Subgroups — C₁₃×#32789 #15719128

Order 3328.

672 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2851	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2101	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2077	C₂	1	2	yes	maximal
7	C₁₃×#2076	C₂	1	2	yes	maximal
8	C₁₃×#2059	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1817	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₁₃×#391	—	2	1	no	—
20	C₁₃×#389	—	2	1	no	—
21	C₁₃×#389	C₂²	1	1	yes	characteristic
22	C₁₃×#389	C₂²	1	1	yes	characteristic
23	C₁₃×#389	C₂²	1	2	yes	—
24	C₁₃×#387	—	2	1	no	—
25	C₁₃×#387	—	2	1	no	—
26	C₁₃×#385	—	2	1	no	—
27	C₁₃×#385	—	2	1	no	—
28	C₁₃×#384	C₂²	1	1	yes	characteristic
29	C₁₃×#382	C₂²	1	1	yes	characteristic
30	C₁₃×#380	—	2	1	no	—
31	C₁₃×#380	C₂²	1	1	yes	characteristic
32	C₁₃×#380	C₂²	1	2	yes	—
33	C₁₃×#380	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₁₃×C₄⋊Q₈	—	4	2	no	—
50	C₁₃×#125	—	4	2	no	—
51	C₁₃×C₂²⋊Q₈	—	4	4	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₁₃	—	4	2	no	—
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#107	—	4	2	no	—
75	C₁₃×#106	—	4	2	no	—
76	C₁₃×C₂²⋊C₈	—	4	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	—	2	1	no	—
79	C₁₃×#95	—	2	1	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	1	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	1	no	—
85	#32789	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂×Q₈×C₁₃	—	4	2	no	—
88	C₂×Q₈×C₁₃	—	4	2	no	—
89	C₂×Q₈×C₁₃	—	4	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	4	1	no	—
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	—	4	1	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	1	no	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	4	4	no	—
128	C₁₃×C₄⋊C₄	—	4	2	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	—	4	2	no	—
131	C₁₃×C₄⋊C₄	—	4	2	no	—
132	C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₂²⋊C₄	—	4	2	no	—
136	C₁₃×C₂²⋊C₄	—	4	4	no	—
137	C₁₃×C₂²⋊C₄	—	4	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	—	4	1	no	—
141	C₄²×C₁₃	—	4	1	no	—
142	#2857	C₂×C₁₃	1	1	yes	characteristic
143	#2851	C₂×C₁₃	1	1	yes	characteristic
144	#2101	C₂×C₁₃	1	2	yes	complemented
145	#2099	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2099	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2077	C₂×C₁₃	1	2	yes	—
148	#2076	C₂×C₁₃	1	2	yes	—
149	#2059	C₂×C₁₃	1	2	yes	complemented
150	#2058	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2057	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1817	C₂×C₁₃	1	1	yes	characteristic
153	C₂³×C₁₃	—	2	1	no	—
154	C₂³×C₁₃	—	2	1	no	—
155	C₂³×C₁₃	—	2	1	no	—
156	C₂³×C₁₃	—	2	1	no	—
157	C₂³×C₁₃	—	2	1	no	—
158	C₂³×C₁₃	—	2	1	no	—
159	C₂³×C₁₃	#137	1	2	yes	—
160	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₁₃	—	8	4	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	—	4	4	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	#135	1	2	yes	—
198	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
200	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
201	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
202	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
203	C₈×C₁₃	—	4	2	no	—
204	C₈×C₁₃	—	4	2	no	—
205	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×C₂²⋊Q₈	—	2	1	no	—
208	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#107	C₂²×C₁₃	1	2	yes	—
210	C₂×#106	C₂²×C₁₃	1	2	yes	—
211	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
212	#391	—	2	1	no	—
213	#389	—	2	1	no	—
214	#389	C₂²×C₁₃	1	1	yes	characteristic
215	#389	C₂²×C₁₃	1	1	yes	characteristic
216	#389	C₂²×C₁₃	1	2	yes	—
217	#387	—	2	1	no	—
218	#387	—	2	1	no	—
219	#385	—	2	1	no	—
220	#385	—	2	1	no	—
221	#384	C₂²×C₁₃	1	1	yes	characteristic
222	#382	C₂²×C₁₃	1	1	yes	characteristic
223	#380	—	2	1	no	—
224	#380	C₂²×C₁₃	1	1	yes	characteristic
225	#380	C₂²×C₁₃	1	2	yes	—
226	#380	C₂²×C₁₃	1	1	yes	characteristic
227	#340	C₂²×C₁₃	1	2	yes	—
228	#340	C₂²×C₁₃	1	2	yes	—
229	#340	C₂²×C₁₃	1	2	yes	—
230	#340	C₂²×C₁₃	1	2	yes	—
231	#340	C₂²×C₁₃	1	2	yes	—
232	#340	C₂²×C₁₃	1	2	yes	—
233	#336	C₂²×C₁₃	1	1	yes	characteristic
