Subgroups — C₁₃×#36702 #15723041

Order 3328.

4154 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2846	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2684	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2669	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2668	C₂	1	8	yes	maximal, complemented
7	C₁₃×#2622	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2482	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2410	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2404	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2308	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#535	—	2	8	no	—
17	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
18	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
21	C₂×C₁₃×#120	—	2	8	no	—
22	C₂×C₁₃×#120	C₂²	1	2	yes	—
23	C₂×C₁₃×#120	C₂²	1	4	yes	—
24	C₂×C₁₃×#120	C₂²	1	4	yes	—
25	C₂×C₁₃×#120	C₂²	1	4	yes	—
26	C₂×C₁₃×#120	C₂²	1	8	yes	complemented
27	C₂×C₁₃×#120	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
32	C₁₃×#399	C₂²	1	4	yes	complemented
33	C₁₃×#397	C₂²	1	8	yes	complemented
34	C₁₃×#397	C₂²	1	4	yes	complemented
35	C₁₃×#394	C₂²	1	8	yes	complemented
36	C₁₃×#394	C₂²	1	8	yes	complemented
37	C₁₃×#393	C₂²	1	4	yes	complemented
38	C₁₃×#392	C₂²	1	4	yes	complemented
39	C₁₃×#392	C₂²	1	8	yes	complemented
40	C₁₃×#388	C₂²	1	8	yes	complemented
41	C₁₃×#386	C₂²	1	4	yes	complemented
42	C₁₃×#386	C₂²	1	4	yes	complemented
43	C₁₃×#386	C₂²	1	8	yes	complemented
44	C₁₃×#386	C₂²	1	8	yes	complemented
45	C₁₃×#386	C₂²	1	4	yes	complemented
46	C₁₃×#385	C₂²	1	4	yes	complemented
47	C₁₃×#381	C₂²	1	2	yes	complemented
48	C₁₃×#379	C₂²	1	2	yes	—
49	C₁₃×#379	C₂²	1	4	yes	—
50	C₁₃×#379	C₂²	1	8	yes	complemented
51	C₂⁵×C₁₃	—	2	4	no	—
52	C₂⁵×C₁₃	—	4	8	no	—
53	C₂⁵×C₁₃	—	4	4	no	—
54	C₂⁵×C₁₃	C₂³	1	2	yes	—
55	C₂⁵×C₁₃	C₂³	1	4	yes	—
56	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
57	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×#41	—	2	4	no	—
59	C₂×C₁₃×#41	—	4	4	no	—
60	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic, complemented
61	C₂²×D₄×C₁₃	—	2	8	no	—
62	C₂²×D₄×C₁₃	—	4	4	no	—
63	C₂²×D₄×C₁₃	—	4	8	no	—
64	C₂²×D₄×C₁₃	D₄	1	8	yes	complemented
65	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
72	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	complemented
76	C₂³×C₄×C₁₃	C₂³	1	4	yes	complemented
77	C₁₃×#127	—	2	8	no	—
78	C₁₃×#124	—	2	8	no	—
79	C₁₃×#121	—	2	16	no	—
80	C₁₃×#121	—	4	16	no	—
81	C₁₃×#120	—	2	8	no	—
82	C₁₃×#120	—	2	8	no	—
83	C₁₃×#120	—	2	16	no	—
84	C₁₃×#120	—	2	16	no	—
85	C₁₃×#120	—	4	8	no	—
86	C₁₃×#120	—	4	16	no	—
87	C₁₃×#117	—	2	4	no	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
90	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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	4	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
106	C₂×C₄²×C₁₃	C₂³	1	2	yes	complemented
107	C₁₃×#95	C₂³	1	4	yes	complemented
108	C₁₃×#95	C₂³	1	4	yes	complemented
109	C₁₃×#95	C₂³	1	8	yes	complemented
110	C₁₃×#95	C₂³	1	8	yes	complemented
111	#36702	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₃	—	2	4	no	—
113	C₂⁴×C₁₃	—	2	8	no	—
114	C₂⁴×C₁₃	—	2	4	no	—
115	C₂⁴×C₁₃	—	2	4	no	—
116	C₂⁴×C₁₃	—	2	8	no	—
117	C₂⁴×C₁₃	—	2	16	no	—
118	C₂⁴×C₁₃	—	2	8	no	—
119	C₂⁴×C₁₃	—	4	4	no	—
120	C₂⁴×C₁₃	—	4	4	no	—
121	C₂⁴×C₁₃	—	4	8	no	—
