Subgroups — C₁₃×#3558 #13112616

Order 1664.

1160 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#562	C₂	1	2	yes	maximal, complemented
2	C₁₃×H(3,𝔽₄)	C₂	1	2	yes	maximal, complemented
3	C₁₃×#559	C₂	1	2	yes	maximal, complemented
4	C₁₃×#548	C₂	1	2	yes	maximal, complemented
5	C₁₃×#546	C₂	1	2	yes	maximal, complemented
6	C₁₃×#546	C₂	1	4	yes	maximal, complemented
7	D₄²×C₁₃	C₂	1	2	yes	maximal, complemented
8	C₁₃×#542	C₂	1	2	yes	maximal, complemented
9	C₁₃×#538	C₂	1	2	yes	maximal, complemented
10	C₁₃×#538	C₂	1	4	yes	maximal, complemented
11	C₁₃×#535	C₂	1	2	yes	maximal, complemented
12	C₁₃×#534	C₂	1	2	yes	maximal, complemented
13	C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
17	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
18	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₁₃	C₂²	1	4	yes	complemented
21	C₂²×D₄×C₁₃	C₂²	1	2	yes	complemented
22	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#127	C₂²	1	2	yes	—
24	C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#126	C₂²	1	2	yes	complemented
26	C₁₃×#126	C₂²	1	4	yes	complemented
27	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#124	C₂²	1	2	yes	complemented
29	C₁₃×#124	C₂²	1	2	yes	complemented
30	C₁₃×#124	C₂²	1	2	yes	complemented
31	C₁₃×#124	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	2	yes	complemented
35	C₁₃×#124	C₂²	1	4	yes	complemented
36	C₁₃×#124	C₂²	1	4	yes	complemented
37	C₁₃×#124	C₂²	1	4	yes	complemented
38	C₁₃×#123	C₂²	1	2	yes	complemented
39	C₁₃×#123	C₂²	1	4	yes	complemented
40	C₁₃×#123	C₂²	1	4	yes	complemented
41	C₁₃×#123	C₂²	1	4	yes	complemented
42	C₁₃×#123	C₂²	1	4	yes	complemented
43	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
45	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
46	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
47	C₁₃×#121	C₂²	1	1	yes	characteristic
48	C₁₃×#121	C₂²	1	2	yes	—
49	C₁₃×#121	C₂²	1	2	yes	complemented
50	C₁₃×#121	C₂²	1	2	yes	complemented
51	C₁₃×#121	C₂²	1	4	yes	complemented
52	C₁₃×#121	C₂²	1	4	yes	complemented
53	C₁₃×#121	C₂²	1	4	yes	complemented
54	C₁₃×#121	C₂²	1	4	yes	complemented
55	C₁₃×#121	C₂²	1	4	yes	complemented
56	C₁₃×#120	C₂²	1	4	yes	complemented
57	C₁₃×#120	C₂²	1	4	yes	complemented
58	C₁₃×#120	C₂²	1	4	yes	complemented
59	C₁₃×#120	C₂²	1	4	yes	complemented
60	C₁₃×#120	C₂²	1	4	yes	complemented
61	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
62	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
63	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
64	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
66	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
67	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
68	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
69	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
70	C₁₃×#117	C₂²	1	2	yes	complemented
71	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
72	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
73	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
74	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
75	C₂⁴×C₁₃	C₂³	1	2	yes	—
76	C₂⁴×C₁₃	C₂³	1	4	yes	—
77	C₁₃×#41	—	4	4	no	—
78	C₁₃×#41	—	4	4	no	—
79	C₂×Q₈×C₁₃	—	4	2	no	—
80	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
81	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
83	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
84	C₂×D₄×C₁₃	—	4	2	no	—
85	C₂×D₄×C₁₃	—	4	4	no	—
86	C₂×D₄×C₁₃	—	4	8	no	—
87	C₂×D₄×C₁₃	C₂³	1	4	yes	—
88	C₂×D₄×C₁₃	C₂³	1	2	yes	—
89	C₂×D₄×C₁₃	C₂³	1	2	yes	—
