Subgroups — C₁₃×#3555 #13112613

Order 1664.

910 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#563	C₂	1	4	yes	maximal, complemented
2	Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#557	C₂	1	2	yes	maximal, complemented
5	C₁₃×#556	C₂	1	2	yes	maximal, complemented
6	C₁₃×#556	C₂	1	2	yes	maximal, complemented
7	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#552	C₂	1	2	yes	maximal, complemented
10	C₁₃×#544	C₂	1	2	yes	maximal, complemented
11	C₁₃×#542	C₂	1	2	yes	maximal
12	C₁₃×#541	C₂	1	2	yes	maximal, complemented
13	C₁₃×#541	C₂	1	2	yes	maximal, complemented
14	C₁₃×#541	C₂	1	4	yes	maximal, complemented
15	C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#529	C₂	1	1	yes	maximal, characteristic
18	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
24	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
25	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
27	C₁₃×#126	C₂²	1	2	yes	—
28	C₁₃×#126	C₂²	1	4	yes	—
29	C₁₃×#126	C₂²	1	4	yes	—
30	C₁₃×#126	C₂²	1	4	yes	—
31	C₁₃×#126	C₂²	1	4	yes	—
32	C₁₃×#126	C₂²	1	4	yes	—
33	C₁₃×#126	C₂²	1	4	yes	—
34	C₁₃×#125	C₂²	1	1	yes	characteristic
35	C₁₃×#125	C₂²	1	2	yes	—
36	C₁₃×#125	C₂²	1	2	yes	—
37	C₁₃×#125	C₂²	1	4	yes	—
38	C₁₃×#125	C₂²	1	4	yes	—
39	C₁₃×#125	C₂²	1	4	yes	—
40	C₁₃×#125	C₂²	1	2	yes	—
41	C₁₃×#125	C₂²	1	4	yes	—
42	C₁₃×#125	C₂²	1	4	yes	—
43	C₁₃×#125	C₂²	1	2	yes	—
44	C₁₃×#124	C₂²	1	1	yes	characteristic
45	C₁₃×#124	C₂²	1	2	yes	—
46	C₁₃×#124	C₂²	1	4	yes	—
47	C₁₃×#123	C₂²	1	2	yes	—
48	C₁₃×#123	C₂²	1	4	yes	—
49	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
50	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
52	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
53	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
54	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
55	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
56	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
57	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
58	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
59	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
60	C₁₃×#121	C₂²	1	1	yes	characteristic
61	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
62	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
63	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
64	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
65	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
66	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
67	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
68	C₄×Q₈×C₁₃	C₂²	1	4	yes	—
69	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
70	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
71	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
72	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
73	C₄×D₄×C₁₃	C₂²	1	2	yes	—
74	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
75	C₄×D₄×C₁₃	C₂²	1	2	yes	—
76	C₁₃×#117	C₂²	1	2	yes	—
77	C₁₃×#117	C₂²	1	2	yes	—
78	C₁₃×#117	C₂²	1	2	yes	—
79	C₁₃×#117	C₂²	1	4	yes	—
80	C₁₃×#117	C₂²	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
83	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
87	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
88	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
89	C₂×Q₈×C₁₃	C₂³	1	4	yes	—
90	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
97	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
99	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
106	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
126	C₁₃×C₂²⋊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	2	yes	—
130	C₁₃×C₂²⋊C₄	C₂³	1	4	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	2	yes	—
135	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₄²×C₁₃	C₂³	1	1	yes	characteristic
139	C₄²×C₁₃	C₂³	1	1	yes	characteristic
140	C₄²×C₁₃	C₂³	1	1	yes	characteristic
141	C₄²×C₁₃	C₂³	1	4	yes	—
142	C₄²×C₁₃	C₂³	1	2	yes	—
143	C₄²×C₁₃	C₂³	1	2	yes	—
144	C₄²×C₁₃	C₂³	1	2	yes	—
145	C₄²×C₁₃	C₂³	1	4	yes	—
146	C₄²×C₁₃	C₂³	1	4	yes	—
147	C₄²×C₁₃	C₂³	1	4	yes	—
148	#3555	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₂³×C₁₃	C₂⁴	1	2	yes	—
151	Q₈×C₁₃	—	2	2	no	—
152	Q₈×C₁₃	—	2	2	no	—
153	Q₈×C₁₃	—	2	2	no	—
154	Q₈×C₁₃	—	2	4	no	—
155	Q₈×C₁₃	—	4	2	no	—
156	Q₈×C₁₃	—	4	2	no	—
157	Q₈×C₁₃	—	4	4	no	—
158	D₄×C₁₃	—	2	2	no	—
159	D₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	4	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	4	4	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
177	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	#563	C₂×C₁₃	1	4	yes	complemented
181	Q₈²	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#557	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#557	C₂×C₁₃	1	2	yes	complemented
