Subgroups — C₁₃×#33490 #15719829

Order 3328.

574 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2169	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2168	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2168	C₂	1	2	yes	maximal, complemented
5	D₄×C₁₃×C₁₆	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2164	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2113	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#525	C₄	1	1	yes	characteristic
13	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
16	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
19	C₁₃×#435	C₄	1	2	yes	—
20	C₁₃×#435	C₄	1	2	yes	—
21	C₈×D₄×C₁₃	C₂²	1	2	yes	—
22	C₈×D₄×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#424	C₄	1	1	yes	characteristic
24	C₁₃×#408	C₄	1	1	yes	characteristic
25	C₁₃×#407	C₄	1	1	yes	characteristic
26	C₁₃×#405	C₂²	1	1	yes	characteristic
27	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
28	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
29	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
30	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
31	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
32	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
33	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
34	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
35	C₁₃×#346	C₂²	1	2	yes	complemented
36	C₄×C₁₃×C₁₆	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₁₃×#131	—	4	1	no	—
40	C₁₃×#131	—	4	1	no	—
41	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
42	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
43	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₃	—	4	1	no	—
45	C₂²×C₈×C₁₃	—	4	1	no	—
46	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₁₃×#123	C₈	1	2	yes	—
54	C₁₃×C₂²⋊Q₈	C₈	1	1	yes	characteristic
55	C₁₃×C₂²⋊Q₈	C₈	1	1	yes	characteristic
56	C₁₃×#121	C₈	1	1	yes	characteristic
57	C₁₃×#121	C₈	1	1	yes	characteristic
58	C₁₃×#120	C₈	1	2	yes	—
59	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
60	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
61	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
62	C₁₃×M₃₂	—	4	1	no	—
63	C₁₃×M₃₂	—	4	1	no	—
64	C₁₃×M₃₂	—	4	2	no	—
65	C₂×C₁₃×C₁₆	—	4	1	no	—
66	C₂×C₁₃×C₁₆	—	4	1	no	—
67	C₂×C₁₃×C₁₆	—	4	2	no	—
68	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
69	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
70	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
71	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
72	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
73	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
74	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
75	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
76	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
77	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
78	C₁₃×#97	C₂×C₄	1	2	yes	—
79	C₄×C₈×C₁₃	C₂³	1	2	yes	—
80	#33490	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
82	C₁₃×#41	—	4	1	no	—
83	C₁₃×#41	—	4	1	no	—
84	C₂×Q₈×C₁₃	C₂×C₈	1	1	yes	characteristic
85	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
86	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
87	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
88	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	—	4	1	no	—
90	C₂²×C₄×C₁₃	—	4	1	no	—
91	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₁₃×M₁₆	—	4	1	no	—
99	C₁₃×M₁₆	—	4	2	no	—
100	C₁₃×M₁₆	—	4	1	no	—
101	C₂×C₈×C₁₃	—	2	1	no	—
102	C₂×C₈×C₁₃	—	2	1	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	1	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	4	1	no	—
110	C₂×C₈×C₁₃	—	4	1	no	—
111	C₂×C₈×C₁₃	—	4	1	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
119	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
120	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
121	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
122	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
123	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
124	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
125	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
126	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
127	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
128	C₁₃×C₁₆	—	2	2	no	—
129	C₁₃×C₁₆	—	2	2	no	—
130	C₁₃×C₁₆	—	2	2	no	—
131	C₁₃×C₁₆	—	2	2	no	—
132	#2929	C₂×C₁₃	1	1	yes	characteristic
133	#2169	C₂×C₁₃	1	2	yes	complemented
134	#2168	C₂×C₁₃	1	2	yes	complemented
135	#2168	C₂×C₁₃	1	2	yes	complemented
