Subgroups — C₁₃×#3552 #13112610

Order 1664.

1004 conjugacy classes of subgroups.

The subgroup lattice has 436 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	C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#554	C₂	1	2	yes	maximal, complemented
5	C₁₃×#553	C₂	1	2	yes	maximal, complemented
6	D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×Q₈×C₁₃	C₂	1	2	yes	maximal, complemented
8	C₁₃×#548	C₂	1	2	yes	maximal, complemented
9	C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#544	C₂	1	2	yes	maximal, complemented
11	C₁₃×#542	C₂	1	2	yes	maximal, complemented
12	C₁₃×#541	C₂	1	2	yes	maximal, complemented
13	C₁₃×#539	C₂	1	4	yes	maximal, complemented
14	C₁₃×#536	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#41	C₂²	1	2	yes	—
19	C₂²×Q₈×C₁₃	C₂²	1	2	yes	—
20	C₂²×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
28	C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
29	C₁₃×#126	C₂²	1	2	yes	—
30	C₁₃×#126	C₂²	1	2	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	1	yes	characteristic
36	C₁₃×#125	C₂²	1	4	yes	—
37	C₁₃×#125	C₂²	1	4	yes	—
38	C₁₃×#125	C₂²	1	4	yes	—
39	C₁₃×#125	C₂²	1	2	yes	—
40	C₁₃×#124	C₂²	1	1	yes	characteristic
41	C₁₃×#124	C₂²	1	1	yes	characteristic
42	C₁₃×#124	C₂²	1	2	yes	—
43	C₁₃×#124	C₂²	1	4	yes	—
44	C₁₃×#123	C₂²	1	2	yes	—
45	C₁₃×#123	C₂²	1	2	yes	—
46	C₁₃×#123	C₂²	1	4	yes	—
47	C₁₃×#123	C₂²	1	4	yes	—
48	C₁₃×#123	C₂²	1	4	yes	—
49	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
50	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
51	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
52	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
53	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
54	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
55	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
56	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
57	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
58	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
59	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
60	C₁₃×#121	C₂²	1	1	yes	characteristic
61	C₁₃×#121	C₂²	1	1	yes	characteristic
62	C₁₃×#121	C₂²	1	4	yes	—
63	C₁₃×#121	C₂²	1	2	yes	—
64	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
65	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
66	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
67	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
68	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
69	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
70	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
71	C₄×D₄×C₁₃	C₂²	1	2	yes	—
72	C₄×D₄×C₁₃	C₂²	1	2	yes	—
73	C₄×D₄×C₁₃	C₂²	1	4	yes	—
74	C₄×D₄×C₁₃	C₂²	1	4	yes	—
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	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
83	C₁₃×#41	—	4	4	no	—
84	C₂×Q₈×C₁₃	—	4	4	no	—
85	C₂×Q₈×C₁₃	—	4	4	no	—
86	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
89	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
90	C₂×Q₈×C₁₃	C₂³	1	4	yes	—
91	C₂×Q₈×C₁₃	C₂³	1	4	yes	—
92	C₂×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×D₄×C₁₃	C₂³	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
103	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
104	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
105	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
109	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₁₃×C₄⋊C₄	C₂³	1	2	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	2	yes	—
117	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
124	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
126	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
127	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₁₃×C₄⋊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	2	yes	—
133	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₁₃×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
143	C₄²×C₁₃	C₂³	1	1	yes	characteristic
144	C₄²×C₁₃	C₂³	1	1	yes	characteristic
145	C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₄²×C₁₃	C₂³	1	1	yes	characteristic
147	C₄²×C₁₃	C₂³	1	2	yes	—
148	C₄²×C₁₃	C₂³	1	2	yes	—
149	C₄²×C₁₃	C₂³	1	4	yes	—
150	C₄²×C₁₃	C₂³	1	4	yes	—
151	#3552	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₁₃	C₂⁴	1	2	yes	—
153	C₂³×C₁₃	C₂⁴	1	2	yes	—
154	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
155	Q₈×C₁₃	—	2	4	no	—
156	Q₈×C₁₃	—	2	2	no	—
157	Q₈×C₁₃	—	2	4	no	—
158	Q₈×C₁₃	—	2	2	no	—
159	Q₈×C₁₃	—	4	4	no	—
160	Q₈×C₁₃	—	4	4	no	—
161	D₄×C₁₃	—	2	4	no	—
162	D₄×C₁₃	—	2	4	no	—
163	D₄×C₁₃	—	2	2	no	—
164	D₄×C₁₃	—	2	2	no	—
165	D₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	4	4	no	—
172	C₂×C₄×C₁₃	—	4	4	no	—
173	C₂×C₄×C₁₃	—	4	4	no	—
174	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
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	2	yes	—
181	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
184	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
185	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