184	#556	C₂×C₁₃	1	2	yes	complemented
185	#556	C₂×C₁₃	1	2	yes	complemented
186	#556	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#554	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#552	C₂×C₁₃	1	2	yes	complemented
189	#544	C₂×C₁₃	1	2	yes	complemented
190	#542	C₂×C₁₃	1	2	yes	—
191	#541	C₂×C₁₃	1	2	yes	complemented
192	#541	C₂×C₁₃	1	2	yes	complemented
193	#541	C₂×C₁₃	1	4	yes	complemented
194	#533	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#533	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#529	C₂×C₁₃	1	1	yes	characteristic
197	C₂²×C₁₃	—	2	1	no	—
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	2	1	no	—
203	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
204	C₄×C₁₃	—	2	1	no	—
205	C₄×C₁₃	—	2	2	no	—
206	C₄×C₁₃	—	2	1	no	—
207	C₄×C₁₃	—	2	2	no	—
208	C₄×C₁₃	—	2	2	no	—
209	C₄×C₁₃	—	2	4	no	—
210	C₄×C₁₃	—	2	2	no	—
211	C₄×C₁₃	—	2	2	no	—
212	C₄×C₁₃	—	2	4	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	2	2	no	—
216	C₄×C₁₃	—	2	2	no	—
217	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
218	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
219	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
223	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
224	C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
225	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
226	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
227	C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
228	#126	C₂²×C₁₃	1	2	yes	—
229	#126	C₂²×C₁₃	1	4	yes	—
230	#126	C₂²×C₁₃	1	4	yes	—
231	#126	C₂²×C₁₃	1	4	yes	—
232	#126	C₂²×C₁₃	1	4	yes	—
233	#126	C₂²×C₁₃	1	4	yes	—
234	#126	C₂²×C₁₃	1	4	yes	—
235	#125	C₂²×C₁₃	1	1	yes	characteristic
236	#125	C₂²×C₁₃	1	2	yes	—
237	#125	C₂²×C₁₃	1	2	yes	—
238	#125	C₂²×C₁₃	1	4	yes	—
239	#125	C₂²×C₁₃	1	4	yes	—
240	#125	C₂²×C₁₃	1	4	yes	—
241	#125	C₂²×C₁₃	1	2	yes	—
242	#125	C₂²×C₁₃	1	4	yes	—
243	#125	C₂²×C₁₃	1	4	yes	—
244	#125	C₂²×C₁₃	1	2	yes	—
245	#124	C₂²×C₁₃	1	1	yes	characteristic
246	#124	C₂²×C₁₃	1	2	yes	—
247	#124	C₂²×C₁₃	1	4	yes	—
248	#123	C₂²×C₁₃	1	2	yes	—
249	#123	C₂²×C₁₃	1	4	yes	—
250	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
252	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
254	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
255	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
256	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
257	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
258	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
259	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
260	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
261	#121	C₂²×C₁₃	1	1	yes	characteristic
262	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
263	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
264	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
266	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
267	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
269	C₄×Q₈	C₂²×C₁₃	1	4	yes	—
270	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
271	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
272	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
273	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
274	C₄×D₄	C₂²×C₁₃	1	2	yes	—
275	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
276	C₄×D₄	C₂²×C₁₃	1	2	yes	—
277	#117	C₂²×C₁₃	1	2	yes	—
278	#117	C₂²×C₁₃	1	2	yes	—
279	#117	C₂²×C₁₃	1	2	yes	—
280	#117	C₂²×C₁₃	1	4	yes	—
281	#117	C₂²×C₁₃	1	2	yes	—
282	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
283	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₁₃	—	4	1	no	—
285	C₂×C₁₃	—	4	2	no	—
286	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
287	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
288	C₂×C₁₃	#585	1	1	yes	characteristic
289	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
293	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
294	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
295	C₂×Q₈	C₂³×C₁₃	1	4	yes	—
296	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂×D₄	C₂³×C₁₃	1	2	yes	—
298	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
301	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
303	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
304	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
305	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
306	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
307	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
308	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
309	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
310	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
