Subgroups — C₁₃×#25031 #15711370

Order 3328.

850 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2420	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, complemented
7	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#465	—	2	4	no	—
23	C₄×C₁₃×SD₁₆	—	2	4	no	—
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#400	—	2	1	no	—
39	C₁₃×#397	—	2	1	no	—
40	C₁₃×#397	—	2	1	no	—
41	C₁₃×#394	—	2	1	no	—
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#389	C₂²	1	1	yes	characteristic
46	C₁₃×#388	—	2	1	no	—
47	C₁₃×#387	—	2	1	no	—
48	C₁₃×#386	—	2	1	no	—
49	C₁₃×#382	C₂²	1	1	yes	characteristic
50	C₁₃×#382	C₂²	1	1	yes	characteristic
51	C₁₃×#381	—	2	1	no	—
52	C₁₃×#380	C₂²	1	1	yes	characteristic
53	C₁₃×#380	C₂²	1	1	yes	characteristic
54	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×SD₁₆	—	2	2	no	—
67	C₂×C₁₃×SD₁₆	—	2	2	no	—
68	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
69	C₂²×C₈×C₁₃	—	2	2	no	—
70	C₂²×C₈×C₁₃	—	2	2	no	—
71	C₂²×C₈×C₁₃	—	2	2	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×C₂²⋊Q₈	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	4	1	no	—
78	C₁₃×#121	—	2	2	no	—
79	C₁₃×#121	—	4	1	no	—
80	C₄×Q₈×C₁₃	—	2	2	no	—
81	C₄×Q₈×C₁₃	—	4	1	no	—
82	C₄×D₄×C₁₃	—	2	2	no	—
83	C₄×D₄×C₁₃	—	4	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
102	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×#107	—	4	1	no	—
107	C₁₃×#107	—	4	1	no	—
108	C₁₃×#106	—	2	2	no	—
109	C₁₃×#106	—	2	2	no	—
110	C₁₃×#106	—	2	2	no	—
111	C₁₃×#103	—	2	2	no	—
112	C₁₃×#103	—	2	2	no	—
113	C₁₃×#103	—	2	2	no	—
114	C₁₃×#102	—	2	2	no	—
115	C₁₃×#102	—	2	2	no	—
116	C₁₃×#102	—	2	2	no	—
117	C₁₃×C₂²⋊C₈	—	2	2	no	—
118	C₄×C₈×C₁₃	—	2	2	no	—
119	C₄×C₈×C₁₃	—	2	2	no	—
120	C₁₃×#95	—	2	1	no	—
121	C₁₃×#95	—	2	1	no	—
122	C₁₃×#95	—	2	1	no	—
123	C₁₃×#95	—	2	1	no	—
124	C₁₃×#95	—	2	1	no	—
125	C₁₃×#95	—	2	1	no	—
126	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	D₄	1	1	yes	characteristic
131	C₁₃×#95	D₄	1	1	yes	characteristic
132	#25031	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂⁴×C₁₃	—	2	1	no	—
134	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
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	—	4	2	no	—
147	C₂×D₄×C₁₃	—	4	2	no	—
148	C₂×D₄×C₁₃	—	8	1	no	—
149	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	4	2	no	—
164	C₂²×C₄×C₁₃	—	4	2	no	—
165	C₂²×C₄×C₁₃	—	8	1	no	—
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	—	2	8	no	—
173	C₂×C₈×C₁₃	—	2	1	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	—	4	4	no	—
182	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
183	C₂×C₈×C₁₃	#41	1	2	yes	—
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	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	4	2	no	—
199	C₁₃×C₄⋊C₄	—	4	2	no	—
200	C₁₃×C₄⋊C₄	—	4	2	no	—
201	C₁₃×C₄⋊C₄	—	8	1	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	4	2	no	—
205	C₁₃×C₂²⋊C₄	—	4	2	no	—
206	C₁₃×C₂²⋊C₄	—	4	2	no	—
207	C₁₃×C₂²⋊C₄	—	4	2	no	—
208	C₁₃×C₂²⋊C₄	—	8	1	no	—
209	C₁₃×C₂²⋊C₄	—	8	1	no	—
210	C₁₃×C₂²⋊C₄	—	8	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	4	2	no	—
216	C₂×#465	C₂×C₁₃	1	1	yes	characteristic
