Subgroups — C₁₃×#36717 #15723056

Order 3328.

3394 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#534	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2847	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2703	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2669	C₂	1	8	yes	maximal, complemented
6	C₁₃×#2617	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2591	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2433	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2403	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2403	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
17	C₁₃×#534	—	2	8	no	—
18	C₂×C₁₃×#127	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#121	—	2	8	no	—
21	C₂×C₁₃×#121	C₂²	1	2	yes	—
22	C₂×C₁₃×#121	C₂²	1	2	yes	—
23	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
24	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
26	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
27	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
28	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
29	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#400	C₂²	1	4	yes	complemented
34	C₁₃×#397	C₂²	1	4	yes	complemented
35	C₁₃×#394	C₂²	1	4	yes	complemented
36	C₁₃×#394	C₂²	1	8	yes	complemented
37	C₁₃×#392	C₂²	1	4	yes	complemented
38	C₁₃×#392	C₂²	1	8	yes	complemented
39	C₁₃×#392	C₂²	1	8	yes	complemented
40	C₁₃×#392	C₂²	1	8	yes	complemented
41	C₁₃×#390	C₂²	1	4	yes	complemented
42	C₁₃×#388	C₂²	1	8	yes	complemented
43	C₁₃×#388	C₂²	1	8	yes	complemented
44	C₁₃×#386	C₂²	1	4	yes	complemented
45	C₁₃×#386	C₂²	1	4	yes	complemented
46	C₁₃×#386	C₂²	1	8	yes	complemented
47	C₁₃×#386	C₂²	1	4	yes	complemented
48	C₁₃×#386	C₂²	1	4	yes	complemented
49	C₁₃×#380	C₂²	1	2	yes	complemented
50	C₁₃×#380	C₂²	1	4	yes	complemented
51	C₁₃×#379	C₂²	1	2	yes	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
53	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
54	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
55	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
56	C₂⁵×C₁₃	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₃	—	2	4	no	—
58	C₂²×D₄×C₁₃	—	2	4	no	—
59	C₂²×D₄×C₁₃	—	2	8	no	—
60	C₂²×D₄×C₁₃	—	2	4	no	—
61	C₂²×D₄×C₁₃	—	4	4	no	—
62	C₂²×D₄×C₁₃	—	4	4	no	—
63	C₂²×D₄×C₁₃	—	4	8	no	—
64	C₂²×D₄×C₁₃	—	4	4	no	—
65	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
74	C₂³×C₄×C₁₃	—	2	4	no	—
75	C₂³×C₄×C₁₃	—	4	4	no	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×#127	—	4	8	no	—
83	C₁₃×#123	—	2	16	no	—
84	C₁₃×#121	—	2	8	no	—
85	C₁₃×#121	—	2	8	no	—
86	C₁₃×#121	—	2	32	no	—
87	C₁₃×#121	—	4	8	no	—
88	C₁₃×#120	—	2	16	no	—
89	C₁₃×#120	—	4	8	no	—
90	C₁₃×#120	—	4	8	no	—
91	C₁₃×#120	—	4	8	no	—
92	C₁₃×#120	—	4	8	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
99	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
112	C₁₃×#95	C₂³	1	4	yes	—
113	C₁₃×#95	C₂³	1	8	yes	—
114	C₁₃×#95	C₂³	1	4	yes	—
115	C₁₃×#95	C₂³	1	8	yes	—
116	#36717	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂⁴×C₁₃	—	2	2	no	—
118	C₂⁴×C₁₃	—	2	4	no	—
119	C₂⁴×C₁₃	—	2	4	no	—
120	C₂⁴×C₁₃	—	2	2	no	—
121	C₂⁴×C₁₃	—	2	4	no	—
122	C₂⁴×C₁₃	—	2	4	no	—
123	C₂⁴×C₁₃	—	2	4	no	—
124	C₂⁴×C₁₃	—	4	2	no	—
125	C₂⁴×C₁₃	—	4	2	no	—
126	C₂⁴×C₁₃	—	4	2	no	—
127	C₂⁴×C₁₃	—	4	2	no	—
128	C₂⁴×C₁₃	—	4	2	no	—
129	C₂⁴×C₁₃	—	4	4	no	—
130	C₂⁴×C₁₃	—	4	4	no	—
