Subgroups — C₁₃×#25032 #15711371

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2420	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2073	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2034	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1864	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#121	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#466	—	2	4	no	—
17	C₄×C₁₃×D₈	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#397	—	2	2	no	—
29	C₁₃×#394	—	2	2	no	—
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#386	—	2	2	no	—
33	C₁₃×#382	C₂²	1	2	yes	—
34	C₁₃×#381	—	2	2	no	—
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	—	2	2	no	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×D₈	—	2	2	no	—
46	C₂×C₁₃×D₈	—	2	2	no	—
47	C₂×C₁₃×D₈	D₄	1	4	yes	—
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#121	—	2	4	no	—
56	C₁₃×#121	—	4	2	no	—
57	C₄×D₄×C₁₃	—	2	4	no	—
58	C₄×D₄×C₁₃	—	4	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×#107	—	2	2	no	—
73	C₁₃×#107	—	2	2	no	—
74	C₁₃×#107	—	2	2	no	—
75	C₁₃×#106	—	4	2	no	—
76	C₁₃×#102	—	2	4	no	—
77	C₁₃×#102	—	2	4	no	—
78	C₁₃×#102	—	2	4	no	—
79	C₁₃×C₂²⋊C₈	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	D₄	1	1	yes	characteristic
87	C₁₃×#95	D₄	1	1	yes	characteristic
88	#25032	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	2	no	—
90	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	4	4	no	—
97	C₂×D₄×C₁₃	—	4	4	no	—
98	C₂×D₄×C₁₃	—	8	2	no	—
99	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	4	4	no	—
110	C₂²×C₄×C₁₃	—	4	4	no	—
111	C₂²×C₄×C₁₃	—	8	2	no	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×D₈	—	2	8	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	4	4	no	—
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃	#41	1	2	yes	—
130	C₂×C₈×C₁₃	#41	1	2	yes	—
131	C₂×C₈×C₁₃	#41	1	2	yes	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	8	2	no	—
139	C₁₃×C₂²⋊C₄	—	2	2	no	—
140	C₁₃×C₂²⋊C₄	—	2	2	no	—
141	C₁₃×C₂²⋊C₄	—	4	4	no	—
142	C₁₃×C₂²⋊C₄	—	4	4	no	—
143	C₁₃×C₂²⋊C₄	—	8	2	no	—
144	C₁₃×C₂²⋊C₄	—	8	2	no	—
145	C₁₃×C₂²⋊C₄	—	8	2	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₂×#466	C₂×C₁₃	1	1	yes	characteristic
151	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#2420	C₂×C₁₃	1	2	yes	complemented
153	#2073	C₂×C₁₃	1	2	yes	complemented
154	#2034	C₂×C₁₃	1	2	yes	complemented
155	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#1864	C₂×C₁₃	1	2	yes	complemented
158	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1808	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂³×C₁₃	—	2	1	no	—
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	—	2	1	no	—
164	C₂³×C₁₃	—	2	1	no	—
165	C₂³×C₁₃	—	2	1	no	—
166	C₂³×C₁₃	—	2	1	no	—
167	C₂³×C₁₃	—	2	4	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	#135	1	2	yes	—
175	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	D₄×C₁₃	—	2	4	no	—
177	D₄×C₁₃	—	2	4	no	—
178	D₄×C₁₃	—	4	2	no	—
179	D₄×C₁₃	—	4	2	no	—
180	D₄×C₁₃	—	8	8	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	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	2	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	8	8	no	—
209	C₂×C₄×C₁₃	#135	1	2	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
216	C₈×C₁₃	—	2	2	no	—