186	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	#563	C₂×C₁₃	1	4	yes	complemented
189	#557	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#556	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#554	C₂×C₁₃	1	2	yes	complemented
192	#553	C₂×C₁₃	1	2	yes	complemented
193	D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
194	D₄×Q₈	C₂×C₁₃	1	2	yes	complemented
195	#548	C₂×C₁₃	1	2	yes	complemented
196	#547	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#544	C₂×C₁₃	1	2	yes	complemented
198	#542	C₂×C₁₃	1	2	yes	complemented
199	#541	C₂×C₁₃	1	2	yes	complemented
200	#539	C₂×C₁₃	1	4	yes	complemented
201	#536	C₂×C₁₃	1	2	yes	complemented
202	C₂×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂²×C₁₃	—	2	1	no	—
206	C₂²×C₁₃	—	2	1	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	2	2	no	—
209	C₂²×C₁₃	—	2	2	no	—
210	C₂²×C₁₃	—	2	2	no	—
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	—	2	2	no	—
213	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
214	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
215	C₄×C₁₃	—	2	2	no	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	—	2	4	no	—
218	C₄×C₁₃	—	2	4	no	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	1	no	—
221	C₄×C₁₃	—	2	1	no	—
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	—	2	2	no	—
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
228	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
229	C₂×#41	C₂²×C₁₃	1	2	yes	—
230	C₂²×Q₈	C₂²×C₁₃	1	2	yes	—
231	C₂²×Q₈	C₂²×C₁₃	1	2	yes	—
232	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
233	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
234	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
235	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
236	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
237	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
238	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
239	C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
240	#126	C₂²×C₁₃	1	2	yes	—
241	#126	C₂²×C₁₃	1	2	yes	—
242	#126	C₂²×C₁₃	1	4	yes	—
243	#126	C₂²×C₁₃	1	4	yes	—
244	#126	C₂²×C₁₃	1	4	yes	—
245	#125	C₂²×C₁₃	1	1	yes	characteristic
246	#125	C₂²×C₁₃	1	1	yes	characteristic
247	#125	C₂²×C₁₃	1	4	yes	—
248	#125	C₂²×C₁₃	1	4	yes	—
249	#125	C₂²×C₁₃	1	4	yes	—
250	#125	C₂²×C₁₃	1	2	yes	—
251	#124	C₂²×C₁₃	1	1	yes	characteristic
252	#124	C₂²×C₁₃	1	1	yes	characteristic
253	#124	C₂²×C₁₃	1	2	yes	—
254	#124	C₂²×C₁₃	1	4	yes	—
255	#123	C₂²×C₁₃	1	2	yes	—
256	#123	C₂²×C₁₃	1	2	yes	—
257	#123	C₂²×C₁₃	1	4	yes	—
258	#123	C₂²×C₁₃	1	4	yes	—
259	#123	C₂²×C₁₃	1	4	yes	—
260	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
263	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
264	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
265	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
266	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
267	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
268	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
269	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
270	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
271	#121	C₂²×C₁₃	1	1	yes	characteristic
272	#121	C₂²×C₁₃	1	1	yes	characteristic
273	#121	C₂²×C₁₃	1	4	yes	—
274	#121	C₂²×C₁₃	1	2	yes	—
275	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
276	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
277	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
278	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
279	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
280	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
281	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
282	C₄×D₄	C₂²×C₁₃	1	2	yes	—
283	C₄×D₄	C₂²×C₁₃	1	2	yes	—
284	C₄×D₄	C₂²×C₁₃	1	4	yes	—
285	C₄×D₄	C₂²×C₁₃	1	4	yes	—
286	C₄×D₄	C₂²×C₁₃	1	2	yes	—
287	#117	C₂²×C₁₃	1	2	yes	—
288	#117	C₂²×C₁₃	1	2	yes	—
289	#117	C₂²×C₁₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
293	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₁₃	—	2	2	no	—
295	C₂×C₁₃	—	4	2	no	—
296	C₂×C₁₃	—	4	2	no	—
297	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
299	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
300	#41	—	4	4	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂×Q₈	—	4	4	no	—
303	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
304	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
306	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
307	C₂×Q₈	C₂³×C₁₃	1	4	yes	—
308	C₂×Q₈	C₂³×C₁₃	1	4	yes	—
309	C₂×D₄	C₂³×C₁₃	1	2	yes	—
310	C₂×D₄	C₂³×C₁₃	1	2	yes	—
311	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
313	C₂×D₄	C₂³×C₁₃	1	4	yes	—
314	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
316	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
318	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
319	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
320	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
321	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
322	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