131	C₂⁴×C₁₃	—	4	4	no	—
132	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
133	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
134	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
135	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
136	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
137	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂×D₄×C₁₃	—	2	8	no	—
139	C₂×D₄×C₁₃	—	2	8	no	—
140	C₂×D₄×C₁₃	—	2	8	no	—
141	C₂×D₄×C₁₃	—	2	8	no	—
142	C₂×D₄×C₁₃	—	2	8	no	—
143	C₂×D₄×C₁₃	—	2	8	no	—
144	C₂×D₄×C₁₃	—	2	8	no	—
145	C₂×D₄×C₁₃	—	2	8	no	—
146	C₂×D₄×C₁₃	—	2	16	no	—
147	C₂×D₄×C₁₃	—	2	8	no	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	8	no	—
151	C₂×D₄×C₁₃	—	4	4	no	—
152	C₂×D₄×C₁₃	—	4	4	no	—
153	C₂×D₄×C₁₃	—	4	4	no	—
154	C₂×D₄×C₁₃	—	4	4	no	—
155	C₂×D₄×C₁₃	—	4	4	no	—
156	C₂×D₄×C₁₃	—	4	16	no	—
157	C₂×D₄×C₁₃	—	4	8	no	—
158	C₂×D₄×C₁₃	—	4	8	no	—
159	C₂×D₄×C₁₃	—	4	8	no	—
160	C₂×D₄×C₁₃	—	4	4	no	—
161	C₂×D₄×C₁₃	—	4	8	no	—
162	C₂×D₄×C₁₃	—	4	4	no	—
163	C₂×D₄×C₁₃	—	4	8	no	—
164	C₂×D₄×C₁₃	—	4	16	no	—
165	C₂×D₄×C₁₃	—	4	16	no	—
166	C₂×D₄×C₁₃	—	4	32	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	8	no	—
172	C₂²×C₄×C₁₃	—	2	8	no	—
173	C₂²×C₄×C₁₃	—	4	2	no	—
174	C₂²×C₄×C₁₃	—	4	4	no	—
175	C₂²×C₄×C₁₃	—	4	2	no	—
176	C₂²×C₄×C₁₃	—	4	2	no	—
177	C₂²×C₄×C₁₃	—	4	4	no	—
178	C₂²×C₄×C₁₃	—	4	16	no	—
179	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₁₃×C₄⋊C₄	—	2	8	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	4	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	8	no	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₁₃×C₂²⋊C₄	—	2	8	no	—
194	C₁₃×C₂²⋊C₄	—	2	8	no	—
195	C₁₃×C₂²⋊C₄	—	2	16	no	—
196	C₁₃×C₂²⋊C₄	—	4	4	no	—
197	C₁₃×C₂²⋊C₄	—	4	8	no	—
198	C₁₃×C₂²⋊C₄	—	4	8	no	—
199	C₁₃×C₂²⋊C₄	—	4	8	no	—
200	C₁₃×C₂²⋊C₄	—	4	4	no	—
201	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
202	C₄²×C₁₃	—	4	4	no	—
203	C₂×#534	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#2847	C₂×C₁₃	1	2	yes	complemented
206	#2703	C₂×C₁₃	1	8	yes	complemented
207	#2669	C₂×C₁₃	1	8	yes	complemented
208	#2617	C₂×C₁₃	1	2	yes	complemented
209	#2591	C₂×C₁₃	1	2	yes	complemented
210	#2433	C₂×C₁₃	1	2	yes	complemented
211	#2403	C₂×C₁₃	1	2	yes	complemented
212	#2403	C₂×C₁₃	1	2	yes	complemented
213	#2312	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂³×C₁₃	—	2	2	no	—
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	8	no	—
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	2	4	no	—
219	C₂³×C₁₃	—	2	4	no	—
220	C₂³×C₁₃	—	2	4	no	—
221	C₂³×C₁₃	—	2	4	no	—
222	C₂³×C₁₃	—	2	4	no	—
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	8	no	—
225	C₂³×C₁₃	—	2	4	no	—
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	—	2	8	no	—
228	C₂³×C₁₃	—	2	4	no	—
229	C₂³×C₁₃	—	2	8	no	—
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	—	2	4	no	—
234	C₂³×C₁₃	—	4	4	no	—
235	C₂³×C₁₃	—	4	4	no	—
236	C₂³×C₁₃	—	4	16	no	—
237	C₂³×C₁₃	—	4	4	no	—
238	C₂³×C₁₃	—	4	4	no	—
239	C₂³×C₁₃	—	4	4	no	—
240	C₂³×C₁₃	—	4	8	no	—
241	C₂³×C₁₃	—	4	4	no	—
242	C₂³×C₁₃	—	4	4	no	—
243	C₂³×C₁₃	—	8	8	no	—
244	C₂³×C₁₃	—	8	8	no	—
245	C₂³×C₁₃	—	8	4	no	—
246	C₂³×C₁₃	—	8	4	no	—
247	C₂³×C₁₃	—	8	16	no	—
248	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
249	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
250	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
251	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
