Subgroups — C₁₃×#3514 #13112572

Order 1664.

1142 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#555	C₂	1	2	yes	maximal, complemented
4	C₁₃×#551	C₂	1	4	yes	maximal, complemented
5	D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#548	C₂	1	2	yes	maximal, complemented
7	C₁₃×#546	C₂	1	2	yes	maximal, complemented
8	C₁₃×#546	C₂	1	2	yes	maximal, complemented
9	D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#542	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×#529	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#124	C₂	1	2	yes	maximal, complemented
16	C₁₃×#518	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
20	C₂²×Q₈×C₁₃	C₂²	1	2	yes	complemented
21	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
22	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
23	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₁₃×#127	C₂²	1	1	yes	characteristic
26	C₁₃×#126	C₂²	1	4	yes	complemented
27	C₁₃×#126	C₂²	1	2	yes	complemented
28	C₁₃×#126	C₂²	1	4	yes	complemented
29	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#124	C₂²	1	1	yes	characteristic
31	C₁₃×#124	C₂²	1	2	yes	—
32	C₁₃×#124	C₂²	1	2	yes	complemented
33	C₁₃×#124	C₂²	1	4	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	2	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×C₂²⋊Q₈	C₂²	1	2	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	2	yes	—
48	C₁₃×#121	C₂²	1	1	yes	characteristic
49	C₁₃×#121	C₂²	1	2	yes	—
50	C₁₃×#121	C₂²	1	2	yes	complemented
51	C₁₃×#121	C₂²	1	2	yes	complemented
52	C₁₃×#121	C₂²	1	4	yes	complemented
53	C₁₃×#121	C₂²	1	4	yes	complemented
54	C₁₃×#120	C₂²	1	4	yes	—
55	C₁₃×#120	C₂²	1	4	yes	complemented
56	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
58	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
59	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
60	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
61	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
62	C₄×D₄×C₁₃	C₂²	1	2	yes	—
63	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
64	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
65	C₄×D₄×C₁₃	C₂²	1	2	yes	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	2	yes	complemented
71	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
72	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
73	C₁₃×#117	C₂²	1	2	yes	complemented
74	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#117	C₂²	1	2	yes	complemented
76	C₁₃×#117	C₂²	1	2	yes	complemented
77	C₁₃×#117	C₂²	1	4	yes	complemented
78	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
79	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
80	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
81	C₂×C₄²×C₁₃	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
83	C₂⁴×C₁₃	C₂³	1	4	yes	—
84	C₁₃×#41	—	2	4	no	—
85	C₁₃×#41	—	4	4	no	—
86	C₂×Q₈×C₁₃	—	4	4	no	—
87	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
90	C₂×Q₈×C₁₃	C₂³	1	4	yes	—
91	C₂×D₄×C₁₃	—	2	8	no	—
92	C₂×D₄×C₁₃	—	4	4	no	—
93	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×D₄×C₁₃	C₂³	1	4	yes	—
95	C₂×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂×D₄×C₁₃	C₂³	1	2	yes	—
98	C₂×D₄×C₁₃	C₂³	1	2	yes	—
99	C₂×D₄×C₁₃	C₂³	1	2	yes	—
100	C₂×D₄×C₁₃	C₂³	1	4	yes	—
101	C₂×D₄×C₁₃	C₂³	1	4	yes	—
102	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
111	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
112	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
113	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
127	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₄²×C₁₃	C₂³	1	1	yes	characteristic
