Subgroups — C₁₃×#3519 #13112577

Order 1664.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#553	C₂	1	2	yes	maximal, complemented
4	C₁₃×#553	C₂	1	2	yes	maximal, complemented
5	C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#546	C₂	1	4	yes	maximal, complemented
7	C₁₃×#546	C₂	1	2	yes	maximal, complemented
8	D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄²×C₁₃	C₂	1	2	yes	maximal, complemented
10	C₁₃×#540	C₂	1	2	yes	maximal, complemented
11	C₁₃×#538	C₂	1	4	yes	maximal, complemented
12	C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#525	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#121	C₂	1	2	yes	maximal, complemented
16	C₁₃×#518	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
20	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
22	C₂²×D₄×C₁₃	C₂²	1	2	yes	complemented
23	C₂²×D₄×C₁₃	C₂²	1	4	yes	complemented
24	C₂³×C₄×C₁₃	C₂²	1	2	yes	complemented
25	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#127	C₂²	1	2	yes	complemented
28	C₁₃×#126	C₂²	1	2	yes	complemented
29	C₁₃×#126	C₂²	1	4	yes	complemented
30	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#125	C₂²	1	2	yes	complemented
32	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#124	C₂²	1	2	yes	complemented
34	C₁₃×#124	C₂²	1	4	yes	complemented
35	C₁₃×#123	C₂²	1	4	yes	complemented
36	C₁₃×#123	C₂²	1	2	yes	complemented
37	C₁₃×#123	C₂²	1	4	yes	complemented
38	C₁₃×#123	C₂²	1	4	yes	complemented
39	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
41	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
42	C₁₃×#121	C₂²	1	1	yes	characteristic
43	C₁₃×#121	C₂²	1	2	yes	complemented
44	C₁₃×#121	C₂²	1	4	yes	complemented
45	C₁₃×#121	C₂²	1	4	yes	complemented
46	C₁₃×#121	C₂²	1	2	yes	complemented
47	C₁₃×#121	C₂²	1	2	yes	complemented
48	C₁₃×#121	C₂²	1	2	yes	complemented
49	C₁₃×#121	C₂²	1	2	yes	complemented
50	C₁₃×#121	C₂²	1	4	yes	complemented
51	C₁₃×#121	C₂²	1	4	yes	complemented
52	C₁₃×#121	C₂²	1	2	yes	complemented
53	C₁₃×#121	C₂²	1	2	yes	complemented
54	C₁₃×#121	C₂²	1	4	yes	complemented
55	C₁₃×#120	C₂²	1	4	yes	complemented
56	C₁₃×#120	C₂²	1	4	yes	complemented
57	C₁₃×#120	C₂²	1	4	yes	complemented
58	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
59	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
60	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
61	C₄×D₄×C₁₃	C₂²	1	2	yes	—
62	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
63	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
64	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
65	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
66	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
67	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
68	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
69	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
70	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
71	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
72	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
73	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
74	C₁₃×#117	C₂²	1	2	yes	complemented
75	C₁₃×#117	C₂²	1	2	yes	complemented
76	C₁₃×#117	C₂²	1	2	yes	complemented
77	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
79	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
80	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
81	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
82	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
