Subgroups — C₁₃×#24778 #15711117

Order 3328.

1066 conjugacy classes of subgroups.

The subgroup lattice has 576 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, complemented
2	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₁₃	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×#2065	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2034	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1875	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1808	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	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×#466	—	2	4	no	—
20	C₁₃×#466	—	2	4	no	—
21	C₈×D₄×C₁₃	—	2	4	no	—
22	C₁₃×#427	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	2	yes	—
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×C₄×C₈×C₁₃	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	C₂²×C₈×C₁₃	—	2	2	no	—
53	C₂²×C₈×C₁₃	—	2	2	no	—
54	C₂²×C₈×C₁₃	—	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	2	no	—
87	C₁₃×#107	D₄	1	4	yes	complemented
88	C₁₃×#106	—	2	4	no	—
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	C₄×C₈×C₁₃	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	C₁₃×#95	—	2	2	no	—
98	#24778	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	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	4	4	no	—
112	C₂×D₄×C₁₃	—	4	4	no	—
113	C₂×D₄×C₁₃	—	4	4	no	—
114	C₂×D₄×C₁₃	—	8	2	no	—
115	C₂×D₄×C₁₃	—	8	2	no	—
116	C₂×D₄×C₁₃	—	8	2	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	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	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	1	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	#41	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×D₈	—	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	—	4	4	no	—
148	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₃	#41	1	2	yes	—
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	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	8	2	no	—
159	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
160	C₁₃×C₂²⋊C₄	—	2	2	no	—
161	C₁₃×C₂²⋊C₄	—	2	2	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	—	4	4	no	—
166	C₁₃×C₂²⋊C₄	—	8	2	no	—
167	C₁₃×C₂²⋊C₄	—	8	2	no	—
168	C₄²×C₁₃	—	2	1	no	—
169	C₄²×C₁₃	—	2	1	no	—
170	C₄²×C₁₃	—	4	4	no	—
171	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#2414	C₂×C₁₃	1	2	yes	complemented
176	#2065	C₂×C₁₃	1	2	yes	complemented
177	#2034	C₂×C₁₃	1	2	yes	complemented
178	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#1875	C₂×C₁₃	1	2	yes	complemented
181	#1808	C₂×C₁₃	1	1	yes	characteristic, complemented
182	C₂³×C₁₃	—	2	1	no	—
183	C₂³×C₁₃	—	2	1	no	—
184	C₂³×C₁₃	—	2	1	no	—
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	2	1	no	—
189	C₂³×C₁₃	—	2	1	no	—
190	C₂³×C₁₃	—	2	1	no	—
191	C₂³×C₁₃	—	2	1	no	—
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	—	2	1	no	—
194	C₂³×C₁₃	—	4	2	no	—
195	C₂³×C₁₃	—	4	2	no	—
196	C₂³×C₁₃	—	4	2	no	—
197	C₂³×C₁₃	—	4	2	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	—	4	2	no	—
200	C₂³×C₁₃	—	4	2	no	—
201	C₂³×C₁₃	#121	1	2	yes	—
202	C₂³×C₁₃	#135	1	2	yes	—
203	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	D₄×C₁₃	—	2	8	no	—
205	D₄×C₁₃	—	4	2	no	—
206	D₄×C₁₃	—	4	2	no	—
207	D₄×C₁₃	—	4	2	no	—
208	D₄×C₁₃	—	4	2	no	—
209	D₄×C₁₃	—	8	8	no	—
210	D₄×C₁₃	—	8	8	no	—
211	C₂×C₄×C₁₃	—	2	1	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	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	#121	1	2	yes	—
239	C₂×C₄×C₁₃	#135	1	2	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
246	C₈×C₁₃	—	2	2	no	—
247	C₈×C₁₃	—	4	1	no	—
248	C₈×C₁₃	—	4	1	no	—
249	C₈×C₁₃	#121	1	4	yes	—
250	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#121	C₂²×C₁₃	1	2	yes	—
254	C₂×#121	C₂²×C₁₃	1	2	yes	—
255	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#117	C₂²×C₁₃	1	2	yes	—
257	#466	—	2	4	no	—
258	#466	—	2	4	no	—
259	C₈×D₄	—	2	4	no	—
260	#427	—	2	4	no	—
261	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#106	C₂²×C₁₃	1	2	yes	—
265	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#102	C₂²×C₁₃	1	2	yes	—
267	C₂×#102	C₂²×C₁₃	1	2	yes	—
268	C₂×#102	C₂²×C₁₃	1	2	yes	—
269	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
272	#394	—	2	2	no	—
273	#392	—	2	2	no	—
274	#390	—	2	2	no	—
275	#390	C₂²×C₁₃	1	2	yes	—
276	#389	C₂²×C₁₃	1	2	yes	—
277	#388	—	2	2	no	—
278	#380	C₂²×C₁₃	1	2	yes	—
279	#340	C₂²×C₁₃	1	2	yes	—
280	#340	C₂²×C₁₃	1	2	yes	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	2	2	no	—
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	2	2	no	—
285	C₂²×C₁₃	—	2	2	no	—
286	C₂²×C₁₃	—	2	2	no	—
287	C₂²×C₁₃	—	4	1	no	—
288	C₂²×C₁₃	—	4	1	no	—
289	C₂²×C₁₃	—	4	1	no	—
290	C₂²×C₁₃	—	4	1	no	—
291	C₂²×C₁₃	—	4	1	no	—
292	C₂²×C₁₃	—	4	1	no	—
293	C₂²×C₁₃	—	4	1	no	—
294	C₂²×C₁₃	—	4	1	no	—
295	C₂²×C₁₃	—	8	2	no	—
296	C₂²×C₁₃	—	8	2	no	—
297	C₂²×C₁₃	—	8	2	no	—
298	C₂²×C₁₃	—	8	2	no	—
299	C₂²×C₁₃	—	8	2	no	—
300	C₂²×C₁₃	—	8	2	no	—
301	C₂²×C₁₃	—	8	2	no	—
302	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
