Subgroups — C₁₃×#62589 #15748928

Order 3328.

1702 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×#3518	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3363	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3359	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3329	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3328	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3237	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3218	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3172	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3139	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈²×C₁₃	—	2	1	no	—
13	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#557	C₂²	1	2	yes	—
15	C₁₃×#556	—	2	3	no	—
16	C₁₃×#556	C₂²	1	3	yes	—
17	C₁₃×#555	C₂²	1	3	yes	—
18	C₁₃×#554	—	2	3	no	—
19	D₄×Q₈×C₁₃	C₂²	1	6	yes	—
20	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#548	—	2	1	no	—
22	C₁₃×#544	—	2	3	no	—
23	C₁₃×#542	—	2	3	no	—
24	C₁₃×#533	C₂²	1	3	yes	—
25	C₁₃×#533	C₂²	1	3	yes	—
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
27	C₁₃×#529	C₂²	1	3	yes	—
28	C₁₃×#520	—	2	1	no	—
29	C₁₃×#519	—	2	1	no	—
30	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
31	C₁₃×#501	C₂²	1	3	yes	—
32	C₁₃×#497	C₂²	1	3	yes	—
33	C₁₃×#491	C₂²	1	3	yes	—
34	C₁₃×#491	C₂²	1	6	yes	—
35	C₁₃×#489	C₂²	1	1	yes	characteristic
36	C₁₃×#487	C₂²	1	6	yes	—
37	C₁₃×#487	C₂²	1	6	yes	—
38	C₁₃×#485	C₂²	1	12	yes	—
39	C₁₃×#477	C₂²	1	6	yes	—
40	C₁₃×#475	C₂²	1	6	yes	—
41	C₁₃×#470	C₂²	1	6	yes	—
42	C₁₃×#468	C₂²	1	6	yes	—
43	C₁₃×#462	C₂²	1	6	yes	—
44	C₁₃×#461	C₂²	1	6	yes	—
45	C₁₃×#451	C₂²	1	6	yes	—
46	C₁₃×#448	C₂²	1	6	yes	—
47	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
48	C₄×C₁₃×Q₁₆	C₂²	1	6	yes	—
49	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
50	C₁₃×#436	C₂²	1	6	yes	—
51	C₁₃×#432	C₂²	1	3	yes	—
52	C₁₃×#419	C₂²	1	12	yes	—
53	C₄×C₁₃×M₁₆	C₂²	1	3	yes	—
54	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	—	2	1	no	—
56	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
57	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
58	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
59	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
60	C₁₃×C₄⋊Q₈	—	2	3	no	—
61	C₁₃×C₄⋊Q₈	—	2	6	no	—
62	C₁₃×C₄⋊Q₈	—	2	3	no	—
63	C₁₃×C₄⋊Q₈	—	2	3	no	—
64	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
65	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
67	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₁₃×#126	—	2	6	no	—
70	C₁₃×#126	—	2	3	no	—
71	C₁₃×#125	—	2	6	no	—
72	C₁₃×#125	—	2	3	no	—
73	C₁₃×#125	C₂³	1	3	yes	—
74	C₁₃×#124	—	2	3	no	—
75	C₁₃×#124	—	2	6	no	—
76	C₁₃×#124	C₂³	1	1	yes	characteristic
77	C₁₃×#123	—	2	3	no	—
78	C₁₃×C₂²⋊Q₈	—	2	3	no	—
79	C₁₃×C₂²⋊Q₈	—	2	3	no	—
80	C₁₃×C₂²⋊Q₈	—	2	3	no	—
81	C₁₃×C₂²⋊Q₈	—	2	3	no	—
82	C₁₃×C₂²⋊Q₈	—	2	12	no	—
83	C₁₃×C₂²⋊Q₈	C₂³	1	3	yes	—
84	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
85	C₁₃×#121	—	2	3	no	—
86	C₁₃×#121	C₂³	1	3	yes	—
87	C₄×Q₈×C₁₃	—	2	1	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	—	2	3	no	—
90	C₄×Q₈×C₁₃	—	2	3	no	—
91	C₄×Q₈×C₁₃	—	2	3	no	—
