Subgroups — C₁₃×#29504 #15715843

Order 3328.

788 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2645	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2328	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2085	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2074	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×#1973	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1746	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#401	—	2	1	no	—
34	C₁₃×#400	—	2	1	no	—
35	C₁₃×#400	—	2	1	no	—
36	C₁₃×#400	—	2	1	no	—
37	C₁₃×#391	C₂²	1	1	yes	characteristic
38	C₁₃×#391	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	1	yes	characteristic
40	C₁₃×#390	C₂²	1	1	yes	characteristic
41	C₁₃×#390	C₂²	1	1	yes	characteristic
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#386	—	2	1	no	—
46	C₁₃×#386	—	2	1	no	—
47	C₁₃×#386	—	2	1	no	—
48	C₁₃×#386	—	2	1	no	—
49	C₁₃×#382	C₂²	1	1	yes	characteristic
50	C₁₃×#376	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#336	C₂²	1	1	yes	characteristic
56	C₁₃×#336	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂×C₁₃×SD₁₆	—	2	2	no	—
67	C₂×C₁₃×SD₁₆	—	2	2	no	—
68	C₂×C₁₃×SD₁₆	—	2	2	no	—
69	C₂×C₁₃×SD₁₆	—	2	2	no	—
70	C₂×C₁₃×SD₁₆	—	4	1	no	—
71	C₂×C₁₃×SD₁₆	—	4	1	no	—
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#127	—	2	2	no	—
77	C₁₃×#127	—	2	2	no	—
78	C₄×D₄×C₁₃	—	4	1	no	—
79	C₄×D₄×C₁₃	—	4	1	no	—
80	C₄×D₄×C₁₃	—	4	1	no	—
81	C₄×D₄×C₁₃	—	4	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#107	—	4	1	no	—
100	C₁₃×#106	—	4	1	no	—
101	C₁₃×#103	—	4	1	no	—
102	C₁₃×#103	—	4	1	no	—
103	C₁₃×#102	—	2	2	no	—
104	C₁₃×#102	—	2	2	no	—
105	C₁₃×#102	—	2	2	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	4	1	no	—
108	C₁₃×#102	—	4	1	no	—
109	C₁₃×#97	—	2	2	no	—
110	C₄×C₈×C₁₃	—	2	2	no	—
111	C₁₃×#95	—	2	1	no	—
112	C₁₃×#95	—	2	1	no	—
113	C₁₃×#95	—	2	1	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	—	2	1	no	—
120	C₁₃×#95	—	2	1	no	—
121	C₁₃×#95	—	2	1	no	—
122	C₁₃×#95	D₄	1	1	yes	characteristic
123	C₁₃×#95	D₄	1	1	yes	characteristic
124	C₁₃×#95	D₄	1	1	yes	characteristic
125	C₁₃×#95	D₄	1	1	yes	characteristic
126	#29504	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	—	2	1	no	—
128	C₂⁴×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	—	2	4	no	—
136	C₂×D₄×C₁₃	—	2	4	no	—
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	8	1	no	—
148	C₂×D₄×C₁₃	—	8	1	no	—
149	C₂×D₄×C₁₃	—	8	1	no	—
150	C₂×D₄×C₁₃	—	8	1	no	—
151	C₂×D₄×C₁₃	#41	1	2	yes	—
152	C₂×D₄×C₁₃	#41	1	2	yes	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	4	2	no	—
160	C₂²×C₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	—	8	1	no	—
162	C₂²×C₄×C₁₃	—	8	1	no	—
163	C₂²×C₄×C₁₃	—	8	1	no	—
164	C₂²×C₄×C₁₃	—	8	1	no	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₁₃×SD₁₆	—	4	4	no	—
173	C₁₃×SD₁₆	—	4	4	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	#41	1	2	yes	—
185	C₂×C₈×C₁₃	#41	1	2	yes	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	8	1	no	—
197	C₁₃×C₄⋊C₄	—	8	1	no	—
198	C₁₃×C₄⋊C₄	—	8	1	no	—
199	C₁₃×C₂²⋊C₄	—	4	2	no	—