252	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
253	D₄×C₁₃	—	4	16	no	—
254	D₄×C₁₃	—	4	16	no	—
255	D₄×C₁₃	—	4	16	no	—
256	D₄×C₁₃	—	4	16	no	—
257	D₄×C₁₃	—	4	16	no	—
258	D₄×C₁₃	—	8	4	no	—
259	D₄×C₁₃	—	8	4	no	—
260	D₄×C₁₃	—	8	16	no	—
261	D₄×C₁₃	—	8	16	no	—
262	C₂×C₄×C₁₃	—	2	8	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	8	no	—
270	C₂×C₄×C₁₃	—	2	8	no	—
271	C₂×C₄×C₁₃	—	2	8	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	2	4	no	—
275	C₂×C₄×C₁₃	—	4	4	no	—
276	C₂×C₄×C₁₃	—	4	4	no	—
277	C₂×C₄×C₁₃	—	4	16	no	—
278	C₂×C₄×C₁₃	—	4	8	no	—
279	C₂×C₄×C₁₃	—	4	4	no	—
280	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
281	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
282	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
283	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
284	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
285	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
286	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
287	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
288	#534	—	2	8	no	—
289	C₂×#127	C₂²×C₁₃	1	4	yes	complemented
290	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
291	C₂×#121	—	2	8	no	—
292	C₂×#121	C₂²×C₁₃	1	2	yes	—
293	C₂×#121	C₂²×C₁₃	1	2	yes	—
294	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
295	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
296	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
297	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
298	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
299	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
300	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
301	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
302	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
303	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
304	#400	C₂²×C₁₃	1	4	yes	complemented
305	#397	C₂²×C₁₃	1	4	yes	complemented
306	#394	C₂²×C₁₃	1	4	yes	complemented
307	#394	C₂²×C₁₃	1	8	yes	complemented
308	#392	C₂²×C₁₃	1	4	yes	complemented
309	#392	C₂²×C₁₃	1	8	yes	complemented
310	#392	C₂²×C₁₃	1	8	yes	complemented
311	#392	C₂²×C₁₃	1	8	yes	complemented
312	#390	C₂²×C₁₃	1	4	yes	complemented
313	#388	C₂²×C₁₃	1	8	yes	complemented
314	#388	C₂²×C₁₃	1	8	yes	complemented
315	#386	C₂²×C₁₃	1	4	yes	complemented
316	#386	C₂²×C₁₃	1	4	yes	complemented
317	#386	C₂²×C₁₃	1	8	yes	complemented
318	#386	C₂²×C₁₃	1	4	yes	complemented
319	#386	C₂²×C₁₃	1	4	yes	complemented
320	#380	C₂²×C₁₃	1	2	yes	complemented
321	#380	C₂²×C₁₃	1	4	yes	complemented
322	#379	C₂²×C₁₃	1	2	yes	—
323	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	2	8	no	—
327	C₂²×C₁₃	—	2	4	no	—
328	C₂²×C₁₃	—	2	4	no	—
329	C₂²×C₁₃	—	2	4	no	—
330	C₂²×C₁₃	—	2	4	no	—
331	C₂²×C₁₃	—	2	8	no	—
332	C₂²×C₁₃	—	4	16	no	—
333	C₂²×C₁₃	—	4	2	no	—
334	C₂²×C₁₃	—	4	2	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	—	4	8	no	—
337	C₂²×C₁₃	—	4	4	no	—
338	C₂²×C₁₃	—	4	2	no	—
339	C₂²×C₁₃	—	4	2	no	—
340	C₂²×C₁₃	—	4	2	no	—
341	C₂²×C₁₃	—	4	4	no	—
342	C₂²×C₁₃	—	4	4	no	—
343	C₂²×C₁₃	—	4	8	no	—
344	C₂²×C₁₃	—	4	8	no	—
345	C₂²×C₁₃	—	4	8	no	—
346	C₂²×C₁₃	—	8	8	no	—
347	C₂²×C₁₃	—	8	8	no	—
348	C₂²×C₁₃	—	8	16	no	—
349	C₂²×C₁₃	#535	1	4	yes	—
350	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
351	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