92	C₄×Q₈×C₁₃	—	2	3	no	—
93	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
96	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₁₃	—	2	6	no	—
98	C₄×D₄×C₁₃	—	2	3	no	—
99	C₄×D₄×C₁₃	D₄	1	3	yes	—
100	C₄×D₄×C₁₃	C₂³	1	3	yes	—
101	C₄×D₄×C₁₃	C₂³	1	3	yes	—
102	C₁₃×#117	—	2	3	no	—
103	C₁₃×#117	—	2	3	no	—
104	C₁₃×#117	—	2	3	no	—
105	C₁₃×#117	D₄	1	3	yes	—
106	C₁₃×#117	C₂³	1	6	yes	—
107	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
109	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
110	C₁₃×#107	C₂³	1	6	yes	—
111	C₁₃×#106	C₂³	1	6	yes	—
112	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
113	C₁₃×#103	C₂³	1	6	yes	—
114	C₁₃×#103	C₂³	1	6	yes	—
115	C₁₃×#103	C₂³	1	12	yes	—
116	C₁₃×#103	C₂³	1	12	yes	—
117	C₁₃×#103	C₂³	1	2	yes	—
118	C₁₃×#102	C₂³	1	2	yes	—
119	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
120	C₁₃×#97	C₂³	1	1	yes	characteristic
121	C₁₃×#97	C₂³	1	3	yes	—
122	C₄×C₈×C₁₃	C₂³	1	6	yes	—
123	#62589	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₁₃×#41	—	2	4	no	—
125	C₂×Q₈×C₁₃	—	2	1	no	—
126	C₂×Q₈×C₁₃	—	2	3	no	—
127	C₂×Q₈×C₁₃	—	2	3	no	—
128	C₂×Q₈×C₁₃	—	2	6	no	—
129	C₂×Q₈×C₁₃	—	4	12	no	—
130	C₂×Q₈×C₁₃	—	4	4	no	—
131	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
133	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂×D₄×C₁₃	—	2	3	no	—
135	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
136	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	—	2	6	no	—
138	C₂²×C₄×C₁₃	—	2	3	no	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
142	C₁₃×Q₁₆	—	4	6	no	—
143	C₁₃×SD₁₆	—	4	6	no	—
144	C₁₃×M₁₆	—	4	6	no	—
145	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
146	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
147	C₁₃×C₄⋊C₄	—	2	3	no	—
148	C₁₃×C₄⋊C₄	—	2	3	no	—
149	C₁₃×C₄⋊C₄	—	2	6	no	—
150	C₁₃×C₄⋊C₄	—	2	6	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	3	no	—
153	C₁₃×C₄⋊C₄	—	2	3	no	—
154	C₁₃×C₄⋊C₄	—	2	3	no	—
155	C₁₃×C₄⋊C₄	—	2	3	no	—
156	C₁₃×C₄⋊C₄	—	2	3	no	—
157	C₁₃×C₄⋊C₄	—	2	6	no	—
158	C₁₃×C₄⋊C₄	—	2	6	no	—
159	C₁₃×C₄⋊C₄	—	2	3	no	—
160	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
162	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
164	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
165	C₁₃×C₂²⋊C₄	—	2	6	no	—
166	C₁₃×C₂²⋊C₄	—	2	6	no	—
167	C₁₃×C₂²⋊C₄	—	2	3	no	—
168	C₁₃×C₂²⋊C₄	—	2	3	no	—
169	C₁₃×C₂²⋊C₄	—	2	1	no	—
170	C₁₃×C₂²⋊C₄	—	2	1	no	—
171	C₁₃×C₂²⋊C₄	—	2	3	no	—
172	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
173	C₄²×C₁₃	—	2	6	no	—
174	C₄²×C₁₃	—	2	3	no	—
175	C₄²×C₁₃	—	2	6	no	—
176	C₄²×C₁₃	C₂×D₄	1	3	yes	—
177	C₄²×C₁₃	C₂×D₄	1	3	yes	—
178	C₄²×C₁₃	C₂⁴	1	3	yes	—
179	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
180	#3518	C₂×C₁₃	1	1	yes	characteristic
181	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#3363	C₂×C₁₃	1	2	yes	complemented
183	#3359	C₂×C₁₃	1	2	yes	complemented
184	#3329	C₂×C₁₃	1	6	yes	complemented
185	#3328	C₂×C₁₃	1	6	yes	complemented
186	#3237	C₂×C₁₃	1	3	yes	complemented
187	#3218	C₂×C₁₃	1	3	yes	complemented
188	#3172	C₂×C₁₃	1	3	yes	complemented
189	#3139	C₂×C₁₃	1	3	yes	complemented
