Subgroups — C₁₃×#19263 #15705602

Order 3328.

628 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×#3167	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1684	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1682	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1672	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1666	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1552	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1551	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₁₃×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#498	C₂²	1	1	yes	characteristic
16	C₁₃×#492	C₂²	1	1	yes	characteristic
17	C₁₃×#487	C₂²	1	1	yes	characteristic
18	C₁₃×#486	C₂²	1	1	yes	characteristic
19	C₁₃×#483	—	2	1	no	—
20	C₁₃×#480	—	2	1	no	—
21	C₁₃×#477	C₂²	1	2	yes	—
22	C₁₃×#475	C₂²	1	2	yes	—
23	C₁₃×#465	—	2	1	no	—
24	C₁₃×#465	—	2	1	no	—
25	C₁₃×#462	C₂²	1	2	yes	—
26	C₁₃×#460	C₂²	1	2	yes	—
27	C₁₃×#451	—	2	1	no	—
28	C₁₃×#448	—	2	1	no	—
29	C₈×Q₈×C₁₃	—	2	1	no	—
30	C₈×Q₈×C₁₃	—	2	1	no	—
31	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
33	C₁₃×#441	—	2	2	no	—
34	C₁₃×#440	—	2	2	no	—
35	C₄×C₁₃×SD₁₆	—	2	1	no	—
36	C₄×C₁₃×SD₁₆	—	2	1	no	—
37	C₁₃×#432	C₂²	1	1	yes	characteristic
38	C₁₃×#432	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
40	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₁₃	—	2	1	no	—
42	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#335	C₂²	1	2	yes	—
44	C₁₃×#334	C₂²	1	2	yes	—
45	C₁₃×#333	C₂²	1	2	yes	—
46	C₁₃×#332	C₂²	1	2	yes	—
47	C₁₃×#332	C₂²	1	2	yes	—
48	C₁₃×#331	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂×C₁₃×Q₁₆	—	2	2	no	—
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×SD₁₆	—	2	1	no	—
54	C₂×C₁₃×SD₁₆	—	2	1	no	—
55	C₂²×C₈×C₁₃	—	2	1	no	—
56	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
58	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₃×#127	C₂³	1	1	yes	characteristic
62	C₁₃×#125	—	2	1	no	—
63	C₁₃×#124	—	2	1	no	—
64	C₁₃×C₂²⋊Q₈	—	2	1	no	—
65	C₁₃×C₂²⋊Q₈	—	2	1	no	—
66	C₁₃×#121	—	2	1	no	—
67	C₁₃×#121	—	2	1	no	—
68	C₄×Q₈×C₁₃	—	2	1	no	—
69	C₄×Q₈×C₁₃	—	2	1	no	—
70	C₄×Q₈×C₁₃	—	2	1	no	—
71	C₄×Q₈×C₁₃	—	2	1	no	—
72	C₄×Q₈×C₁₃	D₄	1	2	yes	—
73	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
74	C₄×D₄×C₁₃	—	2	1	no	—
75	C₄×D₄×C₁₃	—	2	1	no	—
76	C₁₃×#117	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	—	2	1	no	—
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×#107	—	2	2	no	—
82	C₁₃×#106	—	2	1	no	—
83	C₁₃×#106	—	2	1	no	—
84	C₁₃×#106	—	2	2	no	—
85	C₁₃×C₄⋊C₈	—	2	2	no	—
86	C₁₃×C₄⋊C₈	—	2	2	no	—
87	C₁₃×C₄⋊C₈	—	2	1	no	—
88	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
89	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
90	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
91	C₁₃×#103	—	2	2	no	—
92	C₁₃×#103	—	2	2	no	—
93	C₁₃×#103	—	2	1	no	—
94	C₁₃×#103	—	2	1	no	—
95	C₁₃×#103	—	2	2	no	—
96	C₁₃×#102	—	2	1	no	—
97	C₁₃×#102	—	2	1	no	—
98	C₁₃×#102	—	2	2	no	—
99	C₁₃×C₂²⋊C₈	—	2	1	no	—
100	C₁₃×C₂²⋊C₈	—	2	1	no	—
101	C₁₃×#97	—	2	1	no	—
102	C₁₃×#97	—	2	1	no	—
103	C₄×C₈×C₁₃	—	2	2	no	—
104	C₄×C₈×C₁₃	—	2	2	no	—
105	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
106	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
107	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	#19263	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₁₃×#41	—	8	2	no	—
111	C₂×Q₈×C₁₃	—	2	4	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	4	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	4	1	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
127	C₁₃×Q₁₆	—	4	4	no	—
128	C₁₃×SD₁₆	—	4	2	no	—
129	C₁₃×SD₁₆	—	4	4	no	—
130	C₁₃×SD₁₆	—	4	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	4	1	no	—
136	C₂×C₈×C₁₃	—	4	2	no	—