145	C₄²×C₁₃	C₂³	1	2	yes	—
146	C₄²×C₁₃	C₂³	1	1	yes	characteristic
147	C₄²×C₁₃	C₂³	1	1	yes	characteristic
148	C₄²×C₁₃	C₂³	1	1	yes	characteristic
149	C₄²×C₁₃	C₂³	1	2	yes	—
150	C₄²×C₁₃	C₂³	1	2	yes	—
151	C₄²×C₁₃	C₂³	1	4	yes	—
152	C₄²×C₁₃	C₂³	1	2	yes	—
153	#3514	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₃	—	2	8	no	—
155	C₂³×C₁₃	—	4	4	no	—
156	C₂³×C₁₃	—	4	4	no	—
157	C₂³×C₁₃	C₂⁴	1	2	yes	—
158	C₂³×C₁₃	C₂⁴	1	4	yes	—
159	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂³×C₁₃	C₂⁴	1	2	yes	—
161	Q₈×C₁₃	—	2	2	no	—
162	Q₈×C₁₃	—	2	2	no	—
163	Q₈×C₁₃	—	2	4	no	—
164	Q₈×C₁₃	—	4	4	no	—
165	D₄×C₁₃	—	2	8	no	—
166	D₄×C₁₃	—	2	4	no	—
167	D₄×C₁₃	—	2	4	no	—
168	D₄×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	2	4	no	—
170	D₄×C₁₃	—	4	4	no	—
171	D₄×C₁₃	—	4	2	no	—
172	D₄×C₁₃	—	4	2	no	—
173	D₄×C₁₃	—	4	4	no	—
174	D₄×C₁₃	#41	1	4	yes	complemented
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	4	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	4	no	—
184	C₂×C₄×C₁₃	—	4	4	no	—
185	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
189	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
190	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
195	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
196	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
198	#559	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#556	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#555	C₂×C₁₃	1	2	yes	complemented
201	#551	C₂×C₁₃	1	4	yes	complemented
202	D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#548	C₂×C₁₃	1	2	yes	complemented
204	#546	C₂×C₁₃	1	2	yes	complemented
205	#546	C₂×C₁₃	1	2	yes	complemented
206	D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#542	C₂×C₁₃	1	2	yes	complemented
208	#538	C₂×C₁₃	1	4	yes	complemented
209	#532	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#529	C₂×C₁₃	1	2	yes	complemented
212	C₂×#124	C₂×C₁₃	1	2	yes	complemented
213	#518	C₂×C₁₃	1	2	yes	complemented
214	C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂²×C₁₃	—	2	2	no	—
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	2	1	no	—
218	C₂²×C₁₃	—	2	2	no	—
219	C₂²×C₁₃	—	2	4	no	—
220	C₂²×C₁₃	—	2	1	no	—
221	C₂²×C₁₃	—	2	4	no	—
222	C₂²×C₁₃	—	2	2	no	—
223	C₂²×C₁₃	—	2	1	no	—
224	C₂²×C₁₃	—	2	4	no	—
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	—	8	8	no	—
227	C₂²×C₁₃	C₂×#41	1	4	yes	—
228	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	2	no	—
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	2	1	no	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	4	no	—
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	C₂×#41	1	2	yes	—
241	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
242	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#41	C₂²×C₁₃	1	2	yes	complemented
244	C₂²×Q₈	C₂²×C₁₃	1	2	yes	complemented
245	C₂²×D₄	C₂²×C₁₃	1	2	yes	—
246	C₂²×D₄	C₂²×C₁₃	1	2	yes	—
247	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
248	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
249	#127	C₂²×C₁₃	1	1	yes	characteristic
250	#126	C₂²×C₁₃	1	4	yes	complemented
251	#126	C₂²×C₁₃	1	2	yes	complemented
252	#126	C₂²×C₁₃	1	4	yes	complemented
253	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
254	#124	C₂²×C₁₃	1	1	yes	characteristic
255	#124	C₂²×C₁₃	1	2	yes	—
256	#124	C₂²×C₁₃	1	2	yes	complemented
257	#124	C₂²×C₁₃	1	4	yes	complemented
258	#124	C₂²×C₁₃	1	2	yes	complemented
259	#124	C₂²×C₁₃	1	4	yes	complemented
260	#124	C₂²×C₁₃	1	4	yes	complemented
261	#124	C₂²×C₁₃	1	2	yes	complemented
262	#123	C₂²×C₁₃	1	2	yes	complemented
