Subgroups — C₁₃×#32568 #15718907

Order 3328.

716 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2088	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1934	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	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×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	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×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#396	—	2	1	no	—
31	C₁₃×#396	—	2	1	no	—
32	C₁₃×#395	—	2	1	no	—
33	C₁₃×#395	—	2	1	no	—
34	C₁₃×#391	—	2	1	no	—
35	C₁₃×#390	C₂²	1	1	yes	characteristic
36	C₁₃×#390	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×#389	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	1	yes	characteristic
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#384	—	2	1	no	—
44	C₁₃×#384	C₂²	1	1	yes	characteristic
45	C₁₃×#380	—	2	1	no	—
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₁₃×#340	C₂²	1	1	yes	characteristic
48	C₁₃×#340	C₂²	1	1	yes	characteristic
49	C₁₃×#340	C₂²	1	1	yes	characteristic
50	C₁₃×#340	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	—	2	1	no	—
60	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×C₄⋊Q₈	—	4	1	no	—
68	C₁₃×C₄⋊Q₈	—	4	1	no	—
69	C₁₃×C₂²⋊Q₈	—	4	4	no	—
70	C₄×Q₈×C₁₃	—	4	1	no	—
71	C₄×Q₈×C₁₃	—	4	1	no	—
72	C₄×D₄×C₁₃	—	4	1	no	—
73	C₄×D₄×C₁₃	—	4	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₄²×C₁₃	—	2	1	no	—
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#106	—	2	2	no	—
103	C₁₃×#106	—	2	2	no	—
104	C₁₃×#106	—	4	1	no	—
105	C₁₃×#106	—	4	1	no	—
106	C₁₃×C₄⋊C₈	—	4	1	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₁₃×#102	—	4	1	no	—
109	C₁₃×#102	—	4	1	no	—
110	C₁₃×#102	Q₈	1	4	yes	complemented
111	C₄×C₈×C₁₃	—	4	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	#32568	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	4	1	no	—
122	C₂×Q₈×C₁₃	—	4	1	no	—
123	C₂×Q₈×C₁₃	—	4	2	no	—
124	C₂×Q₈×C₁₃	—	8	1	no	—
125	C₂×Q₈×C₁₃	—	8	1	no	—
126	C₂×Q₈×C₁₃	SD₁₆	1	4	yes	—
127	C₂×D₄×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	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×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	—	4	2	no	—
141	C₂²×C₄×C₁₃	—	4	2	no	—
142	C₂²×C₄×C₁₃	—	4	2	no	—
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	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
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	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	4	1	no	—
175	C₁₃×C₄⋊C₄	—	4	1	no	—
176	C₁₃×C₄⋊C₄	—	4	1	no	—
177	C₁₃×C₄⋊C₄	—	4	2	no	—
178	C₁₃×C₄⋊C₄	—	4	2	no	—
179	C₁₃×C₄⋊C₄	—	4	2	no	—
180	C₁₃×C₄⋊C₄	—	4	2	no	—
181	C₁₃×C₄⋊C₄	—	8	1	no	—
182	C₁₃×C₄⋊C₄	—	8	1	no	—
183	C₁₃×C₄⋊C₄	—	8	1	no	—
184	C₁₃×C₄⋊C₄	—	8	1	no	—
185	C₁₃×C₄⋊C₄	—	8	1	no	—
186	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
187	C₁₃×C₄⋊C₄	#41	1	2	yes	—
188	C₁₃×C₂²⋊C₄	—	4	2	no	—
189	C₁₃×C₂²⋊C₄	—	4	2	no	—
190	C₁₃×C₂²⋊C₄	—	4	2	no	—
191	C₁₃×C₂²⋊C₄	—	8	1	no	—
192	C₁₃×C₂²⋊C₄	—	8	1	no	—
193	C₄²×C₁₃	—	2	1	no	—
194	C₄²×C₁₃	—	2	1	no	—
195	C₄²×C₁₃	—	2	1	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	—	2	1	no	—
199	C₄²×C₁₃	—	4	2	no	—
200	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#2538	C₂×C₁₃	1	1	yes	characteristic
202	#2099	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#2088	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#2084	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#2065	C₂×C₁₃	1	1	yes	characteristic
206	#2058	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#2023	C₂×C₁₃	1	1	yes	characteristic
208	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1934	C₂×C₁₃	1	1	yes	characteristic
211	#1926	C₂×C₁₃	1	1	yes	characteristic
212	#1919	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1864	C₂×C₁₃	1	1	yes	characteristic
214	#1864	C₂×C₁₃	1	1	yes	characteristic
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	4	1	no	—
217	C₂³×C₁₃	—	4	1	no	—
