Subgroups — C₁₃×#29102 #15715441

Order 3328.

668 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2513	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2088	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2074	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1935	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#102	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×#97	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#400	—	2	1	no	—
31	C₁₃×#398	—	2	1	no	—
32	C₁₃×#397	—	2	1	no	—
33	C₁₃×#397	—	2	1	no	—
34	C₁₃×#391	C₂²	1	1	yes	characteristic
35	C₁₃×#391	C₂²	1	1	yes	characteristic
36	C₁₃×#390	C₂²	1	1	yes	characteristic
37	C₁₃×#390	C₂²	1	1	yes	characteristic
38	C₁₃×#390	C₂²	1	1	yes	characteristic
39	C₁₃×#389	—	2	1	no	—
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×#388	—	2	1	no	—
44	C₁₃×#388	—	2	1	no	—
45	C₁₃×#387	—	2	1	no	—
46	C₁₃×#382	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×C₄⋊C₄	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×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	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	C₂×C₁₃×SD₁₆	—	2	2	no	—
62	C₂×C₁₃×SD₁₆	—	2	2	no	—
63	C₂×C₁₃×SD₁₆	—	4	1	no	—
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	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#125	—	2	2	no	—
69	C₁₃×#125	—	4	1	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	—	4	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	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₄²×C₁₃	—	2	1	no	—
93	C₂×C₄²×C₁₃	—	2	1	no	—
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#106	—	2	2	no	—
98	C₁₃×C₄⋊C₈	—	2	2	no	—
99	C₁₃×#103	—	2	2	no	—
100	C₁₃×#103	—	2	2	no	—
101	C₁₃×#103	—	2	2	no	—
102	C₁₃×#102	—	2	2	no	—
103	C₁₃×#102	—	2	2	no	—
104	C₁₃×#102	—	4	1	no	—
105	C₁₃×#97	—	2	2	no	—
106	C₁₃×#97	—	4	1	no	—
107	C₄×C₈×C₁₃	—	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	D₄	1	1	yes	characteristic
119	C₁₃×#95	D₄	1	1	yes	characteristic
120	#29102	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	#41	1	2	yes	—
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	C₁₃×SD₁₆	—	4	4	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	#41	1	2	yes	—
160	C₂×C₈×C₁₃	#41	1	2	yes	—
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	1	no	—
173	C₁₃×C₄⋊C₄	—	4	1	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×C₄⋊C₄	—	4	2	no	—
179	C₁₃×C₄⋊C₄	—	8	1	no	—
180	C₁₃×C₄⋊C₄	#41	1	2	yes	—
181	C₁₃×C₂²⋊C₄	—	4	2	no	—
182	C₁₃×C₂²⋊C₄	—	4	2	no	—
183	C₁₃×C₂²⋊C₄	—	8	1	no	—
184	C₁₃×C₂²⋊C₄	—	8	1	no	—
185	C₁₃×C₂²⋊C₄	—	8	1	no	—
186	C₁₃×C₂²⋊C₄	—	8	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	—	2	1	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	4	2	no	—
194	C₄²×C₁₃	—	8	1	no	—
195	#2513	C₂×C₁₃	1	1	yes	characteristic
196	#2453	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#2088	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#2074	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#2055	C₂×C₁₃	1	1	yes	characteristic
200	#2025	C₂×C₁₃	1	1	yes	characteristic
201	#1991	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#1968	C₂×C₁₃	1	1	yes	characteristic
203	#1936	C₂×C₁₃	1	1	yes	characteristic
204	#1936	C₂×C₁₃	1	1	yes	characteristic
205	#1935	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1920	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#1880	C₂×C₁₃	1	1	yes	characteristic
208	#1771	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1763	C₂×C₁₃	1	1	yes	characteristic, complemented
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	—	4	1	no	—