190	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂³×C₁₃	—	2	1	no	—
192	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
193	Q₈×C₁₃	—	2	6	no	—
194	Q₈×C₁₃	—	2	2	no	—
195	Q₈×C₁₃	—	2	6	no	—
196	Q₈×C₁₃	—	4	2	no	—
197	Q₈×C₁₃	—	4	6	no	—
198	Q₈×C₁₃	—	8	3	no	—
199	Q₈×C₁₃	—	8	6	no	—
200	Q₈×C₁₃	#137	1	4	yes	—
201	D₄×C₁₃	—	2	6	no	—
202	D₄×C₁₃	—	2	2	no	—
203	D₄×C₁₃	—	8	3	no	—
204	C₂×C₄×C₁₃	—	2	6	no	—
205	C₂×C₄×C₁₃	—	2	6	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	3	no	—
209	C₂×C₄×C₁₃	—	2	3	no	—
210	C₂×C₄×C₁₃	—	2	6	no	—
211	C₂×C₄×C₁₃	—	4	3	no	—
212	C₂×C₄×C₁₃	—	4	6	no	—
213	C₂×C₄×C₁₃	—	8	6	no	—
214	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
215	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
219	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
220	C₈×C₁₃	—	2	2	no	—
221	C₈×C₁₃	—	2	6	no	—
222	Q₈²	—	2	1	no	—
223	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
224	#557	C₂²×C₁₃	1	2	yes	—
225	#556	—	2	3	no	—
226	#556	C₂²×C₁₃	1	3	yes	—
227	#555	C₂²×C₁₃	1	3	yes	—
228	#554	—	2	3	no	—
229	D₄×Q₈	C₂²×C₁₃	1	6	yes	—
230	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
231	#548	—	2	1	no	—
232	#544	—	2	3	no	—
233	#542	—	2	3	no	—
234	#533	C₂²×C₁₃	1	3	yes	—
235	#533	C₂²×C₁₃	1	3	yes	—
236	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
237	#529	C₂²×C₁₃	1	3	yes	—
238	#520	—	2	1	no	—
239	#519	—	2	1	no	—
240	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
241	#501	C₂²×C₁₃	1	3	yes	—
242	#497	C₂²×C₁₃	1	3	yes	—
243	#491	C₂²×C₁₃	1	3	yes	—
244	#491	C₂²×C₁₃	1	6	yes	—
245	#489	C₂²×C₁₃	1	1	yes	characteristic
246	#487	C₂²×C₁₃	1	6	yes	—
247	#487	C₂²×C₁₃	1	6	yes	—
248	#485	C₂²×C₁₃	1	12	yes	—
249	#477	C₂²×C₁₃	1	6	yes	—
250	#475	C₂²×C₁₃	1	6	yes	—
251	#470	C₂²×C₁₃	1	6	yes	—
252	#468	C₂²×C₁₃	1	6	yes	—
253	#462	C₂²×C₁₃	1	6	yes	—
254	#461	C₂²×C₁₃	1	6	yes	—
255	#451	C₂²×C₁₃	1	6	yes	—
256	#448	C₂²×C₁₃	1	6	yes	—
257	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
258	C₄×Q₁₆	C₂²×C₁₃	1	6	yes	—
259	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
260	#436	C₂²×C₁₃	1	6	yes	—
261	#432	C₂²×C₁₃	1	3	yes	—
262	#419	C₂²×C₁₃	1	12	yes	—
263	C₄×M₁₆	C₂²×C₁₃	1	3	yes	—
264	C₂²×C₁₃	—	2	3	no	—
265	C₂²×C₁₃	—	2	3	no	—
266	C₂²×C₁₃	—	2	3	no	—
267	C₂²×C₁₃	—	4	1	no	—
268	C₂²×C₁₃	—	4	1	no	—
269	C₂²×C₁₃	—	4	1	no	—
270	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
271	C₄×C₁₃	—	2	1	no	—
272	C₄×C₁₃	—	2	3	no	—
273	C₄×C₁₃	—	2	3	no	—
274	C₄×C₁₃	—	2	1	no	—
275	C₄×C₁₃	—	4	3	no	—
276	C₄×C₁₃	—	4	2	no	—
277	C₄×C₁₃	—	4	6	no	—
278	C₄×C₁₃	—	4	1	no	—
279	C₄×C₁₃	—	4	3	no	—
280	C₄×C₁₃	C₂×#137	1	6	yes	—
281	C₄×C₁₃	#585	1	2	yes	—
282	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
283	C₂²×Q₈	—	2	1	no	—
284	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
285	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
286	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
287	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
288	C₄⋊Q₈	—	2	3	no	—
289	C₄⋊Q₈	—	2	6	no	—
290	C₄⋊Q₈	—	2	3	no	—
291	C₄⋊Q₈	—	2	3	no	—
292	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
