Subgroups — C₁₃×#3554 #13112612

Order 1664.

1022 conjugacy classes of subgroups.

The subgroup lattice has 442 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	4	yes	maximal, complemented
2	C₁₃×#559	C₂	1	2	yes	maximal, complemented
3	C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#554	C₂	1	2	yes	maximal, complemented
6	C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#548	C₂	1	2	yes	maximal, complemented
9	C₁₃×#547	C₂	1	2	yes	maximal, complemented
10	C₁₃×#542	C₂	1	2	yes	maximal, complemented
11	C₁₃×#542	C₂	1	2	yes	maximal, complemented
12	C₁₃×#540	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	C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#532	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	C₂×C₁₃×#41	C₂²	1	2	yes	—
20	C₂²×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
25	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₁₃×#127	C₂²	1	1	yes	characteristic
27	C₁₃×#127	C₂²	1	2	yes	—
28	C₁₃×#126	C₂²	1	2	yes	—
29	C₁₃×#126	C₂²	1	4	yes	—
30	C₁₃×#125	C₂²	1	1	yes	characteristic
31	C₁₃×#125	C₂²	1	2	yes	—
32	C₁₃×#125	C₂²	1	4	yes	—
33	C₁₃×#125	C₂²	1	2	yes	—
34	C₁₃×#124	C₂²	1	1	yes	characteristic
35	C₁₃×#124	C₂²	1	2	yes	—
36	C₁₃×#124	C₂²	1	2	yes	—
37	C₁₃×#124	C₂²	1	4	yes	—
38	C₁₃×#124	C₂²	1	2	yes	—
39	C₁₃×#124	C₂²	1	4	yes	—
40	C₁₃×#123	C₂²	1	2	yes	—
41	C₁₃×#123	C₂²	1	4	yes	—
42	C₁₃×#123	C₂²	1	4	yes	—
43	C₁₃×#123	C₂²	1	4	yes	—
44	C₁₃×#123	C₂²	1	4	yes	—
45	C₁₃×#123	C₂²	1	4	yes	—
46	C₁₃×#123	C₂²	1	4	yes	—
47	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
50	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
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	4	yes	—
57	C₁₃×#121	C₂²	1	1	yes	characteristic
58	C₁₃×#121	C₂²	1	2	yes	—
59	C₁₃×#121	C₂²	1	2	yes	—
60	C₁₃×#121	C₂²	1	4	yes	—
61	C₁₃×#121	C₂²	1	4	yes	—
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	1	yes	characteristic
67	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
68	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
69	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
70	C₄×D₄×C₁₃	C₂²	1	2	yes	—
71	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
72	C₄×D₄×C₁₃	C₂²	1	2	yes	—
73	C₄×D₄×C₁₃	C₂²	1	2	yes	—
74	C₄×D₄×C₁₃	C₂²	1	4	yes	—
75	C₄×D₄×C₁₃	C₂²	1	2	yes	—
76	C₄×D₄×C₁₃	C₂²	1	2	yes	—
77	C₄×D₄×C₁₃	C₂²	1	2	yes	—
78	C₄×D₄×C₁₃	C₂²	1	2	yes	—
79	C₁₃×#117	C₂²	1	2	yes	—
80	C₁₃×#117	C₂²	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
82	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
83	C₁₃×#41	—	4	4	no	—
84	C₁₃×#41	—	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	1	yes	characteristic
90	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
91	C₂×Q₈×C₁₃	C₂³	1	4	yes	—
92	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂×D₄×C₁₃	C₂³	1	2	yes	—
95	C₂×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂×D₄×C₁₃	C₂³	1	4	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	4	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	4	yes	—
111	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
118	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
128	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₁₃×C₂²⋊C₄	C₂³	1	2	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	4	yes	—
136	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₁₃×C₂²⋊C₄	C₂³	1	4	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	4	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	2	yes	—
150	C₄²×C₁₃	C₂³	1	4	yes	—
151	#3554	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₁₃	C₂⁴	1	2	yes	—
153	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂³×C₁₃	C₂⁴	1	4	yes	—
155	Q₈×C₁₃	—	2	2	no	—
156	Q₈×C₁₃	—	2	4	no	—
157	Q₈×C₁₃	—	2	2	no	—
158	Q₈×C₁₃	—	2	2	no	—
159	Q₈×C₁₃	—	4	4	no	—
160	Q₈×C₁₃	—	4	2	no	—
161	D₄×C₁₃	—	2	4	no	—
162	D₄×C₁₃	—	2	2	no	—
163	D₄×C₁₃	—	2	4	no	—
164	D₄×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	4	4	no	—
167	D₄×C₁₃	—	4	4	no	—
168	D₄×C₁₃	—	4	4	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	4	4	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	4	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	—	4	4	no	—
177	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
184	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
186	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