90	C₂×D₄×C₁₃	C₂³	1	2	yes	—
91	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂×D₄×C₁₃	C₂³	1	4	yes	—
93	C₂×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂×D₄×C₁₃	C₂³	1	4	yes	—
95	C₂×D₄×C₁₃	C₂³	1	4	yes	—
96	C₂×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂×D₄×C₁₃	C₂³	1	2	yes	—
98	C₂×D₄×C₁₃	C₂³	1	4	yes	—
99	C₂×D₄×C₁₃	C₂³	1	4	yes	—
100	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
106	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
107	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
108	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₄²×C₁₃	C₂³	1	1	yes	characteristic
137	C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₄²×C₁₃	C₂³	1	2	yes	—
139	C₄²×C₁₃	C₂³	1	4	yes	—
140	#3558	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₁₃	—	2	4	no	—
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	—	4	4	no	—
144	C₂³×C₁₃	—	4	4	no	—
145	C₂³×C₁₃	—	4	2	no	—
146	C₂³×C₁₃	—	4	4	no	—
147	C₂³×C₁₃	C₂⁴	1	2	yes	—
148	C₂³×C₁₃	C₂⁴	1	4	yes	—
149	C₂³×C₁₃	C₂⁴	1	4	yes	—
150	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
151	Q₈×C₁₃	—	2	4	no	—
152	Q₈×C₁₃	—	4	2	no	—
153	Q₈×C₁₃	—	4	1	no	—
154	Q₈×C₁₃	—	4	2	no	—
155	D₄×C₁₃	—	2	4	no	—
156	D₄×C₁₃	—	2	8	no	—
157	D₄×C₁₃	—	2	4	no	—
158	D₄×C₁₃	—	2	4	no	—
159	D₄×C₁₃	—	4	4	no	—
160	D₄×C₁₃	—	4	2	no	—
161	D₄×C₁₃	—	4	4	no	—
162	D₄×C₁₃	—	4	4	no	—
163	D₄×C₁₃	—	4	2	no	—
164	D₄×C₁₃	—	4	1	no	—
165	D₄×C₁₃	—	4	4	no	—
166	D₄×C₁₃	—	4	2	no	—
167	D₄×C₁₃	—	4	4	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	4	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	4	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
183	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
184	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
186	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	#562	C₂×C₁₃	1	2	yes	complemented
188	H(3,𝔽₄)	C₂×C₁₃	1	2	yes	complemented
189	#559	C₂×C₁₃	1	2	yes	complemented
190	#548	C₂×C₁₃	1	2	yes	complemented
191	#546	C₂×C₁₃	1	2	yes	complemented
192	#546	C₂×C₁₃	1	4	yes	complemented
193	D₄²	C₂×C₁₃	1	2	yes	complemented
194	#542	C₂×C₁₃	1	2	yes	complemented
195	#538	C₂×C₁₃	1	2	yes	complemented
196	#538	C₂×C₁₃	1	4	yes	complemented
197	#535	C₂×C₁₃	1	2	yes	complemented
198	#534	C₂×C₁₃	1	2	yes	complemented
199	#532	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂²×C₁₃	—	2	1	no	—
203	C₂²×C₁₃	—	2	1	no	—
204	C₂²×C₁₃	—	2	2	no	—
205	C₂²×C₁₃	—	2	4	no	—
206	C₂²×C₁₃	—	2	4	no	—
207	C₂²×C₁₃	—	2	4	no	—
208	C₂²×C₁₃	—	2	2	no	—
209	C₂²×C₁₃	—	2	4	no	—
210	C₂²×C₁₃	—	2	4	no	—
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	—	2	4	no	—
213	C₂²×C₁₃	—	8	4	no	—
214	C₂²×C₁₃	—	8	8	no	—
215	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
216	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
217	C₄×C₁₃	—	2	1	no	—
218	C₄×C₁₃	—	2	2	no	—
219	C₄×C₁₃	—	2	1	no	—
220	C₄×C₁₃	—	2	1	no	—
221	C₄×C₁₃	—	2	2	no	—
222	C₄×C₁₃	—	2	4	no	—
223	C₄×C₁₃	—	2	4	no	—
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
228	C₂×#41	C₂²×C₁₃	1	2	yes	complemented
229	C₂×#41	C₂²×C₁₃	1	2	yes	complemented
230	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
231	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
232	C₂²×D₄	C₂²×C₁₃	1	4	yes	complemented
233	C₂²×D₄	C₂²×C₁₃	1	2	yes	complemented
234	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
235	#127	C₂²×C₁₃	1	2	yes	—
236	#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
237	#126	C₂²×C₁₃	1	2	yes	complemented
238	#126	C₂²×C₁₃	1	4	yes	complemented
239	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
