Subgroups — C₁₃×#29494 #15715833

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 478 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	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2013	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1968	C₂	1	2	yes	maximal
8	C₁₃×#1933	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1880	C₂	1	2	yes	maximal
10	C₁₃×#1865	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#126	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₂×C₁₃×#106	C₂²	1	2	yes	—
17	C₂×C₁₃×#103	C₂²	1	2	yes	—
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#391	C₂²	1	2	yes	—
23	C₁₃×#390	C₂²	1	1	yes	characteristic
24	C₁₃×#390	C₂²	1	1	yes	characteristic
25	C₁₃×#390	C₂²	1	1	yes	characteristic
26	C₁₃×#389	—	2	1	no	—
27	C₁₃×#389	—	2	1	no	—
28	C₁₃×#389	C₂²	1	1	yes	characteristic
29	C₁₃×#389	C₂²	1	1	yes	characteristic
30	C₁₃×#389	C₂²	1	1	yes	characteristic
31	C₁₃×#388	—	2	1	no	—
32	C₁₃×#388	—	2	1	no	—
33	C₁₃×#388	—	2	1	no	—
34	C₁₃×#384	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
36	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
37	C₄³×C₁₃	C₂²	1	1	yes	characteristic
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	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×SD₁₆	—	2	4	no	—
46	C₂×C₁₃×SD₁₆	—	2	4	no	—
47	C₂×C₁₃×SD₁₆	—	4	2	no	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₁₃×C₄⋊Q₈	—	2	4	no	—
51	C₁₃×#126	—	4	4	no	—
52	C₄×Q₈×C₁₃	—	4	2	no	—
53	C₄×Q₈×C₁₃	—	4	2	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	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
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	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	2	no	—
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#106	—	4	2	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#103	—	4	2	no	—
84	C₁₃×#102	—	4	2	no	—
85	C₄×C₈×C₁₃	—	2	4	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	1	no	—
91	#29494	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	#41	1	4	yes	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×SD₁₆	—	4	8	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	#41	1	4	yes	—
122	C₁₃×C₄⋊C₄	—	2	4	no	—
123	C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	4	2	no	—
131	C₁₃×C₄⋊C₄	—	4	4	no	—
132	C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₂²⋊C₄	—	4	2	no	—
137	C₁₃×C₂²⋊C₄	—	4	2	no	—
138	C₁₃×C₂²⋊C₄	—	4	2	no	—
139	C₁₃×C₂²⋊C₄	—	4	2	no	—
140	C₁₃×C₂²⋊C₄	—	4	2	no	—
141	C₁₃×C₂²⋊C₄	—	4	2	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	4	1	no	—
149	C₄²×C₁₃	—	4	4	no	—
150	C₄²×C₁₃	SD₁₆	1	4	yes	complemented
151	#2860	C₂×C₁₃	1	1	yes	characteristic
152	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#2084	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2071	C₂×C₁₃	1	1	yes	characteristic
155	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2013	C₂×C₁₃	1	1	yes	characteristic
157	#1968	C₂×C₁₃	1	2	yes	—
158	#1933	C₂×C₁₃	1	2	yes	complemented
159	#1880	C₂×C₁₃	1	2	yes	—
160	#1865	C₂×C₁₃	1	2	yes	complemented
161	#1744	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	—	4	1	no	—
167	C₂³×C₁₃	—	4	1	no	—
168	C₂³×C₁₃	—	4	1	no	—
169	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	4	no	—
171	Q₈×C₁₃	—	2	4	no	—
172	Q₈×C₁₃	—	4	2	no	—
173	Q₈×C₁₃	—	4	2	no	—
174	D₄×C₁₃	—	4	2	no	—
175	D₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	4	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	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	1	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	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
205	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
206	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
207	C₂×C₄×C₁₃	#135	1	2	yes	—
208	C₂×C₄×C₁₃	#137	1	2	yes	—
209	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
210	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
211	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
213	C₈×C₁₃	—	2	4	no	—
214	C₈×C₁₃	—	4	2	no	—
215	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
216	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#126	—	2	1	no	—
218	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
219	C₂×#106	C₂²×C₁₃	1	2	yes	—
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×#103	C₂²×C₁₃	1	2	yes	—
222	C₂×#103	C₂²×C₁₃	1	2	yes	—
223	C₂×#102	C₂²×C₁₃	1	2	yes	—
224	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
225	#391	C₂²×C₁₃	1	2	yes	—
226	#390	C₂²×C₁₃	1	1	yes	characteristic
227	#390	C₂²×C₁₃	1	1	yes	characteristic
228	#390	C₂²×C₁₃	1	1	yes	characteristic
229	#389	—	2	1	no	—
230	#389	—	2	1	no	—
231	#389	C₂²×C₁₃	1	1	yes	characteristic
232	#389	C₂²×C₁₃	1	1	yes	characteristic
233	#389	C₂²×C₁₃	1	1	yes	characteristic
234	#388	—	2	1	no	—
235	#388	—	2	1	no	—
236	#388	—	2	1	no	—
237	#384	C₂²×C₁₃	1	1	yes	characteristic
238	C₄×C₄⋊C₄	—	2	1	no	—
