Subgroups — C₁₃×#24497 #15710836

Order 3328.

950 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2436	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2068	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1983	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1927	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1895	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#124	C₂²	1	2	yes	—
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₁₃×#482	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₁₃×#419	—	2	4	no	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₃×#393	—	2	1	no	—
31	C₁₃×#393	—	2	1	no	—
32	C₁₃×#391	C₂²	1	2	yes	—
33	C₁₃×#389	C₂²	1	2	yes	—
34	C₁₃×#388	—	2	2	no	—
35	C₁₃×#386	—	2	2	no	—
36	C₁₃×#383	—	2	1	no	—
37	C₁₃×#380	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
40	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	—	2	4	no	—
45	C₂²×Q₈×C₁₃	—	2	2	no	—
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	—	4	2	no	—
48	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂×C₁₃×M₁₆	—	4	2	no	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₁₃×#124	—	2	4	no	—
59	C₁₃×#124	—	4	2	no	—
60	C₁₃×#121	—	2	2	no	—
61	C₁₃×#121	—	2	2	no	—
62	C₁₃×#117	—	2	2	no	—
63	C₁₃×#117	D₄	1	4	yes	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	—	2	2	no	—
77	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
78	C₁₃×#107	—	2	2	no	—
79	C₁₃×#106	—	2	2	no	—
80	C₁₃×C₄⋊C₈	—	4	2	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₁₃×#103	—	4	2	no	—
85	C₁₃×#102	—	2	2	no	—
86	C₁₃×#102	—	2	2	no	—
87	C₁₃×#102	—	4	2	no	—
88	C₁₃×C₂²⋊C₈	—	2	2	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	2	no	—
93	C₁₃×#95	—	2	2	no	—
94	C₁₃×#95	D₄	1	1	yes	characteristic
95	C₁₃×#95	D₄	1	1	yes	characteristic
96	#24497	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	—	2	1	no	—
98	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	2	8	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	4	4	no	—
106	C₂×Q₈×C₁₃	—	4	8	no	—
107	C₂×Q₈×C₁₃	—	4	4	no	—
108	C₂×Q₈×C₁₃	—	4	2	no	—
109	C₂×Q₈×C₁₃	#41	1	4	yes	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	4	4	no	—
115	C₂×D₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	4	4	no	—
124	C₂²×C₄×C₁₃	—	4	2	no	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	#41	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₁₃×M₁₆	—	4	4	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	4	4	no	—
146	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
147	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
148	C₁₃×C₂²⋊C₄	—	2	4	no	—
149	C₁₃×C₂²⋊C₄	—	4	2	no	—
150	C₁₃×C₂²⋊C₄	—	4	4	no	—
151	C₁₃×C₂²⋊C₄	—	4	4	no	—
152	C₁₃×C₂²⋊C₄	—	4	2	no	—
153	C₁₃×C₂²⋊C₄	—	8	1	no	—
154	C₄²×C₁₃	—	2	4	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	8	2	no	—
158	C₂×#482	C₂×C₁₃	1	1	yes	characteristic
159	C₂×#419	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#2436	C₂×C₁₃	1	1	yes	characteristic
161	#2347	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#2068	C₂×C₁₃	1	2	yes	complemented
163	#2042	C₂×C₁₃	1	2	yes	complemented
164	#1983	C₂×C₁₃	1	2	yes	complemented
165	#1927	C₂×C₁₃	1	2	yes	complemented
166	#1895	C₂×C₁₃	1	1	yes	characteristic
167	#1851	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	—	2	2	no	—
171	C₂³×C₁₃	—	2	1	no	—
172	C₂³×C₁₃	—	2	1	no	—
173	C₂³×C₁₃	—	4	1	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	#121	1	2	yes	—
179	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₃	—	2	4	no	—
181	Q₈×C₁₃	—	2	4	no	—
182	Q₈×C₁₃	—	4	8	no	—
183	Q₈×C₁₃	—	4	2	no	—
184	Q₈×C₁₃	—	4	2	no	—
185	D₄×C₁₃	—	4	1	no	—
186	D₄×C₁₃	—	4	1	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	8	4	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	4	8	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	#121	1	2	yes	—
214	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
216	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
218	C₈×C₁₃	—	4	1	no	—
219	C₈×C₁₃	—	4	1	no	—
220	C₈×C₁₃	—	4	2	no	—
221	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×#124	C₂²×C₁₃	1	2	yes	—
224	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
226	#482	—	2	4	no	—
227	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
230	#419	—	2	4	no	—
231	C₂×#103	C₂²×C₁₃	1	2	yes	—
232	C₂×#103	C₂²×C₁₃	1	2	yes	—
233	C₂×#103	C₂²×C₁₃	1	2	yes	—
234	C₂×#103	C₂²×C₁₃	1	2	yes	—
235	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#102	C₂²×C₁₃	1	2	yes	—
238	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
239	#393	—	2	1	no	—
240	#393	—	2	1	no	—
241	#391	C₂²×C₁₃	1	2	yes	—
242	#389	C₂²×C₁₃	1	2	yes	—
243	#388	—	2	2	no	—
244	#386	—	2	2	no	—
245	#383	—	2	1	no	—
246	#380	C₂²×C₁₃	1	1	yes	characteristic
247	C₄×C₄⋊C₄	—	2	1	no	—
248	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
249	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
250	#340	C₂²×C₁₃	1	2	yes	—
251	#336	C₂²×C₁₃	1	2	yes	—
252	C₂²×C₁₃	—	2	2	no	—
253	C₂²×C₁₃	—	2	2	no	—
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	—	4	2	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	—	8	1	no	—
258	C₂²×C₁₃	—	8	1	no	—
259	C₂²×C₁₃	—	8	1	no	—
260	C₂²×C₁₃	—	8	2	no	—
261	C₂²×C₁₃	—	8	2	no	—
262	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
263	C₂²×C₁₃	#546	1	2	yes	—
264	C₂²×C₁₃	#575	1	2	yes	—
265	C₂²×C₁₃	#577	1	1	yes	characteristic
266	C₂²×C₁₃	#578	1	1	yes	characteristic
267	C₄×C₁₃	—	2	2	no	—
268	C₄×C₁₃	—	4	4	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	4	2	no	—
271	C₄×C₁₃	—	4	2	no	—
272	C₄×C₁₃	—	4	2	no	—
273	C₄×C₁₃	—	8	1	no	—
274	C₄×C₁₃	—	8	2	no	—
275	C₄×C₁₃	#525	1	1	yes	characteristic
276	C₄×C₁₃	#535	1	1	yes	characteristic
277	C₄×C₁₃	#551	1	2	yes	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×Q₈	—	2	4	no	—
280	C₂²×Q₈	—	2	2	no	—
281	C₂²×Q₈	—	2	2	no	—
282	C₂²×Q₈	—	4	2	no	—
283	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂³×C₄	—	2	1	no	—
287	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	4	2	no	—
290	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
293	#124	—	2	4	no	—
294	#124	—	4	2	no	—
295	#121	—	2	2	no	—
296	#121	—	2	2	no	—
297	#117	—	2	2	no	—
298	#117	D₄×C₁₃	1	4	yes	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
313	#107	—	2	2	no	—
314	#106	—	2	2	no	—
315	C₄⋊C₈	—	4	2	no	—
316	#103	—	2	4	no	—
317	#103	—	2	4	no	—
318	#103	—	2	4	no	—
319	#103	—	4	2	no	—
320	#102	—	2	2	no	—
321	#102	—	2	2	no	—
322	#102	—	4	2	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	#95	—	2	1	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	#95	—	2	2	no	—
329	#95	D₄×C₁₃	1	1	yes	characteristic
330	#95	D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₁₃	—	4	2	no	—
332	C₂×C₁₃	—	16	1	no	—
333	C₂×C₁₃	#2411	1	1	yes	characteristic
334	C₂×C₁₃	#3040	1	1	yes	characteristic
335	C₂×C₁₃	#3046	1	1	yes	characteristic
336	C₂×C₁₃	#3313	1	2	yes	—
337	C₂×C₁₃	#3326	1	2	yes	—
338	C₂⁴	—	2	1	no	—
339	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	8	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	4	4	no	—
347	C₂×Q₈	—	4	8	no	—
348	C₂×Q₈	—	4	4	no	—
349	C₂×Q₈	—	4	2	no	—
350	C₂×Q₈	C₁₃×#41	1	4	yes	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
370	C₂²×C₄	C₁₃×#41	1	2	yes	—
371	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
372	M₁₆	—	4	4	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
388	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	8	1	no	—
395	C₄²	—	2	4	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	8	2	no	—
399	C₁₃	#24497	1	1	yes	characteristic, direct product factor, Sylow
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	C₁₃×#121	1	2	yes	—
410	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	8	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	2	no	—
419	D₄	—	8	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	4	8	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	C₁₃×#121	1	2	yes	—
445	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
446	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
447	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
448	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
449	C₈	—	4	1	no	—
450	C₈	—	4	1	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	1	no	—
462	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
463	C₂²	C₁₃×#546	1	2	yes	—
464	C₂²	C₁₃×#575	1	2	yes	—
465	C₂²	C₁₃×#577	1	1	yes	characteristic
466	C₂²	C₁₃×#578	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	4	no	—
473	C₄	—	8	1	no	—
474	C₄	—	8	2	no	—
475	C₄	C₁₃×#525	1	1	yes	characteristic
476	C₄	C₁₃×#535	1	1	yes	characteristic
477	C₄	C₁₃×#551	1	2	yes	—
478	C₂	—	4	2	no	—
479	C₂	—	16	1	no	—
480	C₂	C₁₃×#2411	1	1	yes	characteristic
481	C₂	C₁₃×#3040	1	1	yes	characteristic
482	C₂	C₁₃×#3046	1	1	yes	characteristic
483	C₂	C₁₃×#3313	1	2	yes	—
484	C₂	C₁₃×#3326	1	2	yes	—