311	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
312	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
313	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
314	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
315	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
316	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
317	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
318	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
319	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
320	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
321	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
322	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
323	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
324	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
325	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
326	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
327	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
329	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
330	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
331	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
332	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
333	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
334	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
335	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
336	C₂²⋊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	2	yes	—
341	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
342	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
343	C₄²	C₂³×C₁₃	1	1	yes	characteristic
344	C₄²	C₂³×C₁₃	1	1	yes	characteristic
345	C₄²	C₂³×C₁₃	1	1	yes	characteristic
346	C₄²	C₂³×C₁₃	1	1	yes	characteristic
347	C₄²	C₂³×C₁₃	1	4	yes	—
348	C₄²	C₂³×C₁₃	1	2	yes	—
349	C₄²	C₂³×C₁₃	1	2	yes	—
350	C₄²	C₂³×C₁₃	1	2	yes	—
351	C₄²	C₂³×C₁₃	1	4	yes	—
352	C₄²	C₂³×C₁₃	1	4	yes	—
353	C₄²	C₂³×C₁₃	1	4	yes	—
354	C₁₃	#3555	1	1	yes	characteristic, direct product factor, Sylow
355	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
356	C₂³	C₂⁴×C₁₃	1	2	yes	—
357	Q₈	—	2	2	no	—
358	Q₈	—	2	2	no	—
359	Q₈	—	2	2	no	—
360	Q₈	—	2	4	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	4	4	no	—
364	D₄	—	2	2	no	—
365	D₄	—	4	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
373	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
374	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
375	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
376	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
377	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
378	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
379	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
380	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
382	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
383	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
384	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
385	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	1	no	—
392	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	4	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	4	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
407	C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
408	C₂	—	4	1	no	—
409	C₂	—	4	2	no	—
410	C₂	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
411	C₂	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
412	C₂	C₁₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
prime radical	C₁₃×#121	C₂²
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×#563	C₂	semidirect
2. Q₈²×C₁₃	C₂	semidirect
3. C₁₃×#557	C₂	semidirect
4. C₁₃×#557	C₂	semidirect
5. C₁₃×#556	C₂	semidirect
6. C₁₃×#556	C₂	semidirect
7. C₁₃×#556	C₂	semidirect
8. C₁₃×#554	C₂	semidirect
9. C₁₃×#552	C₂	semidirect
10. C₁₃×#544	C₂	semidirect
12. C₁₃×#541	C₂	semidirect
13. C₁₃×#541	C₂	semidirect
14. C₁₃×#541	C₂	semidirect
15. C₁₃×#533	C₂	semidirect
16. C₁₃×#533	C₂	semidirect
148. #3555	C₁₃	direct (N × H)
180. #563	C₂×C₁₃	semidirect
181. Q₈²	C₂×C₁₃	semidirect
182. #557	C₂×C₁₃	semidirect
183. #557	C₂×C₁₃	semidirect
184. #556	C₂×C₁₃	semidirect
185. #556	C₂×C₁₃	semidirect
186. #556	C₂×C₁₃	semidirect
187. #554	C₂×C₁₃	semidirect
188. #552	C₂×C₁₃	semidirect
189. #544	C₂×C₁₃	semidirect
191. #541	C₂×C₁₃	semidirect
192. #541	C₂×C₁₃	semidirect
193. #541	C₂×C₁₃	semidirect
194. #533	C₂×C₁₃	semidirect
195. #533	C₂×C₁₃	semidirect
354. C₁₃	#3555	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×#563	2
Q₈²×C₁₃	2
C₁₃×#557	2
C₁₃×#556	2
C₁₃×#554	2
C₁₃×#552	2
C₁₃×#544	2
C₁₃×#542	2
C₁₃×#541	2
C₁₃×#533	2
C₁₃×#529	2
#3555	13

Subgroups — C13×#3555 #13112613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3555 #13112613