Subgroups — C₁₃×#24784 #15711123

Order 3328.

1040 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2414	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1944	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1875	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	C₂²	1	2	yes	—
16	C₂×C₁₃×#121	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	C₂²	1	2	yes	—
19	C₁₃×#469	—	2	4	no	—
20	C₁₃×#466	—	2	4	no	—
21	C₁₃×#435	—	2	4	no	—
22	C₁₃×#427	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	C₂²	1	2	yes	—
25	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	C₂²	1	2	yes	—
31	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₁₃×#394	—	2	2	no	—
35	C₁₃×#392	—	2	2	no	—
36	C₁₃×#390	—	2	2	no	—
37	C₁₃×#390	C₂²	1	2	yes	—
38	C₁₃×#389	C₂²	1	2	yes	—
39	C₁₃×#388	—	2	2	no	—
40	C₁₃×#380	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×D₈	—	2	2	no	—
50	C₂×C₁₃×D₈	—	2	2	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂²×C₈×C₁₃	—	2	2	no	—
56	C₂²×C₈×C₁₃	—	2	2	no	—
57	C₂²×C₈×C₁₃	D₄	1	4	yes	complemented
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×#121	—	2	4	no	—
63	C₁₃×#121	—	2	4	no	—
64	C₁₃×#121	—	2	4	no	—
65	C₁₃×#121	—	4	2	no	—
66	C₄×D₄×C₁₃	—	2	2	no	—
67	C₄×D₄×C₁₃	—	2	2	no	—
68	C₁₃×#117	—	2	4	no	—
69	C₁₃×#117	—	4	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	—	2	2	no	—
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#107	—	2	2	no	—
86	C₁₃×#107	—	2	4	no	—
87	C₁₃×#106	—	2	2	no	—
88	C₁₃×#106	D₄	1	4	yes	complemented
89	C₁₃×C₄⋊C₈	—	2	2	no	—
90	C₁₃×#102	—	2	4	no	—
91	C₁₃×#102	—	2	4	no	—
92	C₁₃×#102	—	4	2	no	—
93	C₁₃×C₂²⋊C₈	—	2	2	no	—
94	C₁₃×C₂²⋊C₈	—	2	2	no	—
95	C₁₃×#97	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	C₁₃×#95	—	2	2	no	—
98	#24784	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	—	2	2	no	—
100	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	4	2	no	—
110	C₂×D₄×C₁₃	—	4	4	no	—
111	C₂×D₄×C₁₃	—	4	4	no	—
112	C₂×D₄×C₁₃	—	4	4	no	—
113	C₂×D₄×C₁₃	—	8	2	no	—
114	C₂×D₄×C₁₃	—	8	2	no	—
115	C₂×D₄×C₁₃	—	8	2	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	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	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	#41	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₁₃×D₈	—	4	4	no	—
137	C₁₃×M₁₆	—	4	4	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	8	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₁₃	#41	1	2	yes	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	8	2	no	—
158	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
159	C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₁₃×C₂²⋊C₄	—	2	2	no	—
161	C₁₃×C₂²⋊C₄	—	4	4	no	—
162	C₁₃×C₂²⋊C₄	—	4	4	no	—
163	C₁₃×C₂²⋊C₄	—	4	4	no	—
164	C₁₃×C₂²⋊C₄	—	4	4	no	—
165	C₁₃×C₂²⋊C₄	—	8	2	no	—
166	C₁₃×C₂²⋊C₄	—	8	2	no	—
167	C₄²×C₁₃	—	2	1	no	—
168	C₄²×C₁₃	—	2	1	no	—
169	C₄²×C₁₃	—	4	4	no	—
170	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#2414	C₂×C₁₃	1	2	yes	complemented
175	#2067	C₂×C₁₃	1	2	yes	complemented
176	#2033	C₂×C₁₃	1	2	yes	complemented
177	#1972	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#1944	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#1875	C₂×C₁₃	1	2	yes	complemented
180	#1809	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂³×C₁₃	—	2	1	no	—
182	C₂³×C₁₃	—	2	1	no	—
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	—	2	2	no	—
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	4	2	no	—
191	C₂³×C₁₃	—	4	2	no	—
192	C₂³×C₁₃	—	4	2	no	—
193	C₂³×C₁₃	—	4	2	no	—
194	C₂³×C₁₃	—	4	2	no	—
