Subgroups — C₁₃×#35051 #15721390

Order 3328.

3078 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2847	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2656	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2639	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2564	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2543	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2498	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2430	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2325	C₂	1	4	yes	maximal, complemented
11	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#525	—	2	16	no	—
16	C₂×C₁₃×#123	C₂²	1	4	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#121	C₂²	1	2	yes	—
20	C₂×C₁₃×#121	C₂²	1	4	yes	—
21	C₂×C₁₃×#121	C₂²	1	2	yes	—
22	C₂×C₁₃×#121	C₂²	1	4	yes	—
23	C₂×C₁₃×#121	C₂²	1	4	yes	—
24	C₂×C₁₃×#120	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
27	C₂×C₁₃×#117	C₂²	1	2	yes	—
28	C₁₃×#400	C₂²	1	4	yes	complemented
29	C₁₃×#399	C₂²	1	4	yes	complemented
30	C₁₃×#398	C₂²	1	4	yes	complemented
31	C₁₃×#397	C₂²	1	4	yes	complemented
32	C₁₃×#395	C₂²	1	4	yes	complemented
33	C₁₃×#394	C₂²	1	4	yes	complemented
34	C₁₃×#393	C₂²	1	4	yes	complemented
35	C₁₃×#392	C₂²	1	4	yes	complemented
36	C₁₃×#388	C₂²	1	8	yes	complemented
37	C₁₃×#387	C₂²	1	8	yes	complemented
38	C₁₃×#386	C₂²	1	8	yes	—
39	C₁₃×#386	C₂²	1	8	yes	—
40	C₁₃×#386	C₂²	1	8	yes	—
41	C₁₃×#386	C₂²	1	8	yes	complemented
42	C₁₃×#385	C₂²	1	8	yes	complemented
43	C₁₃×#380	C₂²	1	4	yes	—
44	C₁₃×#380	C₂²	1	4	yes	—
45	C₁₃×#380	C₂²	1	4	yes	—
46	C₂×C₁₃×#95	C₂²	1	4	yes	—
47	C₂×C₁₃×#95	C₂²	1	4	yes	—
48	C₂×C₁₃×#95	C₂²	1	2	yes	—
49	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
51	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×#41	—	2	8	no	—
53	C₂×C₁₃×#41	—	4	8	no	—
54	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	—	2	8	no	—
61	C₂³×C₄×C₁₃	—	4	4	no	—
62	C₂³×C₄×C₁₃	—	4	4	no	—
63	C₂³×C₄×C₁₃	—	4	4	no	—
64	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
65	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
74	C₁₃×#123	—	2	16	no	—
75	C₁₃×C₂²⋊Q₈	—	2	8	no	—
76	C₁₃×C₂²⋊Q₈	—	2	8	no	—
77	C₁₃×#121	—	2	8	no	—
78	C₁₃×#121	—	2	8	no	—
79	C₁₃×#121	—	2	16	no	—
80	C₁₃×#121	—	4	8	no	—
81	C₁₃×#121	—	4	8	no	—
82	C₁₃×#120	—	2	16	no	—
83	C₄×D₄×C₁₃	—	2	16	no	—
84	C₄×D₄×C₁₃	—	2	16	no	—
85	C₁₃×#117	—	2	8	no	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
102	C₁₃×#95	C₂³	1	8	yes	—
103	C₁₃×#95	C₂³	1	8	yes	—
104	C₁₃×#95	C₂³	1	8	yes	—
105	C₁₃×#95	C₂³	1	8	yes	—
106	C₁₃×#95	C₂³	1	4	yes	—
107	C₁₃×#95	C₂³	1	4	yes	—
108	#35051	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	4	no	—
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	—	2	4	no	—
112	C₂⁴×C₁₃	—	2	2	no	—
113	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
114	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
115	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×#41	—	4	32	no	—
119	C₂×Q₈×C₁₃	—	2	4	no	—
120	C₂×Q₈×C₁₃	—	4	4	no	—
121	C₂×D₄×C₁₃	—	2	8	no	—
122	C₂×D₄×C₁₃	—	2	8	no	—
123	C₂×D₄×C₁₃	—	2	8	no	—
124	C₂×D₄×C₁₃	—	2	16	no	—
125	C₂×D₄×C₁₃	—	2	8	no	—
126	C₂×D₄×C₁₃	—	2	16	no	—
127	C₂×D₄×C₁₃	—	2	8	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	8	no	—
130	C₂×D₄×C₁₃	—	4	4	no	—