218	C₂³×C₁₃	—	4	1	no	—
219	C₂³×C₁₃	—	4	1	no	—
220	C₂³×C₁₃	—	4	1	no	—
221	C₂³×C₁₃	—	4	1	no	—
222	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	Q₈×C₁₃	—	4	4	no	—
224	Q₈×C₁₃	—	8	4	no	—
225	D₄×C₁₃	—	2	2	no	—
226	D₄×C₁₃	—	2	2	no	—
227	D₄×C₁₃	—	4	1	no	—
228	D₄×C₁₃	—	4	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	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	8	4	no	—
266	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
267	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
268	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
269	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
272	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
274	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
275	C₈×C₁₃	—	2	2	no	—
276	C₈×C₁₃	—	4	1	no	—
277	C₈×C₁₃	—	4	1	no	—
278	C₈×C₁₃	—	4	1	no	—
279	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₂²⋊Q₈	—	2	1	no	—
281	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×C₄⋊C₈	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	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
293	#396	—	2	1	no	—
294	#396	—	2	1	no	—
295	#395	—	2	1	no	—
296	#395	—	2	1	no	—
297	#391	—	2	1	no	—
298	#390	C₂²×C₁₃	1	1	yes	characteristic
299	#390	C₂²×C₁₃	1	1	yes	characteristic
300	#389	C₂²×C₁₃	1	1	yes	characteristic
301	#389	C₂²×C₁₃	1	1	yes	characteristic
302	#389	C₂²×C₁₃	1	1	yes	characteristic
303	#389	C₂²×C₁₃	1	1	yes	characteristic
304	#389	C₂²×C₁₃	1	1	yes	characteristic
305	#389	C₂²×C₁₃	1	1	yes	characteristic
306	#384	—	2	1	no	—
307	#384	C₂²×C₁₃	1	1	yes	characteristic
308	#380	—	2	1	no	—
309	C₄×C₄⋊C₄	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	#340	C₂²×C₁₃	1	1	yes	characteristic
314	#340	C₂²×C₁₃	1	1	yes	characteristic
315	#340	C₂²×C₁₃	1	1	yes	characteristic
316	#340	C₂²×C₁₃	1	1	yes	characteristic
317	#340	C₂²×C₁₃	1	1	yes	characteristic
318	#336	C₂²×C₁₃	1	1	yes	characteristic
319	#336	C₂²×C₁₃	1	1	yes	characteristic
320	#336	C₂²×C₁₃	1	1	yes	characteristic
321	#336	C₂²×C₁₃	1	1	yes	characteristic
322	C₂²×C₁₃	—	4	2	no	—
323	C₂²×C₁₃	—	4	2	no	—
324	C₂²×C₁₃	—	4	2	no	—
325	C₂²×C₁₃	—	8	1	no	—
326	C₂²×C₁₃	—	8	1	no	—
327	C₂²×C₁₃	—	8	1	no	—
328	C₂²×C₁₃	—	8	1	no	—
329	C₂²×C₁₃	#534	1	1	yes	characteristic
330	C₂²×C₁₃	#548	1	1	yes	characteristic
331	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
332	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
333	C₂²×C₁₃	#575	1	1	yes	characteristic
334	C₂²×C₁₃	#576	1	1	yes	characteristic
335	C₂²×C₁₃	#577	1	1	yes	characteristic
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	—	4	2	no	—
341	C₄×C₁₃	—	4	1	no	—
342	C₄×C₁₃	—	4	1	no	—
343	C₄×C₁₃	—	4	1	no	—
344	C₄×C₁₃	—	8	1	no	—
345	C₄×C₁₃	—	8	1	no	—
346	C₄×C₁₃	—	8	1	no	—
347	C₄×C₁₃	—	8	1	no	—
348	C₄×C₁₃	—	8	1	no	—
349	C₄×C₁₃	#542	1	1	yes	characteristic
350	C₄×C₁₃	#544	1	1	yes	characteristic
351	C₄×C₁₃	#554	1	1	yes	characteristic
352	C₄×C₁₃	#563	1	1	yes	characteristic
353	C₂²×Q₈	—	2	1	no	—
354	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
355	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
356	C₂³×C₄	—	2	1	no	—
357	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
360	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
361	C₄⋊Q₈	—	4	1	no	—
362	C₄⋊Q₈	—	4	1	no	—
363	C₂²⋊Q₈	—	4	4	no	—
364	C₄×Q₈	—	4	1	no	—
365	C₄×Q₈	—	4	1	no	—
366	C₄×D₄	—	4	1	no	—
367	C₄×D₄	—	4	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
379	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
396	#106	—	2	2	no	—
397	#106	—	2	2	no	—
398	#106	—	4	1	no	—
399	#106	—	4	1	no	—
400	C₄⋊C₈	—	4	1	no	—
401	#102	—	2	2	no	—
402	#102	—	4	1	no	—
403	#102	—	4	1	no	—
404	#102	Q₈×C₁₃	1	4	yes	complemented
405	C₄×C₈	—	4	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	C₂×C₁₃	—	8	2	no	—
414	C₂×C₁₃	#2729	1	1	yes	characteristic
415	C₂×C₁₃	#3187	1	1	yes	characteristic
416	C₂×C₁₃	#3198	1	1	yes	characteristic
417	C₂×C₁₃	#3362	1	1	yes	characteristic