263	#123	C₂²×C₁₃	1	4	yes	complemented
264	#123	C₂²×C₁₃	1	4	yes	complemented
265	#123	C₂²×C₁₃	1	4	yes	complemented
266	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
267	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
268	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
269	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
270	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
271	#121	C₂²×C₁₃	1	2	yes	—
272	#121	C₂²×C₁₃	1	1	yes	characteristic
273	#121	C₂²×C₁₃	1	2	yes	—
274	#121	C₂²×C₁₃	1	2	yes	complemented
275	#121	C₂²×C₁₃	1	2	yes	complemented
276	#121	C₂²×C₁₃	1	4	yes	complemented
277	#121	C₂²×C₁₃	1	4	yes	complemented
278	#120	C₂²×C₁₃	1	4	yes	—
279	#120	C₂²×C₁₃	1	4	yes	complemented
280	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
281	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
282	C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
283	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
284	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
285	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
286	C₄×D₄	C₂²×C₁₃	1	2	yes	—
287	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
288	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
289	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
290	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
291	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
292	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
293	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
294	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
295	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
296	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
297	#117	C₂²×C₁₃	1	2	yes	complemented
298	#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
299	#117	C₂²×C₁₃	1	2	yes	complemented
300	#117	C₂²×C₁₃	1	2	yes	complemented
301	#117	C₂²×C₁₃	1	4	yes	complemented
302	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
303	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
304	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
305	C₂×C₄²	C₂²×C₁₃	1	2	yes	complemented
306	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
307	C₂×C₁₃	—	2	4	no	—
308	C₂×C₁₃	—	4	1	no	—
309	C₂×C₁₃	—	4	4	no	—
310	C₂×C₁₃	—	4	2	no	—
311	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
312	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₁₃	#585	1	1	yes	characteristic
314	C₂⁴	C₂³×C₁₃	1	4	yes	—
315	#41	—	2	4	no	—
316	#41	—	4	4	no	—
317	C₂×Q₈	—	4	4	no	—
318	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
320	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
321	C₂×Q₈	C₂³×C₁₃	1	4	yes	—
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂×D₄	C₂³×C₁₃	1	4	yes	—
326	C₂×D₄	C₂³×C₁₃	1	2	yes	—
327	C₂×D₄	C₂³×C₁₃	1	2	yes	—
328	C₂×D₄	C₂³×C₁₃	1	2	yes	—
329	C₂×D₄	C₂³×C₁₃	1	2	yes	—
330	C₂×D₄	C₂³×C₁₃	1	2	yes	—
331	C₂×D₄	C₂³×C₁₃	1	4	yes	—
332	C₂×D₄	C₂³×C₁₃	1	4	yes	—
333	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
335	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
337	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
339	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
340	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
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	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
347	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
349	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
350	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
351	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