122	C₂⁴×C₁₃	—	4	4	no	—
123	C₂⁴×C₁₃	—	4	4	no	—
124	C₂⁴×C₁₃	—	4	4	no	—
125	C₂⁴×C₁₃	—	4	32	no	—
126	C₂⁴×C₁₃	—	4	16	no	—
127	C₂⁴×C₁₃	—	4	64	no	—
128	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
129	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
130	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
131	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
132	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
133	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
134	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₁₃×#41	—	4	16	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	4	2	no	—
138	C₂×D₄×C₁₃	—	2	16	no	—
139	C₂×D₄×C₁₃	—	2	4	no	—
140	C₂×D₄×C₁₃	—	2	8	no	—
141	C₂×D₄×C₁₃	—	2	16	no	—
142	C₂×D₄×C₁₃	—	2	8	no	—
143	C₂×D₄×C₁₃	—	2	8	no	—
144	C₂×D₄×C₁₃	—	2	16	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	4	16	no	—
147	C₂×D₄×C₁₃	—	4	2	no	—
148	C₂×D₄×C₁₃	—	4	2	no	—
149	C₂×D₄×C₁₃	—	4	2	no	—
150	C₂×D₄×C₁₃	—	4	2	no	—
151	C₂×D₄×C₁₃	—	4	8	no	—
152	C₂×D₄×C₁₃	—	4	2	no	—
153	C₂×D₄×C₁₃	—	4	8	no	—
154	C₂×D₄×C₁₃	—	4	8	no	—
155	C₂×D₄×C₁₃	—	4	8	no	—
156	C₂×D₄×C₁₃	—	4	8	no	—
157	C₂×D₄×C₁₃	—	4	32	no	—
158	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
159	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	4	4	no	—
164	C₂²×C₄×C₁₃	—	4	4	no	—
165	C₂²×C₄×C₁₃	—	4	4	no	—
166	C₂²×C₄×C₁₃	—	4	8	no	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	4	8	no	—
176	C₁₃×C₂²⋊C₄	—	2	8	no	—
177	C₁₃×C₂²⋊C₄	—	2	4	no	—
178	C₁₃×C₂²⋊C₄	—	2	8	no	—
179	C₁₃×C₂²⋊C₄	—	2	8	no	—
180	C₁₃×C₂²⋊C₄	—	2	8	no	—
181	C₁₃×C₂²⋊C₄	—	2	16	no	—
182	C₁₃×C₂²⋊C₄	—	2	8	no	—
183	C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₁₃×C₂²⋊C₄	—	4	4	no	—
185	C₁₃×C₂²⋊C₄	—	4	8	no	—
186	C₁₃×C₂²⋊C₄	—	4	8	no	—
187	C₁₃×C₂²⋊C₄	—	4	8	no	—
188	C₁₃×C₂²⋊C₄	—	4	8	no	—
189	C₄²×C₁₃	—	2	4	no	—
190	C₂×#535	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂²×#120	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#2846	C₂×C₁₃	1	2	yes	complemented
193	#2684	C₂×C₁₃	1	4	yes	complemented
194	#2669	C₂×C₁₃	1	4	yes	complemented
195	#2668	C₂×C₁₃	1	8	yes	complemented
196	#2622	C₂×C₁₃	1	2	yes	complemented
197	#2482	C₂×C₁₃	1	2	yes	complemented
198	#2410	C₂×C₁₃	1	4	yes	complemented
199	#2404	C₂×C₁₃	1	2	yes	complemented
200	#2308	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂³×C₁₃	—	2	4	no	—
202	C₂³×C₁₃	—	2	16	no	—
203	C₂³×C₁₃	—	2	8	no	—
204	C₂³×C₁₃	—	2	4	no	—
205	C₂³×C₁₃	—	2	2	no	—
206	C₂³×C₁₃	—	2	8	no	—
207	C₂³×C₁₃	—	2	8	no	—
208	C₂³×C₁₃	—	2	8	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	2	8	no	—
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	—	2	2	no	—
213	C₂³×C₁₃	—	2	4	no	—
214	C₂³×C₁₃	—	2	8	no	—
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	8	no	—
217	C₂³×C₁₃	—	2	4	no	—
218	C₂³×C₁₃	—	4	8	no	—
219	C₂³×C₁₃	—	4	8	no	—
220	C₂³×C₁₃	—	4	32	no	—
221	C₂³×C₁₃	—	4	32	no	—
222	C₂³×C₁₃	—	4	16	no	—
223	C₂³×C₁₃	—	4	8	no	—
224	C₂³×C₁₃	—	4	16	no	—
225	C₂³×C₁₃	—	4	16	no	—
226	C₂³×C₁₃	—	4	32	no	—
227	C₂³×C₁₃	—	4	128	no	—
228	C₂³×C₁₃	—	4	16	no	—
229	C₂³×C₁₃	—	4	8	no	—
230	C₂³×C₁₃	—	8	8	no	—
231	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
232	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
233	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
234	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
