Subgroups — C₁₃×#60624 #15746963

Order 3328.

2038 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3142	C₂	1	3	yes	maximal, complemented
4	C₁₃×#3140	C₂	1	3	yes	maximal, complemented
5	C₁₃×#3137	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3136	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3131	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₃×#488	C₂	1	3	yes	maximal, complemented
9	C₁₃×#2898	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2897	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	2	yes	—
15	C₁₃×#557	—	2	2	no	—
16	C₁₃×#554	—	2	6	no	—
17	C₁₃×#548	—	2	2	no	—
18	C₁₃×#546	—	2	6	no	—
19	C₁₃×#544	C₂²	1	6	yes	complemented
20	C₁₃×#536	C₂²	1	3	yes	—
21	C₁₃×#535	C₂²	1	3	yes	—
22	C₁₃×#533	C₂²	1	3	yes	complemented
23	C₁₃×#532	C₂²	1	3	yes	—
24	C₂×C₁₃×#125	C₂²	1	3	yes	complemented
25	C₂×C₁₃×#124	C₂²	1	3	yes	—
26	C₁₃×#520	C₂²	1	2	yes	—
27	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
28	C₁₃×#491	C₂²	1	6	yes	complemented
29	C₁₃×#490	C₂²	1	6	yes	complemented
30	C₁₃×#489	C₂²	1	12	yes	complemented
31	C₁₃×#488	C₂²	1	3	yes	complemented
32	C₁₃×#488	C₂²	1	12	yes	complemented
33	C₁₃×#488	C₂²	1	6	yes	complemented
34	C₁₃×#488	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#488	C₂²	1	3	yes	complemented
36	C₁₃×#488	C₂²	1	3	yes	complemented
37	C₁₃×#487	C₂²	1	6	yes	complemented
38	C₁₃×#486	C₂²	1	6	yes	complemented
39	C₁₃×#419	C₂²	1	6	yes	complemented
40	C₁₃×#418	C₂²	1	6	yes	—
41	C₁₃×#417	C₂²	1	6	yes	—
42	C₁₃×#417	C₂²	1	6	yes	complemented
43	C₁₃×#416	C₂²	1	6	yes	—
44	C₁₃×#416	C₂²	1	6	yes	complemented
45	C₂×C₁₃×#103	C₂²	1	6	yes	complemented
46	C₂×C₁₃×#102	C₂²	1	6	yes	—
47	C₁₃×#405	C₂²	1	6	yes	complemented
48	C₄×C₁₃×M₁₆	C₂²	1	3	yes	complemented
49	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	complemented
50	C₁₃×2₋¹⁺⁴	—	2	8	no	—
51	C₁₃×H(5,𝔽₂)	—	2	8	no	—
52	C₂×C₁₃×#41	—	2	1	no	—
53	C₂×C₁₃×#41	—	2	3	no	—
54	C₂×C₁₃×#41	C₂³	1	3	yes	—
55	C₂×C₁₃×#41	C₂³	1	3	yes	—
56	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	—	2	1	no	—
58	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
59	C₂²×D₄×C₁₃	—	2	3	no	—
60	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
61	C₁₃×#131	—	2	8	no	—
62	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
63	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
64	C₁₃×C₄⋊Q₈	—	2	6	no	—
65	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
67	C₁₃×#127	C₂³	1	3	yes	—
68	C₁₃×#125	—	2	6	no	—
69	C₁₃×#125	—	2	6	no	—
70	C₁₃×#125	C₂³	1	3	yes	—
71	C₁₃×#125	C₂³	1	1	yes	characteristic
72	C₁₃×#125	C₂³	1	6	yes	—
73	C₁₃×#124	—	2	6	no	—
74	C₁₃×#124	C₂³	1	3	yes	—