240	#124	C₂²×C₁₃	1	2	yes	complemented
241	#124	C₂²×C₁₃	1	2	yes	complemented
242	#124	C₂²×C₁₃	1	2	yes	complemented
243	#124	C₂²×C₁₃	1	2	yes	complemented
244	#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
245	#124	C₂²×C₁₃	1	2	yes	complemented
246	#124	C₂²×C₁₃	1	2	yes	complemented
247	#124	C₂²×C₁₃	1	4	yes	complemented
248	#124	C₂²×C₁₃	1	4	yes	complemented
249	#124	C₂²×C₁₃	1	4	yes	complemented
250	#123	C₂²×C₁₃	1	2	yes	complemented
251	#123	C₂²×C₁₃	1	4	yes	complemented
252	#123	C₂²×C₁₃	1	4	yes	complemented
253	#123	C₂²×C₁₃	1	4	yes	complemented
254	#123	C₂²×C₁₃	1	4	yes	complemented
255	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
256	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
257	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
258	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
259	#121	C₂²×C₁₃	1	1	yes	characteristic
260	#121	C₂²×C₁₃	1	2	yes	—
261	#121	C₂²×C₁₃	1	2	yes	complemented
262	#121	C₂²×C₁₃	1	2	yes	complemented
263	#121	C₂²×C₁₃	1	4	yes	complemented
264	#121	C₂²×C₁₃	1	4	yes	complemented
265	#121	C₂²×C₁₃	1	4	yes	complemented
266	#121	C₂²×C₁₃	1	4	yes	complemented
267	#121	C₂²×C₁₃	1	4	yes	complemented
268	#120	C₂²×C₁₃	1	4	yes	complemented
269	#120	C₂²×C₁₃	1	4	yes	complemented
270	#120	C₂²×C₁₃	1	4	yes	complemented
271	#120	C₂²×C₁₃	1	4	yes	complemented
272	#120	C₂²×C₁₃	1	4	yes	complemented
273	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
274	C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
275	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
276	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
277	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
278	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
279	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
280	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
281	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
282	#117	C₂²×C₁₃	1	2	yes	complemented
283	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
284	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
285	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
286	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
287	C₂×C₁₃	—	2	2	no	—
288	C₂×C₁₃	—	4	4	no	—
289	C₂×C₁₃	—	4	2	no	—
290	C₂×C₁₃	—	4	4	no	—
291	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
293	C₂×C₁₃	#585	1	1	yes	characteristic
294	C₂⁴	C₂³×C₁₃	1	2	yes	—
295	C₂⁴	C₂³×C₁₃	1	4	yes	—
296	#41	—	4	4	no	—
297	#41	—	4	4	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
300	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
302	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	8	no	—
306	C₂×D₄	C₂³×C₁₃	1	4	yes	—
307	C₂×D₄	C₂³×C₁₃	1	2	yes	—
308	C₂×D₄	C₂³×C₁₃	1	2	yes	—
309	C₂×D₄	C₂³×C₁₃	1	2	yes	—
310	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₂×D₄	C₂³×C₁₃	1	4	yes	—
312	C₂×D₄	C₂³×C₁₃	1	2	yes	—
313	C₂×D₄	C₂³×C₁₃	1	4	yes	—
314	C₂×D₄	C₂³×C₁₃	1	4	yes	—
315	C₂×D₄	C₂³×C₁₃	1	2	yes	—
316	C₂×D₄	C₂³×C₁₃	1	2	yes	—
317	C₂×D₄	C₂³×C₁₃	1	4	yes	—
318	C₂×D₄	C₂³×C₁₃	1	4	yes	—
319	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
322	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
324	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
325	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
326	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
327	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
329	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
330	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
331	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