235	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
236	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
237	Q₈×C₁₃	—	4	4	no	—
238	D₄×C₁₃	—	4	8	no	—
239	D₄×C₁₃	—	4	8	no	—
240	D₄×C₁₃	—	4	4	no	—
241	D₄×C₁₃	—	4	32	no	—
242	D₄×C₁₃	—	4	8	no	—
243	D₄×C₁₃	—	8	8	no	—
244	D₄×C₁₃	—	8	8	no	—
245	D₄×C₁₃	—	8	16	no	—
246	C₂×C₄×C₁₃	—	2	8	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	8	no	—
253	C₂×C₄×C₁₃	—	2	8	no	—
254	C₂×C₄×C₁₃	—	2	8	no	—
255	C₂×C₄×C₁₃	—	2	8	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	8	no	—
258	C₂×C₄×C₁₃	—	4	8	no	—
259	C₂×C₄×C₁₃	—	4	8	no	—
260	C₂×C₄×C₁₃	—	8	8	no	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
263	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
264	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
265	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
266	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
267	#535	—	2	8	no	—
268	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
269	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
270	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
271	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
272	C₂×#120	—	2	8	no	—
273	C₂×#120	C₂²×C₁₃	1	2	yes	—
274	C₂×#120	C₂²×C₁₃	1	4	yes	—
275	C₂×#120	C₂²×C₁₃	1	4	yes	—
276	C₂×#120	C₂²×C₁₃	1	4	yes	—
277	C₂×#120	C₂²×C₁₃	1	8	yes	complemented
278	C₂×#120	C₂²×C₁₃	1	2	yes	complemented
279	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
280	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
282	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
283	#399	C₂²×C₁₃	1	4	yes	complemented
284	#397	C₂²×C₁₃	1	8	yes	complemented
285	#397	C₂²×C₁₃	1	4	yes	complemented
286	#394	C₂²×C₁₃	1	8	yes	complemented
287	#394	C₂²×C₁₃	1	8	yes	complemented
288	#393	C₂²×C₁₃	1	4	yes	complemented
289	#392	C₂²×C₁₃	1	4	yes	complemented
290	#392	C₂²×C₁₃	1	8	yes	complemented
291	#388	C₂²×C₁₃	1	8	yes	complemented
292	#386	C₂²×C₁₃	1	4	yes	complemented
293	#386	C₂²×C₁₃	1	4	yes	complemented
294	#386	C₂²×C₁₃	1	8	yes	complemented
295	#386	C₂²×C₁₃	1	8	yes	complemented
296	#386	C₂²×C₁₃	1	4	yes	complemented
297	#385	C₂²×C₁₃	1	4	yes	complemented
298	#381	C₂²×C₁₃	1	2	yes	complemented
299	#379	C₂²×C₁₃	1	2	yes	—
300	#379	C₂²×C₁₃	1	4	yes	—
301	#379	C₂²×C₁₃	1	8	yes	complemented
302	C₂²×C₁₃	—	2	4	no	—
303	C₂²×C₁₃	—	2	8	no	—
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	4	no	—
306	C₂²×C₁₃	—	2	8	no	—
307	C₂²×C₁₃	—	2	8	no	—
308	C₂²×C₁₃	—	2	8	no	—
309	C₂²×C₁₃	—	2	16	no	—
310	C₂²×C₁₃	—	4	32	no	—
311	C₂²×C₁₃	—	4	16	no	—
312	C₂²×C₁₃	—	4	64	no	—
313	C₂²×C₁₃	—	4	4	no	—
314	C₂²×C₁₃	—	4	4	no	—
315	C₂²×C₁₃	—	4	4	no	—
316	C₂²×C₁₃	—	4	4	no	—
317	C₂²×C₁₃	—	4	8	no	—
318	C₂²×C₁₃	—	4	4	no	—
319	C₂²×C₁₃	—	4	4	no	—
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	—	4	4	no	—
322	C₂²×C₁₃	—	4	8	no	—
323	C₂²×C₁₃	—	8	8	no	—
324	C₂²×C₁₃	#534	1	4	yes	—
325	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
326	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
327	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	4	2	no	—
331	C₄×C₁₃	—	4	4	no	—
332	C₄×C₁₃	—	4	4	no	—
333	C₄×C₁₃	—	4	8	no	—
334	C₂⁵	—	2	4	no	—
335	C₂⁵	—	4	8	no	—
336	C₂⁵	—	4	4	no	—
337	C₂⁵	C₂³×C₁₃	1	2	yes	—
338	C₂⁵	C₂³×C₁₃	1	4	yes	—
339	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