83	C₂⁴×C₁₃	C₂³	1	2	yes	—
84	C₂⁴×C₁₃	C₂³	1	4	yes	—
85	C₁₃×#41	—	4	4	no	—
86	C₁₃×#41	—	4	4	no	—
87	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
89	C₂×D₄×C₁₃	—	2	4	no	—
90	C₂×D₄×C₁₃	—	2	8	no	—
91	C₂×D₄×C₁₃	—	4	4	no	—
92	C₂×D₄×C₁₃	—	4	8	no	—
93	C₂×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂×D₄×C₁₃	C₂³	1	4	yes	—
95	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂×D₄×C₁₃	C₂³	1	4	yes	—
98	C₂×D₄×C₁₃	C₂³	1	2	yes	—
99	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×D₄×C₁₃	C₂³	1	2	yes	—
101	C₂×D₄×C₁₃	C₂³	1	4	yes	—
102	C₂×D₄×C₁₃	C₂³	1	2	yes	—
103	C₂×D₄×C₁₃	C₂³	1	4	yes	—
104	C₂×D₄×C₁₃	C₂³	1	4	yes	—
105	C₂×D₄×C₁₃	C₂³	1	4	yes	—
106	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	—	4	4	no	—
108	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
116	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
118	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
120	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
124	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
126	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
132	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₄²×C₁₃	C₂³	1	1	yes	characteristic
151	C₄²×C₁₃	C₂³	1	1	yes	characteristic
152	C₄²×C₁₃	C₂³	1	1	yes	characteristic
153	C₄²×C₁₃	C₂³	1	4	yes	—
154	C₄²×C₁₃	C₂³	1	2	yes	—
155	#3519	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₁₃	—	2	4	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	2	8	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	4	4	no	—
161	C₂³×C₁₃	—	4	4	no	—
162	C₂³×C₁₃	C₂⁴	1	2	yes	—
163	C₂³×C₁₃	C₂⁴	1	2	yes	—
164	C₂³×C₁₃	C₂⁴	1	4	yes	—
165	C₂³×C₁₃	C₂⁴	1	2	yes	—
166	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
167	Q₈×C₁₃	—	2	2	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	D₄×C₁₃	—	2	4	no	—
170	D₄×C₁₃	—	2	8	no	—
171	D₄×C₁₃	—	2	4	no	—
172	D₄×C₁₃	—	2	8	no	—
173	D₄×C₁₃	—	2	2	no	—
174	D₄×C₁₃	—	2	4	no	—
175	D₄×C₁₃	—	2	2	no	—
176	D₄×C₁₃	—	2	4	no	—
177	D₄×C₁₃	—	4	4	no	—
178	D₄×C₁₃	—	4	4	no	—
179	D₄×C₁₃	—	4	4	no	—
180	D₄×C₁₃	—	4	2	no	—
181	D₄×C₁₃	—	4	4	no	—
182	D₄×C₁₃	#41	1	4	yes	complemented
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	—	4	4	no	—
194	C₂×C₄×C₁₃	—	4	4	no	—
195	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
197	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
200	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
202	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
203	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
204	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
205	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
207	#555	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#554	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#553	C₂×C₁₃	1	2	yes	complemented
210	#553	C₂×C₁₃	1	2	yes	complemented
211	#550	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#546	C₂×C₁₃	1	4	yes	complemented
213	#546	C₂×C₁₃	1	2	yes	complemented
214	D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
215	D₄²	C₂×C₁₃	1	2	yes	complemented
216	#540	C₂×C₁₃	1	2	yes	complemented
217	#538	C₂×C₁₃	1	4	yes	complemented
218	#532	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#525	C₂×C₁₃	1	2	yes	complemented
221	C₂×#121	C₂×C₁₃	1	2	yes	complemented
222	#518	C₂×C₁₃	1	2	yes	complemented
223	C₂×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂²×C₁₃	—	2	1	no	—
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	2	2	no	—
228	C₂²×C₁₃	—	2	2	no	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	—	2	4	no	—