217	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₁₃	—	2	2	no	—
219	Q₈×C₁₃	—	2	2	no	—
220	Q₈×C₁₃	—	4	1	no	—
221	Q₈×C₁₃	—	4	1	no	—
222	D₄×C₁₃	—	4	1	no	—
223	D₄×C₁₃	—	4	1	no	—
224	D₄×C₁₃	—	4	1	no	—
225	D₄×C₁₃	—	4	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	2	no	—
233	C₂×C₄×C₁₃	—	2	2	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	—	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	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
270	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
271	C₈×C₁₃	—	2	2	no	—
272	C₈×C₁₃	—	2	2	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₈×C₁₃	—	4	1	no	—
275	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
289	#400	—	2	1	no	—
290	#398	—	2	1	no	—
291	#397	—	2	1	no	—
292	#397	—	2	1	no	—
293	#391	C₂²×C₁₃	1	1	yes	characteristic
294	#391	C₂²×C₁₃	1	1	yes	characteristic
295	#390	C₂²×C₁₃	1	1	yes	characteristic
296	#390	C₂²×C₁₃	1	1	yes	characteristic
297	#390	C₂²×C₁₃	1	1	yes	characteristic
298	#389	—	2	1	no	—
299	#389	C₂²×C₁₃	1	1	yes	characteristic
300	#389	C₂²×C₁₃	1	1	yes	characteristic
301	#389	C₂²×C₁₃	1	1	yes	characteristic
302	#388	—	2	1	no	—
303	#388	—	2	1	no	—
304	#387	—	2	1	no	—
305	#382	C₂²×C₁₃	1	1	yes	characteristic
306	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
307	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
308	#340	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	#340	C₂²×C₁₃	1	1	yes	characteristic
314	#340	C₂²×C₁₃	1	1	yes	characteristic
315	#340	C₂²×C₁₃	1	1	yes	characteristic
316	#336	C₂²×C₁₃	1	1	yes	characteristic
317	#336	C₂²×C₁₃	1	1	yes	characteristic
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	—	8	1	no	—
325	C₂²×C₁₃	#532	1	1	yes	characteristic
326	C₂²×C₁₃	#546	1	1	yes	characteristic
327	C₂²×C₁₃	#548	1	1	yes	characteristic
328	C₂²×C₁₃	#575	1	1	yes	characteristic
329	C₂²×C₁₃	#575	1	1	yes	characteristic
330	C₂²×C₁₃	#577	1	1	yes	characteristic
331	C₂²×C₁₃	#577	1	1	yes	characteristic
332	C₄×C₁₃	—	4	2	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	—	4	2	no	—
338	C₄×C₁₃	—	4	1	no	—
339	C₄×C₁₃	—	4	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	—	8	1	no	—
345	C₄×C₁₃	#529	1	1	yes	characteristic
346	C₄×C₁₃	#539	1	1	yes	characteristic
347	C₄×C₁₃	#551	1	1	yes	characteristic
348	C₄×C₁₃	#556	1	1	yes	characteristic
349	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
350	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂×SD₁₆	—	2	2	no	—
352	C₂×SD₁₆	—	2	2	no	—
353	C₂×SD₁₆	—	4	1	no	—
354	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
358	#125	—	2	2	no	—
359	#125	—	4	1	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	—	4	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
387	#106	—	2	2	no	—
388	C₄⋊C₈	—	2	2	no	—
389	#103	—	2	2	no	—
390	#103	—	2	2	no	—
391	#103	—	2	2	no	—
392	#102	—	2	2	no	—
393	#102	—	2	2	no	—
394	#102	—	4	1	no	—
395	#97	—	2	2	no	—
396	#97	—	4	1	no	—
397	C₄×C₈	—	4	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	D₄×C₁₃	1	1	yes	characteristic
409	#95	D₄×C₁₃	1	1	yes	characteristic
410	C₂×C₁₃	—	16	1	no	—
411	C₂×C₁₃	#2560	1	1	yes	characteristic
412	C₂×C₁₃	#3174	1	1	yes	characteristic
413	C₂×C₁₃	#3183	1	1	yes	characteristic
414	C₂×C₁₃	#3307	1	1	yes	characteristic
415	C₂×C₁₃	#3321	1	1	yes	characteristic
416	C₂×C₁₃	#3371	1	1	yes	characteristic
417	C₂×C₁₃	#3371	1	1	yes	characteristic
418	C₂⁴	—	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×Q₈	C₁₃×#41	1	2	yes	—
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	C₂×D₄	—	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	—	2	1	no	—