75	C₁₃×#124	C₂³	1	1	yes	characteristic
76	C₁₃×#124	C₂³	1	6	yes	—
77	C₁₃×#123	—	2	6	no	—
78	C₁₃×C₂²⋊Q₈	—	2	6	no	—
79	C₁₃×C₂²⋊Q₈	—	2	6	no	—
80	C₁₃×C₂²⋊Q₈	—	2	12	no	—
81	C₁₃×#121	—	2	6	no	—
82	C₁₃×#121	—	2	6	no	—
83	C₁₃×#120	—	2	6	no	—
84	C₄×Q₈×C₁₃	—	2	2	no	—
85	C₄×Q₈×C₁₃	—	2	6	no	—
86	C₄×Q₈×C₁₃	D₄	1	2	yes	—
87	C₄×D₄×C₁₃	—	2	6	no	—
88	C₄×D₄×C₁₃	—	2	6	no	—
89	C₄×D₄×C₁₃	D₄	1	6	yes	—
90	C₁₃×#117	C₂³	1	6	yes	—
91	C₁₃×#117	C₂³	1	3	yes	—
92	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
95	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
96	C₁₃×#103	C₂³	1	6	yes	—
97	C₁₃×#103	C₂³	1	12	yes	—
98	C₁₃×#103	C₂³	1	2	yes	—
99	C₁₃×#103	C₂³	1	6	yes	—
100	C₁₃×#103	C₂³	1	6	yes	—
101	C₁₃×#102	C₂³	1	6	yes	—
102	C₁₃×#102	C₂³	1	12	yes	—
103	C₁₃×#102	C₂³	1	6	yes	—
104	C₁₃×#102	C₂³	1	2	yes	—
105	C₁₃×#102	C₂³	1	6	yes	—
106	C₁₃×#97	C₂³	1	6	yes	—
107	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₁₃	C₂³	1	3	yes	—
109	C₄×C₈×C₁₃	C₂³	1	6	yes	—
110	#60624	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂⁴×C₁₃	—	2	3	no	—
112	C₁₃×#41	—	2	12	no	—
113	C₁₃×#41	—	2	12	no	—
114	C₁₃×#41	—	4	4	no	—
115	C₁₃×#41	—	4	12	no	—
116	C₁₃×#41	#41	1	8	yes	—
117	C₂×Q₈×C₁₃	—	2	3	no	—
118	C₂×Q₈×C₁₃	—	2	6	no	—
119	C₂×Q₈×C₁₃	—	2	12	no	—
120	C₂×Q₈×C₁₃	—	4	4	no	—
121	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
123	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₂×D₄×C₁₃	—	2	3	no	—
125	C₂×D₄×C₁₃	—	2	3	no	—
126	C₂×D₄×C₁₃	—	2	3	no	—
127	C₂×D₄×C₁₃	—	2	6	no	—
128	C₂×D₄×C₁₃	—	2	12	no	—
129	C₂×D₄×C₁₃	—	4	12	no	—
130	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
131	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
132	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	—	2	3	no	—
134	C₂²×C₄×C₁₃	—	2	6	no	—
135	C₂²×C₄×C₁₃	—	2	3	no	—
136	C₂²×C₄×C₁₃	—	2	3	no	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
139	C₁₃×M₁₆	—	2	12	no	—
140	C₂×C₈×C₁₃	—	2	12	no	—
141	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
142	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
143	C₁₃×C₄⋊C₄	—	2	6	no	—
144	C₁₃×C₄⋊C₄	—	2	12	no	—
145	C₁₃×C₄⋊C₄	—	2	6	no	—
146	C₁₃×C₄⋊C₄	—	2	6	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	6	no	—
149	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
150	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
151	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
152	C₁₃×C₂²⋊C₄	—	2	6	no	—
153	C₁₃×C₂²⋊C₄	—	2	6	no	—
154	C₁₃×C₂²⋊C₄	—	2	12	no	—
155	C₁₃×C₂²⋊C₄	—	2	2	no	—
156	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
157	C₄²×C₁₃	—	2	6	no	—
158	C₄²×C₁₃	C₂×D₄	1	6	yes	—
159	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₄²×C₁₃	C₂⁴	1	3	yes	—