231	C₂²×C₁₃	—	2	2	no	—
232	C₂²×C₁₃	—	2	4	no	—
233	C₂²×C₁₃	—	2	4	no	—
234	C₂²×C₁₃	—	2	2	no	—
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	4	8	no	—
238	C₂²×C₁₃	—	8	8	no	—
239	C₂²×C₁₃	C₂×#41	1	4	yes	—
240	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
241	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	—	2	2	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	2	4	no	—
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	C₂×#41	1	2	yes	—
253	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
254	C₂×#41	C₂²×C₁₃	1	2	yes	complemented
255	C₂×#41	C₂²×C₁₃	1	2	yes	complemented
256	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂²×D₄	C₂²×C₁₃	1	2	yes	—
258	C₂²×D₄	C₂²×C₁₃	1	2	yes	complemented
259	C₂²×D₄	C₂²×C₁₃	1	4	yes	complemented
260	C₂³×C₄	C₂²×C₁₃	1	2	yes	complemented
261	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
262	#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
263	#127	C₂²×C₁₃	1	2	yes	complemented
264	#126	C₂²×C₁₃	1	2	yes	complemented
265	#126	C₂²×C₁₃	1	4	yes	complemented
266	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
267	#125	C₂²×C₁₃	1	2	yes	complemented
268	#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
269	#124	C₂²×C₁₃	1	2	yes	complemented
270	#124	C₂²×C₁₃	1	4	yes	complemented
271	#123	C₂²×C₁₃	1	4	yes	complemented
272	#123	C₂²×C₁₃	1	2	yes	complemented
273	#123	C₂²×C₁₃	1	4	yes	complemented
274	#123	C₂²×C₁₃	1	4	yes	complemented
275	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
276	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
277	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
278	#121	C₂²×C₁₃	1	1	yes	characteristic
279	#121	C₂²×C₁₃	1	2	yes	complemented
280	#121	C₂²×C₁₃	1	4	yes	complemented
281	#121	C₂²×C₁₃	1	4	yes	complemented
282	#121	C₂²×C₁₃	1	2	yes	complemented
283	#121	C₂²×C₁₃	1	2	yes	complemented
284	#121	C₂²×C₁₃	1	2	yes	complemented
285	#121	C₂²×C₁₃	1	2	yes	complemented
286	#121	C₂²×C₁₃	1	4	yes	complemented
287	#121	C₂²×C₁₃	1	4	yes	complemented
288	#121	C₂²×C₁₃	1	2	yes	complemented
289	#121	C₂²×C₁₃	1	2	yes	complemented
290	#121	C₂²×C₁₃	1	4	yes	complemented
291	#120	C₂²×C₁₃	1	4	yes	complemented
292	#120	C₂²×C₁₃	1	4	yes	complemented
293	#120	C₂²×C₁₃	1	4	yes	complemented
294	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
295	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
296	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
297	C₄×D₄	C₂²×C₁₃	1	2	yes	—
298	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
299	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
300	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
301	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
302	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
303	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
304	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
305	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
306	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
307	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
308	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
309	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
310	#117	C₂²×C₁₃	1	2	yes	complemented
311	#117	C₂²×C₁₃	1	2	yes	complemented
312	#117	C₂²×C₁₃	1	2	yes	complemented
313	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
314	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
315	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