332	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
333	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
334	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
337	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
338	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
339	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
340	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
341	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
342	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
343	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
344	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
347	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
348	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
349	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
350	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
351	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
352	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
353	C₄²	C₂³×C₁₃	1	1	yes	characteristic
354	C₄²	C₂³×C₁₃	1	1	yes	characteristic
355	C₄²	C₂³×C₁₃	1	1	yes	characteristic
356	C₄²	C₂³×C₁₃	1	1	yes	characteristic
357	C₄²	C₂³×C₁₃	1	2	yes	—
358	C₄²	C₂³×C₁₃	1	4	yes	—
359	C₁₃	#3558	1	1	yes	characteristic, direct product factor, Sylow
360	C₂³	—	2	4	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	4	no	—
366	C₂³	C₂⁴×C₁₃	1	2	yes	—
367	C₂³	C₂⁴×C₁₃	1	4	yes	—
368	C₂³	C₂⁴×C₁₃	1	4	yes	—
369	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	1	no	—
374	D₄	—	2	4	no	—
375	D₄	—	2	8	no	—
376	D₄	—	2	4	no	—
377	D₄	—	2	4	no	—
378	D₄	—	4	4	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	4	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
396	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
397	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
398	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
399	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
400	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
402	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
403	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
404	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
405	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	8	4	no	—
418	C₂²	—	8	8	no	—
419	C₂²	C₁₃×H(5,𝔽₂)	1	2	yes	—
420	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	4	no	—
427	C₄	—	2	4	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	2	no	—
431	C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
432	C₂	—	2	2	no	—
433	C₂	—	4	2	no	—
434	C₂	—	4	4	no	—
435	C₂	—	4	4	no	—
436	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂	C₁₃×#585	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×#562	C₂	semidirect
2. C₁₃×H(3,𝔽₄)	C₂	semidirect
3. C₁₃×#559	C₂	semidirect
4. C₁₃×#548	C₂	semidirect
5. C₁₃×#546	C₂	semidirect
6. C₁₃×#546	C₂	semidirect
7. D₄²×C₁₃	C₂	semidirect
8. C₁₃×#542	C₂	semidirect
9. C₁₃×#538	C₂	semidirect
10. C₁₃×#538	C₂	semidirect
11. C₁₃×#535	C₂	semidirect
12. C₁₃×#534	C₂	semidirect
13. C₁₃×#532	C₂	semidirect
14. C₁₃×#529	C₂	semidirect
15. C₂×C₁₃×#124	C₂	semidirect
16. C₂×C₁₃×#41	C₂²	semidirect
17. C₂×C₁₃×#41	C₂²	semidirect
18. C₂²×Q₈×C₁₃	C₂²	semidirect
20. C₂²×D₄×C₁₃	C₂²	semidirect
21. C₂²×D₄×C₁₃	C₂²	semidirect
22. C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₁₃×#127	C₂²	semidirect
25. C₁₃×#126	C₂²	semidirect
26. C₁₃×#126	C₂²	semidirect
27. C₁₃×#125	C₂²	semidirect
28. C₁₃×#124	C₂²	semidirect
29. C₁₃×#124	C₂²	semidirect
30. C₁₃×#124	C₂²	semidirect
