Subgroups — C₁₃×#29366 #15715705

Order 3328.

914 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2014	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1926	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1880	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1877	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1864	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1839	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	—	2	1	no	—
16	C₂×C₄×D₄×C₁₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
18	C₂×C₁₃×#106	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₁₃×#391	C₂²	1	1	yes	characteristic
24	C₁₃×#391	C₂²	1	1	yes	characteristic
25	C₁₃×#390	—	2	1	no	—
26	C₁₃×#390	—	2	1	no	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#389	C₂²	1	1	yes	characteristic
29	C₁₃×#389	C₂²	1	1	yes	characteristic
30	C₁₃×#387	—	2	1	no	—
31	C₁₃×#387	—	2	1	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₁₃×#376	—	2	1	no	—
36	C₄³×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	4	no	—
49	C₂×C₁₃×SD₁₆	—	2	4	no	—
50	C₂×C₁₃×SD₁₆	—	4	2	no	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₁₃×#127	—	2	4	no	—
54	C₄×Q₈×C₁₃	—	2	2	no	—
55	C₄×Q₈×C₁₃	—	2	2	no	—
56	C₄×D₄×C₁₃	—	4	2	no	—
57	C₄×D₄×C₁₃	—	4	2	no	—
58	C₄×D₄×C₁₃	—	4	4	no	—
59	C₄×D₄×C₁₃	—	4	4	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×#106	—	4	2	no	—
82	C₁₃×#103	—	4	2	no	—
83	C₁₃×#102	—	2	4	no	—
84	C₁₃×#102	—	2	4	no	—
85	C₁₃×#102	—	4	2	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	1	no	—
91	C₁₃×#95	—	2	1	no	—
92	C₁₃×#95	—	2	1	no	—
93	#29366	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	#41	1	2	yes	—
99	C₂×D₄×C₁₃	—	2	4	no	—
100	C₂×D₄×C₁₃	—	2	4	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	—	4	2	no	—
109	C₂×D₄×C₁₃	—	4	2	no	—
110	C₂×D₄×C₁₃	#41	1	4	yes	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	4	4	no	—
117	C₂²×C₄×C₁₃	—	4	4	no	—
118	C₂²×C₄×C₁₃	—	4	4	no	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×SD₁₆	—	4	8	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	4	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₄⋊C₄	#41	1	2	yes	—
144	C₁₃×C₂²⋊C₄	—	4	4	no	—
145	C₁₃×C₂²⋊C₄	—	4	4	no	—
146	C₁₃×C₂²⋊C₄	—	4	4	no	—
147	C₄²×C₁₃	—	2	4	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	—	4	1	no	—
154	C₄²×C₁₃	—	4	1	no	—
155	C₄²×C₁₃	—	4	2	no	—
156	C₄²×C₁₃	SD₁₆	1	4	yes	complemented
157	C₄×#127	C₂×C₁₃	1	1	yes	characteristic
158	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#2099	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#2096	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#2041	C₂×C₁₃	1	1	yes	characteristic
162	#2014	C₂×C₁₃	1	1	yes	characteristic
163	#1926	C₂×C₁₃	1	2	yes	complemented
164	#1880	C₂×C₁₃	1	2	yes	complemented
165	#1877	C₂×C₁₃	1	2	yes	complemented
166	#1864	C₂×C₁₃	1	2	yes	complemented
167	#1839	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂³×C₁₃	—	2	4	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₁₃	—	2	4	no	—
177	Q₈×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	2	4	no	—
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	4	8	no	—
181	D₄×C₁₃	—	4	8	no	—
182	D₄×C₁₃	—	4	2	no	—
183	D₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	8	8	no	—
214	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