418	C₂×C₁₃	#3376	1	1	yes	characteristic
419	C₂×C₁₃	Q₈×SD₁₆	1	1	yes	characteristic
420	C₂×C₁₃	#3389	1	1	yes	characteristic
421	C₂⁴	—	2	1	no	—
422	C₂×Q₈	—	4	1	no	—
423	C₂×Q₈	—	4	1	no	—
424	C₂×Q₈	—	4	2	no	—
425	C₂×Q₈	—	8	1	no	—
426	C₂×Q₈	—	8	1	no	—
427	C₂×Q₈	C₁₃×SD₁₆	1	4	yes	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
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	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	2	no	—
479	C₄⋊C₄	—	4	2	no	—
480	C₄⋊C₄	—	4	2	no	—
481	C₄⋊C₄	—	4	2	no	—
482	C₄⋊C₄	—	8	1	no	—
483	C₄⋊C₄	—	8	1	no	—
484	C₄⋊C₄	—	8	1	no	—
485	C₄⋊C₄	—	8	1	no	—
486	C₄⋊C₄	—	8	1	no	—
487	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
488	C₄⋊C₄	C₁₃×#41	1	2	yes	—
489	C₂²⋊C₄	—	4	2	no	—
490	C₂²⋊C₄	—	4	2	no	—
491	C₂²⋊C₄	—	4	2	no	—
492	C₂²⋊C₄	—	8	1	no	—
493	C₂²⋊C₄	—	8	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	4	2	no	—
501	C₁₃	#32568	1	1	yes	characteristic, direct product factor, Sylow
502	C₂³	—	2	2	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	4	1	no	—
509	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
510	Q₈	—	4	4	no	—
511	Q₈	—	8	4	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	2	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	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	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	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	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	8	4	no	—
553	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
554	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
555	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
556	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
557	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
558	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
559	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
561	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
562	C₈	—	2	2	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	8	1	no	—
570	C₂²	—	8	1	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	8	1	no	—
573	C₂²	C₁₃×#534	1	1	yes	characteristic
574	C₂²	C₁₃×#548	1	1	yes	characteristic
575	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
576	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
577	C₂²	C₁₃×#575	1	1	yes	characteristic
578	C₂²	C₁₃×#576	1	1	yes	characteristic
579	C₂²	C₁₃×#577	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	—	8	1	no	—
591	C₄	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	C₁₃×#542	1	1	yes	characteristic
594	C₄	C₁₃×#544	1	1	yes	characteristic
595	C₄	C₁₃×#554	1	1	yes	characteristic
596	C₄	C₁₃×#563	1	1	yes	characteristic
597	C₂	—	8	2	no	—
598	C₂	C₁₃×#2729	1	1	yes	characteristic
599	C₂	C₁₃×#3187	1	1	yes	characteristic
600	C₂	C₁₃×#3198	1	1	yes	characteristic
601	C₂	C₁₃×#3362	1	1	yes	characteristic
602	C₂	C₁₃×#3376	1	1	yes	characteristic
603	C₂	Q₈×C₁₃×SD₁₆	1	1	yes	characteristic
604	C₂	C₁₃×#3389	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2567	C₂	semidirect
3. C₁₃×#2099	C₂	semidirect
4. C₁₃×#2088	C₂	semidirect
5. C₁₃×#2084	C₂	semidirect
7. C₁₃×#2058	C₂	semidirect
9. C₁₃×#1984	C₂	semidirect
10. C₁₃×#1941	C₂	semidirect
13. C₁₃×#1919	C₂	semidirect
110. C₁₃×#102	Q₈	semidirect
119. #32568	C₁₃	direct (N × H)
200. #2567	C₂×C₁₃	semidirect
202. #2099	C₂×C₁₃	semidirect
203. #2088	C₂×C₁₃	semidirect
204. #2084	C₂×C₁₃	semidirect
206. #2058	C₂×C₁₃	semidirect
208. #1984	C₂×C₁₃	semidirect
209. #1941	C₂×C₁₃	semidirect
212. #1919	C₂×C₁₃	semidirect
404. #102	Q₈×C₁₃	semidirect
501. C₁₃	#32568	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×#2567	2
C₁₃×#2538	2
C₁₃×#2099	2
C₁₃×#2088	2
C₁₃×#2084	2
C₁₃×#2065	2
C₁₃×#2058	2
C₁₃×#2023	2
C₁₃×#1984	2
C₁₃×#1941	2
C₁₃×#1934	2
C₁₃×#1926	2
C₁₃×#1919	2
C₁₃×#1864	2
#32568	13

Subgroups — C13×#32568 #15718907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32568 #15718907