₂×C₁₃	semidirect
158. #3138	C₂×C₁₃	semidirect
159. #3136	C₂×C₁₃	semidirect
160. #3131	C₂×C₁₃	semidirect
161. C₂×#486	C₂×C₁₃	semidirect
162. #2897	C₂×C₁₃	semidirect
163. C₄×#131	C₂×C₁₃	semidirect
208. #544	C₂²×C₁₃	semidirect
210. #533	C₂²×C₁₃	semidirect
212. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
216. #490	C₂²×C₁₃	semidirect
217. #489	C₂²×C₁₃	semidirect
218. #488	C₂²×C₁₃	semidirect
219. #487	C₂²×C₁₃	semidirect
220. #487	C₂²×C₁₃	semidirect
221. #486	C₂²×C₁₃	semidirect
222. #486	C₂²×C₁₃	semidirect
223. #486	C₂²×C₁₃	semidirect
224. #486	C₂²×C₁₃	semidirect
225. #418	C₂²×C₁₃	semidirect
226. #417	C₂²×C₁₃	semidirect
227. #416	C₂²×C₁₃	semidirect
228. C₂×#102	C₂²×C₁₃	semidirect
229. #405	C₂²×C₁₃	semidirect
230. C₄×M₁₆	C₂²×C₁₃	semidirect
231. C₂×C₄×C₈	C₂²×C₁₃	semidirect
364. C₁₃	#60622	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×#3503	2
C₁₃×#3498	2
C₁₃×#3141	2
C₁₃×#3138	2
C₁₃×#3136	2
C₁₃×#3131	2
C₂×C₁₃×#486	2
C₁₃×#2897	2
C₄×C₁₃×#131	2
#60622	13

Subgroups — C13×#60622 #15746961

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60622 #15746961