161	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#3500	C₂×C₁₃	1	1	yes	characteristic
163	#3142	C₂×C₁₃	1	3	yes	complemented
164	#3140	C₂×C₁₃	1	3	yes	complemented
165	#3137	C₂×C₁₃	1	6	yes	complemented
166	#3136	C₂×C₁₃	1	6	yes	complemented
167	#3131	C₂×C₁₃	1	3	yes	complemented
168	C₂×#488	C₂×C₁₃	1	3	yes	complemented
169	#2898	C₂×C₁₃	1	2	yes	complemented
170	#2897	C₂×C₁₃	1	2	yes	complemented
171	C₄×#131	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂³×C₁₃	—	2	3	no	—
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	—	4	6	no	—
175	C₂³×C₁₃	—	8	6	no	—
176	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
177	Q₈×C₁₃	—	2	6	no	—
178	Q₈×C₁₃	—	2	2	no	—
179	Q₈×C₁₃	—	4	6	no	—
180	Q₈×C₁₃	—	8	6	no	—
181	Q₈×C₁₃	#124	1	4	yes	—
182	D₄×C₁₃	—	2	6	no	—
183	D₄×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	4	6	no	—
185	D₄×C₁₃	—	4	6	no	—
186	D₄×C₁₃	—	4	6	no	—
187	D₄×C₁₃	—	8	6	no	—
188	D₄×C₁₃	#124	1	12	yes	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	6	no	—
191	C₂×C₄×C₁₃	—	2	3	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	4	6	no	—
194	C₂×C₄×C₁₃	—	4	6	no	—
195	C₂×C₄×C₁₃	—	4	6	no	—
196	C₂×C₄×C₁₃	—	4	6	no	—
197	C₂×C₄×C₁₃	—	8	6	no	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
201	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
202	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
203	C₈×C₁₃	—	2	2	no	—
204	C₈×C₁₃	—	2	6	no	—
205	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×#131	C₂²×C₁₃	1	2	yes	—
208	#557	—	2	2	no	—
209	#554	—	2	6	no	—
210	#548	—	2	2	no	—
211	#546	—	2	6	no	—
212	#544	C₂²×C₁₃	1	6	yes	complemented
213	#536	C₂²×C₁₃	1	3	yes	—
214	#535	C₂²×C₁₃	1	3	yes	—
215	#533	C₂²×C₁₃	1	3	yes	complemented
216	#532	C₂²×C₁₃	1	3	yes	—
217	C₂×#125	C₂²×C₁₃	1	3	yes	complemented
218	C₂×#124	C₂²×C₁₃	1	3	yes	—
219	#520	C₂²×C₁₃	1	2	yes	—
220	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
221	#491	C₂²×C₁₃	1	6	yes	complemented
222	#490	C₂²×C₁₃	1	6	yes	complemented
223	#489	C₂²×C₁₃	1	12	yes	complemented
224	#488	C₂²×C₁₃	1	3	yes	complemented
225	#488	C₂²×C₁₃	1	12	yes	complemented
226	#488	C₂²×C₁₃	1	6	yes	complemented
227	#488	C₂²×C₁₃	1	1	yes	characteristic, complemented
228	#488	C₂²×C₁₃	1	3	yes	complemented
229	#488	C₂²×C₁₃	1	3	yes	complemented
230	#487	C₂²×C₁₃	1	6	yes	complemented
231	#486	C₂²×C₁₃	1	6	yes	complemented
232	#419	C₂²×C₁₃	1	6	yes	complemented
233	#418	C₂²×C₁₃	1	6	yes	—
234	#417	C₂²×C₁₃	1	6	yes	—
235	#417	C₂²×C₁₃	1	6	yes	complemented
236	#416	C₂²×C₁₃	1	6	yes	—
237	#416	C₂²×C₁₃	1	6	yes	complemented
238	C₂×#103	C₂²×C₁₃	1	6	yes	complemented
239	C₂×#102	C₂²×C₁₃	1	6	yes	—