200	C₁₃×C₂²⋊C₄	—	4	2	no	—
201	C₁₃×C₂²⋊C₄	—	8	1	no	—
202	C₁₃×C₂²⋊C₄	—	8	1	no	—
203	C₁₃×C₂²⋊C₄	—	8	1	no	—
204	C₁₃×C₂²⋊C₄	—	8	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	#2645	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#2328	C₂×C₁₃	1	1	yes	characteristic
213	#2085	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#2074	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2041	C₂×C₁₃	1	1	yes	characteristic
216	#2014	C₂×C₁₃	1	1	yes	characteristic
217	#1973	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1968	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1936	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1934	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1746	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	—	2	2	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	C₂³×C₁₃	—	4	1	no	—
230	C₂³×C₁₃	—	4	1	no	—
231	C₂³×C₁₃	—	4	1	no	—
232	C₂³×C₁₃	—	4	1	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	C₂³×C₁₃	—	4	1	no	—
235	C₂³×C₁₃	—	4	1	no	—
236	C₂³×C₁₃	—	4	1	no	—
237	C₂³×C₁₃	—	4	1	no	—
238	C₂³×C₁₃	—	4	1	no	—
239	C₂³×C₁₃	—	4	1	no	—
240	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₁₃	—	4	1	no	—
242	Q₈×C₁₃	—	4	1	no	—
243	Q₈×C₁₃	—	4	1	no	—
244	Q₈×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	2	2	no	—
246	D₄×C₁₃	—	2	2	no	—
247	D₄×C₁₃	—	2	2	no	—
248	D₄×C₁₃	—	2	2	no	—
249	D₄×C₁₃	—	4	1	no	—
250	D₄×C₁₃	—	4	1	no	—
251	D₄×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	4	1	no	—
253	D₄×C₁₃	—	8	4	no	—
254	D₄×C₁₃	—	8	4	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	—	4	1	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	1	no	—
291	C₂×C₄×C₁₃	—	8	4	no	—
292	C₂×C₄×C₁₃	—	8	4	no	—
293	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
299	C₈×C₁₃	—	2	2	no	—
300	C₈×C₁₃	—	2	2	no	—
301	C₈×C₁₃	—	4	1	no	—
302	C₈×C₁₃	—	4	1	no	—
303	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
304	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
320	#401	—	2	1	no	—
321	#400	—	2	1	no	—
322	#400	—	2	1	no	—
323	#400	—	2	1	no	—
324	#391	C₂²×C₁₃	1	1	yes	characteristic
325	#391	C₂²×C₁₃	1	1	yes	characteristic
326	#391	C₂²×C₁₃	1	1	yes	characteristic
327	#390	C₂²×C₁₃	1	1	yes	characteristic
328	#390	C₂²×C₁₃	1	1	yes	characteristic
329	#389	C₂²×C₁₃	1	1	yes	characteristic
330	#389	C₂²×C₁₃	1	1	yes	characteristic
331	#389	C₂²×C₁₃	1	1	yes	characteristic
332	#386	—	2	1	no	—
333	#386	—	2	1	no	—
334	#386	—	2	1	no	—
335	#386	—	2	1	no	—
336	#382	C₂²×C₁₃	1	1	yes	characteristic
337	#376	C₂²×C₁₃	1	1	yes	characteristic
338	#340	C₂²×C₁₃	1	1	yes	characteristic
339	#340	C₂²×C₁₃	1	1	yes	characteristic
340	#340	C₂²×C₁₃	1	1	yes	characteristic
341	#340	C₂²×C₁₃	1	1	yes	characteristic
342	#336	C₂²×C₁₃	1	1	yes	characteristic
343	#336	C₂²×C₁₃	1	1	yes	characteristic
344	#336	C₂²×C₁₃	1	1	yes	characteristic
345	#336	C₂²×C₁₃	1	1	yes	characteristic
346	C₂²×C₁₃	—	4	2	no	—
347	C₂²×C₁₃	—	4	2	no	—
348	C₂²×C₁₃	—	4	2	no	—
349	C₂²×C₁₃	—	4	2	no	—
350	C₂²×C₁₃	—	4	2	no	—
351	C₂²×C₁₃	—	4	2	no	—
352	C₂²×C₁₃	—	8	1	no	—
353	C₂²×C₁₃	—	8	1	no	—