340	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
341	C₂×#41	—	2	4	no	—
342	C₂×#41	—	4	4	no	—
343	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
344	C₂²×D₄	—	2	8	no	—
345	C₂²×D₄	—	4	4	no	—
346	C₂²×D₄	—	4	8	no	—
347	C₂²×D₄	D₄×C₁₃	1	8	yes	complemented
348	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
349	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
350	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
351	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
352	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
353	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
354	C₂²×D₄	C₂³×C₁₃	1	4	yes	complemented
355	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
356	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
358	C₂³×C₄	C₂³×C₁₃	1	2	yes	complemented
359	C₂³×C₄	C₂³×C₁₃	1	4	yes	complemented
360	#127	—	2	8	no	—
361	#124	—	2	8	no	—
362	#121	—	2	16	no	—
363	#121	—	4	16	no	—
364	#120	—	2	8	no	—
365	#120	—	2	8	no	—
366	#120	—	2	16	no	—
367	#120	—	2	16	no	—
368	#120	—	4	8	no	—
369	#120	—	4	16	no	—
370	#117	—	2	4	no	—
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
373	C₂×C₂²⋊C₄	—	2	4	no	—
374	C₂×C₂²⋊C₄	—	2	8	no	—
375	C₂×C₂²⋊C₄	—	4	4	no	—
376	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
387	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
388	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	complemented
389	C₂×C₄²	C₂³×C₁₃	1	2	yes	complemented
390	#95	C₂³×C₁₃	1	4	yes	complemented
391	#95	C₂³×C₁₃	1	4	yes	complemented
392	#95	C₂³×C₁₃	1	8	yes	complemented
393	#95	C₂³×C₁₃	1	8	yes	complemented
394	C₂×C₁₃	—	2	4	no	—
395	C₂×C₁₃	—	4	4	no	—
396	C₂×C₁₃	—	4	8	no	—
397	C₂×C₁₃	—	4	4	no	—
398	C₂×C₁₃	—	8	2	no	—
399	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
400	C₂×C₁₃	#3484	1	2	yes	—
401	C₂×C₁₃	#3532	1	4	yes	—
402	C₂⁴	—	2	4	no	—
403	C₂⁴	—	2	8	no	—
404	C₂⁴	—	2	4	no	—
405	C₂⁴	—	2	4	no	—
406	C₂⁴	—	2	8	no	—
407	C₂⁴	—	2	16	no	—
408	C₂⁴	—	2	8	no	—
409	C₂⁴	—	4	4	no	—
410	C₂⁴	—	4	4	no	—
411	C₂⁴	—	4	4	no	—
412	C₂⁴	—	4	8	no	—
413	C₂⁴	—	4	4	no	—
414	C₂⁴	—	4	4	no	—
415	C₂⁴	—	4	32	no	—
416	C₂⁴	—	4	16	no	—
417	C₂⁴	—	4	64	no	—
418	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
419	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
420	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
421	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
422	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
423	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
424	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
425	#41	—	4	16	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	4	2	no	—
428	C₂×D₄	—	2	16	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	8	no	—
431	C₂×D₄	—	2	16	no	—
432	C₂×D₄	—	2	8	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	16	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	4	16	no	—
437	C₂×D₄	—	4	2	no	—
438	C₂×D₄	—	4	2	no	—
439	C₂×D₄	—	4	2	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	8	no	—
442	C₂×D₄	—	4	2	no	—
443	C₂×D₄	—	4	8	no	—
444	C₂×D₄	—	4	8	no	—
445	C₂×D₄	—	4	8	no	—
446	C₂×D₄	—	4	8	no	—
447	C₂×D₄	—	4	32	no	—
448	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
449	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	—	4	8	no	—
457	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