136	D₄×C₁₆	C₂×C₁₃	1	2	yes	complemented
137	#2164	C₂×C₁₃	1	2	yes	complemented
138	#2113	C₂×C₁₃	1	2	yes	complemented
139	#2112	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂×C₂²⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂³×C₁₃	—	2	2	no	—
142	C₂³×C₁₃	—	4	1	no	—
143	C₂³×C₁₃	—	4	1	no	—
144	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
145	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
146	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
147	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
148	Q₈×C₁₃	—	4	1	no	—
149	D₄×C₁₃	—	2	4	no	—
150	D₄×C₁₃	—	4	2	no	—
151	D₄×C₁₃	—	4	1	no	—
152	D₄×C₁₃	—	4	2	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
165	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
166	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
169	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
171	C₈×C₁₃	—	2	1	no	—
172	C₈×C₁₃	—	2	1	no	—
173	C₈×C₁₃	—	2	1	no	—
174	C₈×C₁₃	—	2	2	no	—
175	C₈×C₁₃	—	2	2	no	—
176	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
177	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
179	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
180	#525	C₄×C₁₃	1	1	yes	characteristic
181	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
183	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
184	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
185	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
186	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
187	#435	C₄×C₁₃	1	2	yes	—
188	#435	C₄×C₁₃	1	2	yes	—
189	C₈×D₄	C₂²×C₁₃	1	2	yes	—
190	C₈×D₄	C₂²×C₁₃	1	2	yes	—
191	#424	C₄×C₁₃	1	1	yes	characteristic
192	#408	C₄×C₁₃	1	1	yes	characteristic
193	#407	C₄×C₁₃	1	1	yes	characteristic
194	#405	C₂²×C₁₃	1	1	yes	characteristic
195	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
196	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
197	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
198	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
199	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
200	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
201	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
202	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
203	#346	C₂²×C₁₃	1	2	yes	complemented
204	C₄×C₁₆	C₂²×C₁₃	1	2	yes	complemented
205	C₂²×C₁₃	—	2	1	no	—
206	C₂²×C₁₃	—	2	1	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	2	1	no	—
209	C₂²×C₁₃	—	2	1	no	—
210	C₂²×C₁₃	—	2	1	no	—
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	—	2	1	no	—
213	C₂²×C₁₃	—	2	1	no	—
214	C₂²×C₁₃	—	2	1	no	—
215	C₂²×C₁₃	—	2	2	no	—
216	C₂²×C₁₃	—	4	4	no	—
217	C₂²×C₁₃	#504	1	2	yes	—
218	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	2	1	no	—
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	—	2	1	no	—
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	#518	1	1	yes	characteristic
226	C₄×C₁₃	#568	1	1	yes	characteristic
227	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
228	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
229	#131	—	4	1	no	—
230	#131	—	4	1	no	—
231	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
232	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
233	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
234	C₂²×C₈	—	4	1	no	—
235	C₂²×C₈	—	4	1	no	—
236	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
237	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
238	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
243	#123	C₈×C₁₃	1	2	yes	—
244	C₂²⋊Q₈	C₈×C₁₃	1	1	yes	characteristic
245	C₂²⋊Q₈	C₈×C₁₃	1	1	yes	characteristic
246	#121	C₈×C₁₃	1	1	yes	characteristic
247	#121	C₈×C₁₃	1	1	yes	characteristic
248	#120	C₈×C₁₃	1	2	yes	—
249	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
250	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
251	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
252	M₃₂	—	4	1	no	—
253	M₃₂	—	4	1	no	—
254	M₃₂	—	4	2	no	—
255	C₂×C₁₆	—	4	1	no	—
256	C₂×C₁₆	—	4	1	no	—
257	C₂×C₁₆	—	4	2	no	—
258	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
259	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
260	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
261	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
262	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
263	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
264	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
265	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
266	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