234	#336	C₂²×C₁₃	1	1	yes	characteristic
235	#336	C₂²×C₁₃	1	2	yes	—
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	4	1	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	—	4	1	no	—
243	C₂²×C₁₃	#534	1	1	yes	characteristic
244	C₂²×C₁₃	#536	1	1	yes	characteristic
245	C₂²×C₁₃	#536	1	1	yes	characteristic
246	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
247	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
249	C₂²×C₁₃	#575	1	1	yes	characteristic
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	4	1	no	—
253	C₄×C₁₃	—	4	1	no	—
254	C₄×C₁₃	—	4	1	no	—
255	C₄×C₁₃	—	8	1	no	—
256	C₄×C₁₃	—	8	1	no	—
257	C₄×C₁₃	—	8	2	no	—
258	C₄×C₁₃	—	8	2	no	—
259	C₄×C₁₃	—	8	1	no	—
260	C₄×C₁₃	—	8	1	no	—
261	C₄×C₁₃	#563	1	2	yes	—
262	C₄×C₁₃	#563	1	2	yes	—
263	C₂²×Q₈	—	2	1	no	—
264	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
265	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
266	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
268	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
269	C₄⋊Q₈	—	4	2	no	—
270	#125	—	4	2	no	—
271	C₂²⋊Q₈	—	4	4	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₄²	—	4	2	no	—
290	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
291	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
294	#107	—	4	2	no	—
295	#106	—	4	2	no	—
296	C₂²⋊C₈	—	4	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	1	no	—
299	#95	—	2	1	no	—
300	#95	—	2	2	no	—
301	#95	—	2	1	no	—
302	#95	—	2	1	no	—
303	#95	—	2	1	no	—
304	#95	—	2	1	no	—
305	C₂×C₁₃	—	4	2	no	—
306	C₂×C₁₃	#2817	1	1	yes	characteristic
307	C₂×C₁₃	#3190	1	1	yes	characteristic
308	C₂×C₁₃	#3194	1	1	yes	characteristic
309	C₂×C₁₃	#3228	1	1	yes	characteristic
310	C₂×C₁₃	#3233	1	1	yes	characteristic
311	C₂×C₁₃	#3236	1	1	yes	characteristic
312	C₂×C₁₃	#3239	1	1	yes	characteristic
313	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	4	4	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	4	1	no	—
368	C₄²	—	4	1	no	—
369	C₁₃	#32789	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	C₁₃×#137	1	2	yes	—
377	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	Q₈	—	8	4	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	C₁₃×#135	1	2	yes	—
415	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
416	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
417	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
418	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
419	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
420	C₈	—	4	2	no	—
421	C₈	—	4	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	C₁₃×#534	1	1	yes	characteristic
430	C₂²	C₁₃×#536	1	1	yes	characteristic
431	C₂²	C₁₃×#536	1	1	yes	characteristic
432	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
433	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
434	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
435	C₂²	C₁₃×#575	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	2	no	—
444	C₄	—	8	2	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	1	no	—
447	C₄	C₁₃×#563	1	2	yes	—
448	C₄	C₁₃×#563	1	2	yes	—
449	C₂	—	4	2	no	—
450	C₂	C₁₃×#2817	1	1	yes	characteristic
451	C₂	C₁₃×#3190	1	1	yes	characteristic
452	C₂	C₁₃×#3194	1	1	yes	characteristic
453	C₂	C₁₃×#3228	1	1	yes	characteristic
454	C₂	C₁₃×#3233	1	1	yes	characteristic
455	C₂	C₁₃×#3236	1	1	yes	characteristic
456	C₂	C₁₃×#3239	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2101	C₂	semidirect
4. C₁₃×#2099	C₂	semidirect
5. C₁₃×#2099	C₂	semidirect
8. C₁₃×#2059	C₂	semidirect
9. C₁₃×#2058	C₂	semidirect
10. C₁₃×#2057	C₂	semidirect
85. #32789	C₁₃	direct (N × H)
144. #2101	C₂×C₁₃	semidirect
145. #2099	C₂×C₁₃	semidirect
146. #2099	C₂×C₁₃	semidirect
149. #2059	C₂×C₁₃	semidirect
150. #2058	C₂×C₁₃	semidirect
151. #2057	C₂×C₁₃	semidirect
369. C₁₃	#32789	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×#2857	2
C₁₃×#2851	2
C₁₃×#2101	2
C₁₃×#2099	2
C₁₃×#2077	2
C₁₃×#2076	2
C₁₃×#2059	2
C₁₃×#2058	2
C₁₃×#2057	2
C₁₃×#1817	2
#32789	13

Subgroups — C13×#32789 #15719128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32789 #15719128