240	#405	C₂²×C₁₃	1	6	yes	complemented
241	C₄×M₁₆	C₂²×C₁₃	1	3	yes	complemented
242	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	complemented
243	C₂²×C₁₃	—	2	6	no	—
244	C₂²×C₁₃	—	4	2	no	—
245	C₂²×C₁₃	—	4	6	no	—
246	C₂²×C₁₃	—	4	1	no	—
247	C₂²×C₁₃	—	4	3	no	—
248	C₂²×C₁₃	—	16	6	no	—
249	C₂²×C₁₃	C₂×#124	1	6	yes	—
250	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	2	6	no	—
253	C₄×C₁₃	—	4	6	no	—
254	C₄×C₁₃	—	4	2	no	—
255	C₄×C₁₃	—	4	1	no	—
256	C₄×C₁₃	—	4	3	no	—
257	C₄×C₁₃	C₂×#124	1	6	yes	—
258	C₄×C₁₃	C₂²×#41	1	2	yes	—
259	2₋¹⁺⁴	—	2	8	no	—
260	H(5,𝔽₂)	—	2	8	no	—
261	C₂×#41	—	2	1	no	—
262	C₂×#41	—	2	3	no	—
263	C₂×#41	C₂³×C₁₃	1	3	yes	—
264	C₂×#41	C₂³×C₁₃	1	3	yes	—
265	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
266	C₂²×Q₈	—	2	1	no	—
267	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
268	C₂²×D₄	—	2	3	no	—
269	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
270	#131	—	2	8	no	—
271	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
272	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
273	C₄⋊Q₈	—	2	6	no	—
274	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
275	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
276	#127	C₂³×C₁₃	1	3	yes	—
277	#125	—	2	6	no	—
278	#125	—	2	6	no	—
279	#125	C₂³×C₁₃	1	3	yes	—
280	#125	C₂³×C₁₃	1	6	yes	—
281	#125	C₂³×C₁₃	1	1	yes	characteristic
282	#124	—	2	6	no	—
283	#124	C₂³×C₁₃	1	3	yes	—
284	#124	C₂³×C₁₃	1	6	yes	—
285	#124	C₂³×C₁₃	1	1	yes	characteristic
286	#123	—	2	6	no	—
287	C₂²⋊Q₈	—	2	6	no	—
288	C₂²⋊Q₈	—	2	6	no	—
289	C₂²⋊Q₈	—	2	12	no	—
290	#121	—	2	6	no	—
291	#121	—	2	6	no	—
292	#120	—	2	6	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	6	no	—
295	C₄×Q₈	D₄×C₁₃	1	2	yes	—
296	C₄×D₄	—	2	6	no	—
297	C₄×D₄	—	2	6	no	—
298	C₄×D₄	D₄×C₁₃	1	6	yes	—
299	#117	C₂³×C₁₃	1	6	yes	—
300	#117	C₂³×C₁₃	1	3	yes	—
301	C₂×C₄⋊C₄	—	2	6	no	—
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
303	C₂×C₂²⋊C₄	—	2	6	no	—
304	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
305	#103	C₂³×C₁₃	1	6	yes	—
306	#103	C₂³×C₁₃	1	12	yes	—
307	#103	C₂³×C₁₃	1	2	yes	—
308	#103	C₂³×C₁₃	1	6	yes	—
309	#103	C₂³×C₁₃	1	6	yes	—
310	#102	C₂³×C₁₃	1	6	yes	—
311	#102	C₂³×C₁₃	1	12	yes	—
312	#102	C₂³×C₁₃	1	6	yes	—
313	#102	C₂³×C₁₃	1	2	yes	—
314	#102	C₂³×C₁₃	1	6	yes	—
315	#97	C₂³×C₁₃	1	6	yes	—
316	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
317	C₄×C₈	C₂³×C₁₃	1	3	yes	—
318	C₄×C₈	C₂³×C₁₃	1	6	yes	—
319	C₂×C₁₃	—	2	6	no	—
320	C₂×C₁₃	—	8	1	no	—
321	C₂×C₁₃	—	8	3	no	—
322	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
323	C₂×C₁₃	#3584	1	2	yes	—
324	C₂⁴	—	2	3	no	—
325	#41	—	2	12	no	—
326	#41	—	2	12	no	—