267	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
268	#97	C₂×C₄×C₁₃	1	2	yes	—
269	C₄×C₈	C₂³×C₁₃	1	2	yes	—
270	C₂×C₁₃	—	2	2	no	—
271	C₂×C₁₃	—	4	2	no	—
272	C₂×C₁₃	—	4	1	no	—
273	C₂×C₁₃	—	4	1	no	—
274	C₂×C₁₃	#2972	1	1	yes	characteristic
275	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
276	C₂×C₁₃	#3407	1	1	yes	characteristic
277	C₂⁴	C₂×C₈×C₁₃	1	1	yes	characteristic
278	#41	—	4	1	no	—
279	#41	—	4	1	no	—
280	C₂×Q₈	C₂×C₈×C₁₃	1	1	yes	characteristic
281	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
282	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
283	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
284	C₂×D₄	C₂×C₈×C₁₃	1	1	yes	characteristic
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
294	M₁₆	—	4	2	no	—
295	M₁₆	—	4	1	no	—
296	M₁₆	—	4	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
309	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
310	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
311	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
312	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
313	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
314	C₄⋊C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
315	C₄⋊C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
316	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
317	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
318	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
319	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
320	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
321	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
322	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
323	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
324	C₁₆	—	2	2	no	—
325	C₁₆	—	2	2	no	—
326	C₁₆	—	2	2	no	—
327	C₁₆	—	2	2	no	—
328	C₁₃	#33490	1	1	yes	characteristic, direct product factor, Sylow
329	C₂³	—	2	2	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
333	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
334	C₂³	C₂²×C₈×C₁₃	1	2	yes	—
335	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
336	Q₈	—	4	1	no	—
337	D₄	—	2	4	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	1	no	—
340	D₄	—	4	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
353	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
354	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
357	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
358	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	2	2	no	—
363	C₈	—	2	2	no	—
364	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
365	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	4	4	no	—
378	C₂²	C₁₃×#504	1	2	yes	—
379	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	C₁₃×#518	1	1	yes	characteristic
387	C₄	C₁₃×#568	1	1	yes	characteristic
388	C₂	—	2	2	no	—
389	C₂	—	4	1	no	—
390	C₂	—	4	1	no	—
391	C₂	—	4	2	no	—
392	C₂	C₁₃×#2972	1	1	yes	characteristic
393	C₂	C₂×C₁₃×#504	1	1	yes	characteristic
394	C₂	C₁₃×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂³×C₈
prime radical	C₁₃×#525	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃×#2169	C₂	semidirect
3. C₁₃×#2168	C₂	semidirect
4. C₁₃×#2168	C₂	semidirect
5. D₄×C₁₃×C₁₆	C₂	semidirect
6. C₁₃×#2164	C₂	semidirect
7. C₁₃×#2113	C₂	semidirect
8. C₁₃×#2112	C₂	semidirect
9. C₂×C₁₃×C₂²⋊C₁₆	C₂	semidirect
15. C₂×C₁₃×M₃₂	C₂²	semidirect
18. C₂²×C₁₃×C₁₆	C₂²	semidirect
27. C₁₃×C₄⋊C₁₆	C₂²	semidirect
28. C₁₃×C₄⋊C₁₆	C₂²	semidirect
33. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
34. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
35. C₁₃×#346	C₂²	semidirect
36. C₄×C₁₃×C₁₆	C₂²	semidirect
80. #33490	C₁₃	direct (N × H)
133. #2169	C₂×C₁₃	semidirect
134. #2168	C₂×C₁₃	semidirect
135. #2168	C₂×C₁₃	semidirect
136. D₄×C₁₆	C₂×C₁₃	semidirect
137. #2164	C₂×C₁₃	semidirect
138. #2113	C₂×C₁₃	semidirect
139. #2112	C₂×C₁₃	semidirect
140. C₂×C₂²⋊C₁₆	C₂×C₁₃	semidirect
183. C₂×M₃₂	C₂²×C₁₃	semidirect
186. C₂²×C₁₆	C₂²×C₁₃	semidirect
195. C₄⋊C₁₆	C₂²×C₁₃	semidirect
196. C₄⋊C₁₆	C₂²×C₁₃	semidirect
201. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
202. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
203. #346	C₂²×C₁₃	semidirect
204. C₄×C₁₆	C₂²×C₁₃	semidirect
328. C₁₃	#33490	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×#2929	2
C₁₃×#2169	2
C₁₃×#2168	2
D₄×C₁₃×C₁₆	2
C₁₃×#2164	2
C₁₃×#2113	2
C₁₃×#2112	2
C₂×C₁₃×C₂²⋊C₁₆	2
#33490	13

Subgroups — C13×#33490 #15719829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33490 #15719829