131	C₂×D₄×C₁₃	—	4	4	no	—
132	C₂×D₄×C₁₃	—	4	4	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	8	no	—
136	C₂²×C₄×C₁₃	—	2	8	no	—
137	C₂²×C₄×C₁₃	—	2	8	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	2	8	no	—
140	C₂²×C₄×C₁₃	—	4	16	no	—
141	C₂²×C₄×C₁₃	—	4	2	no	—
142	C₂²×C₄×C₁₃	—	4	2	no	—
143	C₂²×C₄×C₁₃	—	4	4	no	—
144	C₂²×C₄×C₁₃	—	4	4	no	—
145	C₂²×C₄×C₁₃	—	4	2	no	—
146	C₂²×C₄×C₁₃	—	4	4	no	—
147	C₂²×C₄×C₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₃	—	4	2	no	—
149	C₂²×C₄×C₁₃	—	4	2	no	—
150	C₂²×C₄×C₁₃	—	4	8	no	—
151	C₂²×C₄×C₁₃	—	4	32	no	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
153	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₁₃×C₄⋊C₄	—	2	8	no	—
167	C₁₃×C₄⋊C₄	—	2	8	no	—
168	C₁₃×C₄⋊C₄	—	2	8	no	—
169	C₁₃×C₄⋊C₄	—	4	4	no	—
170	C₁₃×C₄⋊C₄	—	4	4	no	—
171	C₁₃×C₂²⋊C₄	—	2	8	no	—
172	C₁₃×C₂²⋊C₄	—	2	8	no	—
173	C₁₃×C₂²⋊C₄	—	2	8	no	—
174	C₁₃×C₂²⋊C₄	—	2	8	no	—
175	C₁₃×C₂²⋊C₄	—	2	8	no	—
176	C₁₃×C₂²⋊C₄	—	2	16	no	—
177	C₁₃×C₂²⋊C₄	—	4	8	no	—
178	C₁₃×C₂²⋊C₄	—	4	8	no	—
179	C₄²×C₁₃	—	2	8	no	—
180	C₂×#525	C₂×C₁₃	1	2	yes	complemented
181	#2847	C₂×C₁₃	1	4	yes	complemented
182	#2659	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#2656	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#2639	C₂×C₁₃	1	2	yes	complemented
185	#2564	C₂×C₁₃	1	4	yes	complemented
186	#2543	C₂×C₁₃	1	4	yes	complemented
187	#2498	C₂×C₁₃	1	4	yes	complemented
188	#2430	C₂×C₁₃	1	4	yes	complemented
189	#2325	C₂×C₁₃	1	4	yes	complemented
190	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂³×C₁₃	—	2	16	no	—
192	C₂³×C₁₃	—	2	16	no	—
193	C₂³×C₁₃	—	2	8	no	—
194	C₂³×C₁₃	—	2	8	no	—
195	C₂³×C₁₃	—	2	8	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	2	2	no	—
200	C₂³×C₁₃	—	2	1	no	—
201	C₂³×C₁₃	—	2	1	no	—
202	C₂³×C₁₃	—	2	1	no	—
203	C₂³×C₁₃	—	2	1	no	—
204	C₂³×C₁₃	—	2	4	no	—
205	C₂³×C₁₃	—	2	8	no	—
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	2	8	no	—
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
210	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
212	C₂³×C₁₃	C₂×#41	1	4	yes	—
213	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
214	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
215	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
216	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
217	Q₈×C₁₃	—	4	8	no	—
218	D₄×C₁₃	—	4	8	no	—
219	D₄×C₁₃	—	4	16	no	—
220	D₄×C₁₃	—	4	16	no	—
221	D₄×C₁₃	—	4	16	no	—
222	D₄×C₁₃	—	8	8	no	—
223	C₂×C₄×C₁₃	—	2	16	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	8	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	8	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	4	4	no	—
239	C₂×C₄×C₁₃	—	4	8	no	—
240	C₂×C₄×C₁₃	—	4	4	no	—
241	C₂×C₄×C₁₃	—	4	8	no	—
242	C₂×C₄×C₁₃	—	4	16	no	—
243	C₂×C₄×C₁₃	—	4	16	no	—
244	C₂×C₄×C₁₃	—	4	16	no	—
245	C₂×C₄×C₁₃	—	4	8	no	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
249	C₂²×#41	C₂²×C₁₃	1	2	yes	—
250	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
251	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
252	#525	—	2	16	no	—
253	C₂×#123	C₂²×C₁₃	1	4	yes	—
254	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
255	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
256	C₂×#121	C₂²×C₁₃	1	4	yes	—
257	C₂×#121	C₂²×C₁₃	1	2	yes	—