195	C₂³×C₁₃	—	4	2	no	—
196	C₂³×C₁₃	—	4	2	no	—
197	C₂³×C₁₃	#121	1	2	yes	—
198	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	D₄×C₁₃	—	4	4	no	—
200	D₄×C₁₃	—	4	2	no	—
201	D₄×C₁₃	—	4	2	no	—
202	D₄×C₁₃	—	4	2	no	—
203	D₄×C₁₃	—	4	2	no	—
204	D₄×C₁₃	—	8	8	no	—
205	D₄×C₁₃	—	8	8	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	#121	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
239	C₈×C₁₃	—	2	2	no	—
240	C₈×C₁₃	—	4	1	no	—
241	C₈×C₁₃	—	4	1	no	—
242	C₈×C₁₃	#121	1	4	yes	—
243	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
245	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#121	C₂²×C₁₃	1	2	yes	—
247	C₂×#121	C₂²×C₁₃	1	2	yes	—
248	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×#117	C₂²×C₁₃	1	2	yes	—
250	#469	—	2	4	no	—
251	#466	—	2	4	no	—
252	#435	—	2	4	no	—
253	#427	—	2	4	no	—
254	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×#107	C₂²×C₁₃	1	2	yes	—
256	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#102	C₂²×C₁₃	1	2	yes	—
260	C₂×#102	C₂²×C₁₃	1	2	yes	—
261	C₂×#102	C₂²×C₁₃	1	2	yes	—
262	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
265	#394	—	2	2	no	—
266	#392	—	2	2	no	—
267	#390	—	2	2	no	—
268	#390	C₂²×C₁₃	1	2	yes	—
269	#389	C₂²×C₁₃	1	2	yes	—
270	#388	—	2	2	no	—
271	#380	C₂²×C₁₃	1	2	yes	—
272	#340	C₂²×C₁₃	1	2	yes	—
273	#340	C₂²×C₁₃	1	2	yes	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	2	2	no	—
277	C₂²×C₁₃	—	4	2	no	—
278	C₂²×C₁₃	—	4	2	no	—
279	C₂²×C₁₃	—	4	2	no	—
280	C₂²×C₁₃	—	4	1	no	—
281	C₂²×C₁₃	—	4	2	no	—
282	C₂²×C₁₃	—	4	1	no	—
283	C₂²×C₁₃	—	4	1	no	—
284	C₂²×C₁₃	—	8	2	no	—
285	C₂²×C₁₃	—	8	2	no	—
286	C₂²×C₁₃	—	8	2	no	—
287	C₂²×C₁₃	—	8	2	no	—
288	C₂²×C₁₃	—	8	2	no	—
289	C₂²×C₁₃	—	8	2	no	—
290	C₂²×C₁₃	—	8	2	no	—
291	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
292	C₂²×C₁₃	D₄²	1	1	yes	characteristic
293	C₂²×C₁₃	#547	1	1	yes	characteristic
294	C₂²×C₁₃	#575	1	2	yes	—
295	C₂²×C₁₃	#576	1	2	yes	—
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	4	1	no	—
298	C₄×C₁₃	—	4	4	no	—
299	C₄×C₁₃	—	4	1	no	—
300	C₄×C₁₃	—	4	1	no	—
301	C₄×C₁₃	—	8	2	no	—
302	C₄×C₁₃	—	8	2	no	—
303	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
304	C₄×C₁₃	#537	1	1	yes	characteristic
305	C₄×C₁₃	#548	1	1	yes	characteristic
306	C₄×C₁₃	#553	1	1	yes	characteristic
307	C₂²×D₄	—	2	2	no	—
308	C₂²×D₄	—	2	2	no	—
309	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
310	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
311	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
313	C₂×D₈	—	2	2	no	—
314	C₂×D₈	—	2	2	no	—
315	C₂×D₈	—	2	2	no	—
316	C₂×M₁₆	—	2	2	no	—
317	C₂×M₁₆	—	2	2	no	—
318	C₂×M₁₆	—	2	2	no	—
319	C₂²×C₈	—	2	2	no	—
320	C₂²×C₈	—	2	2	no	—
321	C₂²×C₈	D₄×C₁₃	1	4	yes	complemented
322	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
326	#121	—	2	4	no	—
327	#121	—	2	4	no	—
328	#121	—	2	4	no	—
329	#121	—	4	2	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	#117	—	2	4	no	—
333	#117	—	4	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
346	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
349	#107	—	2	2	no	—
350	#107	—	2	4	no	—
351	#106	—	2	2	no	—
352	#106	D₄×C₁₃	1	4	yes	complemented
353	C₄⋊C₈	—	2	2	no	—
354	#102	—	2	4	no	—
355	#102	—	2	4	no	—
356	#102	—	4	2	no	—
357	C₂²⋊C₈	—	2	2	no	—
358	C₂²⋊C₈	—	2	2	no	—
359	#97	—	2	2	no	—
360	#95	—	2	2	no	—
361	#95	—	2	2	no	—
362	C₂×C₁₃	—	4	2	no	—
363	C₂×C₁₃	—	8	1	no	—
364	C₂×C₁₃	—	16	2	no	—
365	C₂×C₁₃	#2416	1	1	yes	characteristic
366	C₂×C₁₃	#3054	1	1	yes	characteristic
367	C₂×C₁₃	#3058	1	1	yes	characteristic