217	C₈×C₁₃	—	4	1	no	—
218	C₈×C₁₃	—	4	1	no	—
219	C₈×C₁₃	#123	1	4	yes	—
220	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#121	C₂²×C₁₃	1	2	yes	—
223	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
224	#466	—	2	4	no	—
225	C₄×D₈	—	2	4	no	—
226	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#106	C₂²×C₁₃	1	2	yes	—
230	C₂×#102	C₂²×C₁₃	1	2	yes	—
231	C₂×#102	C₂²×C₁₃	1	2	yes	—
232	C₂×#102	C₂²×C₁₃	1	2	yes	—
233	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
236	#397	—	2	2	no	—
237	#394	—	2	2	no	—
238	#390	C₂²×C₁₃	1	2	yes	—
239	#389	C₂²×C₁₃	1	2	yes	—
240	#386	—	2	2	no	—
241	#382	C₂²×C₁₃	1	2	yes	—
242	#381	—	2	2	no	—
243	#380	C₂²×C₁₃	1	2	yes	—
244	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
245	#340	C₂²×C₁₃	1	2	yes	—
246	#340	C₂²×C₁₃	1	2	yes	—
247	#336	C₂²×C₁₃	1	1	yes	characteristic
248	#336	C₂²×C₁₃	1	1	yes	characteristic
249	C₂²×C₁₃	—	2	2	no	—
250	C₂²×C₁₃	—	2	2	no	—
251	C₂²×C₁₃	—	2	2	no	—
252	C₂²×C₁₃	—	4	1	no	—
253	C₂²×C₁₃	—	4	1	no	—
254	C₂²×C₁₃	—	4	1	no	—
255	C₂²×C₁₃	—	4	1	no	—
256	C₂²×C₁₃	—	4	4	no	—
257	C₂²×C₁₃	—	4	4	no	—
258	C₂²×C₁₃	—	4	4	no	—
259	C₂²×C₁₃	—	8	2	no	—
260	C₂²×C₁₃	—	8	2	no	—
261	C₂²×C₁₃	—	8	2	no	—
262	C₂²×C₁₃	—	8	2	no	—
263	C₂²×C₁₃	#532	1	1	yes	characteristic
264	C₂²×C₁₃	D₄²	1	1	yes	characteristic
265	C₂²×C₁₃	#547	1	1	yes	characteristic
266	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
267	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
268	C₂²×C₁₃	#576	1	1	yes	characteristic
269	C₂²×C₁₃	#576	1	1	yes	characteristic
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	4	1	no	—
272	C₄×C₁₃	—	4	1	no	—
273	C₄×C₁₃	—	4	1	no	—
274	C₄×C₁₃	—	4	1	no	—
275	C₄×C₁₃	—	8	2	no	—
276	C₄×C₁₃	—	8	2	no	—
277	C₄×C₁₃	—	8	2	no	—
278	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
279	C₄×C₁₃	#542	1	1	yes	characteristic
280	C₄×C₁₃	#547	1	1	yes	characteristic
281	C₄×C₁₃	#553	1	1	yes	characteristic
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
284	C₂³×C₄	—	2	2	no	—
285	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×D₈	—	2	2	no	—
287	C₂×D₈	—	2	2	no	—
288	C₂×D₈	D₄×C₁₃	1	4	yes	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
296	#121	—	2	4	no	—
297	#121	—	4	2	no	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	4	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
313	#107	—	2	2	no	—
314	#107	—	2	2	no	—
315	#107	—	2	2	no	—
316	#106	—	4	2	no	—
317	#102	—	2	4	no	—
318	#102	—	2	4	no	—
319	#102	—	2	4	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	D₄×C₁₃	1	1	yes	characteristic
328	#95	D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₁₃	—	4	2	no	—
330	C₂×C₁₃	—	8	4	no	—
331	C₂×C₁₃	#2422	1	1	yes	characteristic
332	C₂×C₁₃	#3168	1	1	yes	characteristic
333	C₂×C₁₃	#3176	1	1	yes	characteristic
334	C₂×C₁₃	#3280	1	1	yes	characteristic
335	C₂×C₁₃	#3280	1	1	yes	characteristic
336	C₂×C₁₃	#3339	1	1	yes	characteristic
337	C₂×C₁₃	#3341	1	1	yes	characteristic
338	C₂⁴	—	2	2	no	—
339	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	—	8	2	no	—
348	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	4	no	—
360	C₂²×C₄	—	8	2	no	—
361	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
367	D₈	—	2	8	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	4	4	no	—