	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×C₁₃×#419	C₂	semidirect
4. C₁₃×#2347	C₂	semidirect
5. C₁₃×#2068	C₂	semidirect
6. C₁₃×#2042	C₂	semidirect
7. C₁₃×#1983	C₂	semidirect
8. C₁₃×#1927	C₂	semidirect
10. C₁₃×#1851	C₂	semidirect
11. C₁₃×#1787	C₂	semidirect
96. #24497	C₁₃	direct (N × H)
159. C₂×#419	C₂×C₁₃	semidirect
161. #2347	C₂×C₁₃	semidirect
162. #2068	C₂×C₁₃	semidirect
163. #2042	C₂×C₁₃	semidirect
164. #1983	C₂×C₁₃	semidirect
165. #1927	C₂×C₁₃	semidirect
167. #1851	C₂×C₁₃	semidirect
168. #1787	C₂×C₁₃	semidirect
399. C₁₃	#24497	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×#482	2
C₂×C₁₃×#419	2
C₁₃×#2436	2
C₁₃×#2347	2
C₁₃×#2068	2
C₁₃×#2042	2
C₁₃×#1983	2
C₁₃×#1927	2
C₁₃×#1895	2
C₁₃×#1851	2
C₁₃×#1787	2
#24497	13

Subgroups — C13×#24497 #15710836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24497 #15710836