368	C₂×C₁₃	#3268	1	2	yes	—
369	C₂×C₁₃	#3347	1	2	yes	—
370	C₂⁴	—	2	2	no	—
371	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	—	8	2	no	—
385	C₂×D₄	—	8	2	no	—
386	C₂×D₄	—	8	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
405	C₂²×C₄	C₁₃×#41	1	2	yes	—
406	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
407	D₈	—	4	4	no	—
408	M₁₆	—	4	4	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	8	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
419	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
420	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
421	C₂×C₈	C₁₃×#41	1	2	yes	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	8	2	no	—
429	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₂²⋊C₄	—	4	4	no	—
435	C₂²⋊C₄	—	4	4	no	—
436	C₂²⋊C₄	—	8	2	no	—
437	C₂²⋊C₄	—	8	2	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	4	4	no	—
441	C₁₃	#24784	1	1	yes	characteristic, direct product factor, Sylow
442	C₂³	—	2	1	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	C₁₃×#121	1	2	yes	—
459	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
460	D₄	—	4	4	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	2	no	—
465	D₄	—	8	8	no	—
466	D₄	—	8	8	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	C₁₃×#121	1	2	yes	—
494	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
496	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
497	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
498	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
499	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
500	C₈	—	2	2	no	—
501	C₈	—	4	1	no	—
502	C₈	—	4	1	no	—
503	C₈	C₁₃×#121	1	4	yes	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
522	C₂²	D₄²×C₁₃	1	1	yes	characteristic
523	C₂²	C₁₃×#547	1	1	yes	characteristic
524	C₂²	C₁₃×#575	1	2	yes	—
525	C₂²	C₁₃×#576	1	2	yes	—
526	C₄	—	2	2	no	—
527	C₄	—	4	4	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	8	2	no	—
532	C₄	—	8	2	no	—
533	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
534	C₄	C₁₃×#537	1	1	yes	characteristic
535	C₄	C₁₃×#548	1	1	yes	characteristic
536	C₄	C₁₃×#553	1	1	yes	characteristic
537	C₂	—	4	2	no	—
538	C₂	—	8	1	no	—
539	C₂	—	16	2	no	—
540	C₂	C₁₃×#2416	1	1	yes	characteristic
541	C₂	C₁₃×#3054	1	1	yes	characteristic
542	C₂	C₁₃×#3058	1	1	yes	characteristic
543	C₂	C₁₃×#3268	1	2	yes	—
544	C₂	C₁₃×#3347	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#469	C₂	semidirect
2. C₂×C₁₃×#466	C₂	semidirect
3. C₂×C₁₃×#435	C₂	semidirect
4. C₂×C₁₃×#427	C₂	semidirect
5. C₁₃×#2414	C₂	semidirect
6. C₁₃×#2067	C₂	semidirect
7. C₁₃×#2033	C₂	semidirect
8. C₁₃×#1972	C₂	semidirect
9. C₁₃×#1944	C₂	semidirect
10. C₁₃×#1875	C₂	semidirect
11. C₁₃×#1809	C₂	semidirect
57. C₂²×C₈×C₁₃	D₄	semidirect
88. C₁₃×#106	D₄	semidirect
98. #24784	C₁₃	direct (N × H)
170. C₂×#469	C₂×C₁₃	semidirect
171. C₂×#466	C₂×C₁₃	semidirect
172. C₂×#435	C₂×C₁₃	semidirect
173. C₂×#427	C₂×C₁₃	semidirect
174. #2414	C₂×C₁₃	semidirect
175. #2067	C₂×C₁₃	semidirect
176. #2033	C₂×C₁₃	semidirect
177. #1972	C₂×C₁₃	semidirect
178. #1944	C₂×C₁₃	semidirect
179. #1875	C₂×C₁₃	semidirect
180. #1809	C₂×C₁₃	semidirect
321. C₂²×C₈	D₄×C₁₃	semidirect
352. #106	D₄×C₁₃	semidirect
441. C₁₃	#24784	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×#469	2
C₂×C₁₃×#466	2
C₂×C₁₃×#435	2
C₂×C₁₃×#427	2
C₁₃×#2414	2
C₁₃×#2067	2
C₁₃×#2033	2
C₁₃×#1972	2
C₁₃×#1944	2
C₁₃×#1875	2
C₁₃×#1809	2
#24784	13

Subgroups — C13×#24784 #15711123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24784 #15711123