377	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
378	C₂×C₈	C₁₃×#41	1	2	yes	—
379	C₂×C₈	C₁₃×#41	1	2	yes	—
380	C₂×C₈	C₁₃×#41	1	2	yes	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	8	2	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	8	2	no	—
393	C₂²⋊C₄	—	8	2	no	—
394	C₂²⋊C₄	—	8	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₁₃	#25032	1	1	yes	characteristic, direct product factor, Sylow
400	C₂³	—	2	1	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	C₁₃×#135	1	2	yes	—
414	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
415	D₄	—	2	4	no	—
416	D₄	—	2	4	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	8	8	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	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	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	8	8	no	—
448	C₂×C₄	C₁₃×#135	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
451	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
452	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
453	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	4	1	no	—
457	C₈	—	4	1	no	—
458	C₈	C₁₃×#123	1	4	yes	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	2	no	—
471	C₂²	—	8	2	no	—
472	C₂²	—	8	2	no	—
473	C₂²	C₁₃×#532	1	1	yes	characteristic
474	C₂²	D₄²×C₁₃	1	1	yes	characteristic
475	C₂²	C₁₃×#547	1	1	yes	characteristic
476	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
477	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
478	C₂²	C₁₃×#576	1	1	yes	characteristic
479	C₂²	C₁₃×#576	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	4	1	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	8	2	no	—
486	C₄	—	8	2	no	—
487	C₄	—	8	2	no	—
488	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
489	C₄	C₁₃×#542	1	1	yes	characteristic
490	C₄	C₁₃×#547	1	1	yes	characteristic
491	C₄	C₁₃×#553	1	1	yes	characteristic
492	C₂	—	4	2	no	—
493	C₂	—	8	4	no	—
494	C₂	C₁₃×#2422	1	1	yes	characteristic
495	C₂	C₁₃×#3168	1	1	yes	characteristic
496	C₂	C₁₃×#3176	1	1	yes	characteristic
497	C₂	C₁₃×#3280	1	1	yes	characteristic
498	C₂	C₁₃×#3280	1	1	yes	characteristic
499	C₂	C₁₃×#3339	1	1	yes	characteristic
500	C₂	C₁₃×#3341	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#466	C₂
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×D₈	C₂	semidirect
3. C₁₃×#2420	C₂	semidirect
4. C₁₃×#2073	C₂	semidirect
5. C₁₃×#2034	C₂	semidirect
6. C₁₃×#1970	C₂	semidirect
7. C₁₃×#1942	C₂	semidirect
8. C₁₃×#1864	C₂	semidirect
9. C₁₃×#1846	C₂	semidirect
10. C₁₃×#1808	C₂	semidirect
11. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
88. #25032	C₁₃	direct (N × H)
151. C₂×C₄×D₈	C₂×C₁₃	semidirect
152. #2420	C₂×C₁₃	semidirect
153. #2073	C₂×C₁₃	semidirect
154. #2034	C₂×C₁₃	semidirect
155. #1970	C₂×C₁₃	semidirect
156. #1942	C₂×C₁₃	semidirect
157. #1864	C₂×C₁₃	semidirect
158. #1846	C₂×C₁₃	semidirect
159. #1808	C₂×C₁₃	semidirect
160. C₈×C₂²⋊C₄	C₂×C₁₃	semidirect
399. C₁₃	#25032	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×#466	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2420	2
C₁₃×#2073	2
C₁₃×#2034	2
C₁₃×#1970	2
C₁₃×#1942	2
C₁₃×#1864	2
C₁₃×#1846	2
C₁₃×#1808	2
C₈×C₁₃×C₂²⋊C₄	2
#25032	13

Subgroups — C13×#25032 #15711371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25032 #15711371