Subgroups — C₁₃×#32822 #15719161

Order 3328.

626 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2861	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2097	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2092	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2073	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#2059	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2059	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#103	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×#102	C₂²	1	1	yes	characteristic
32	C₁₃×#391	C₂²	1	1	yes	characteristic
33	C₁₃×#391	C₂²	1	1	yes	characteristic
34	C₁₃×#390	C₂²	1	1	yes	characteristic
35	C₁₃×#390	C₂²	1	1	yes	characteristic
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#389	C₂²	1	1	yes	characteristic
38	C₁₃×#389	C₂²	1	1	yes	characteristic
39	C₁₃×#389	C₂²	1	1	yes	characteristic
40	C₁₃×#388	—	2	1	no	—
41	C₁₃×#388	—	2	1	no	—
42	C₁₃×#388	—	2	1	no	—
43	C₁₃×#388	—	2	1	no	—
44	C₁₃×#387	—	2	1	no	—
45	C₁₃×#387	—	2	1	no	—
46	C₁₃×#387	—	2	1	no	—
47	C₁₃×#387	—	2	1	no	—
48	C₁₃×#382	C₂²	1	1	yes	characteristic
49	C₁₃×#382	C₂²	1	1	yes	characteristic
50	C₄³×C₁₃	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	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#125	—	4	1	no	—
66	C₁₃×#125	—	4	1	no	—
67	C₁₃×#124	—	4	1	no	—
68	C₁₃×#124	—	4	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
94	C₁₃×#107	—	4	1	no	—
95	C₁₃×#107	—	4	1	no	—
96	C₁₃×#106	—	4	1	no	—
97	C₁₃×#106	—	4	1	no	—
98	C₁₃×C₄⋊C₈	—	4	1	no	—
99	C₁₃×C₄⋊C₈	—	4	1	no	—
100	C₁₃×#103	—	4	1	no	—
101	C₁₃×#103	—	4	1	no	—
102	C₁₃×#103	—	4	1	no	—
103	C₁₃×#103	—	4	1	no	—
104	C₁₃×#102	—	4	1	no	—
105	C₁₃×#102	—	4	1	no	—
106	C₁₃×#102	—	4	1	no	—
107	C₁₃×#102	—	4	1	no	—
108	C₁₃×#95	—	2	1	no	—
109	C₁₃×#95	—	2	1	no	—
110	C₁₃×#95	—	2	1	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	#32822	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	—	2	1	no	—
122	C₂×Q₈×C₁₃	—	2	1	no	—
123	C₂×Q₈×C₁₃	—	2	1	no	—
124	C₂×Q₈×C₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	2	1	no	—
126	C₂×Q₈×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	4	2	no	—
173	C₁₃×C₄⋊C₄	—	4	2	no	—
174	C₁₃×C₄⋊C₄	—	4	2	no	—
175	C₁₃×C₄⋊C₄	—	4	2	no	—
176	C₁₃×C₄⋊C₄	—	4	2	no	—
177	C₁₃×C₄⋊C₄	—	4	2	no	—
178	C₁₃×C₂²⋊C₄	—	4	2	no	—
179	C₁₃×C₂²⋊C₄	—	4	2	no	—
180	C₁₃×C₂²⋊C₄	—	4	2	no	—
181	C₁₃×C₂²⋊C₄	—	4	2	no	—
182	C₁₃×C₂²⋊C₄	—	4	2	no	—
183	C₁₃×C₂²⋊C₄	—	4	2	no	—
184	C₄²×C₁₃	—	2	2	no	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	—	2	1	no	—
187	C₄²×C₁₃	—	2	1	no	—
188	C₄²×C₁₃	—	2	1	no	—
189	C₄²×C₁₃	—	2	1	no	—
190	C₄²×C₁₃	—	2	1	no	—
191	C₄²×C₁₃	—	4	1	no	—
192	C₄²×C₁₃	—	4	1	no	—
193	C₄²×C₁₃	—	4	1	no	—
194	#2864	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#2861	C₂×C₁₃	1	1	yes	characteristic
196	#2097	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#2092	C₂×C₁₃	1	1	yes	characteristic
198	#2074	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#2073	C₂×C₁₃	1	1	yes	characteristic
200	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#2067	C₂×C₁₃	1	1	yes	characteristic
202	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#2065	C₂×C₁₃	1	1	yes	characteristic
204	#2059	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#2059	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#2042	C₂×C₁₃	1	1	yes	characteristic