316	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
317	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
318	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
319	C₂×C₁₃	—	2	2	no	—
320	C₂×C₁₃	—	2	4	no	—
321	C₂×C₁₃	—	4	2	no	—
322	C₂×C₁₃	—	4	4	no	—
323	C₂×C₁₃	—	4	2	no	—
324	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
325	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
327	C₂⁴	C₂³×C₁₃	1	2	yes	—
328	C₂⁴	C₂³×C₁₃	1	4	yes	—
329	#41	—	4	4	no	—
330	#41	—	4	4	no	—
331	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
332	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	8	no	—
335	C₂×D₄	—	4	4	no	—
336	C₂×D₄	—	4	8	no	—
337	C₂×D₄	C₂³×C₁₃	1	2	yes	—
338	C₂×D₄	C₂³×C₁₃	1	4	yes	—
339	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
340	C₂×D₄	C₂³×C₁₃	1	2	yes	—
341	C₂×D₄	C₂³×C₁₃	1	4	yes	—
342	C₂×D₄	C₂³×C₁₃	1	2	yes	—
343	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
344	C₂×D₄	C₂³×C₁₃	1	2	yes	—
345	C₂×D₄	C₂³×C₁₃	1	4	yes	—
346	C₂×D₄	C₂³×C₁₃	1	2	yes	—
347	C₂×D₄	C₂³×C₁₃	1	4	yes	—
348	C₂×D₄	C₂³×C₁₃	1	4	yes	—
349	C₂×D₄	C₂³×C₁₃	1	4	yes	—
350	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
356	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
357	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
358	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
359	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
360	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
361	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
362	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
363	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
364	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
367	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
369	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
370	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
371	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
372	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
373	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
374	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
375	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
376	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
377	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
378	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
379	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
380	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
381	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
382	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
383	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
384	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
385	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
386	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
387	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
388	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
389	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
390	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
391	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
392	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
393	C₄²	C₂³×C₁₃	1	1	yes	characteristic
394	C₄²	C₂³×C₁₃	1	1	yes	characteristic
395	C₄²	C₂³×C₁₃	1	1	yes	characteristic
396	C₄²	C₂³×C₁₃	1	1	yes	characteristic
397	C₄²	C₂³×C₁₃	1	4	yes	—
398	C₄²	C₂³×C₁₃	1	2	yes	—
399	C₁₃	#3519	1	1	yes	characteristic, direct product factor, Sylow