303	C₂²×C₁₃	D₄²	1	1	yes	characteristic
304	C₂²×C₁₃	#547	1	1	yes	characteristic
305	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
306	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
307	C₂²×C₁₃	#576	1	1	yes	characteristic
308	C₂²×C₁₃	#576	1	1	yes	characteristic
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	2	2	no	—
311	C₄×C₁₃	—	4	1	no	—
312	C₄×C₁₃	—	4	4	no	—
313	C₄×C₁₃	—	4	1	no	—
314	C₄×C₁₃	—	8	2	no	—
315	C₄×C₁₃	—	8	2	no	—
316	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
317	C₄×C₁₃	#537	1	1	yes	characteristic
318	C₄×C₁₃	#548	1	1	yes	characteristic
319	C₄×C₁₃	#553	1	1	yes	characteristic
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
323	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
324	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
326	C₂×D₈	—	2	2	no	—
327	C₂×D₈	—	2	2	no	—
328	C₂×D₈	—	2	2	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₂²×C₈	—	2	2	no	—
331	C₂²×C₈	—	2	2	no	—
332	C₂²×C₈	—	2	2	no	—
333	C₂²×C₈	—	2	2	no	—
334	C₂²×C₈	D₄×C₁₃	1	4	yes	complemented
335	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
339	#121	—	2	4	no	—
340	#121	—	2	4	no	—
341	#121	—	2	4	no	—
342	#121	—	4	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	2	no	—
345	#117	—	2	4	no	—
346	#117	—	4	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
362	#107	—	2	2	no	—
363	#107	—	2	2	no	—
364	#107	D₄×C₁₃	1	4	yes	complemented
365	#106	—	2	4	no	—
366	C₄⋊C₈	—	2	2	no	—
367	#102	—	2	4	no	—
368	#102	—	2	4	no	—
369	#102	—	4	2	no	—
370	C₂²⋊C₈	—	2	2	no	—
371	C₂²⋊C₈	—	2	2	no	—
372	C₄×C₈	—	2	2	no	—
373	#95	—	2	2	no	—
374	#95	—	2	2	no	—
375	C₂×C₁₃	—	4	2	no	—
376	C₂×C₁₃	—	4	2	no	—
377	C₂×C₁₃	—	16	2	no	—
378	C₂×C₁₃	#2416	1	1	yes	characteristic
379	C₂×C₁₃	#3050	1	1	yes	characteristic
380	C₂×C₁₃	#3058	1	1	yes	characteristic
381	C₂×C₁₃	#3280	1	1	yes	characteristic
382	C₂×C₁₃	#3287	1	1	yes	characteristic
383	C₂×C₁₃	#3339	1	1	yes	characteristic
384	C₂×C₁₃	#3341	1	1	yes	characteristic
385	C₂⁴	—	2	2	no	—
386	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	8	2	no	—
401	C₂×D₄	—	8	2	no	—
402	C₂×D₄	—	8	2	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
420	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₂²×C₄	C₁₃×#41	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
423	D₈	—	4	4	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	8	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	4	4	no	—
434	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
435	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
436	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
437	C₂×C₈	C₁₃×#41	1	2	yes	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	8	2	no	—
445	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	4	4	no	—
449	C₂²⋊C₄	—	4	4	no	—
450	C₂²⋊C₄	—	4	4	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₂²⋊C₄	—	8	2	no	—
453	C₂²⋊C₄	—	8	2	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	4	4	no	—
457	C₁₃	#24778	1	1	yes	characteristic, direct product factor, Sylow
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	C₁₃×#121	1	2	yes	—
478	C₂³	C₁₃×#135	1	2	yes	—
479	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
480	D₄	—	2	8	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	4	2	no	—
485	D₄	—	8	8	no	—
486	D₄	—	8	8	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	C₁₃×#121	1	2	yes	—
515	C₂×C₄	C₁₃×#135	1	2	yes	—
516	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
518	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
519	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
520	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
521	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
522	C₈	—	2	2	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₈	C₁₃×#121	1	4	yes	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	8	2	no	—
541	C₂²	—	8	2	no	—
542	C₂²	—	8	2	no	—
543	C₂²	—	8	2	no	—
544	C₂²	—	8	2	no	—
545	C₂²	—	8	2	no	—
546	C₂²	—	8	2	no	—
547	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
548	C₂²	D₄²×C₁₃	1	1	yes	characteristic
549	C₂²	C₁₃×#547	1	1	yes	characteristic
550	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
551	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
552	C₂²	C₁₃×#576	1	1	yes	characteristic
553	C₂²	C₁₃×#576	1	1	yes	characteristic
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	4	4	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	8	2	no	—
560	C₄	—	8	2	no	—
561	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
562	C₄	C₁₃×#537	1	1	yes	characteristic
563	C₄	C₁₃×#548	1	1	yes	characteristic
564	C₄	C₁₃×#553	1	1	yes	characteristic
565	C₂	—	4	2	no	—
566	C₂	—	4	2	no	—
567	C₂	—	16	2	no	—
568	C₂	C₁₃×#2416	1	1	yes	characteristic
569	C₂	C₁₃×#3050	1	1	yes	characteristic
570	C₂	C₁₃×#3058	1	1	yes	characteristic
571	C₂	C₁₃×#3280	1	1	yes	characteristic
572	C₂	C₁₃×#3287	1	1	yes	characteristic
573	C₂	C₁₃×#3339	1	1	yes	characteristic
574	C₂	C₁₃×#3341	1	1	yes	characteristic