293	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
294	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
295	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
296	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
297	#126	—	2	6	no	—
298	#126	—	2	3	no	—
299	#125	—	2	6	no	—
300	#125	—	2	3	no	—
301	#125	C₂³×C₁₃	1	3	yes	—
302	#124	—	2	3	no	—
303	#124	—	2	6	no	—
304	#124	C₂³×C₁₃	1	1	yes	characteristic
305	#123	—	2	3	no	—
306	C₂²⋊Q₈	—	2	3	no	—
307	C₂²⋊Q₈	—	2	3	no	—
308	C₂²⋊Q₈	—	2	3	no	—
309	C₂²⋊Q₈	—	2	3	no	—
310	C₂²⋊Q₈	—	2	12	no	—
311	C₂²⋊Q₈	C₂³×C₁₃	1	3	yes	—
312	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
313	#121	—	2	3	no	—
314	#121	C₂³×C₁₃	1	3	yes	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	3	no	—
318	C₄×Q₈	—	2	3	no	—
319	C₄×Q₈	—	2	3	no	—
320	C₄×Q₈	—	2	3	no	—
321	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
322	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
323	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
324	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
325	C₄×D₄	—	2	6	no	—
326	C₄×D₄	—	2	3	no	—
327	C₄×D₄	D₄×C₁₃	1	3	yes	—
328	C₄×D₄	C₂³×C₁₃	1	3	yes	—
329	C₄×D₄	C₂³×C₁₃	1	3	yes	—
330	#117	—	2	3	no	—
331	#117	—	2	3	no	—
332	#117	—	2	3	no	—
333	#117	D₄×C₁₃	1	3	yes	—
334	#117	C₂³×C₁₃	1	6	yes	—
335	C₂×C₄⋊C₄	—	2	3	no	—
336	C₂×C₄⋊C₄	—	2	3	no	—
337	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
338	#107	C₂³×C₁₃	1	6	yes	—
339	#106	C₂³×C₁₃	1	6	yes	—
340	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
341	#103	C₂³×C₁₃	1	6	yes	—
342	#103	C₂³×C₁₃	1	6	yes	—
343	#103	C₂³×C₁₃	1	12	yes	—
344	#103	C₂³×C₁₃	1	12	yes	—
345	#103	C₂³×C₁₃	1	2	yes	—
346	#102	C₂³×C₁₃	1	2	yes	—
347	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
348	#97	C₂³×C₁₃	1	1	yes	characteristic
349	#97	C₂³×C₁₃	1	3	yes	—
350	C₄×C₈	C₂³×C₁₃	1	6	yes	—
351	C₂×C₁₃	—	4	3	no	—
352	C₂×C₁₃	—	8	1	no	—
353	C₂×C₁₃	#3500	1	1	yes	characteristic
354	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
355	C₂×C₁₃	#3586	1	1	yes	characteristic
356	#41	—	2	4	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	3	no	—
359	C₂×Q₈	—	2	3	no	—
360	C₂×Q₈	—	2	6	no	—
361	C₂×Q₈	—	4	12	no	—
362	C₂×Q₈	—	4	4	no	—
363	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
365	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
366	C₂×D₄	—	2	3	no	—
367	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
368	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	—	2	6	no	—
370	C₂²×C₄	—	2	3	no	—
371	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
372	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
373	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
374	Q₁₆	—	4	6	no	—
375	SD₁₆	—	4	6	no	—
376	M₁₆	—	4	6	no	—
377	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
378	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
379	C₄⋊C₄	—	2	3	no	—
380	C₄⋊C₄	—	2	3	no	—
381	C₄⋊C₄	—	2	6	no	—
382	C₄⋊C₄	—	2	6	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	3	no	—
385	C₄⋊C₄	—	2	3	no	—
386	C₄⋊C₄	—	2	3	no	—
387	C₄⋊C₄	—	2	3	no	—
388	C₄⋊C₄	—	2	3	no	—
389	C₄⋊C₄	—	2	6	no	—
390	C₄⋊C₄	—	2	6	no	—
391	C₄⋊C₄	—	2	3	no	—