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	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
445	SD₁₆	—	4	4	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	C₂×C₈	C₁₃×#41	1	2	yes	—
457	C₂×C₈	C₁₃×#41	1	2	yes	—
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	—	2	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	2	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₄⋊C₄	—	4	2	no	—
476	C₄⋊C₄	—	8	1	no	—
477	C₄⋊C₄	C₁₃×#41	1	2	yes	—
478	C₂²⋊C₄	—	4	2	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₂²⋊C₄	—	8	1	no	—
481	C₂²⋊C₄	—	8	1	no	—
482	C₂²⋊C₄	—	8	1	no	—
483	C₂²⋊C₄	—	8	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	4	2	no	—
491	C₄²	—	8	1	no	—
492	C₁₃	#29102	1	1	yes	characteristic, direct product factor, Sylow
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	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
501	Q₈	—	2	2	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	D₄	—	4	1	no	—
506	D₄	—	4	1	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	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	2	no	—
516	C₂×C₄	—	2	2	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	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	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	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
549	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
550	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
551	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
552	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
554	C₈	—	2	2	no	—
555	C₈	—	2	2	no	—
556	C₈	—	4	1	no	—
557	C₈	—	4	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	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	C₁₃×#532	1	1	yes	characteristic
566	C₂²	C₁₃×#546	1	1	yes	characteristic
567	C₂²	C₁₃×#548	1	1	yes	characteristic
568	C₂²	C₁₃×#575	1	1	yes	characteristic
569	C₂²	C₁₃×#575	1	1	yes	characteristic
570	C₂²	C₁₃×#577	1	1	yes	characteristic
571	C₂²	C₁₃×#577	1	1	yes	characteristic
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	8	1	no	—
581	C₄	—	8	1	no	—
582	C₄	—	8	1	no	—
583	C₄	—	8	1	no	—
584	C₄	—	8	1	no	—
585	C₄	C₁₃×#529	1	1	yes	characteristic
586	C₄	C₁₃×#539	1	1	yes	characteristic
587	C₄	C₁₃×#551	1	1	yes	characteristic
588	C₄	C₁₃×#556	1	1	yes	characteristic
589	C₂	—	16	1	no	—
590	C₂	C₁₃×#2560	1	1	yes	characteristic
591	C₂	C₁₃×#3174	1	1	yes	characteristic
592	C₂	C₁₃×#3183	1	1	yes	characteristic
593	C₂	C₁₃×#3307	1	1	yes	characteristic
594	C₂	C₁₃×#3321	1	1	yes	characteristic
595	C₂	C₁₃×#3371	1	1	yes	characteristic
596	C₂	C₁₃×#3371	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 ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2453	C₂	semidirect
3. C₁₃×#2088	C₂	semidirect
4. C₁₃×#2074	C₂	semidirect
7. C₁₃×#1991	C₂	semidirect
11. C₁₃×#1935	C₂	semidirect
12. C₁₃×#1920	C₂	semidirect
14. C₁₃×#1771	C₂	semidirect
15. C₁₃×#1763	C₂	semidirect
120. #29102	C₁₃	direct (N × H)
196. #2453	C₂×C₁₃	semidirect
197. #2088	C₂×C₁₃	semidirect
198. #2074	C₂×C₁₃	semidirect
201. #1991	C₂×C₁₃	semidirect
205. #1935	C₂×C₁₃	semidirect
206. #1920	C₂×C₁₃	semidirect
208. #1771	C₂×C₁₃	semidirect
209. #1763	C₂×C₁₃	semidirect
492. C₁₃	#29102	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×#2513	2
C₁₃×#2453	2
C₁₃×#2088	2
C₁₃×#2074	2
C₁₃×#2055	2
C₁₃×#2025	2
C₁₃×#1991	2
C₁₃×#1968	2
C₁₃×#1936	2
C₁₃×#1935	2
C₁₃×#1920	2
C₁₃×#1880	2
C₁₃×#1771	2
C₁₃×#1763	2
#29102	13

Subgroups — C13×#29102 #15715441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29102 #15715441