352	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
353	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
354	C₄×C₁₃	—	2	4	no	—
355	C₄×C₁₃	—	2	4	no	—
356	C₄×C₁₃	—	2	4	no	—
357	C₄×C₁₃	—	4	4	no	—
358	C₄×C₁₃	—	4	2	no	—
359	C₄×C₁₃	—	4	8	no	—
360	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
361	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
362	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
363	C₂⁵	C₂³×C₁₃	1	2	yes	—
364	C₂²×D₄	—	2	4	no	—
365	C₂²×D₄	—	2	4	no	—
366	C₂²×D₄	—	2	8	no	—
367	C₂²×D₄	—	2	4	no	—
368	C₂²×D₄	—	4	4	no	—
369	C₂²×D₄	—	4	4	no	—
370	C₂²×D₄	—	4	8	no	—
371	C₂²×D₄	—	4	4	no	—
372	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
373	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
374	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
375	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
376	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
377	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
378	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
379	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
380	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
381	C₂³×C₄	—	2	4	no	—
382	C₂³×C₄	—	4	4	no	—
383	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
385	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
387	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
389	#127	—	4	8	no	—
390	#123	—	2	16	no	—
391	#121	—	2	8	no	—
392	#121	—	2	8	no	—
393	#121	—	2	32	no	—
394	#121	—	4	8	no	—
395	#120	—	2	16	no	—
396	#120	—	4	8	no	—
397	#120	—	4	8	no	—
398	#120	—	4	8	no	—
399	#120	—	4	8	no	—
400	C₂×C₄⋊C₄	—	2	4	no	—
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
405	C₂×C₂²⋊C₄	—	2	4	no	—
406	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
407	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
418	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
419	#95	C₂³×C₁₃	1	4	yes	—
420	#95	C₂³×C₁₃	1	8	yes	—
421	#95	C₂³×C₁₃	1	4	yes	—
422	#95	C₂³×C₁₃	1	8	yes	—
423	C₂×C₁₃	—	2	4	no	—
424	C₂×C₁₃	—	4	4	no	—
425	C₂×C₁₃	—	4	4	no	—
426	C₂×C₁₃	—	8	4	no	—
427	C₂×C₁₃	—	8	2	no	—
428	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
429	C₂×C₁₃	#3484	1	1	yes	characteristic
430	C₂×C₁₃	#3484	1	1	yes	characteristic
431	C₂×C₁₃	#3537	1	4	yes	—
432	C₂⁴	—	2	2	no	—
433	C₂⁴	—	2	4	no	—
434	C₂⁴	—	2	4	no	—
435	C₂⁴	—	2	2	no	—
436	C₂⁴	—	2	4	no	—
437	C₂⁴	—	2	4	no	—
438	C₂⁴	—	2	4	no	—
439	C₂⁴	—	4	2	no	—
440	C₂⁴	—	4	2	no	—
441	C₂⁴	—	4	2	no	—
442	C₂⁴	—	4	2	no	—
443	C₂⁴	—	4	2	no	—
444	C₂⁴	—	4	4	no	—
445	C₂⁴	—	4	4	no	—
446	C₂⁴	—	4	4	no	—
447	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
448	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
449	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
450	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
451	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
452	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	8	no	—
456	C₂×D₄	—	2	8	no	—
457	C₂×D₄	—	2	8	no	—
458	C₂×D₄	—	2	8	no	—
459	C₂×D₄	—	2	8	no	—
460	C₂×D₄	—	2	8	no	—
461	C₂×D₄	—	2	16	no	—
462	C₂×D₄	—	2	8	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	8	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	—	4	4	no	—
468	C₂×D₄	—	4	4	no	—
469	C₂×D₄	—	4	4	no	—
470	C₂×D₄	—	4	4	no	—
471	C₂×D₄	—	4	16	no	—
472	C₂×D₄	—	4	8	no	—
473	C₂×D₄	—	4	8	no	—