217	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2421	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2420	C₂×C₁₃	1	1	yes	characteristic
220	#2074	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2073	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#2033	C₂×C₁₃	1	1	yes	characteristic
224	#1968	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1807	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	—	2	1	no	—
235	C₂³×C₁₃	—	2	1	no	—
236	C₂³×C₁₃	—	2	1	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	4	1	no	—
239	C₂³×C₁₃	—	4	1	no	—
240	C₂³×C₁₃	—	4	1	no	—
241	C₂³×C₁₃	—	4	1	no	—
242	C₂³×C₁₃	—	4	1	no	—
243	C₂³×C₁₃	—	4	1	no	—
244	C₂³×C₁₃	#135	1	2	yes	—
245	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	Q₈×C₁₃	—	2	2	no	—
247	Q₈×C₁₃	—	2	2	no	—
248	Q₈×C₁₃	—	4	1	no	—
249	Q₈×C₁₃	—	4	1	no	—
250	D₄×C₁₃	—	2	2	no	—
251	D₄×C₁₃	—	2	2	no	—
252	D₄×C₁₃	—	4	1	no	—
253	D₄×C₁₃	—	4	1	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	2	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	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	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	—	4	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	8	4	no	—
295	C₂×C₄×C₁₃	#135	1	2	yes	—
296	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
300	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
301	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
302	C₈×C₁₃	—	2	2	no	—
303	C₈×C₁₃	—	4	1	no	—
304	C₈×C₁₃	—	4	1	no	—
305	C₈×C₁₃	#123	1	4	yes	—
306	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
307	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
312	#465	—	2	4	no	—
313	C₄×SD₁₆	—	2	4	no	—
314	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
328	#400	—	2	1	no	—
329	#397	—	2	1	no	—
330	#397	—	2	1	no	—
331	#394	—	2	1	no	—
332	#391	C₂²×C₁₃	1	1	yes	characteristic
333	#390	C₂²×C₁₃	1	1	yes	characteristic
334	#389	C₂²×C₁₃	1	1	yes	characteristic
335	#389	C₂²×C₁₃	1	1	yes	characteristic
336	#388	—	2	1	no	—
337	#387	—	2	1	no	—
338	#386	—	2	1	no	—
339	#382	C₂²×C₁₃	1	1	yes	characteristic
340	#382	C₂²×C₁₃	1	1	yes	characteristic
341	#381	—	2	1	no	—
342	#380	C₂²×C₁₃	1	1	yes	characteristic
343	#380	C₂²×C₁₃	1	1	yes	characteristic
344	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
345	#340	C₂²×C₁₃	1	1	yes	characteristic
346	#340	C₂²×C₁₃	1	1	yes	characteristic
347	#340	C₂²×C₁₃	1	1	yes	characteristic
348	#340	C₂²×C₁₃	1	1	yes	characteristic
349	#336	C₂²×C₁₃	1	1	yes	characteristic
350	#336	C₂²×C₁₃	1	1	yes	characteristic
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	2	2	no	—
353	C₂²×C₁₃	—	2	2	no	—
354	C₂²×C₁₃	—	4	1	no	—
355	C₂²×C₁₃	—	4	1	no	—
356	C₂²×C₁₃	—	4	1	no	—
357	C₂²×C₁₃	—	4	1	no	—
358	C₂²×C₁₃	—	4	2	no	—
359	C₂²×C₁₃	—	4	2	no	—
360	C₂²×C₁₃	—	4	2	no	—
361	C₂²×C₁₃	—	8	1	no	—
362	C₂²×C₁₃	—	8	1	no	—
363	C₂²×C₁₃	—	8	1	no	—
364	C₂²×C₁₃	—	8	1	no	—
365	C₂²×C₁₃	#532	1	1	yes	characteristic
366	C₂²×C₁₃	D₄²	1	1	yes	characteristic
367	C₂²×C₁₃	#547	1	1	yes	characteristic
368	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
369	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
370	C₂²×C₁₃	#577	1	1	yes	characteristic
371	C₂²×C₁₃	#577	1	1	yes	characteristic