258	C₂×#121	C₂²×C₁₃	1	2	yes	—
259	C₂×#121	C₂²×C₁₃	1	4	yes	—
260	C₂×#121	C₂²×C₁₃	1	4	yes	—
261	C₂×#120	C₂²×C₁₃	1	4	yes	—
262	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
263	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
264	C₂×#117	C₂²×C₁₃	1	2	yes	—
265	#400	C₂²×C₁₃	1	4	yes	complemented
266	#399	C₂²×C₁₃	1	4	yes	complemented
267	#398	C₂²×C₁₃	1	4	yes	complemented
268	#397	C₂²×C₁₃	1	4	yes	complemented
269	#395	C₂²×C₁₃	1	4	yes	complemented
270	#394	C₂²×C₁₃	1	4	yes	complemented
271	#393	C₂²×C₁₃	1	4	yes	complemented
272	#392	C₂²×C₁₃	1	4	yes	complemented
273	#388	C₂²×C₁₃	1	8	yes	complemented
274	#387	C₂²×C₁₃	1	8	yes	complemented
275	#386	C₂²×C₁₃	1	8	yes	—
276	#386	C₂²×C₁₃	1	8	yes	—
277	#386	C₂²×C₁₃	1	8	yes	—
278	#386	C₂²×C₁₃	1	8	yes	complemented
279	#385	C₂²×C₁₃	1	8	yes	complemented
280	#380	C₂²×C₁₃	1	4	yes	—
281	#380	C₂²×C₁₃	1	4	yes	—
282	#380	C₂²×C₁₃	1	4	yes	—
283	C₂×#95	C₂²×C₁₃	1	4	yes	—
284	C₂×#95	C₂²×C₁₃	1	2	yes	—
285	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#95	C₂²×C₁₃	1	4	yes	—
288	C₂²×C₁₃	—	2	32	no	—
289	C₂²×C₁₃	—	2	2	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	2	2	no	—
293	C₂²×C₁₃	—	2	2	no	—
294	C₂²×C₁₃	—	2	2	no	—
295	C₂²×C₁₃	—	2	4	no	—
296	C₂²×C₁₃	—	2	4	no	—
297	C₂²×C₁₃	—	2	4	no	—
298	C₂²×C₁₃	—	2	4	no	—
299	C₂²×C₁₃	—	2	4	no	—
300	C₂²×C₁₃	—	2	4	no	—
301	C₂²×C₁₃	—	4	4	no	—
302	C₂²×C₁₃	—	4	4	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	4	8	no	—
305	C₂²×C₁₃	—	4	8	no	—
306	C₂²×C₁₃	#532	1	4	yes	—
307	C₂²×C₁₃	#534	1	4	yes	—
308	C₂²×C₁₃	#537	1	4	yes	—
309	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
310	C₂²×C₁₃	C₂²×#41	1	2	yes	—
311	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
312	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
314	C₄×C₁₃	—	2	4	no	—
315	C₄×C₁₃	—	2	4	no	—
316	C₄×C₁₃	—	2	8	no	—
317	C₄×C₁₃	—	4	4	no	—
318	C₄×C₁₃	—	4	4	no	—
319	C₄×C₁₃	—	4	4	no	—
320	C₄×C₁₃	—	4	4	no	—
321	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
322	C₂×#41	—	2	8	no	—
323	C₂×#41	—	4	8	no	—
324	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
325	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
326	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
327	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
328	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
329	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
330	C₂³×C₄	—	2	8	no	—
331	C₂³×C₄	—	4	4	no	—
332	C₂³×C₄	—	4	4	no	—
333	C₂³×C₄	—	4	4	no	—
334	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
335	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
336	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
337	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
338	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
339	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
340	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
342	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
344	#123	—	2	16	no	—
345	C₂²⋊Q₈	—	2	8	no	—
346	C₂²⋊Q₈	—	2	8	no	—
347	#121	—	2	8	no	—
348	#121	—	2	8	no	—
349	#121	—	2	16	no	—
350	#121	—	4	8	no	—
351	#121	—	4	8	no	—
352	#120	—	2	16	no	—
353	C₄×D₄	—	2	16	no	—
354	C₄×D₄	—	2	16	no	—
355	#117	—	2	8	no	—
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