354	C₂²×C₁₃	—	8	1	no	—
355	C₂²×C₁₃	—	8	1	no	—
356	C₂²×C₁₃	—	8	1	no	—
357	C₂²×C₁₃	—	8	1	no	—
358	C₂²×C₁₃	—	8	1	no	—
359	C₂²×C₁₃	—	8	1	no	—
360	C₂²×C₁₃	#525	1	1	yes	characteristic
361	C₂²×C₁₃	#532	1	1	yes	characteristic
362	C₂²×C₁₃	#535	1	1	yes	characteristic
363	C₂²×C₁₃	#576	1	1	yes	characteristic
364	C₂²×C₁₃	#577	1	1	yes	characteristic
365	C₂²×C₁₃	#577	1	1	yes	characteristic
366	C₂²×C₁₃	#577	1	1	yes	characteristic
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	—	4	1	no	—
370	C₄×C₁₃	—	4	1	no	—
371	C₄×C₁₃	—	4	1	no	—
372	C₄×C₁₃	—	4	1	no	—
373	C₄×C₁₃	—	8	1	no	—
374	C₄×C₁₃	—	8	1	no	—
375	C₄×C₁₃	—	8	1	no	—
376	C₄×C₁₃	—	8	1	no	—
377	C₄×C₁₃	—	8	1	no	—
378	C₄×C₁₃	—	8	1	no	—
379	C₄×C₁₃	#551	1	1	yes	characteristic
380	C₄×C₁₃	#551	1	1	yes	characteristic
381	C₄×C₁₃	#553	1	1	yes	characteristic
382	C₄×C₁₃	#553	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
384	C₂²×D₄	—	2	1	no	—
385	C₂²×D₄	—	2	1	no	—
386	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	—	2	1	no	—
390	C₂×SD₁₆	—	2	2	no	—
391	C₂×SD₁₆	—	2	2	no	—
392	C₂×SD₁₆	—	2	2	no	—
393	C₂×SD₁₆	—	2	2	no	—
394	C₂×SD₁₆	—	4	1	no	—
395	C₂×SD₁₆	—	4	1	no	—
396	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
400	#127	—	2	2	no	—
401	#127	—	2	2	no	—
402	C₄×D₄	—	4	1	no	—
403	C₄×D₄	—	4	1	no	—
404	C₄×D₄	—	4	1	no	—
405	C₄×D₄	—	4	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
423	#107	—	4	1	no	—
424	#106	—	4	1	no	—
425	#103	—	4	1	no	—
426	#103	—	4	1	no	—
427	#102	—	2	2	no	—
428	#102	—	2	2	no	—
429	#102	—	2	2	no	—
430	#102	—	2	2	no	—
431	#102	—	4	1	no	—
432	#102	—	4	1	no	—
433	#97	—	2	2	no	—
434	C₄×C₈	—	2	2	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	D₄×C₁₃	1	1	yes	characteristic
447	#95	D₄×C₁₃	1	1	yes	characteristic
448	#95	D₄×C₁₃	1	1	yes	characteristic
449	#95	D₄×C₁₃	1	1	yes	characteristic
450	C₂×C₁₃	—	8	2	no	—
451	C₂×C₁₃	—	8	2	no	—
452	C₂×C₁₃	#2603	1	1	yes	characteristic
453	C₂×C₁₃	#3118	1	1	yes	characteristic
454	C₂×C₁₃	#3123	1	1	yes	characteristic
455	C₂×C₁₃	#3174	1	1	yes	characteristic
456	C₂×C₁₃	#3179	1	1	yes	characteristic
457	C₂×C₁₃	#3222	1	1	yes	characteristic
458	C₂×C₁₃	#3224	1	1	yes	characteristic
459	C₂⁴	—	2	1	no	—
460	C₂⁴	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	8	1	no	—
480	C₂×D₄	—	8	1	no	—
481	C₂×D₄	—	8	1	no	—
482	C₂×D₄	—	8	1	no	—
483	C₂×D₄	C₁₃×#41	1	2	yes	—
484	C₂×D₄	C₁₃×#41	1	2	yes	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	8	1	no	—
494	C₂²×C₄	—	8	1	no	—
495	C₂²×C₄	—	8	1	no	—
496	C₂²×C₄	—	8	1	no	—
497	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
504	SD₁₆	—	4	4	no	—
505	SD₁₆	—	4	4	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	C₁₃×#41	1	2	yes	—
517	C₂×C₈	C₁₃×#41	1	2	yes	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	8	1	no	—
529	C₄⋊C₄	—	8	1	no	—
530	C₄⋊C₄	—	8	1	no	—
531	C₂²⋊C₄	—	4	2	no	—
532	C₂²⋊C₄	—	4	2	no	—
533	C₂²⋊C₄	—	8	1	no	—
534	C₂²⋊C₄	—	8	1	no	—
535	C₂²⋊C₄	—	8	1	no	—
536	C₂²⋊C₄	—	8	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₁₃	#29504	1	1	yes	characteristic, direct product factor, Sylow