239	C₄×C₄⋊C₄	—	2	1	no	—
240	C₄³	C₂²×C₁₃	1	1	yes	characteristic
241	#340	C₂²×C₁₃	1	2	yes	—
242	#340	C₂²×C₁₃	1	2	yes	—
243	#336	C₂²×C₁₃	1	1	yes	characteristic
244	#336	C₂²×C₁₃	1	1	yes	characteristic
245	#336	C₂²×C₁₃	1	2	yes	—
246	C₂²×C₁₃	—	8	1	no	—
247	C₂²×C₁₃	—	8	1	no	—
248	C₂²×C₁₃	—	8	1	no	—
249	C₂²×C₁₃	—	8	1	no	—
250	C₂²×C₁₃	—	8	1	no	—
251	C₂²×C₁₃	—	8	1	no	—
252	C₂²×C₁₃	—	8	1	no	—
253	C₂²×C₁₃	#525	1	1	yes	characteristic
254	C₂²×C₁₃	#532	1	1	yes	characteristic
255	C₂²×C₁₃	#535	1	1	yes	characteristic
256	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
257	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
258	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
259	C₂²×C₁₃	#575	1	1	yes	characteristic
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	2	2	no	—
262	C₄×C₁₃	—	2	2	no	—
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	4	4	no	—
266	C₄×C₁₃	—	4	1	no	—
267	C₄×C₁₃	—	8	1	no	—
268	C₄×C₁₃	—	8	1	no	—
269	C₄×C₁₃	—	8	1	no	—
270	C₄×C₁₃	—	8	2	no	—
271	C₄×C₁₃	#551	1	2	yes	—
272	C₄×C₁₃	#553	1	2	yes	—
273	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
274	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×SD₁₆	—	2	4	no	—
276	C₂×SD₁₆	—	2	4	no	—
277	C₂×SD₁₆	—	4	2	no	—
278	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
279	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
280	C₄⋊Q₈	—	2	4	no	—
281	#126	—	4	4	no	—
282	C₄×Q₈	—	4	2	no	—
283	C₄×Q₈	—	4	2	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
304	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
306	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
310	#106	—	4	2	no	—
311	#103	—	2	4	no	—
312	#103	—	2	4	no	—
313	#103	—	4	2	no	—
314	#102	—	4	2	no	—
315	C₄×C₈	—	2	4	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	1	no	—
320	#95	—	2	1	no	—
321	C₂×C₁₃	—	16	1	no	—
322	C₂×C₁₃	#2603	1	1	yes	characteristic
323	C₂×C₁₃	#3103	1	1	yes	characteristic
324	C₂×C₁₃	#3108	1	1	yes	characteristic
325	C₂×C₁₃	#3167	1	1	yes	characteristic
326	C₂×C₁₃	#3181	1	1	yes	characteristic
327	C₂×C₁₃	#3206	1	1	yes	characteristic
328	C₂×C₁₃	#3212	1	1	yes	characteristic
329	C₂⁴	—	2	1	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	C₁₃×#41	1	4	yes	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
352	SD₁₆	—	4	8	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	C₁₃×#41	1	4	yes	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	4	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	4	1	no	—
386	C₄²	—	4	4	no	—
387	C₄²	C₁₃×SD₁₆	1	4	yes	complemented
388	C₁₃	#29494	1	1	yes	characteristic, direct product factor, Sylow
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
397	Q₈	—	2	4	no	—
398	Q₈	—	2	4	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
432	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
433	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
434	C₂×C₄	C₁₃×#135	1	2	yes	—
435	C₂×C₄	C₁₃×#137	1	2	yes	—
436	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
437	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
438	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
440	C₈	—	2	4	no	—
441	C₈	—	4	2	no	—
442	C₂²	—	8	1	no	—
443	C₂²	—	8	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	C₁₃×#525	1	1	yes	characteristic
450	C₂²	C₁₃×#532	1	1	yes	characteristic
451	C₂²	C₁₃×#535	1	1	yes	characteristic
452	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
453	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
454	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
455	C₂²	C₁₃×#575	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	1	no	—
463	C₄	—	8	1	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	1	no	—
466	C₄	—	8	2	no	—
467	C₄	C₁₃×#551	1	2	yes	—
468	C₄	C₁₃×#553	1	2	yes	—
469	C₂	—	16	1	no	—
470	C₂	C₁₃×#2603	1	1	yes	characteristic
471	C₂	C₁₃×#3103	1	1	yes	characteristic
472	C₂	C₁₃×#3108	1	1	yes	characteristic
473	C₂	C₁₃×#3167	1	1	yes	characteristic
474	C₂	C₁₃×#3181	1	1	yes	characteristic
475	C₂	C₁₃×#3206	1	1	yes	characteristic
476	C₂	C₁₃×#3212	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. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#2084	C₂	semidirect
5. C₁₃×#2043	C₂	semidirect
8. C₁₃×#1933	C₂	semidirect
10. C₁₃×#1865	C₂	semidirect
11. C₁₃×#1744	C₂	semidirect
91. #29494	C₁₃	direct (N × H)
150. C₄²×C₁₃	SD₁₆	semidirect
152. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
153. #2084	C₂×C₁₃	semidirect
155. #2043	C₂×C₁₃	semidirect
158. #1933	C₂×C₁₃	semidirect
160. #1865	C₂×C₁₃	semidirect
161. #1744	C₂×C₁₃	semidirect
387. C₄²	C₁₃×SD₁₆	semidirect
388. C₁₃	#29494	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
C₄×C₁₃×C₄⋊Q₈	2
C₁₃×#2084	2
C₁₃×#2071	2
C₁₃×#2043	2
C₁₃×#2013	2
C₁₃×#1968	2
C₁₃×#1933	2
C₁₃×#1880	2
C₁₃×#1865	2
C₁₃×#1744	2
#29494	13

Subgroups — C13×#29494 #15715833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29494 #15715833