137	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	4	1	no	—
151	C₁₃×C₄⋊C₄	—	4	1	no	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₁₃×C₂²⋊C₄	—	4	1	no	—
154	C₁₃×C₂²⋊C₄	—	4	1	no	—
155	C₁₃×C₂²⋊C₄	—	4	1	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	—	4	1	no	—
159	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₃	#41	1	1	yes	characteristic
162	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
163	#3167	C₂×C₁₃	1	1	yes	characteristic
164	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#3112	C₂×C₁₃	1	1	yes	characteristic
166	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1684	C₂×C₁₃	1	2	yes	complemented
168	#1682	C₂×C₁₃	1	2	yes	complemented
169	#1672	C₂×C₁₃	1	2	yes	complemented
170	#1666	C₂×C₁₃	1	2	yes	complemented
171	#1568	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1552	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1551	C₂×C₁₃	1	1	yes	characteristic
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	#121	1	1	yes	characteristic
176	Q₈×C₁₃	—	2	4	no	—
177	Q₈×C₁₃	—	2	2	no	—
178	Q₈×C₁₃	—	4	2	no	—
179	Q₈×C₁₃	—	4	1	no	—
180	Q₈×C₁₃	—	4	1	no	—
181	Q₈×C₁₃	—	8	1	no	—
182	Q₈×C₁₃	#135	1	4	yes	—
183	D₄×C₁₃	—	4	2	no	—
184	D₄×C₁₃	—	4	1	no	—
185	D₄×C₁₃	—	4	1	no	—
186	D₄×C₁₃	—	8	1	no	—
187	D₄×C₁₃	—	8	2	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	8	2	no	—
200	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
201	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
202	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₈×C₁₃	—	2	1	no	—
207	C₈×C₁₃	—	2	1	no	—
208	C₈×C₁₃	—	2	1	no	—
209	C₈×C₁₃	—	4	2	no	—
210	C₈×C₁₃	—	4	2	no	—
211	C₈×C₁₃	—	4	2	no	—
212	C₈×C₁₃	#137	1	2	yes	—
213	#533	C₂²×C₁₃	1	1	yes	characteristic
214	#532	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
216	#498	C₂²×C₁₃	1	1	yes	characteristic
217	#492	C₂²×C₁₃	1	1	yes	characteristic
218	#487	C₂²×C₁₃	1	1	yes	characteristic
219	#486	C₂²×C₁₃	1	1	yes	characteristic
220	#483	—	2	1	no	—
221	#480	—	2	1	no	—
222	#477	C₂²×C₁₃	1	2	yes	—
223	#475	C₂²×C₁₃	1	2	yes	—
224	#465	—	2	1	no	—
225	#465	—	2	1	no	—
226	#462	C₂²×C₁₃	1	2	yes	—
227	#460	C₂²×C₁₃	1	2	yes	—
228	#451	—	2	1	no	—
229	#448	—	2	1	no	—
230	C₈×Q₈	—	2	1	no	—
231	C₈×Q₈	—	2	1	no	—
232	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
233	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
234	#441	—	2	2	no	—
235	#440	—	2	2	no	—
236	C₄×SD₁₆	—	2	1	no	—
237	C₄×SD₁₆	—	2	1	no	—
238	#432	C₂²×C₁₃	1	1	yes	characteristic
239	#432	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₄⋊C₈	—	2	1	no	—
241	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×C₄×C₈	—	2	1	no	—
243	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
244	#335	C₂²×C₁₃	1	2	yes	—
245	#334	C₂²×C₁₃	1	2	yes	—
246	#333	C₂²×C₁₃	1	2	yes	—
247	#332	C₂²×C₁₃	1	2	yes	—
248	#332	C₂²×C₁₃	1	2	yes	—
249	#331	C₂²×C₁₃	1	2	yes	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	—	2	1	no	—
252	C₂²×C₁₃	—	8	1	no	—
253	C₂²×C₁₃	—	8	1	no	—
254	C₂²×C₁₃	—	8	1	no	—
255	C₂²×C₁₃	#471	1	2	yes	—
256	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	2	4	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	—	2	1	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	8	1	no	—
264	C₄×C₁₃	—	8	1	no	—
265	C₄×C₁₃	—	8	1	no	—
266	C₄×C₁₃	C₂×#135	1	2	yes	—
267	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
268	C₄×C₁₃	#575	1	1	yes	characteristic
269	C₂×#41	—	2	1	no	—
270	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
271	C₂×Q₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	2	2	no	—
273	C₂×SD₁₆	—	2	1	no	—
274	C₂×SD₁₆	—	2	1	no	—
275	C₂²×C₈	—	2	1	no	—
276	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
277	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
278	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