392	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
393	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
394	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
395	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
396	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
397	C₂²⋊C₄	—	2	6	no	—
398	C₂²⋊C₄	—	2	6	no	—
399	C₂²⋊C₄	—	2	3	no	—
400	C₂²⋊C₄	—	2	3	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	2	3	no	—
404	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
405	C₄²	—	2	6	no	—
406	C₄²	—	2	3	no	—
407	C₄²	—	2	6	no	—
408	C₄²	C₂×D₄×C₁₃	1	3	yes	—
409	C₄²	C₂×D₄×C₁₃	1	3	yes	—
410	C₄²	C₂⁴×C₁₃	1	3	yes	—
411	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
412	C₁₃	#62589	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	2	1	no	—
414	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
415	Q₈	—	2	6	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	2	6	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	6	no	—
420	Q₈	—	8	6	no	—
421	Q₈	—	8	3	no	—
422	Q₈	C₁₃×#137	1	4	yes	—
423	D₄	—	2	6	no	—
424	D₄	—	2	2	no	—
425	D₄	—	8	3	no	—
426	C₂×C₄	—	2	6	no	—
427	C₂×C₄	—	2	6	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	3	no	—
431	C₂×C₄	—	2	3	no	—
432	C₂×C₄	—	2	6	no	—
433	C₂×C₄	—	4	3	no	—
434	C₂×C₄	—	4	6	no	—
435	C₂×C₄	—	8	6	no	—
436	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
437	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
438	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
440	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
441	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	2	6	no	—
444	C₂²	—	2	3	no	—
445	C₂²	—	2	3	no	—
446	C₂²	—	2	3	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	3	no	—
454	C₄	—	2	3	no	—
455	C₄	—	4	3	no	—
456	C₄	—	4	3	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	6	no	—
459	C₄	—	4	1	no	—
460	C₄	C₂×C₁₃×#137	1	6	yes	—
461	C₄	C₁₃×#585	1	2	yes	—
462	C₂	—	4	3	no	—
463	C₂	—	8	1	no	—
464	C₂	C₁₃×#3500	1	1	yes	characteristic
465	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
466	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3518	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
2. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3363	C₂	semidirect
4. C₁₃×#3359	C₂	semidirect
5. C₁₃×#3329	C₂	semidirect
6. C₁₃×#3328	C₂	semidirect
7. C₁₃×#3237	C₂	semidirect
8. C₁₃×#3218	C₂	semidirect
9. C₁₃×#3172	C₂	semidirect
10. C₁₃×#3139	C₂	semidirect
11. C₁₃×#2971	C₂	semidirect
123. #62589	C₁₃	direct (N × H)
181. #3503	C₂×C₁₃	semidirect
182. #3363	C₂×C₁₃	semidirect
183. #3359	C₂×C₁₃	semidirect
184. #3329	C₂×C₁₃	semidirect
185. #3328	C₂×C₁₃	semidirect
186. #3237	C₂×C₁₃	semidirect
187. #3218	C₂×C₁₃	semidirect
188. #3172	C₂×C₁₃	semidirect
189. #3139	C₂×C₁₃	semidirect
190. #2971	C₂×C₁₃	semidirect
412. C₁₃	#62589	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×#3518	2
C₁₃×#3503	2
C₁₃×#3363	2
C₁₃×#3359	2
C₁₃×#3329	2
C₁₃×#3328	2
C₁₃×#3237	2
C₁₃×#3218	2
C₁₃×#3172	2
C₁₃×#3139	2
C₁₃×#2971	2
#62589	13

Subgroups — C13×#62589 #15748928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62589 #15748928