	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×#466	C₂	semidirect
2. C₂×C₁₃×#466	C₂	semidirect
3. C₂×C₈×D₄×C₁₃	C₂	semidirect
4. C₂×C₁₃×#427	C₂	semidirect
5. C₁₃×#2414	C₂	semidirect
6. C₁₃×#2065	C₂	semidirect
7. C₁₃×#2034	C₂	semidirect
8. C₁₃×#1970	C₂	semidirect
9. C₁₃×#1942	C₂	semidirect
10. C₁₃×#1875	C₂	semidirect
11. C₁₃×#1808	C₂	semidirect
57. C₂²×C₈×C₁₃	D₄	semidirect
87. C₁₃×#107	D₄	semidirect
98. #24778	C₁₃	direct (N × H)
171. C₂×#466	C₂×C₁₃	semidirect
172. C₂×#466	C₂×C₁₃	semidirect
173. C₂×C₈×D₄	C₂×C₁₃	semidirect
174. C₂×#427	C₂×C₁₃	semidirect
175. #2414	C₂×C₁₃	semidirect
176. #2065	C₂×C₁₃	semidirect
177. #2034	C₂×C₁₃	semidirect
178. #1970	C₂×C₁₃	semidirect
179. #1942	C₂×C₁₃	semidirect
180. #1875	C₂×C₁₃	semidirect
181. #1808	C₂×C₁₃	semidirect
334. C₂²×C₈	D₄×C₁₃	semidirect
364. #107	D₄×C₁₃	semidirect
457. C₁₃	#24778	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×C₈×D₄×C₁₃	2
C₂×C₁₃×#427	2
C₁₃×#2414	2
C₁₃×#2065	2
C₁₃×#2034	2
C₁₃×#1970	2
C₁₃×#1942	2
C₁₃×#1875	2
C₁₃×#1808	2
#24778	13

Subgroups — C13×#24778 #15711117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24778 #15711117