371	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
372	#95	C₂³×C₁₃	1	8	yes	—
373	#95	C₂³×C₁₃	1	4	yes	—
374	#95	C₂³×C₁₃	1	4	yes	—
375	#95	C₂³×C₁₃	1	8	yes	—
376	#95	C₂³×C₁₃	1	8	yes	—
377	#95	C₂³×C₁₃	1	8	yes	—
378	C₂×C₁₃	—	2	4	no	—
379	C₂×C₁₃	—	2	4	no	—
380	C₂×C₁₃	—	2	4	no	—
381	C₂×C₁₃	—	8	4	no	—
382	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
383	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
384	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
385	C₂×C₁₃	#3490	1	2	yes	—
386	C₂×C₁₃	#3492	1	2	yes	—
387	C₂⁴	—	2	4	no	—
388	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	4	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
392	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
393	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
394	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
395	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
396	#41	—	4	32	no	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	4	4	no	—
399	C₂×D₄	—	2	8	no	—
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	8	no	—
402	C₂×D₄	—	2	16	no	—
403	C₂×D₄	—	2	8	no	—
404	C₂×D₄	—	2	16	no	—
405	C₂×D₄	—	2	8	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	—	4	4	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂²×C₄	—	2	8	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	8	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	8	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	—	4	16	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	—	4	4	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	4	no	—
425	C₂²×C₄	—	4	2	no	—
426	C₂²×C₄	—	4	2	no	—
427	C₂²×C₄	—	4	2	no	—
428	C₂²×C₄	—	4	8	no	—
429	C₂²×C₄	—	4	32	no	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
431	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
432	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
433	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
434	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
435	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
436	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	8	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	8	no	—
447	C₄⋊C₄	—	4	4	no	—
448	C₄⋊C₄	—	4	4	no	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	2	8	no	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	16	no	—
455	C₂²⋊C₄	—	4	8	no	—
456	C₂²⋊C₄	—	4	8	no	—
457	C₄²	—	2	8	no	—
458	C₁₃	#35051	1	1	yes	characteristic, direct product factor, Sylow
459	C₂³	—	2	16	no	—
460	C₂³	—	2	16	no	—
461	C₂³	—	2	8	no	—
462	C₂³	—	2	8	no	—
463	C₂³	—	2	8	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	8	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	8	no	—
476	C₂³	—	2	4	no	—
477	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
478	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
479	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
480	C₂³	C₂×C₁₃×#41	1	4	yes	—
481	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
482	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
483	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
484	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
485	Q₈	—	4	8	no	—
486	D₄	—	4	8	no	—
487	D₄	—	4	16	no	—
488	D₄	—	4	16	no	—