372	C₄×C₁₃	—	2	2	no	—
373	C₄×C₁₃	—	4	1	no	—
374	C₄×C₁₃	—	4	1	no	—
375	C₄×C₁₃	—	4	1	no	—
376	C₄×C₁₃	—	4	2	no	—
377	C₄×C₁₃	—	4	1	no	—
378	C₄×C₁₃	—	8	1	no	—
379	C₄×C₁₃	—	8	1	no	—
380	C₄×C₁₃	—	8	1	no	—
381	C₄×C₁₃	—	8	1	no	—
382	C₄×C₁₃	—	8	1	no	—
383	C₄×C₁₃	—	8	1	no	—
384	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
385	C₄×C₁₃	#542	1	1	yes	characteristic
386	C₄×C₁₃	#547	1	1	yes	characteristic
387	C₄×C₁₃	#553	1	1	yes	characteristic
388	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₂²×D₄	—	2	1	no	—
390	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
391	C₂³×C₄	—	2	1	no	—
392	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×SD₁₆	—	2	2	no	—
394	C₂×SD₁₆	—	2	2	no	—
395	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
396	C₂²×C₈	—	2	2	no	—
397	C₂²×C₈	—	2	2	no	—
398	C₂²×C₈	—	2	2	no	—
399	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	—	4	1	no	—
405	#121	—	2	2	no	—
406	#121	—	4	1	no	—
407	C₄×Q₈	—	2	2	no	—
408	C₄×Q₈	—	4	1	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	4	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
433	#107	—	4	1	no	—
434	#107	—	4	1	no	—
435	#106	—	2	2	no	—
436	#106	—	2	2	no	—
437	#106	—	2	2	no	—
438	#103	—	2	2	no	—
439	#103	—	2	2	no	—
440	#103	—	2	2	no	—
441	#102	—	2	2	no	—
442	#102	—	2	2	no	—
443	#102	—	2	2	no	—
444	C₂²⋊C₈	—	2	2	no	—
445	C₄×C₈	—	2	2	no	—
446	C₄×C₈	—	2	2	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	D₄×C₁₃	1	1	yes	characteristic
458	#95	D₄×C₁₃	1	1	yes	characteristic
459	C₂×C₁₃	—	4	2	no	—
460	C₂×C₁₃	—	8	2	no	—
461	C₂×C₁₃	#2422	1	1	yes	characteristic
462	C₂×C₁₃	#3168	1	1	yes	characteristic
463	C₂×C₁₃	#3174	1	1	yes	characteristic
464	C₂×C₁₃	#3282	1	1	yes	characteristic
465	C₂×C₁₃	#3282	1	1	yes	characteristic
466	C₂×C₁₃	#3337	1	1	yes	characteristic
467	C₂×C₁₃	#3340	1	1	yes	characteristic
468	C₂⁴	—	2	1	no	—
469	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	4	2	no	—
482	C₂×D₄	—	4	2	no	—
483	C₂×D₄	—	8	1	no	—
484	C₂×D₄	C₂×D₄×C₁₃	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	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	4	2	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	8	1	no	—
501	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
507	SD₁₆	—	2	8	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	—	4	4	no	—
517	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
518	C₂×C₈	C₁₃×#41	1	2	yes	—
519	C₂×C₈	C₁₃×#41	1	2	yes	—
520	C₂×C₈	C₁₃×#41	1	2	yes	—
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	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	4	2	no	—
534	C₄⋊C₄	—	4	2	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	8	1	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	4	2	no	—
540	C₂²⋊C₄	—	4	2	no	—
541	C₂²⋊C₄	—	4	2	no	—
542	C₂²⋊C₄	—	4	2	no	—
543	C₂²⋊C₄	—	8	1	no	—
544	C₂²⋊C₄	—	8	1	no	—
545	C₂²⋊C₄	—	8	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	4	2	no	—
551	C₁₃	#25031	1	1	yes	characteristic, direct product factor, Sylow
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	4	1	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	C₁₃×#135	1	2	yes	—
566	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