327	#41	—	4	4	no	—
328	#41	—	4	12	no	—
329	#41	C₁₃×#41	1	8	yes	—
330	C₂×Q₈	—	2	3	no	—
331	C₂×Q₈	—	2	6	no	—
332	C₂×Q₈	—	2	12	no	—
333	C₂×Q₈	—	4	4	no	—
334	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
336	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
337	C₂×D₄	—	2	3	no	—
338	C₂×D₄	—	2	3	no	—
339	C₂×D₄	—	2	3	no	—
340	C₂×D₄	—	2	6	no	—
341	C₂×D₄	—	2	12	no	—
342	C₂×D₄	—	4	12	no	—
343	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
344	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
345	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
346	C₂²×C₄	—	2	3	no	—
347	C₂²×C₄	—	2	6	no	—
348	C₂²×C₄	—	2	3	no	—
349	C₂²×C₄	—	2	3	no	—
350	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
351	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
352	M₁₆	—	2	12	no	—
353	C₂×C₈	—	2	12	no	—
354	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
355	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
356	C₄⋊C₄	—	2	6	no	—
357	C₄⋊C₄	—	2	12	no	—
358	C₄⋊C₄	—	2	6	no	—
359	C₄⋊C₄	—	2	6	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	6	no	—
362	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
363	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
364	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
365	C₂²⋊C₄	—	2	6	no	—
366	C₂²⋊C₄	—	2	6	no	—
367	C₂²⋊C₄	—	2	12	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
370	C₄²	—	2	6	no	—
371	C₄²	C₂×D₄×C₁₃	1	6	yes	—
372	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
373	C₄²	C₂⁴×C₁₃	1	3	yes	—
374	C₁₃	#60624	1	1	yes	characteristic, direct product factor, Sylow
375	C₂³	—	2	3	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	4	6	no	—
378	C₂³	—	8	6	no	—
379	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
380	Q₈	—	2	6	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	6	no	—
383	Q₈	—	8	6	no	—
384	Q₈	C₁₃×#124	1	4	yes	—
385	D₄	—	2	6	no	—
386	D₄	—	2	2	no	—
387	D₄	—	4	6	no	—
388	D₄	—	4	6	no	—
389	D₄	—	4	6	no	—
390	D₄	—	8	6	no	—
391	D₄	C₁₃×#124	1	12	yes	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	6	no	—
394	C₂×C₄	—	2	3	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	4	6	no	—
397	C₂×C₄	—	4	6	no	—
398	C₂×C₄	—	4	6	no	—
399	C₂×C₄	—	4	6	no	—
400	C₂×C₄	—	8	6	no	—
401	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
403	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
404	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
405	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	6	no	—
408	C₂²	—	2	6	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	6	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	3	no	—
413	C₂²	—	16	6	no	—