279	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
280	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
281	#127	C₂³×C₁₃	1	1	yes	characteristic
282	#125	—	2	1	no	—
283	#124	—	2	1	no	—
284	C₂²⋊Q₈	—	2	1	no	—
285	C₂²⋊Q₈	—	2	1	no	—
286	#121	—	2	1	no	—
287	#121	—	2	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	D₄×C₁₃	1	2	yes	—
293	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	#117	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
301	#107	—	2	2	no	—
302	#106	—	2	1	no	—
303	#106	—	2	1	no	—
304	#106	—	2	2	no	—
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
309	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
310	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
311	#103	—	2	2	no	—
312	#103	—	2	2	no	—
313	#103	—	2	1	no	—
314	#103	—	2	1	no	—
315	#103	—	2	2	no	—
316	#102	—	2	1	no	—
317	#102	—	2	1	no	—
318	#102	—	2	2	no	—
319	C₂²⋊C₈	—	2	1	no	—
320	C₂²⋊C₈	—	2	1	no	—
321	#97	—	2	1	no	—
322	#97	—	2	1	no	—
323	C₄×C₈	—	2	2	no	—
324	C₄×C₈	—	2	2	no	—
325	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
326	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
327	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₁₃	—	2	2	no	—
330	C₂×C₁₃	—	16	1	no	—
331	C₂×C₁₃	#3037	1	1	yes	characteristic
332	C₂×C₁₃	#3050	1	1	yes	characteristic
333	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
334	#41	—	8	2	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
351	Q₁₆	—	4	4	no	—
352	SD₁₆	—	4	2	no	—
353	SD₁₆	—	4	4	no	—
354	SD₁₆	—	4	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	2	no	—
361	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₂²⋊C₄	—	4	1	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	4	1	no	—
383	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
385	C₄²	C₁₃×#41	1	1	yes	characteristic
386	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
387	C₁₃	#19263	1	1	yes	characteristic, direct product factor, Sylow
388	C₂³	—	4	1	no	—
389	C₂³	C₁₃×#121	1	1	yes	characteristic
390	Q₈	—	2	4	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	1	no	—
394	Q₈	—	4	1	no	—
395	Q₈	—	8	1	no	—
396	Q₈	C₁₃×#135	1	4	yes	—
397	D₄	—	4	2	no	—
398	D₄	—	4	1	no	—
399	D₄	—	4	1	no	—
400	D₄	—	8	1	no	—
401	D₄	—	8	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
415	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
416	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	2	no	—
426	C₈	C₁₃×#137	1	2	yes	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	C₁₃×#471	1	2	yes	—
433	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	8	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	C₂×C₁₃×#135	1	2	yes	—
444	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
445	C₄	C₁₃×#575	1	1	yes	characteristic
446	C₂	—	2	2	no	—
447	C₂	—	16	1	no	—
448	C₂	C₁₃×#3037	1	1	yes	characteristic
449	C₂	C₁₃×#3050	1	1	yes	characteristic
450	C₂	C₂×C₁₃×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3113	C₂	semidirect
4. C₂×C₈×Q₈×C₁₃	C₂	semidirect
5. C₁₃×#1684	C₂	semidirect
6. C₁₃×#1682	C₂	semidirect
7. C₁₃×#1672	C₂	semidirect
8. C₁₃×#1666	C₂	semidirect
9. C₁₃×#1568	C₂	semidirect
10. C₁₃×#1552	C₂	semidirect
109. #19263	C₁₃	direct (N × H)
164. #3113	C₂×C₁₃	semidirect
166. C₂×C₈×Q₈	C₂×C₁₃	semidirect
167. #1684	C₂×C₁₃	semidirect
168. #1682	C₂×C₁₃	semidirect
169. #1672	C₂×C₁₃	semidirect
170. #1666	C₂×C₁₃	semidirect
171. #1568	C₂×C₁₃	semidirect
172. #1552	C₂×C₁₃	semidirect
387. C₁₃	#19263	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×#3167	2
C₁₃×#3113	2
C₁₃×#3112	2
C₂×C₈×Q₈×C₁₃	2
C₁₃×#1684	2
C₁₃×#1682	2
C₁₃×#1672	2
C₁₃×#1666	2
C₁₃×#1568	2
C₁₃×#1552	2
C₁₃×#1551	2
#19263	13

Subgroups — C13×#19263 #15705602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19263 #15705602