567	Q₈	—	2	2	no	—
568	Q₈	—	2	2	no	—
569	Q₈	—	4	1	no	—
570	Q₈	—	4	1	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	4	1	no	—
574	D₄	—	4	1	no	—
575	D₄	—	8	4	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	2	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	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	8	4	no	—
616	C₂×C₄	C₁₃×#135	1	2	yes	—
617	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
618	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
619	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
620	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
621	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
622	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
623	C₈	—	2	2	no	—
624	C₈	—	4	1	no	—
625	C₈	—	4	1	no	—
626	C₈	C₁₃×#123	1	4	yes	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	8	1	no	—
638	C₂²	—	8	1	no	—
639	C₂²	—	8	1	no	—
640	C₂²	—	8	1	no	—
641	C₂²	C₁₃×#532	1	1	yes	characteristic
642	C₂²	D₄²×C₁₃	1	1	yes	characteristic
643	C₂²	C₁₃×#547	1	1	yes	characteristic
644	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
645	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
646	C₂²	C₁₃×#577	1	1	yes	characteristic
647	C₂²	C₁₃×#577	1	1	yes	characteristic
648	C₄	—	2	2	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	2	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	—	8	1	no	—
657	C₄	—	8	1	no	—
658	C₄	—	8	1	no	—
659	C₄	—	8	1	no	—
660	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
661	C₄	C₁₃×#542	1	1	yes	characteristic
662	C₄	C₁₃×#547	1	1	yes	characteristic
663	C₄	C₁₃×#553	1	1	yes	characteristic
664	C₂	—	4	2	no	—
665	C₂	—	8	2	no	—
666	C₂	C₁₃×#2422	1	1	yes	characteristic
667	C₂	C₁₃×#3168	1	1	yes	characteristic
668	C₂	C₁₃×#3174	1	1	yes	characteristic
669	C₂	C₁₃×#3282	1	1	yes	characteristic
670	C₂	C₁₃×#3282	1	1	yes	characteristic
671	C₂	C₁₃×#3337	1	1	yes	characteristic
672	C₂	C₁₃×#3340	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
3. C₁₃×#2421	C₂	semidirect
5. C₁₃×#2074	C₂	semidirect
6. C₁₃×#2073	C₂	semidirect
7. C₁₃×#2036	C₂	semidirect
9. C₁₃×#1968	C₂	semidirect
10. C₁₃×#1941	C₂	semidirect
11. C₁₃×#1863	C₂	semidirect
12. C₁₃×#1862	C₂	semidirect
13. C₁₃×#1846	C₂	semidirect
14. C₁₃×#1807	C₂	semidirect
15. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
132. #25031	C₁₃	direct (N × H)
217. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
218. #2421	C₂×C₁₃	semidirect
220. #2074	C₂×C₁₃	semidirect
221. #2073	C₂×C₁₃	semidirect
222. #2036	C₂×C₁₃	semidirect
224. #1968	C₂×C₁₃	semidirect
225. #1941	C₂×C₁₃	semidirect
226. #1863	C₂×C₁₃	semidirect
227. #1862	C₂×C₁₃	semidirect
228. #1846	C₂×C₁₃	semidirect
229. #1807	C₂×C₁₃	semidirect
230. C₈×C₂²⋊C₄	C₂×C₁₃	semidirect
551. C₁₃	#25031	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#465	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2421	2
C₁₃×#2420	2
C₁₃×#2074	2
C₁₃×#2073	2
C₁₃×#2036	2
C₁₃×#2033	2
C₁₃×#1968	2
C₁₃×#1941	2
C₁₃×#1863	2
C₁₃×#1862	2
C₁₃×#1846	2
C₁₃×#1807	2
C₈×C₁₃×C₂²⋊C₄	2
#25031	13

Subgroups — C13×#25031 #15711370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25031 #15711370