459	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	4	8	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	16	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	4	4	no	—
475	C₂²⋊C₄	—	4	8	no	—
476	C₂²⋊C₄	—	4	8	no	—
477	C₂²⋊C₄	—	4	8	no	—
478	C₂²⋊C₄	—	4	8	no	—
479	C₄²	—	2	4	no	—
480	C₁₃	#36702	1	1	yes	characteristic, direct product factor, Sylow
481	C₂³	—	2	4	no	—
482	C₂³	—	2	16	no	—
483	C₂³	—	2	8	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	8	no	—
487	C₂³	—	2	8	no	—
488	C₂³	—	2	8	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	8	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	2	8	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	4	8	no	—
499	C₂³	—	4	8	no	—
500	C₂³	—	4	32	no	—
501	C₂³	—	4	16	no	—
502	C₂³	—	4	32	no	—
503	C₂³	—	4	16	no	—
504	C₂³	—	4	8	no	—
505	C₂³	—	4	32	no	—
506	C₂³	—	4	16	no	—
507	C₂³	—	4	128	no	—
508	C₂³	—	4	16	no	—
509	C₂³	—	4	8	no	—
510	C₂³	—	8	8	no	—
511	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
512	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
513	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
514	C₂³	C₁₃×H(5,𝔽₂)	1	8	yes	—
515	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
516	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
517	Q₈	—	4	4	no	—
518	D₄	—	4	8	no	—
519	D₄	—	4	8	no	—
520	D₄	—	4	4	no	—
521	D₄	—	4	32	no	—
522	D₄	—	4	8	no	—
523	D₄	—	8	16	no	—
524	D₄	—	8	8	no	—
525	D₄	—	8	8	no	—
526	C₂×C₄	—	2	8	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	8	no	—
533	C₂×C₄	—	2	8	no	—
534	C₂×C₄	—	2	8	no	—
535	C₂×C₄	—	2	8	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	8	no	—
538	C₂×C₄	—	4	8	no	—
539	C₂×C₄	—	4	8	no	—
540	C₂×C₄	—	8	8	no	—
541	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
542	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
543	C₂²	—	2	8	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	16	no	—
546	C₂²	—	2	4	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	8	no	—
549	C₂²	—	2	8	no	—
550	C₂²	—	2	8	no	—
551	C₂²	—	4	32	no	—
552	C₂²	—	4	16	no	—
553	C₂²	—	4	64	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	8	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	4	8	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	8	8	no	—
565	C₂²	C₁₃×#534	1	4	yes	—
566	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
567	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
568	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	4	8	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	4	no	—
575	C₂	—	2	4	no	—
576	C₂	—	4	8	no	—
577	C₂	—	4	4	no	—
578	C₂	—	4	4	no	—
579	C₂	—	8	2	no	—
580	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
581	C₂	C₁₃×#3484	1	2	yes	—
582	C₂	C₁₃×#3532	1	4	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×#535	C₂	semidirect
2. C₂²×C₁₃×#120	C₂	semidirect
3. C₁₃×#2846	C₂	semidirect
4. C₁₃×#2684	C₂	semidirect
5. C₁₃×#2669	C₂	semidirect
6. C₁₃×#2668	C₂	semidirect
7. C₁₃×#2622	C₂	semidirect
8. C₁₃×#2482	C₂	semidirect
9. C₁₃×#2410	C₂	semidirect
10. C₁₃×#2404	C₂	semidirect
11. C₁₃×#2308	C₂	semidirect
13. C₂²×C₁₃×#41	C₂²	semidirect
17. C₂×C₁₃×#127	C₂²	semidirect
18. C₂×C₁₃×#124	C₂²	semidirect
19. C₂×C₁₃×#121	C₂²	semidirect
20. C₂×C₁₃×#121	C₂²	semidirect
26. C₂×C₁₃×#120	C₂²	semidirect
27. C₂×C₁₃×#120	C₂²	semidirect
28. C₂×C₁₃×#117	C₂²	semidirect
31. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
32. C₁₃×#399	C₂²	semidirect
33. C₁₃×#397	C₂²	semidirect
34. C₁₃×#397	C₂²	semidirect
35. C₁₃×#394	C₂²	semidirect
36. C₁₃×#394	C₂²	semidirect
37. C₁₃×#393	C₂²	semidirect
38. C₁₃×#392	C₂²	semidirect
39. C₁₃×#392	C₂²	semidirect
40. C₁₃×#388	C₂²	semidirect
41. C₁₃×#386	C₂²	semidirect
42. C₁₃×#386	C₂²	semidirect
43. C₁₃×#386	C₂²	semidirect
44. C₁₃×#386	C₂²	semidirect
45. C₁₃×#386	C₂²	semidirect
46. C₁₃×#385	C₂²	semidirect
47. C₁₃×#381	C₂²	semidirect
50. C₁₃×#379	C₂²	semidirect
60. C₂²×Q₈×C₁₃	C₂³	semidirect
64. C₂²×D₄×C₁₃	D₄	semidirect
71. C₂²×D₄×C₁₃	C₂³	semidirect
72. C₂²×D₄×C₁₃	C₂³	semidirect
75. C₂³×C₄×C₁₃	C₂³	semidirect
76. C₂³×C₄×C₁₃	C₂³	semidirect
88. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
89. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
103. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
104. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
105. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
106. C₂×C₄²×C₁₃	C₂³	semidirect
107. C₁₃×#95	C₂³	semidirect
108. C₁₃×#95	C₂³	semidirect
109. C₁₃×#95	C₂³	semidirect
110. C₁₃×#95	C₂³	semidirect
111. #36702	C₁₃	direct (N × H)
190. C₂×#535	C₂×C₁₃	semidirect
191. C₂²×#120	C₂×C₁₃	semidirect
192. #2846	C₂×C₁₃	semidirect
193. #2684	C₂×C₁₃	semidirect
194. #2669	C₂×C₁₃	semidirect
195. #2668	C₂×C₁₃	semidirect
196. #2622	C₂×C₁₃	semidirect
197. #2482	C₂×C₁₃	semidirect
198. #2410	C₂×C₁₃	semidirect
199. #2404	C₂×C₁₃	semidirect
200. #2308	C₂×C₁₃	semidirect
264. C₂²×#41	C₂²×C₁₃	semidirect
268. C₂×#127	C₂²×C₁₃	semidirect
269. C₂×#124	C₂²×C₁₃	semidirect
270. C₂×#121	C₂²×C₁₃	semidirect
271. C₂×#121	C₂²×C₁₃	semidirect
277. C₂×#120	C₂²×C₁₃	semidirect
278. C₂×#120	C₂²×C₁₃	semidirect
279. C₂×#117	C₂²×C₁₃	semidirect
282. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
283. #399	C₂²×C₁₃	semidirect
284. #397	C₂²×C₁₃	semidirect
285. #397	C₂²×C₁₃	semidirect
286. #394	C₂²×C₁₃	semidirect
287. #394	C₂²×C₁₃	semidirect
288. #393	C₂²×C₁₃	semidirect
289. #392	C₂²×C₁₃	semidirect
290. #392	C₂²×C₁₃	semidirect
291. #388	C₂²×C₁₃	semidirect
292. #386	C₂²×C₁₃	semidirect
293. #386	C₂²×C₁₃	semidirect
294. #386	C₂²×C₁₃	semidirect
295. #386	C₂²×C₁₃	semidirect
296. #386	C₂²×C₁₃	semidirect
297. #385	C₂²×C₁₃	semidirect
298. #381	C₂²×C₁₃	semidirect
301. #379	C₂²×C₁₃	semidirect
343. C₂²×Q₈	C₂³×C₁₃	semidirect
347. C₂²×D₄	D₄×C₁₃	semidirect
354. C₂²×D₄	C₂³×C₁₃	semidirect
355. C₂²×D₄	C₂³×C₁₃	semidirect
358. C₂³×C₄	C₂³×C₁₃	semidirect
359. C₂³×C₄	C₂³×C₁₃	semidirect
371. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
372. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
386. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
387. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
388. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
389. C₂×C₄²	C₂³×C₁₃	semidirect
390. #95	C₂³×C₁₃	semidirect
391. #95	C₂³×C₁₃	semidirect
392. #95	C₂³×C₁₃	semidirect
393. #95	C₂³×C₁₃	semidirect
480. C₁₃	#36702	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×#535	2
C₂²×C₁₃×#120	2
C₁₃×#2846	2
C₁₃×#2684	2
C₁₃×#2669	2
C₁₃×#2668	2
C₁₃×#2622	2
C₁₃×#2482	2
C₁₃×#2410	2
C₁₃×#2404	2
C₁₃×#2308	2
#36702	13

Subgroups — C13×#36702 #15723041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36702 #15723041