207	#2042	C₂×C₁₃	1	1	yes	characteristic
208	#1831	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂³×C₁₃	—	4	1	no	—
210	C₂³×C₁₃	—	4	1	no	—
211	C₂³×C₁₃	—	4	1	no	—
212	C₂³×C₁₃	—	4	1	no	—
213	C₂³×C₁₃	—	4	1	no	—
214	C₂³×C₁₃	—	4	1	no	—
215	C₂³×C₁₃	—	4	1	no	—
216	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₃	—	4	1	no	—
218	Q₈×C₁₃	—	4	1	no	—
219	Q₈×C₁₃	—	4	1	no	—
220	Q₈×C₁₃	—	4	1	no	—
221	D₄×C₁₃	—	4	1	no	—
222	D₄×C₁₃	—	4	1	no	—
223	D₄×C₁₃	—	4	1	no	—
224	D₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	#135	1	2	yes	—
264	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
265	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
267	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
268	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
269	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
270	C₈×C₁₃	—	4	1	no	—
271	C₈×C₁₃	—	4	1	no	—
272	C₈×C₁₃	—	4	1	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
290	#391	C₂²×C₁₃	1	1	yes	characteristic
291	#391	C₂²×C₁₃	1	1	yes	characteristic
292	#390	C₂²×C₁₃	1	1	yes	characteristic
293	#390	C₂²×C₁₃	1	1	yes	characteristic
294	#389	C₂²×C₁₃	1	1	yes	characteristic
295	#389	C₂²×C₁₃	1	1	yes	characteristic
296	#389	C₂²×C₁₃	1	1	yes	characteristic
297	#389	C₂²×C₁₃	1	1	yes	characteristic
298	#388	—	2	1	no	—
299	#388	—	2	1	no	—
300	#388	—	2	1	no	—
301	#388	—	2	1	no	—
302	#387	—	2	1	no	—
303	#387	—	2	1	no	—
304	#387	—	2	1	no	—
305	#387	—	2	1	no	—
306	#382	C₂²×C₁₃	1	1	yes	characteristic
307	#382	C₂²×C₁₃	1	1	yes	characteristic
308	C₄³	C₂²×C₁₃	1	1	yes	characteristic
309	#340	C₂²×C₁₃	1	1	yes	characteristic
310	#340	C₂²×C₁₃	1	1	yes	characteristic
311	#340	C₂²×C₁₃	1	1	yes	characteristic
312	#340	C₂²×C₁₃	1	1	yes	characteristic
313	#336	C₂²×C₁₃	1	1	yes	characteristic
314	#336	C₂²×C₁₃	1	1	yes	characteristic
315	#336	C₂²×C₁₃	1	1	yes	characteristic
316	#336	C₂²×C₁₃	1	1	yes	characteristic
317	C₂²×C₁₃	—	8	1	no	—
318	C₂²×C₁₃	—	8	1	no	—
319	C₂²×C₁₃	—	8	1	no	—
320	C₂²×C₁₃	—	8	1	no	—
321	C₂²×C₁₃	—	8	1	no	—
322	C₂²×C₁₃	—	8	1	no	—
323	C₂²×C₁₃	—	8	1	no	—
324	C₂²×C₁₃	#535	1	1	yes	characteristic
325	C₂²×C₁₃	#536	1	1	yes	characteristic
326	C₂²×C₁₃	#537	1	1	yes	characteristic
327	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
328	C₂²×C₁₃	#575	1	1	yes	characteristic
329	C₂²×C₁₃	#575	1	1	yes	characteristic
330	C₂²×C₁₃	#575	1	1	yes	characteristic
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	4	1	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	4	1	no	—
335	C₄×C₁₃	—	4	1	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	—	8	1	no	—
338	C₄×C₁₃	—	8	1	no	—
339	C₄×C₁₃	—	8	1	no	—
340	C₄×C₁₃	—	8	1	no	—
341	C₄×C₁₃	—	8	1	no	—
342	C₄×C₁₃	—	8	1	no	—
343	C₄×C₁₃	—	8	1	no	—
344	C₄×C₁₃	#562	1	1	yes	characteristic
345	C₄×C₁₃	#562	1	1	yes	characteristic
346	C₄×C₁₃	#563	1	1	yes	characteristic
347	C₄×C₁₃	#563	1	1	yes	characteristic
348	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
349	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
354	#125	—	4	1	no	—
355	#125	—	4	1	no	—
356	#124	—	4	1	no	—
357	#124	—	4	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
377	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
378	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