187	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
189	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	#562	C₂×C₁₃	1	4	yes	complemented
192	#559	C₂×C₁₃	1	2	yes	complemented
193	#559	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#557	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#554	C₂×C₁₃	1	2	yes	complemented
196	#550	C₂×C₁₃	1	1	yes	characteristic, complemented
197	D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#548	C₂×C₁₃	1	2	yes	complemented
199	#547	C₂×C₁₃	1	2	yes	complemented
200	#542	C₂×C₁₃	1	2	yes	complemented
201	#542	C₂×C₁₃	1	2	yes	complemented
202	#540	C₂×C₁₃	1	2	yes	complemented
203	#539	C₂×C₁₃	1	4	yes	complemented
204	#536	C₂×C₁₃	1	2	yes	complemented
205	#533	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#532	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂²×C₁₃	—	2	2	no	—
209	C₂²×C₁₃	—	2	1	no	—
210	C₂²×C₁₃	—	2	4	no	—
211	C₂²×C₁₃	—	2	1	no	—
212	C₂²×C₁₃	—	2	2	no	—
213	C₂²×C₁₃	—	2	4	no	—
214	C₂²×C₁₃	—	2	1	no	—
215	C₂²×C₁₃	—	2	4	no	—
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
218	C₄×C₁₃	—	2	1	no	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	2	4	no	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	2	1	no	—
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	—	2	2	no	—
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	2	2	no	—
230	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
231	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
232	C₂×#41	C₂²×C₁₃	1	2	yes	—
233	C₂×#41	C₂²×C₁₃	1	2	yes	—
234	C₂²×Q₈	C₂²×C₁₃	1	2	yes	—
235	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
236	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
238	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
239	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
240	#127	C₂²×C₁₃	1	1	yes	characteristic
241	#127	C₂²×C₁₃	1	2	yes	—
242	#126	C₂²×C₁₃	1	2	yes	—
243	#126	C₂²×C₁₃	1	4	yes	—
244	#125	C₂²×C₁₃	1	1	yes	characteristic
245	#125	C₂²×C₁₃	1	2	yes	—
246	#125	C₂²×C₁₃	1	4	yes	—
247	#125	C₂²×C₁₃	1	2	yes	—
248	#124	C₂²×C₁₃	1	1	yes	characteristic
249	#124	C₂²×C₁₃	1	2	yes	—
250	#124	C₂²×C₁₃	1	2	yes	—
251	#124	C₂²×C₁₃	1	4	yes	—
252	#124	C₂²×C₁₃	1	2	yes	—
253	#124	C₂²×C₁₃	1	4	yes	—
254	#123	C₂²×C₁₃	1	2	yes	—
255	#123	C₂²×C₁₃	1	4	yes	—
256	#123	C₂²×C₁₃	1	4	yes	—
257	#123	C₂²×C₁₃	1	4	yes	—
258	#123	C₂²×C₁₃	1	4	yes	—
259	#123	C₂²×C₁₃	1	4	yes	—
260	#123	C₂²×C₁₃	1	4	yes	—
261	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
263	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
265	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
266	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
267	C₂²⋊Q₈	C₂²×C₁₃	1	4	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	2	yes	—
273	#121	C₂²×C₁₃	1	2	yes	—
274	#121	C₂²×C₁₃	1	4	yes	—
275	#121	C₂²×C₁₃	1	4	yes	—
276	#121	C₂²×C₁₃	1	4	yes	—
277	#121	C₂²×C₁₃	1	2	yes	—
278	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
279	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
281	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
282	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
283	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
284	C₄×D₄	C₂²×C₁₃	1	2	yes	—
285	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
286	C₄×D₄	C₂²×C₁₃	1	2	yes	—
287	C₄×D₄	C₂²×C₁₃	1	2	yes	—
288	C₄×D₄	C₂²×C₁₃	1	4	yes	—
289	C₄×D₄	C₂²×C₁₃	1	2	yes	—
290	C₄×D₄	C₂²×C₁₃	1	2	yes	—
291	C₄×D₄	C₂²×C₁₃	1	2	yes	—
292	C₄×D₄	C₂²×C₁₃	1	2	yes	—
293	#117	C₂²×C₁₃	1	2	yes	—
294	#117	C₂²×C₁₃	1	2	yes	—
295	C₂×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
296	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₁₃	—	4	2	no	—
298	C₂×C₁₃	—	4	1	no	—
299	C₂×C₁₃	—	4	4	no	—
300	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
301	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
302	C₂×C₁₃	#585	1	1	yes	characteristic
303	#41	—	4	4	no	—
304	#41	—	4	4	no	—
305	C₂×Q₈	—	4	4	no	—
306	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
308	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
309	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
310	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
311	C₂×Q₈	C₂³×C₁₃	1	4	yes	—
312	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
313	C₂×D₄	C₂³×C₁₃	1	2	yes	—
314	C₂×D₄	C₂³×C₁₃	1	2	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	C₂×D₄	C₂³×C₁₃	1	4	yes	—