414	C₂²	C₂×C₁₃×#124	1	6	yes	—
415	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	6	no	—
418	C₄	—	4	6	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	3	no	—
422	C₄	C₂×C₁₃×#124	1	6	yes	—
423	C₄	C₂²×C₁₃×#41	1	2	yes	—
424	C₂	—	2	6	no	—
425	C₂	—	8	3	no	—
426	C₂	—	8	1	no	—
427	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
428	C₂	C₁₃×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3500	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×#3504	C₂	semidirect
3. C₁₃×#3142	C₂	semidirect
4. C₁₃×#3140	C₂	semidirect
5. C₁₃×#3137	C₂	semidirect
6. C₁₃×#3136	C₂	semidirect
7. C₁₃×#3131	C₂	semidirect
8. C₂×C₁₃×#488	C₂	semidirect
9. C₁₃×#2898	C₂	semidirect
10. C₁₃×#2897	C₂	semidirect
11. C₄×C₁₃×#131	C₂	semidirect
19. C₁₃×#544	C₂²	semidirect
22. C₁₃×#533	C₂²	semidirect
24. C₂×C₁₃×#125	C₂²	semidirect
28. C₁₃×#491	C₂²	semidirect
29. C₁₃×#490	C₂²	semidirect
30. C₁₃×#489	C₂²	semidirect
31. C₁₃×#488	C₂²	semidirect
32. C₁₃×#488	C₂²	semidirect
33. C₁₃×#488	C₂²	semidirect
34. C₁₃×#488	C₂²	semidirect
35. C₁₃×#488	C₂²	semidirect
36. C₁₃×#488	C₂²	semidirect
37. C₁₃×#487	C₂²	semidirect
38. C₁₃×#486	C₂²	semidirect
39. C₁₃×#419	C₂²	semidirect
42. C₁₃×#417	C₂²	semidirect
44. C₁₃×#416	C₂²	semidirect
45. C₂×C₁₃×#103	C₂²	semidirect
47. C₁₃×#405	C₂²	semidirect
48. C₄×C₁₃×M₁₆	C₂²	semidirect
49. C₂×C₄×C₈×C₁₃	C₂²	semidirect
110. #60624	C₁₃	direct (N × H)
161. #3504	C₂×C₁₃	semidirect
163. #3142	C₂×C₁₃	semidirect
164. #3140	C₂×C₁₃	semidirect
165. #3137	C₂×C₁₃	semidirect
166. #3136	C₂×C₁₃	semidirect
167. #3131	C₂×C₁₃	semidirect
168. C₂×#488	C₂×C₁₃	semidirect
169. #2898	C₂×C₁₃	semidirect
170. #2897	C₂×C₁₃	semidirect
171. C₄×#131	C₂×C₁₃	semidirect
212. #544	C₂²×C₁₃	semidirect
215. #533	C₂²×C₁₃	semidirect
217. C₂×#125	C₂²×C₁₃	semidirect
221. #491	C₂²×C₁₃	semidirect
222. #490	C₂²×C₁₃	semidirect
223. #489	C₂²×C₁₃	semidirect
224. #488	C₂²×C₁₃	semidirect
225. #488	C₂²×C₁₃	semidirect
226. #488	C₂²×C₁₃	semidirect
227. #488	C₂²×C₁₃	semidirect
228. #488	C₂²×C₁₃	semidirect
229. #488	C₂²×C₁₃	semidirect
230. #487	C₂²×C₁₃	semidirect
231. #486	C₂²×C₁₃	semidirect
232. #419	C₂²×C₁₃	semidirect
235. #417	C₂²×C₁₃	semidirect
237. #416	C₂²×C₁₃	semidirect
238. C₂×#103	C₂²×C₁₃	semidirect
240. #405	C₂²×C₁₃	semidirect
241. C₄×M₁₆	C₂²×C₁₃	semidirect
242. C₂×C₄×C₈	C₂²×C₁₃	semidirect
374. C₁₃	#60624	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×#3504	2
C₁₃×#3500	2
C₁₃×#3142	2
C₁₃×#3140	2
C₁₃×#3137	2
C₁₃×#3136	2
C₁₃×#3131	2
C₂×C₁₃×#488	2
C₁₃×#2898	2
C₁₃×#2897	2
C₄×C₁₃×#131	2
#60624	13

Subgroups — C13×#60624 #15746963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60624 #15746963