215	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
216	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
217	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
218	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
220	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
222	C₈×C₁₃	—	4	2	no	—
223	C₈×C₁₃	—	4	2	no	—
224	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
225	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×C₄×D₄	—	2	1	no	—
228	C₂×C₄×D₄	—	2	1	no	—
229	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
230	C₂×#106	C₂²×C₁₃	1	2	yes	—
231	C₂×#103	C₂²×C₁₃	1	2	yes	—
232	C₂×#102	C₂²×C₁₃	1	2	yes	—
233	C₂×#102	C₂²×C₁₃	1	2	yes	—
234	C₂×#102	C₂²×C₁₃	1	2	yes	—
235	#391	C₂²×C₁₃	1	1	yes	characteristic
236	#391	C₂²×C₁₃	1	1	yes	characteristic
237	#390	—	2	1	no	—
238	#390	—	2	1	no	—
239	#390	C₂²×C₁₃	1	2	yes	—
240	#389	C₂²×C₁₃	1	1	yes	characteristic
241	#389	C₂²×C₁₃	1	1	yes	characteristic
242	#387	—	2	1	no	—
243	#387	—	2	1	no	—
244	#384	C₂²×C₁₃	1	1	yes	characteristic
245	C₄×C₄⋊C₄	—	2	1	no	—
246	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
247	#376	—	2	1	no	—
248	C₄³	C₂²×C₁₃	1	1	yes	characteristic
249	#340	C₂²×C₁₃	1	2	yes	—
250	#340	C₂²×C₁₃	1	2	yes	—
251	#336	C₂²×C₁₃	1	1	yes	characteristic
252	#336	C₂²×C₁₃	1	1	yes	characteristic
253	#336	C₂²×C₁₃	1	2	yes	—
254	#336	C₂²×C₁₃	1	2	yes	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	4	4	no	—
257	C₂²×C₁₃	—	4	4	no	—
258	C₂²×C₁₃	—	8	2	no	—
259	C₂²×C₁₃	—	8	2	no	—
260	C₂²×C₁₃	—	8	2	no	—
261	C₂²×C₁₃	—	8	2	no	—
262	C₂²×C₁₃	#525	1	1	yes	characteristic
263	C₂²×C₁₃	#525	1	1	yes	characteristic
264	C₂²×C₁₃	#535	1	1	yes	characteristic
265	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
266	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
267	C₂²×C₁₃	#575	1	1	yes	characteristic
268	C₂²×C₁₃	#575	1	1	yes	characteristic
269	C₄×C₁₃	—	2	2	no	—
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	4	2	no	—
274	C₄×C₁₃	—	4	1	no	—
275	C₄×C₁₃	—	4	2	no	—
276	C₄×C₁₃	—	4	1	no	—
277	C₄×C₁₃	—	8	1	no	—
278	C₄×C₁₃	—	8	2	no	—
279	C₄×C₁₃	—	8	1	no	—
280	C₄×C₁₃	#551	1	2	yes	—
281	C₄×C₁₃	#553	1	2	yes	—
282	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
286	C₂³×C₄	—	2	2	no	—
287	C₂×SD₁₆	—	2	4	no	—
288	C₂×SD₁₆	—	2	4	no	—
289	C₂×SD₁₆	—	4	2	no	—
290	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
291	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
292	#127	—	2	4	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×D₄	—	4	2	no	—
296	C₄×D₄	—	4	2	no	—
297	C₄×D₄	—	4	4	no	—
298	C₄×D₄	—	4	4	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
314	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
315	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
316	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
320	#106	—	4	2	no	—
321	#103	—	4	2	no	—
322	#102	—	2	4	no	—
323	#102	—	2	4	no	—
324	#102	—	4	2	no	—
325	#95	—	2	1	no	—
326	#95	—	2	1	no	—
327	#95	—	2	1	no	—
328	#95	—	2	1	no	—
329	#95	—	2	1	no	—
330	#95	—	2	1	no	—
331	#95	—	2	1	no	—
332	C₂×C₁₃	—	8	4	no	—
333	C₂×C₁₃	#2598	1	1	yes	characteristic
334	C₂×C₁₃	#3101	1	1	yes	characteristic
335	C₂×C₁₃	#3103	1	1	yes	characteristic
336	C₂×C₁₃	#3114	1	1	yes	characteristic
337	C₂×C₁₃	#3115	1	1	yes	characteristic