474	C₂×D₄	—	4	8	no	—
475	C₂×D₄	—	4	4	no	—
476	C₂×D₄	—	4	8	no	—
477	C₂×D₄	—	4	4	no	—
478	C₂×D₄	—	4	8	no	—
479	C₂×D₄	—	4	16	no	—
480	C₂×D₄	—	4	16	no	—
481	C₂×D₄	—	4	32	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	—	4	4	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	4	no	—
493	C₂²×C₄	—	4	16	no	—
494	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
495	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
497	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
502	C₄⋊C₄	—	2	8	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	4	4	no	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	2	8	no	—
509	C₂²⋊C₄	—	2	8	no	—
510	C₂²⋊C₄	—	2	16	no	—
511	C₂²⋊C₄	—	4	4	no	—
512	C₂²⋊C₄	—	4	8	no	—
513	C₂²⋊C₄	—	4	8	no	—
514	C₂²⋊C₄	—	4	8	no	—
515	C₂²⋊C₄	—	4	4	no	—
516	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
517	C₄²	—	4	4	no	—
518	C₁₃	#36717	1	1	yes	characteristic, direct product factor, Sylow
519	C₂³	—	2	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	8	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	8	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	8	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	8	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	4	4	no	—
540	C₂³	—	4	4	no	—
541	C₂³	—	4	16	no	—
542	C₂³	—	4	4	no	—
543	C₂³	—	4	4	no	—
544	C₂³	—	4	4	no	—
545	C₂³	—	4	8	no	—
546	C₂³	—	4	4	no	—
547	C₂³	—	4	4	no	—
548	C₂³	—	8	8	no	—
549	C₂³	—	8	8	no	—
550	C₂³	—	8	4	no	—
551	C₂³	—	8	4	no	—
552	C₂³	—	8	16	no	—
553	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
554	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
555	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
556	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
557	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
558	D₄	—	4	16	no	—
559	D₄	—	4	16	no	—
560	D₄	—	4	16	no	—
561	D₄	—	4	16	no	—
562	D₄	—	4	16	no	—
563	D₄	—	8	4	no	—
564	D₄	—	8	4	no	—
565	D₄	—	8	16	no	—
566	D₄	—	8	16	no	—
567	C₂×C₄	—	2	8	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	8	no	—
575	C₂×C₄	—	2	8	no	—
576	C₂×C₄	—	2	8	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	4	4	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	16	no	—
583	C₂×C₄	—	4	8	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
586	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
587	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
588	C₂²	—	2	8	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	8	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	4	no	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	4	16	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	8	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	8	no	—
602	C₂²	—	4	8	no	—
603	C₂²	—	4	8	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	8	8	no	—
611	C₂²	—	8	8	no	—
612	C₂²	—	8	16	no	—
613	C₂²	C₁₃×#535	1	4	yes	—
614	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
615	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
616	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
617	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
618	C₄	—	2	4	no	—
619	C₄	—	2	4	no	—
620	C₄	—	2	4	no	—
621	C₄	—	4	8	no	—
622	C₄	—	4	4	no	—
623	C₄	—	4	2	no	—
624	C₂	—	2	4	no	—
625	C₂	—	4	4	no	—
626	C₂	—	4	4	no	—
627	C₂	—	8	4	no	—
628	C₂	—	8	2	no	—
629	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