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	8	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	4	no	—
405	C₂³	—	4	4	no	—
406	C₂³	C₂⁴×C₁₃	1	2	yes	—
407	C₂³	C₂⁴×C₁₃	1	2	yes	—
408	C₂³	C₂⁴×C₁₃	1	4	yes	—
409	C₂³	C₂⁴×C₁₃	1	2	yes	—
410	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
411	Q₈	—	2	2	no	—
412	Q₈	—	4	2	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	8	no	—
415	D₄	—	2	4	no	—
416	D₄	—	2	8	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	4	no	—
419	D₄	—	2	2	no	—
420	D₄	—	2	4	no	—
421	D₄	—	4	4	no	—
422	D₄	—	4	4	no	—
423	D₄	—	4	4	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	4	no	—
426	D₄	C₁₃×#41	1	4	yes	complemented
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
440	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
441	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
442	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
443	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
444	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
445	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
446	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
447	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
448	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
449	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	4	8	no	—
465	C₂²	—	8	8	no	—
466	C₂²	C₂×C₁₃×#41	1	4	yes	—
467	C₂²	C₁₃×H(5,𝔽₂)	1	2	yes	—
468	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	4	no	—
478	C₄	—	2	2	no	—
479	C₄	C₂×C₁₃×#41	1	2	yes	—
480	C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
481	C₂	—	2	2	no	—
482	C₂	—	2	4	no	—
483	C₂	—	4	2	no	—
484	C₂	—	4	2	no	—
485	C₂	—	4	4	no	—
486	C₂	C₂²×C₁₃×#41	1	1	yes	characteristic
487	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#555	C₂	semidirect
2. C₁₃×#554	C₂	semidirect
3. C₁₃×#553	C₂	semidirect
4. C₁₃×#553	C₂	semidirect
5. C₁₃×#550	C₂	semidirect
6. C₁₃×#546	C₂	semidirect
7. C₁₃×#546	C₂	semidirect
8. D₄²×C₁₃	C₂	semidirect
9. D₄²×C₁₃	C₂	semidirect
10. C₁₃×#540	C₂	semidirect
11. C₁₃×#538	C₂	semidirect
12. C₁₃×#532	C₂	semidirect
13. C₁₃×#529	C₂	semidirect
14. C₁₃×#525	C₂	semidirect
15. C₂×C₁₃×#121	C₂	semidirect
16. C₁₃×#518	C₂	semidirect
17. C₂×C₄×D₄×C₁₃	C₂	semidirect
18. C₂×C₁₃×#41	C₂²	semidirect
19. C₂×C₁₃×#41	C₂²	semidirect
22. C₂²×D₄×C₁₃	C₂²	semidirect
23. C₂²×D₄×C₁₃	C₂²	semidirect
24. C₂³×C₄×C₁₃	C₂²	semidirect
25. C₁₃×C₄⋊Q₈	C₂²	semidirect
26. C₁₃×#127	C₂²	semidirect
27. C₁₃×#127	C₂²	semidirect
28. C₁₃×#126	C₂²	semidirect
29. C₁₃×#126	C₂²	semidirect
30. C₁₃×#125	C₂²	semidirect
31. C₁₃×#125	C₂²	semidirect
32. C₁₃×#124	C₂²	semidirect
33. C₁₃×#124	C₂²	semidirect
34. C₁₃×#124	C₂²	semidirect
35. C₁₃×#123	C₂²	semidirect
36. C₁₃×#123	C₂²	semidirect
37. C₁₃×#123	C₂²	semidirect
38. C₁₃×#123	C₂²	semidirect
39. C₁₃×C₂²⋊Q₈	C₂²	semidirect
40. C₁₃×C₂²⋊Q₈	C₂²	semidirect
41. C₁₃×C₂²⋊Q₈	C₂²	semidirect
43. C₁₃×#121	C₂²	semidirect
44. C₁₃×#121	C₂²	semidirect
45. C₁₃×#121	C₂²	semidirect
46. C₁₃×#121	C₂²	semidirect
47. C₁₃×#121	C₂²	semidirect
48. C₁₃×#121	C₂²	semidirect
49. C₁₃×#121	C₂²	semidirect
50. C₁₃×#121	C₂²	semidirect
51. C₁₃×#121	C₂²	semidirect
52. C₁₃×#121	C₂²	semidirect
53. C₁₃×#121	C₂²	semidirect
54. C₁₃×#121	C₂²	semidirect
55. C₁₃×#120	C₂²	semidirect
56. C₁₃×#120	C₂²	semidirect
57. C₁₃×#120	C₂²	semidirect
58. C₄×Q₈×C₁₃	C₂²	semidirect
62. C₄×D₄×C₁₃	C₂²	semidirect
63. C₄×D₄×C₁₃	C₂²	semidirect
64. C₄×D₄×C₁₃	C₂²	semidirect
65. C₄×D₄×C₁₃	C₂²	semidirect
66. C₄×D₄×C₁₃	C₂²	semidirect
