Subgroups — C₁₃×#32841 #15719180

Order 3328.

632 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2860	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2085	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2073	C₂	1	2	yes	maximal
9	C₁₃×#2059	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2025	C₂	1	2	yes	maximal
11	C₁₃×#1839	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#126	—	2	1	no	—
13	C₂×C₁₃×#125	C₂²	1	2	yes	—
14	C₂×C₁₃×#107	C₂²	1	2	yes	—
15	C₂×C₁₃×#106	C₂²	1	2	yes	—
16	C₂×C₁₃×#102	C₂²	1	2	yes	—
17	C₂×C₁₃×#102	C₂²	1	2	yes	—
18	C₁₃×#390	C₂²	1	1	yes	characteristic
19	C₁₃×#390	C₂²	1	1	yes	characteristic
20	C₁₃×#390	C₂²	1	1	yes	characteristic
21	C₁₃×#389	—	2	1	no	—
22	C₁₃×#389	—	2	1	no	—
23	C₁₃×#389	—	2	1	no	—
24	C₁₃×#389	—	2	1	no	—
25	C₁₃×#389	C₂²	1	1	yes	characteristic
26	C₁₃×#389	C₂²	1	1	yes	characteristic
27	C₁₃×#389	C₂²	1	1	yes	characteristic
28	C₁₃×#388	—	2	1	no	—
29	C₁₃×#388	—	2	1	no	—
30	C₁₃×#388	—	2	1	no	—
31	C₁₃×#384	C₂²	1	1	yes	characteristic
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#382	C₂²	1	2	yes	—
34	C₄³×C₁₃	C₂²	1	1	yes	characteristic
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×#336	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₁₃×#126	—	4	4	no	—
47	C₁₃×#125	—	4	2	no	—
48	C₁₃×#125	—	4	2	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
63	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#107	—	4	2	no	—
77	C₁₃×#106	—	4	2	no	—
78	C₁₃×#102	—	4	2	no	—
79	C₁₃×#102	—	4	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	1	no	—
85	#32841	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	2	no	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	2	1	no	—
90	C₂×D₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₁₃×C₄⋊C₄	—	4	2	no	—
119	C₁₃×C₄⋊C₄	—	4	4	no	—
120	C₁₃×C₄⋊C₄	—	4	4	no	—
121	C₁₃×C₄⋊C₄	—	4	2	no	—
122	C₁₃×C₄⋊C₄	—	4	2	no	—
123	C₁₃×C₄⋊C₄	—	4	2	no	—
124	C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₁₃×C₄⋊C₄	—	4	2	no	—
126	C₁₃×C₂²⋊C₄	—	4	2	no	—
127	C₁₃×C₂²⋊C₄	—	4	2	no	—
128	C₁₃×C₂²⋊C₄	—	4	2	no	—
129	C₁₃×C₂²⋊C₄	—	4	2	no	—
130	C₁₃×C₂²⋊C₄	—	4	2	no	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₄²×C₁₃	—	2	2	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	4	1	no	—
139	C₄²×C₁₃	—	4	1	no	—
140	#2860	C₂×C₁₃	1	1	yes	characteristic
141	#2859	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2100	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2099	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2094	C₂×C₁₃	1	1	yes	characteristic
145	#2093	C₂×C₁₃	1	1	yes	characteristic
146	#2085	C₂×C₁₃	1	2	yes	complemented
147	#2073	C₂×C₁₃	1	2	yes	—
148	#2059	C₂×C₁₃	1	2	yes	complemented
149	#2025	C₂×C₁₃	1	2	yes	—
150	#1839	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂³×C₁₃	—	4	1	no	—
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	1	no	—
154	C₂³×C₁₃	—	4	1	no	—
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
159	D₄×C₁₃	—	4	2	no	—
160	D₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	2	1	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	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	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	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	#135	1	2	yes	—
193	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
195	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
196	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
197	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
198	C₈×C₁₃	—	4	2	no	—
199	C₈×C₁₃	—	4	2	no	—
200	C₂×#126	—	2	1	no	—
201	C₂×#125	C₂²×C₁₃	1	2	yes	—
202	C₂×#107	C₂²×C₁₃	1	2	yes	—
203	C₂×#106	C₂²×C₁₃	1	2	yes	—
204	C₂×#102	C₂²×C₁₃	1	2	yes	—
205	C₂×#102	C₂²×C₁₃	1	2	yes	—
206	#390	C₂²×C₁₃	1	1	yes	characteristic
207	#390	C₂²×C₁₃	1	1	yes	characteristic
208	#390	C₂²×C₁₃	1	1	yes	characteristic
209	#389	—	2	1	no	—
210	#389	—	2	1	no	—
211	#389	—	2	1	no	—
212	#389	—	2	1	no	—
213	#389	C₂²×C₁₃	1	1	yes	characteristic
214	#389	C₂²×C₁₃	1	1	yes	characteristic
215	#389	C₂²×C₁₃	1	1	yes	characteristic
216	#388	—	2	1	no	—
217	#388	—	2	1	no	—
218	#388	—	2	1	no	—
219	#384	C₂²×C₁₃	1	1	yes	characteristic
220	#384	C₂²×C₁₃	1	1	yes	characteristic