352	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
353	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
354	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
356	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
357	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
358	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
359	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
360	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
361	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
362	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
363	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
364	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
365	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
366	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
367	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
368	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
369	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
370	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
371	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
372	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
373	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
374	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
375	C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	C₄²	C₂³×C₁₃	1	2	yes	—
377	C₄²	C₂³×C₁₃	1	1	yes	characteristic
378	C₄²	C₂³×C₁₃	1	1	yes	characteristic
379	C₄²	C₂³×C₁₃	1	1	yes	characteristic
380	C₄²	C₂³×C₁₃	1	2	yes	—
381	C₄²	C₂³×C₁₃	1	2	yes	—
382	C₄²	C₂³×C₁₃	1	4	yes	—
383	C₄²	C₂³×C₁₃	1	2	yes	—
384	C₁₃	#3514	1	1	yes	characteristic, direct product factor, Sylow
385	C₂³	—	2	8	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	4	no	—
388	C₂³	C₂⁴×C₁₃	1	2	yes	—
389	C₂³	C₂⁴×C₁₃	1	4	yes	—
390	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
391	C₂³	C₂⁴×C₁₃	1	2	yes	—
392	Q₈	—	2	2	no	—
393	Q₈	—	2	2	no	—
394	Q₈	—	2	4	no	—
395	Q₈	—	4	4	no	—
396	D₄	—	2	8	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	4	no	—
401	D₄	—	4	4	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	4	no	—
405	D₄	C₁₃×#41	1	4	yes	complemented
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
419	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
420	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
421	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
424	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
425	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
426	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
427	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
428	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	8	8	no	—
441	C₂²	C₂×C₁₃×#41	1	4	yes	—
442	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	1	no	—
454	C₄	C₂×C₁₃×#41	1	2	yes	—
455	C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
456	C₂	—	2	4	no	—
457	C₂	—	4	2	no	—
458	C₂	—	4	4	no	—
459	C₂	—	4	1	no	—
460	C₂	C₂²×C₁₃×#41	1	1	yes	characteristic
461	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
462	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×#559	C₂	semidirect
2. C₁₃×#556	C₂	semidirect
3. C₁₃×#555	C₂	semidirect
4. C₁₃×#551	C₂	semidirect
5. D₄×Q₈×C₁₃	C₂	semidirect
6. C₁₃×#548	C₂	semidirect
7. C₁₃×#546	C₂	semidirect
8. C₁₃×#546	C₂	semidirect
9. D₄²×C₁₃	C₂	semidirect
10. C₁₃×#542	C₂	semidirect
11. C₁₃×#538	C₂	semidirect
12. C₁₃×#532	C₂	semidirect
13. C₁₃×#529	C₂	semidirect
14. C₁₃×#529	C₂	semidirect
15. C₂×C₁₃×#124	C₂	semidirect
16. C₁₃×#518	C₂	semidirect
17. C₄×C₁₃×#41	C₂	semidirect