338	C₂×C₁₃	#3208	1	1	yes	characteristic
339	C₂×C₁₃	#3219	1	1	yes	characteristic
340	C₂⁴	—	2	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	C₁₃×#41	1	2	yes	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	2	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	C₁₃×#41	1	4	yes	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	4	4	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
372	SD₁₆	—	4	8	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	C₁₃×#41	1	2	yes	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₄²	—	2	4	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	4	1	no	—
400	C₄²	—	4	1	no	—
401	C₄²	—	4	2	no	—
402	C₄²	C₁₃×SD₁₆	1	4	yes	complemented
403	C₁₃	#29366	1	1	yes	characteristic, direct product factor, Sylow
404	C₂³	—	2	4	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
412	Q₈	—	2	4	no	—
413	Q₈	—	4	2	no	—
414	D₄	—	2	4	no	—
415	D₄	—	2	4	no	—
416	D₄	—	4	8	no	—
417	D₄	—	4	8	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	8	8	no	—
450	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
451	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
452	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
453	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
454	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
455	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
456	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
457	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
458	C₈	—	4	2	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	C₁₃×#525	1	1	yes	characteristic
468	C₂²	C₁₃×#525	1	1	yes	characteristic
469	C₂²	C₁₃×#535	1	1	yes	characteristic
470	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
471	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
472	C₂²	C₁₃×#575	1	1	yes	characteristic
473	C₂²	C₁₃×#575	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	1	no	—
482	C₄	—	8	1	no	—
483	C₄	—	8	2	no	—
484	C₄	—	8	1	no	—
485	C₄	C₁₃×#551	1	2	yes	—
486	C₄	C₁₃×#553	1	2	yes	—
487	C₂	—	8	4	no	—
488	C₂	C₁₃×#2598	1	1	yes	characteristic
489	C₂	C₁₃×#3101	1	1	yes	characteristic
490	C₂	C₁₃×#3103	1	1	yes	characteristic
491	C₂	C₁₃×#3114	1	1	yes	characteristic
492	C₂	C₁₃×#3115	1	1	yes	characteristic
493	C₂	C₁₃×#3208	1	1	yes	characteristic
494	C₂	C₁₃×#3219	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
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×#2295	C₂	semidirect
3. C₁₃×#2099	C₂	semidirect
4. C₁₃×#2096	C₂	semidirect
7. C₁₃×#1926	C₂	semidirect
8. C₁₃×#1880	C₂	semidirect
9. C₁₃×#1877	C₂	semidirect
10. C₁₃×#1864	C₂	semidirect
11. C₁₃×#1839	C₂	semidirect
93. #29366	C₁₃	direct (N × H)
156. C₄²×C₁₃	SD₁₆	semidirect
158. #2295	C₂×C₁₃	semidirect
159. #2099	C₂×C₁₃	semidirect
160. #2096	C₂×C₁₃	semidirect
163. #1926	C₂×C₁₃	semidirect
164. #1880	C₂×C₁₃	semidirect
165. #1877	C₂×C₁₃	semidirect
166. #1864	C₂×C₁₃	semidirect
167. #1839	C₂×C₁₃	semidirect
402. C₄²	C₁₃×SD₁₆	semidirect
403. C₁₃	#29366	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₃×#127	2
C₁₃×#2295	2
C₁₃×#2099	2
C₁₃×#2096	2
C₁₃×#2041	2
C₁₃×#2014	2
C₁₃×#1926	2
C₁₃×#1880	2
C₁₃×#1877	2
C₁₃×#1864	2
C₁₃×#1839	2
#29366	13

Subgroups — C13×#29366 #15715705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29366 #15715705