67. C₄×D₄×C₁₃	C₂²	semidirect
68. C₄×D₄×C₁₃	C₂²	semidirect
69. C₄×D₄×C₁₃	C₂²	semidirect
70. C₄×D₄×C₁₃	C₂²	semidirect
71. C₄×D₄×C₁₃	C₂²	semidirect
72. C₄×D₄×C₁₃	C₂²	semidirect
73. C₄×D₄×C₁₃	C₂²	semidirect
74. C₁₃×#117	C₂²	semidirect
75. C₁₃×#117	C₂²	semidirect
76. C₁₃×#117	C₂²	semidirect
77. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
78. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
79. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
80. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
81. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
82. C₂×C₄²×C₁₃	C₂²	semidirect
155. #3519	C₁₃	direct (N × H)
182. D₄×C₁₃	#41	semidirect
207. #555	C₂×C₁₃	semidirect
208. #554	C₂×C₁₃	semidirect
209. #553	C₂×C₁₃	semidirect
210. #553	C₂×C₁₃	semidirect
211. #550	C₂×C₁₃	semidirect
212. #546	C₂×C₁₃	semidirect
213. #546	C₂×C₁₃	semidirect
214. D₄²	C₂×C₁₃	semidirect
215. D₄²	C₂×C₁₃	semidirect
216. #540	C₂×C₁₃	semidirect
217. #538	C₂×C₁₃	semidirect
218. #532	C₂×C₁₃	semidirect
219. #529	C₂×C₁₃	semidirect
220. #525	C₂×C₁₃	semidirect
221. C₂×#121	C₂×C₁₃	semidirect
222. #518	C₂×C₁₃	semidirect
223. C₂×C₄×D₄	C₂×C₁₃	semidirect
254. C₂×#41	C₂²×C₁₃	semidirect
255. C₂×#41	C₂²×C₁₃	semidirect
258. C₂²×D₄	C₂²×C₁₃	semidirect
259. C₂²×D₄	C₂²×C₁₃	semidirect
260. C₂³×C₄	C₂²×C₁₃	semidirect
261. C₄⋊Q₈	C₂²×C₁₃	semidirect
262. #127	C₂²×C₁₃	semidirect
263. #127	C₂²×C₁₃	semidirect
264. #126	C₂²×C₁₃	semidirect
265. #126	C₂²×C₁₃	semidirect
266. #125	C₂²×C₁₃	semidirect
267. #125	C₂²×C₁₃	semidirect
268. #124	C₂²×C₁₃	semidirect
269. #124	C₂²×C₁₃	semidirect
270. #124	C₂²×C₁₃	semidirect
271. #123	C₂²×C₁₃	semidirect
272. #123	C₂²×C₁₃	semidirect
273. #123	C₂²×C₁₃	semidirect
274. #123	C₂²×C₁₃	semidirect
275. C₂²⋊Q₈	C₂²×C₁₃	semidirect
276. C₂²⋊Q₈	C₂²×C₁₃	semidirect
277. C₂²⋊Q₈	C₂²×C₁₃	semidirect
279. #121	C₂²×C₁₃	semidirect
280. #121	C₂²×C₁₃	semidirect
281. #121	C₂²×C₁₃	semidirect
282. #121	C₂²×C₁₃	semidirect
283. #121	C₂²×C₁₃	semidirect
284. #121	C₂²×C₁₃	semidirect
285. #121	C₂²×C₁₃	semidirect
286. #121	C₂²×C₁₃	semidirect
287. #121	C₂²×C₁₃	semidirect
288. #121	C₂²×C₁₃	semidirect
289. #121	C₂²×C₁₃	semidirect
290. #121	C₂²×C₁₃	semidirect
291. #120	C₂²×C₁₃	semidirect
292. #120	C₂²×C₁₃	semidirect
293. #120	C₂²×C₁₃	semidirect
294. C₄×Q₈	C₂²×C₁₃	semidirect
298. C₄×D₄	C₂²×C₁₃	semidirect
299. C₄×D₄	C₂²×C₁₃	semidirect
300. C₄×D₄	C₂²×C₁₃	semidirect
301. C₄×D₄	C₂²×C₁₃	semidirect
302. C₄×D₄	C₂²×C₁₃	semidirect
303. C₄×D₄	C₂²×C₁₃	semidirect
304. C₄×D₄	C₂²×C₁₃	semidirect
305. C₄×D₄	C₂²×C₁₃	semidirect
306. C₄×D₄	C₂²×C₁₃	semidirect
307. C₄×D₄	C₂²×C₁₃	semidirect
308. C₄×D₄	C₂²×C₁₃	semidirect
309. C₄×D₄	C₂²×C₁₃	semidirect
310. #117	C₂²×C₁₃	semidirect
311. #117	C₂²×C₁₃	semidirect
312. #117	C₂²×C₁₃	semidirect
313. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
314. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
315. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
316. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
317. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
318. C₂×C₄²	C₂²×C₁₃	semidirect
399. C₁₃	#3519	direct (N × H)
426. D₄	C₁₃×#41	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#555	2
C₁₃×#554	2
C₁₃×#553	2
C₁₃×#550	2
C₁₃×#546	2
D₄²×C₁₃	2
C₁₃×#540	2
C₁₃×#538	2
C₁₃×#532	2
C₁₃×#529	2
C₁₃×#525	2
C₂×C₁₃×#121	2
C₁₃×#518	2
C₂×C₄×D₄×C₁₃	2
#3519	13

Subgroups — C13×#3519 #13112577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3519 #13112577