31. C₁₃×#124	C₂²	semidirect
32. C₁₃×#124	C₂²	semidirect
33. C₁₃×#124	C₂²	semidirect
34. C₁₃×#124	C₂²	semidirect
35. C₁₃×#124	C₂²	semidirect
36. C₁₃×#124	C₂²	semidirect
37. C₁₃×#124	C₂²	semidirect
38. C₁₃×#123	C₂²	semidirect
39. C₁₃×#123	C₂²	semidirect
40. C₁₃×#123	C₂²	semidirect
41. C₁₃×#123	C₂²	semidirect
42. C₁₃×#123	C₂²	semidirect
43. C₁₃×C₂²⋊Q₈	C₂²	semidirect
44. C₁₃×C₂²⋊Q₈	C₂²	semidirect
45. C₁₃×C₂²⋊Q₈	C₂²	semidirect
46. C₁₃×C₂²⋊Q₈	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×#121	C₂²	semidirect
56. C₁₃×#120	C₂²	semidirect
57. C₁₃×#120	C₂²	semidirect
58. C₁₃×#120	C₂²	semidirect
59. C₁₃×#120	C₂²	semidirect
60. C₁₃×#120	C₂²	semidirect
61. C₄×Q₈×C₁₃	C₂²	semidirect
62. C₄×Q₈×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. C₁₃×#117	C₂²	semidirect
71. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
72. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
73. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
74. C₂×C₄²×C₁₃	C₂²	semidirect
140. #3558	C₁₃	direct (N × H)
187. #562	C₂×C₁₃	semidirect
188. H(3,𝔽₄)	C₂×C₁₃	semidirect
189. #559	C₂×C₁₃	semidirect
190. #548	C₂×C₁₃	semidirect
191. #546	C₂×C₁₃	semidirect
192. #546	C₂×C₁₃	semidirect
193. D₄²	C₂×C₁₃	semidirect
194. #542	C₂×C₁₃	semidirect
195. #538	C₂×C₁₃	semidirect
196. #538	C₂×C₁₃	semidirect
197. #535	C₂×C₁₃	semidirect
198. #534	C₂×C₁₃	semidirect
199. #532	C₂×C₁₃	semidirect
200. #529	C₂×C₁₃	semidirect
201. C₂×#124	C₂×C₁₃	semidirect
228. C₂×#41	C₂²×C₁₃	semidirect
229. C₂×#41	C₂²×C₁₃	semidirect
230. C₂²×Q₈	C₂²×C₁₃	semidirect
232. C₂²×D₄	C₂²×C₁₃	semidirect
233. C₂²×D₄	C₂²×C₁₃	semidirect
234. C₄⋊Q₈	C₂²×C₁₃	semidirect
236. #127	C₂²×C₁₃	semidirect
237. #126	C₂²×C₁₃	semidirect
238. #126	C₂²×C₁₃	semidirect
239. #125	C₂²×C₁₃	semidirect
240. #124	C₂²×C₁₃	semidirect
241. #124	C₂²×C₁₃	semidirect
242. #124	C₂²×C₁₃	semidirect
243. #124	C₂²×C₁₃	semidirect
244. #124	C₂²×C₁₃	semidirect
245. #124	C₂²×C₁₃	semidirect
246. #124	C₂²×C₁₃	semidirect
247. #124	C₂²×C₁₃	semidirect
248. #124	C₂²×C₁₃	semidirect
249. #124	C₂²×C₁₃	semidirect
250. #123	C₂²×C₁₃	semidirect
251. #123	C₂²×C₁₃	semidirect
252. #123	C₂²×C₁₃	semidirect
253. #123	C₂²×C₁₃	semidirect
254. #123	C₂²×C₁₃	semidirect
255. C₂²⋊Q₈	C₂²×C₁₃	semidirect
256. C₂²⋊Q₈	C₂²×C₁₃	semidirect
257. C₂²⋊Q₈	C₂²×C₁₃	semidirect
258. C₂²⋊Q₈	C₂²×C₁₃	semidirect
261. #121	C₂²×C₁₃	semidirect
262. #121	C₂²×C₁₃	semidirect
263. #121	C₂²×C₁₃	semidirect
264. #121	C₂²×C₁₃	semidirect
265. #121	C₂²×C₁₃	semidirect
266. #121	C₂²×C₁₃	semidirect
267. #121	C₂²×C₁₃	semidirect
268. #120	C₂²×C₁₃	semidirect
269. #120	C₂²×C₁₃	semidirect
270. #120	C₂²×C₁₃	semidirect
271. #120	C₂²×C₁₃	semidirect
272. #120	C₂²×C₁₃	semidirect
273. C₄×Q₈	C₂²×C₁₃	semidirect
274. C₄×Q₈	C₂²×C₁₃	semidirect
275. C₄×D₄	C₂²×C₁₃	semidirect
276. C₄×D₄	C₂²×C₁₃	semidirect
277. C₄×D₄	C₂²×C₁₃	semidirect
278. C₄×D₄	C₂²×C₁₃	semidirect
279. C₄×D₄	C₂²×C₁₃	semidirect
280. C₄×D₄	C₂²×C₁₃	semidirect
281. C₄×D₄	C₂²×C₁₃	semidirect
282. #117	C₂²×C₁₃	semidirect
283. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
284. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
285. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
286. C₂×C₄²	C₂²×C₁₃	semidirect
359. C₁₃	#3558	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#562	2
C₁₃×H(3,𝔽₄)	2
C₁₃×#559	2
C₁₃×#548	2
C₁₃×#546	2
D₄²×C₁₃	2
C₁₃×#542	2
C₁₃×#538	2
C₁₃×#535	2
C₁₃×#534	2
C₁₃×#532	2
C₁₃×#529	2
C₂×C₁₃×#124	2
#3558	13

Subgroups — C13×#3558 #13112616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3558 #13112616