221	#382	C₂²×C₁₃	1	2	yes	—
222	C₄³	C₂²×C₁₃	1	1	yes	characteristic
223	#340	C₂²×C₁₃	1	2	yes	—
224	#340	C₂²×C₁₃	1	2	yes	—
225	#340	C₂²×C₁₃	1	2	yes	—
226	#340	C₂²×C₁₃	1	2	yes	—
227	#336	C₂²×C₁₃	1	2	yes	—
228	#336	C₂²×C₁₃	1	2	yes	—
229	#336	C₂²×C₁₃	1	1	yes	characteristic
230	#336	C₂²×C₁₃	1	1	yes	characteristic
231	C₂²×C₁₃	—	8	1	no	—
232	C₂²×C₁₃	—	8	1	no	—
233	C₂²×C₁₃	—	8	1	no	—
234	C₂²×C₁₃	—	8	1	no	—
235	C₂²×C₁₃	—	8	1	no	—
236	C₂²×C₁₃	—	8	1	no	—
237	C₂²×C₁₃	—	8	1	no	—
238	C₂²×C₁₃	#535	1	1	yes	characteristic
239	C₂²×C₁₃	#536	1	1	yes	characteristic
240	C₂²×C₁₃	#536	1	1	yes	characteristic
241	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₂²×C₁₃	#575	1	1	yes	characteristic
244	C₂²×C₁₃	#575	1	1	yes	characteristic
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	4	1	no	—
248	C₄×C₁₃	—	4	1	no	—
249	C₄×C₁₃	—	4	1	no	—
250	C₄×C₁₃	—	4	1	no	—
251	C₄×C₁₃	—	8	2	no	—
252	C₄×C₁₃	—	8	1	no	—
253	C₄×C₁₃	—	8	2	no	—
254	C₄×C₁₃	—	8	1	no	—
255	C₄×C₁₃	—	8	1	no	—
256	C₄×C₁₃	#563	1	2	yes	—
257	C₄×C₁₃	#563	1	2	yes	—
258	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
260	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
261	#126	—	4	4	no	—
262	#125	—	4	2	no	—
263	#125	—	4	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
286	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
287	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
291	#107	—	4	2	no	—
292	#106	—	4	2	no	—
293	#102	—	4	2	no	—
294	#102	—	4	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	1	no	—
298	#95	—	2	1	no	—
299	#95	—	2	1	no	—
300	C₂×C₁₃	—	16	1	no	—
301	C₂×C₁₃	#2821	1	1	yes	characteristic
302	C₂×C₁₃	#3207	1	1	yes	characteristic
303	C₂×C₁₃	#3219	1	1	yes	characteristic
304	C₂×C₁₃	#3232	1	1	yes	characteristic
305	C₂×C₁₃	#3233	1	1	yes	characteristic
306	C₂×C₁₃	#3234	1	1	yes	characteristic
307	C₂×C₁₃	#3235	1	1	yes	characteristic
308	C₂⁴	—	2	1	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	—	4	4	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₁₃	#32841	1	1	yes	characteristic, direct product factor, Sylow
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	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	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	C₁₃×#135	1	2	yes	—
405	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
406	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
407	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
408	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
409	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
410	C₈	—	4	2	no	—
411	C₈	—	4	2	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	C₁₃×#535	1	1	yes	characteristic
420	C₂²	C₁₃×#536	1	1	yes	characteristic
421	C₂²	C₁₃×#536	1	1	yes	characteristic
422	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
423	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
424	C₂²	C₁₃×#575	1	1	yes	characteristic
425	C₂²	C₁₃×#575	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	8	2	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	2	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	1	no	—
437	C₄	C₁₃×#563	1	2	yes	—
438	C₄	C₁₃×#563	1	2	yes	—
439	C₂	—	16	1	no	—
440	C₂	C₁₃×#2821	1	1	yes	characteristic
441	C₂	C₁₃×#3207	1	1	yes	characteristic
442	C₂	C₁₃×#3219	1	1	yes	characteristic
443	C₂	C₁₃×#3232	1	1	yes	characteristic
444	C₂	C₁₃×#3233	1	1	yes	characteristic
445	C₂	C₁₃×#3234	1	1	yes	characteristic
446	C₂	C₁₃×#3235	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2859	C₂	semidirect
3. C₁₃×#2100	C₂	semidirect
4. C₁₃×#2099	C₂	semidirect
7. C₁₃×#2085	C₂	semidirect
9. C₁₃×#2059	C₂	semidirect
11. C₁₃×#1839	C₂	semidirect
85. #32841	C₁₃	direct (N × H)
141. #2859	C₂×C₁₃	semidirect
142. #2100	C₂×C₁₃	semidirect
143. #2099	C₂×C₁₃	semidirect
146. #2085	C₂×C₁₃	semidirect
148. #2059	C₂×C₁₃	semidirect
150. #1839	C₂×C₁₃	semidirect
362. C₁₃	#32841	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×#2860	2
C₁₃×#2859	2
C₁₃×#2100	2
C₁₃×#2099	2
C₁₃×#2094	2
C₁₃×#2093	2
C₁₃×#2085	2
C₁₃×#2073	2
C₁₃×#2059	2
C₁₃×#2025	2
C₁₃×#1839	2
#32841	13

Subgroups — C13×#32841 #15719180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32841 #15719180