19. C₂×C₁₃×#41	C₂²	semidirect
20. C₂²×Q₈×C₁₃	C₂²	semidirect
23. C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₁₃×C₄⋊Q₈	C₂²	semidirect
26. C₁₃×#126	C₂²	semidirect
27. C₁₃×#126	C₂²	semidirect
28. C₁₃×#126	C₂²	semidirect
29. C₁₃×#125	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×C₂²⋊Q₈	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
50. C₁₃×#121	C₂²	semidirect
51. C₁₃×#121	C₂²	semidirect
52. C₁₃×#121	C₂²	semidirect
53. C₁₃×#121	C₂²	semidirect
55. C₁₃×#120	C₂²	semidirect
56. C₄×Q₈×C₁₃	C₂²	semidirect
57. C₄×Q₈×C₁₃	C₂²	semidirect
58. C₄×Q₈×C₁₃	C₂²	semidirect
59. C₄×Q₈×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. C₁₃×#117	C₂²	semidirect
74. C₁₃×#117	C₂²	semidirect
75. C₁₃×#117	C₂²	semidirect
76. C₁₃×#117	C₂²	semidirect
77. C₁₃×#117	C₂²	semidirect
78. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
79. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
80. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
81. C₂×C₄²×C₁₃	C₂²	semidirect
82. C₂×C₄²×C₁₃	C₂²	semidirect
153. #3514	C₁₃	direct (N × H)
174. D₄×C₁₃	#41	semidirect
198. #559	C₂×C₁₃	semidirect
199. #556	C₂×C₁₃	semidirect
200. #555	C₂×C₁₃	semidirect
201. #551	C₂×C₁₃	semidirect
202. D₄×Q₈	C₂×C₁₃	semidirect
203. #548	C₂×C₁₃	semidirect
204. #546	C₂×C₁₃	semidirect
205. #546	C₂×C₁₃	semidirect
206. D₄²	C₂×C₁₃	semidirect
207. #542	C₂×C₁₃	semidirect
208. #538	C₂×C₁₃	semidirect
209. #532	C₂×C₁₃	semidirect
210. #529	C₂×C₁₃	semidirect
211. #529	C₂×C₁₃	semidirect
212. C₂×#124	C₂×C₁₃	semidirect
213. #518	C₂×C₁₃	semidirect
214. C₄×#41	C₂×C₁₃	semidirect
243. C₂×#41	C₂²×C₁₃	semidirect
244. C₂²×Q₈	C₂²×C₁₃	semidirect
247. C₄⋊Q₈	C₂²×C₁₃	semidirect
248. C₄⋊Q₈	C₂²×C₁₃	semidirect
250. #126	C₂²×C₁₃	semidirect
251. #126	C₂²×C₁₃	semidirect
252. #126	C₂²×C₁₃	semidirect
253. #125	C₂²×C₁₃	semidirect
256. #124	C₂²×C₁₃	semidirect
257. #124	C₂²×C₁₃	semidirect
258. #124	C₂²×C₁₃	semidirect
259. #124	C₂²×C₁₃	semidirect
260. #124	C₂²×C₁₃	semidirect
261. #124	C₂²×C₁₃	semidirect
262. #123	C₂²×C₁₃	semidirect
263. #123	C₂²×C₁₃	semidirect
264. #123	C₂²×C₁₃	semidirect
265. #123	C₂²×C₁₃	semidirect
266. C₂²⋊Q₈	C₂²×C₁₃	semidirect
267. C₂²⋊Q₈	C₂²×C₁₃	semidirect
268. C₂²⋊Q₈	C₂²×C₁₃	semidirect
269. C₂²⋊Q₈	C₂²×C₁₃	semidirect
270. C₂²⋊Q₈	C₂²×C₁₃	semidirect
274. #121	C₂²×C₁₃	semidirect
275. #121	C₂²×C₁₃	semidirect
276. #121	C₂²×C₁₃	semidirect
277. #121	C₂²×C₁₃	semidirect
279. #120	C₂²×C₁₃	semidirect
280. C₄×Q₈	C₂²×C₁₃	semidirect
281. C₄×Q₈	C₂²×C₁₃	semidirect
282. C₄×Q₈	C₂²×C₁₃	semidirect
283. C₄×Q₈	C₂²×C₁₃	semidirect
288. C₄×D₄	C₂²×C₁₃	semidirect
289. C₄×D₄	C₂²×C₁₃	semidirect
290. C₄×D₄	C₂²×C₁₃	semidirect
291. C₄×D₄	C₂²×C₁₃	semidirect
292. C₄×D₄	C₂²×C₁₃	semidirect
293. C₄×D₄	C₂²×C₁₃	semidirect
294. C₄×D₄	C₂²×C₁₃	semidirect
295. C₄×D₄	C₂²×C₁₃	semidirect
296. C₄×D₄	C₂²×C₁₃	semidirect
297. #117	C₂²×C₁₃	semidirect
298. #117	C₂²×C₁₃	semidirect
299. #117	C₂²×C₁₃	semidirect
300. #117	C₂²×C₁₃	semidirect
301. #117	C₂²×C₁₃	semidirect
302. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
303. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
304. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
305. C₂×C₄²	C₂²×C₁₃	semidirect
306. C₂×C₄²	C₂²×C₁₃	semidirect
384. C₁₃	#3514	direct (N × H)
405. 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×#559	2
C₁₃×#556	2
C₁₃×#555	2
C₁₃×#551	2
D₄×Q₈×C₁₃	2
C₁₃×#548	2
C₁₃×#546	2
D₄²×C₁₃	2
C₁₃×#542	2
C₁₃×#538	2
C₁₃×#532	2
C₁₃×#529	2
C₂×C₁₃×#124	2
C₁₃×#518	2
C₄×C₁₃×#41	2
#3514	13

Subgroups — C13×#3514 #13112572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3514 #13112572