324	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
325	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
326	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
327	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
328	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
329	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
330	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
332	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
333	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
334	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
335	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
337	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
338	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
339	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
340	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
341	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
342	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
343	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
344	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
347	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
348	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
349	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
350	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
351	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
352	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
353	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
354	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
355	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
356	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
357	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
358	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
359	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
360	C₄²	C₂³×C₁₃	1	1	yes	characteristic
361	C₄²	C₂³×C₁₃	1	1	yes	characteristic
362	C₄²	C₂³×C₁₃	1	1	yes	characteristic
363	C₄²	C₂³×C₁₃	1	1	yes	characteristic
364	C₄²	C₂³×C₁₃	1	2	yes	—
365	C₄²	C₂³×C₁₃	1	2	yes	—
366	C₄²	C₂³×C₁₃	1	4	yes	—
367	C₄²	C₂³×C₁₃	1	4	yes	—
368	C₁₃	#3552	1	1	yes	characteristic, direct product factor, Sylow
369	C₂³	C₂⁴×C₁₃	1	2	yes	—
370	C₂³	C₂⁴×C₁₃	1	2	yes	—
371	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
372	Q₈	—	2	4	no	—
373	Q₈	—	2	2	no	—
374	Q₈	—	2	4	no	—
375	Q₈	—	2	2	no	—
376	Q₈	—	4	4	no	—
377	Q₈	—	4	4	no	—
378	D₄	—	2	4	no	—
379	D₄	—	2	4	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	2	no	—
382	D₄	—	4	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
392	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
393	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
394	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
397	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
398	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
399	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
400	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
401	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
402	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
403	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
404	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	C₁₃×2₋¹⁺⁴	1	2	yes	—
414	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	4	no	—
418	C₄	—	2	4	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
428	C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
429	C₂	—	2	2	no	—
430	C₂	—	4	2	no	—
431	C₂	—	4	2	no	—
432	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
433	C₂	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
434	C₂	C₂×C₁₃×2₋¹⁺⁴	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×#563	C₂	semidirect
2. C₁₃×#557	C₂	semidirect
3. C₁₃×#556	C₂	semidirect
4. C₁₃×#554	C₂	semidirect
5. C₁₃×#553	C₂	semidirect
6. D₄×Q₈×C₁₃	C₂	semidirect
7. D₄×Q₈×C₁₃	C₂	semidirect
8. C₁₃×#548	C₂	semidirect
9. C₁₃×#547	C₂	semidirect
10. C₁₃×#544	C₂	semidirect
11. C₁₃×#542	C₂	semidirect
12. C₁₃×#541	C₂	semidirect
13. C₁₃×#539	C₂	semidirect
14. C₁₃×#536	C₂	semidirect
15. C₂×C₁₃×C₄⋊Q₈	C₂	semidirect
16. C₁₃×#529	C₂	semidirect
17. C₁₃×#529	C₂	semidirect
151. #3552	C₁₃	direct (N × H)
188. #563	C₂×C₁₃	semidirect
189. #557	C₂×C₁₃	semidirect
190. #556	C₂×C₁₃	semidirect
191. #554	C₂×C₁₃	semidirect
192. #553	C₂×C₁₃	semidirect
193. D₄×Q₈	C₂×C₁₃	semidirect
194. D₄×Q₈	C₂×C₁₃	semidirect
195. #548	C₂×C₁₃	semidirect
196. #547	C₂×C₁₃	semidirect
197. #544	C₂×C₁₃	semidirect
198. #542	C₂×C₁₃	semidirect
199. #541	C₂×C₁₃	semidirect
200. #539	C₂×C₁₃	semidirect
201. #536	C₂×C₁₃	semidirect
202. C₂×C₄⋊Q₈	C₂×C₁₃	semidirect
203. #529	C₂×C₁₃	semidirect
204. #529	C₂×C₁₃	semidirect
368. C₁₃	#3552	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
C₁₃×#557	2
C₁₃×#556	2
C₁₃×#554	2
C₁₃×#553	2
D₄×Q₈×C₁₃	2
C₁₃×#548	2
C₁₃×#547	2
C₁₃×#544	2
C₁₃×#542	2
C₁₃×#541	2
C₁₃×#539	2
C₁₃×#536	2
C₂×C₁₃×C₄⋊Q₈	2
C₁₃×#529	2
#3552	13

Subgroups — C13×#3552 #13112610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3552 #13112610