379	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
383	#107	—	4	1	no	—
384	#107	—	4	1	no	—
385	#106	—	4	1	no	—
386	#106	—	4	1	no	—
387	C₄⋊C₈	—	4	1	no	—
388	C₄⋊C₈	—	4	1	no	—
389	#103	—	4	1	no	—
390	#103	—	4	1	no	—
391	#103	—	4	1	no	—
392	#103	—	4	1	no	—
393	#102	—	4	1	no	—
394	#102	—	4	1	no	—
395	#102	—	4	1	no	—
396	#102	—	4	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	C₂×C₁₃	—	16	1	no	—
410	C₂×C₁₃	#2820	1	1	yes	characteristic
411	C₂×C₁₃	#3212	1	1	yes	characteristic
412	C₂×C₁₃	#3219	1	1	yes	characteristic
413	C₂×C₁₃	#3233	1	1	yes	characteristic
414	C₂×C₁₃	#3240	1	1	yes	characteristic
415	C₂×C₁₃	#3250	1	1	yes	characteristic
416	C₂×C₁₃	#3256	1	1	yes	characteristic
417	C₂⁴	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	—	4	2	no	—
470	C₄⋊C₄	—	4	2	no	—
471	C₄⋊C₄	—	4	2	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₂²⋊C₄	—	4	2	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	4	1	no	—
488	C₄²	—	4	1	no	—
489	C₄²	—	4	1	no	—
490	C₁₃	#32822	1	1	yes	characteristic, direct product factor, Sylow
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	4	1	no	—
498	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	1	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	1	no	—
506	D₄	—	4	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	C₁₃×#135	1	2	yes	—
546	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
549	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
550	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
551	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	—	8	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	C₁₃×#535	1	1	yes	characteristic
564	C₂²	C₁₃×#536	1	1	yes	characteristic
565	C₂²	C₁₃×#537	1	1	yes	characteristic
566	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
567	C₂²	C₁₃×#575	1	1	yes	characteristic
568	C₂²	C₁₃×#575	1	1	yes	characteristic
569	C₂²	C₁₃×#575	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	1	no	—
581	C₄	—	8	1	no	—
582	C₄	—	8	1	no	—
583	C₄	C₁₃×#562	1	1	yes	characteristic
584	C₄	C₁₃×#562	1	1	yes	characteristic
585	C₄	C₁₃×#563	1	1	yes	characteristic
586	C₄	C₁₃×#563	1	1	yes	characteristic
587	C₂	—	16	1	no	—
588	C₂	C₁₃×#2820	1	1	yes	characteristic
589	C₂	C₁₃×#3212	1	1	yes	characteristic
590	C₂	C₁₃×#3219	1	1	yes	characteristic
591	C₂	C₁₃×#3233	1	1	yes	characteristic
592	C₂	C₁₃×#3240	1	1	yes	characteristic
593	C₂	C₁₃×#3250	1	1	yes	characteristic
594	C₂	C₁₃×#3256	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
1. C₁₃×#2864	C₂	semidirect
3. C₁₃×#2097	C₂	semidirect
5. C₁₃×#2074	C₂	semidirect
7. C₁₃×#2068	C₂	semidirect
9. C₁₃×#2066	C₂	semidirect
11. C₁₃×#2059	C₂	semidirect
12. C₁₃×#2059	C₂	semidirect
15. C₁₃×#1831	C₂	semidirect
120. #32822	C₁₃	direct (N × H)
194. #2864	C₂×C₁₃	semidirect
196. #2097	C₂×C₁₃	semidirect
198. #2074	C₂×C₁₃	semidirect
200. #2068	C₂×C₁₃	semidirect
202. #2066	C₂×C₁₃	semidirect
204. #2059	C₂×C₁₃	semidirect
205. #2059	C₂×C₁₃	semidirect
208. #1831	C₂×C₁₃	semidirect
490. C₁₃	#32822	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×#2864	2
C₁₃×#2861	2
C₁₃×#2097	2
C₁₃×#2092	2
C₁₃×#2074	2
C₁₃×#2073	2
C₁₃×#2068	2
C₁₃×#2067	2
C₁₃×#2066	2
C₁₃×#2065	2
C₁₃×#2059	2
C₁₃×#2042	2
C₁₃×#1831	2
#32822	13

Subgroups — C13×#32822 #15719161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32822 #15719161