630	C₂	C₁₃×#3484	1	1	yes	characteristic
631	C₂	C₁₃×#3484	1	1	yes	characteristic
632	C₂	C₁₃×#3537	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×#534	C₂	semidirect
2. C₂²×C₁₃×#121	C₂	semidirect
3. C₁₃×#2847	C₂	semidirect
4. C₁₃×#2703	C₂	semidirect
5. C₁₃×#2669	C₂	semidirect
6. C₁₃×#2617	C₂	semidirect
7. C₁₃×#2591	C₂	semidirect
8. C₁₃×#2433	C₂	semidirect
9. C₁₃×#2403	C₂	semidirect
10. C₁₃×#2403	C₂	semidirect
11. C₁₃×#2312	C₂	semidirect
15. C₂³×D₄×C₁₃	C₂²	semidirect
16. C₂⁴×C₄×C₁₃	C₂²	semidirect
18. C₂×C₁₃×#127	C₂²	semidirect
19. C₂×C₁₃×#123	C₂²	semidirect
23. C₂×C₁₃×#121	C₂²	semidirect
24. C₂×C₁₃×#121	C₂²	semidirect
25. C₂×C₁₃×#120	C₂²	semidirect
26. C₂×C₁₃×#120	C₂²	semidirect
27. C₂×C₁₃×#120	C₂²	semidirect
28. C₂×C₁₃×#120	C₂²	semidirect
29. C₂×C₁₃×#120	C₂²	semidirect
30. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
32. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
33. C₁₃×#400	C₂²	semidirect
34. C₁₃×#397	C₂²	semidirect
35. C₁₃×#394	C₂²	semidirect
36. C₁₃×#394	C₂²	semidirect
37. C₁₃×#392	C₂²	semidirect
38. C₁₃×#392	C₂²	semidirect
39. C₁₃×#392	C₂²	semidirect
40. C₁₃×#392	C₂²	semidirect
41. C₁₃×#390	C₂²	semidirect
42. C₁₃×#388	C₂²	semidirect
43. C₁₃×#388	C₂²	semidirect
44. C₁₃×#386	C₂²	semidirect
45. C₁₃×#386	C₂²	semidirect
46. C₁₃×#386	C₂²	semidirect
47. C₁₃×#386	C₂²	semidirect
48. C₁₃×#386	C₂²	semidirect
49. C₁₃×#380	C₂²	semidirect
50. C₁₃×#380	C₂²	semidirect
52. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
99. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
116. #36717	C₁₃	direct (N × H)
203. C₂×#534	C₂×C₁₃	semidirect
204. C₂²×#121	C₂×C₁₃	semidirect
205. #2847	C₂×C₁₃	semidirect
206. #2703	C₂×C₁₃	semidirect
207. #2669	C₂×C₁₃	semidirect
208. #2617	C₂×C₁₃	semidirect
209. #2591	C₂×C₁₃	semidirect
210. #2433	C₂×C₁₃	semidirect
211. #2403	C₂×C₁₃	semidirect
212. #2403	C₂×C₁₃	semidirect
213. #2312	C₂×C₁₃	semidirect
286. C₂³×D₄	C₂²×C₁₃	semidirect
287. C₂⁴×C₄	C₂²×C₁₃	semidirect
289. C₂×#127	C₂²×C₁₃	semidirect
290. C₂×#123	C₂²×C₁₃	semidirect
294. C₂×#121	C₂²×C₁₃	semidirect
295. C₂×#121	C₂²×C₁₃	semidirect
296. C₂×#120	C₂²×C₁₃	semidirect
297. C₂×#120	C₂²×C₁₃	semidirect
298. C₂×#120	C₂²×C₁₃	semidirect
299. C₂×#120	C₂²×C₁₃	semidirect
300. C₂×#120	C₂²×C₁₃	semidirect
301. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
303. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
304. #400	C₂²×C₁₃	semidirect
305. #397	C₂²×C₁₃	semidirect
306. #394	C₂²×C₁₃	semidirect
307. #394	C₂²×C₁₃	semidirect
308. #392	C₂²×C₁₃	semidirect
309. #392	C₂²×C₁₃	semidirect
310. #392	C₂²×C₁₃	semidirect
311. #392	C₂²×C₁₃	semidirect
312. #390	C₂²×C₁₃	semidirect
313. #388	C₂²×C₁₃	semidirect
314. #388	C₂²×C₁₃	semidirect
315. #386	C₂²×C₁₃	semidirect
316. #386	C₂²×C₁₃	semidirect
317. #386	C₂²×C₁₃	semidirect
318. #386	C₂²×C₁₃	semidirect
319. #386	C₂²×C₁₃	semidirect
320. #380	C₂²×C₁₃	semidirect
321. #380	C₂²×C₁₃	semidirect
323. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
406. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
518. C₁₃	#36717	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×#534	2
C₂²×C₁₃×#121	2
C₁₃×#2847	2
C₁₃×#2703	2
C₁₃×#2669	2
C₁₃×#2617	2
C₁₃×#2591	2
C₁₃×#2433	2
C₁₃×#2403	2
C₁₃×#2312	2
#36717	13

Subgroups — C13×#36717 #15723056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36717 #15723056