320	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
323	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
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	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
328	C₄⋊C₄	C₂³×C₁₃	1	2	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	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	2	yes	—
336	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
339	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
340	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
341	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
342	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
344	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
345	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
347	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
348	C₄⋊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	2	yes	—
354	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
355	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
356	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
357	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
358	C₂²⋊C₄	C₂³×C₁₃	1	4	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	C₄²	C₂³×C₁₃	1	1	yes	characteristic
364	C₄²	C₂³×C₁₃	1	1	yes	characteristic
365	C₄²	C₂³×C₁₃	1	1	yes	characteristic
366	C₄²	C₂³×C₁₃	1	1	yes	characteristic
367	C₄²	C₂³×C₁₃	1	2	yes	—
368	C₄²	C₂³×C₁₃	1	2	yes	—
369	C₄²	C₂³×C₁₃	1	2	yes	—
370	C₄²	C₂³×C₁₃	1	4	yes	—
371	C₁₃	#3554	1	1	yes	characteristic, direct product factor, Sylow
372	C₂³	C₂⁴×C₁₃	1	2	yes	—
373	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
374	C₂³	C₂⁴×C₁₃	1	4	yes	—
375	Q₈	—	2	2	no	—
376	Q₈	—	2	4	no	—
377	Q₈	—	2	2	no	—
378	Q₈	—	2	2	no	—
379	Q₈	—	4	4	no	—
380	Q₈	—	4	2	no	—
381	D₄	—	2	4	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	4	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
398	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
399	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
400	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
403	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
404	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
405	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
406	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
407	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
408	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
409	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
410	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
411	C₂²	—	2	2	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	2	no	—
420	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	2	no	—
433	C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
434	C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
435	C₂	—	4	2	no	—
436	C₂	—	4	1	no	—
437	C₂	—	4	4	no	—
438	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
440	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×#559	C₂	semidirect
3. C₁₃×#559	C₂	semidirect
4. C₁₃×#557	C₂	semidirect
5. C₁₃×#554	C₂	semidirect
6. C₁₃×#550	C₂	semidirect
7. D₄×Q₈×C₁₃	C₂	semidirect
8. C₁₃×#548	C₂	semidirect
9. C₁₃×#547	C₂	semidirect
10. C₁₃×#542	C₂	semidirect
11. C₁₃×#542	C₂	semidirect
12. C₁₃×#540	C₂	semidirect
13. C₁₃×#539	C₂	semidirect
14. C₁₃×#536	C₂	semidirect
15. C₁₃×#533	C₂	semidirect
16. C₁₃×#532	C₂	semidirect
17. C₁₃×#529	C₂	semidirect
151. #3554	C₁₃	direct (N × H)
191. #562	C₂×C₁₃	semidirect
192. #559	C₂×C₁₃	semidirect
193. #559	C₂×C₁₃	semidirect
194. #557	C₂×C₁₃	semidirect
195. #554	C₂×C₁₃	semidirect
196. #550	C₂×C₁₃	semidirect
197. D₄×Q₈	C₂×C₁₃	semidirect
198. #548	C₂×C₁₃	semidirect
199. #547	C₂×C₁₃	semidirect
200. #542	C₂×C₁₃	semidirect
201. #542	C₂×C₁₃	semidirect
202. #540	C₂×C₁₃	semidirect
203. #539	C₂×C₁₃	semidirect
204. #536	C₂×C₁₃	semidirect
205. #533	C₂×C₁₃	semidirect
206. #532	C₂×C₁₃	semidirect
207. #529	C₂×C₁₃	semidirect
371. C₁₃	#3554	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×#559	2
C₁₃×#557	2
C₁₃×#554	2
C₁₃×#550	2
D₄×Q₈×C₁₃	2
C₁₃×#548	2
C₁₃×#547	2
C₁₃×#542	2
C₁₃×#540	2
C₁₃×#539	2
C₁₃×#536	2
C₁₃×#533	2
C₁₃×#532	2
C₁₃×#529	2
#3554	13

Subgroups — C13×#3554 #13112612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3554 #13112612