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
559	Q₈	—	4	1	no	—
560	Q₈	—	4	1	no	—
561	Q₈	—	4	1	no	—
562	Q₈	—	4	1	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	2	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	1	no	—
570	D₄	—	4	1	no	—
571	D₄	—	8	4	no	—
572	D₄	—	8	4	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	8	4	no	—
610	C₂×C₄	—	8	4	no	—
611	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
612	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
613	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
614	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
615	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
617	C₈	—	2	2	no	—
618	C₈	—	2	2	no	—
619	C₈	—	4	1	no	—
620	C₈	—	4	1	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	—	8	1	no	—
630	C₂²	—	8	1	no	—
631	C₂²	—	8	1	no	—
632	C₂²	—	8	1	no	—
633	C₂²	—	8	1	no	—
634	C₂²	—	8	1	no	—
635	C₂²	C₁₃×#525	1	1	yes	characteristic
636	C₂²	C₁₃×#532	1	1	yes	characteristic
637	C₂²	C₁₃×#535	1	1	yes	characteristic
638	C₂²	C₁₃×#576	1	1	yes	characteristic
639	C₂²	C₁₃×#577	1	1	yes	characteristic
640	C₂²	C₁₃×#577	1	1	yes	characteristic
641	C₂²	C₁₃×#577	1	1	yes	characteristic
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	1	no	—
645	C₄	—	4	1	no	—
646	C₄	—	4	1	no	—
647	C₄	—	4	1	no	—
648	C₄	—	8	1	no	—
649	C₄	—	8	1	no	—
650	C₄	—	8	1	no	—
651	C₄	—	8	1	no	—
652	C₄	—	8	1	no	—
653	C₄	—	8	1	no	—
654	C₄	C₁₃×#551	1	1	yes	characteristic
655	C₄	C₁₃×#551	1	1	yes	characteristic
656	C₄	C₁₃×#553	1	1	yes	characteristic
657	C₄	C₁₃×#553	1	1	yes	characteristic
658	C₂	—	8	2	no	—
659	C₂	—	8	2	no	—
660	C₂	C₁₃×#2603	1	1	yes	characteristic
661	C₂	C₁₃×#3118	1	1	yes	characteristic
662	C₂	C₁₃×#3123	1	1	yes	characteristic
663	C₂	C₁₃×#3174	1	1	yes	characteristic
664	C₂	C₁₃×#3179	1	1	yes	characteristic
665	C₂	C₁₃×#3222	1	1	yes	characteristic
666	C₂	C₁₃×#3224	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 ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2645	C₂	semidirect
3. C₁₃×#2085	C₂	semidirect
4. C₁₃×#2074	C₂	semidirect
7. C₁₃×#1973	C₂	semidirect
8. C₁₃×#1968	C₂	semidirect
9. C₁₃×#1936	C₂	semidirect
10. C₁₃×#1934	C₂	semidirect
11. C₁₃×#1877	C₂	semidirect
12. C₁₃×#1877	C₂	semidirect
13. C₁₃×#1864	C₂	semidirect
14. C₁₃×#1862	C₂	semidirect
15. C₁₃×#1746	C₂	semidirect
126. #29504	C₁₃	direct (N × H)
211. #2645	C₂×C₁₃	semidirect
213. #2085	C₂×C₁₃	semidirect
214. #2074	C₂×C₁₃	semidirect
217. #1973	C₂×C₁₃	semidirect
218. #1968	C₂×C₁₃	semidirect
219. #1936	C₂×C₁₃	semidirect
220. #1934	C₂×C₁₃	semidirect
221. #1877	C₂×C₁₃	semidirect
222. #1877	C₂×C₁₃	semidirect
223. #1864	C₂×C₁₃	semidirect
224. #1862	C₂×C₁₃	semidirect
225. #1746	C₂×C₁₃	semidirect
543. C₁₃	#29504	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×#2645	2
C₁₃×#2328	2
C₁₃×#2085	2
C₁₃×#2074	2
C₁₃×#2041	2
C₁₃×#2014	2
C₁₃×#1973	2
C₁₃×#1968	2
C₁₃×#1936	2
C₁₃×#1934	2
C₁₃×#1877	2
C₁₃×#1864	2
C₁₃×#1862	2
C₁₃×#1746	2
#29504	13

Subgroups — C13×#29504 #15715843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29504 #15715843