489	D₄	—	4	16	no	—
490	D₄	—	8	8	no	—
491	C₂×C₄	—	2	16	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	8	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	8	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	8	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	—	4	16	no	—
511	C₂×C₄	—	4	16	no	—
512	C₂×C₄	—	4	16	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
515	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
516	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
517	C₂²	—	2	32	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	4	8	no	—
534	C₂²	—	4	8	no	—
535	C₂²	C₁₃×#532	1	4	yes	—
536	C₂²	C₁₃×#534	1	4	yes	—
537	C₂²	C₁₃×#537	1	4	yes	—
538	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
539	C₂²	C₂²×C₁₃×#41	1	2	yes	—
540	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
541	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
542	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
543	C₄	—	2	4	no	—
544	C₄	—	2	4	no	—
545	C₄	—	2	8	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	4	no	—
549	C₄	—	4	4	no	—
550	C₂	—	2	4	no	—
551	C₂	—	2	4	no	—
552	C₂	—	2	4	no	—
553	C₂	—	8	4	no	—
554	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
555	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
556	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
557	C₂	C₁₃×#3490	1	2	yes	—
558	C₂	C₁₃×#3492	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#525	C₂	semidirect
2. C₁₃×#2847	C₂	semidirect
3. C₁₃×#2659	C₂	semidirect
4. C₁₃×#2656	C₂	semidirect
5. C₁₃×#2639	C₂	semidirect
6. C₁₃×#2564	C₂	semidirect
7. C₁₃×#2543	C₂	semidirect
8. C₁₃×#2498	C₂	semidirect
9. C₁₃×#2430	C₂	semidirect
10. C₁₃×#2325	C₂	semidirect
11. C₂²×C₁₃×#95	C₂	semidirect
28. C₁₃×#400	C₂²	semidirect
29. C₁₃×#399	C₂²	semidirect
30. C₁₃×#398	C₂²	semidirect
31. C₁₃×#397	C₂²	semidirect
32. C₁₃×#395	C₂²	semidirect
33. C₁₃×#394	C₂²	semidirect
34. C₁₃×#393	C₂²	semidirect
35. C₁₃×#392	C₂²	semidirect
36. C₁₃×#388	C₂²	semidirect
37. C₁₃×#387	C₂²	semidirect
41. C₁₃×#386	C₂²	semidirect
42. C₁₃×#385	C₂²	semidirect
64. C₂³×C₄×C₁₃	D₄	semidirect
108. #35051	C₁₃	direct (N × H)
156. C₂²×C₄×C₁₃	#41	semidirect
180. C₂×#525	C₂×C₁₃	semidirect
181. #2847	C₂×C₁₃	semidirect
182. #2659	C₂×C₁₃	semidirect
183. #2656	C₂×C₁₃	semidirect
184. #2639	C₂×C₁₃	semidirect
185. #2564	C₂×C₁₃	semidirect
186. #2543	C₂×C₁₃	semidirect
187. #2498	C₂×C₁₃	semidirect
188. #2430	C₂×C₁₃	semidirect
189. #2325	C₂×C₁₃	semidirect
190. C₂²×#95	C₂×C₁₃	semidirect
265. #400	C₂²×C₁₃	semidirect
266. #399	C₂²×C₁₃	semidirect
267. #398	C₂²×C₁₃	semidirect
268. #397	C₂²×C₁₃	semidirect
269. #395	C₂²×C₁₃	semidirect
270. #394	C₂²×C₁₃	semidirect
271. #393	C₂²×C₁₃	semidirect
272. #392	C₂²×C₁₃	semidirect
273. #388	C₂²×C₁₃	semidirect
274. #387	C₂²×C₁₃	semidirect
278. #386	C₂²×C₁₃	semidirect
279. #385	C₂²×C₁₃	semidirect
334. C₂³×C₄	D₄×C₁₃	semidirect
434. C₂²×C₄	C₁₃×#41	semidirect
458. C₁₃	#35051	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×#525	2
C₁₃×#2847	2
C₁₃×#2659	2
C₁₃×#2656	2
C₁₃×#2639	2
C₁₃×#2564	2
C₁₃×#2543	2
C₁₃×#2498	2
C₁₃×#2430	2
C₁₃×#2325	2
C₂²×C₁₃×#95	2
#35051	13

Subgroups — C13×#35051 #15721390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35051 #15721390