Subgroups — C₁₃×#33522 #15719861

Order 3328.

1170 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2186	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2184	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2140	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
11	C₁₃×#576	—	2	4	no	—
12	C₁₃×#576	—	2	4	no	—
13	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
14	C₂×C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
15	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
21	C₁₃×#535	—	2	1	no	—
22	C₁₃×#509	—	2	4	no	—
23	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
24	C₂×C₁₃×D₁₆	—	2	4	no	—
25	C₂×C₁₃×D₁₆	C₂²	1	4	yes	complemented
26	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
27	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#469	—	2	2	no	—
30	C₁₃×#466	C₂²	1	4	yes	complemented
31	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#418	—	2	1	no	—
33	C₁₃×#358	C₂²	1	2	yes	complemented
34	C₁₃×#357	C₂²	1	2	yes	complemented
35	C₁₃×#357	C₂²	1	4	yes	complemented
36	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
37	C₁₃×H(5,𝔽₂)	—	2	8	no	—
38	C₁₃×H(5,𝔽₂)	—	4	4	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	—	2	2	no	—
41	C₂×C₁₃×#41	—	4	1	no	—
42	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	—	4	2	no	—
47	C₂²×D₄×C₁₃	—	4	1	no	—
48	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
49	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
50	C₁₃×#135	—	2	4	no	—
51	C₁₃×#135	—	2	4	no	—
52	C₁₃×#135	—	2	2	no	—
53	C₁₃×#135	D₄	1	4	yes	complemented
54	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×SD₁₆	—	2	1	no	—
56	C₂×C₁₃×SD₁₆	—	2	2	no	—
57	C₂×C₁₃×D₈	—	2	4	no	—
58	C₂×C₁₃×D₈	—	2	4	no	—
59	C₂×C₁₃×D₈	—	2	1	no	—
60	C₂×C₁₃×D₈	—	2	2	no	—
61	C₂×C₁₃×D₈	—	2	2	no	—
62	C₂×C₁₃×D₈	—	2	2	no	—
63	C₂×C₁₃×D₈	—	2	2	no	—
64	C₂×C₁₃×D₈	—	2	1	no	—
65	C₂×C₁₃×D₈	D₄	1	4	yes	complemented
66	C₂×C₁₃×D₈	C₂³	1	2	yes	—
67	C₂×C₁₃×D₈	C₂³	1	2	yes	—
68	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
69	C₁₃×#131	—	2	2	no	—
70	C₁₃×#131	—	2	2	no	—
71	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
72	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
73	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#127	—	4	1	no	—
76	C₁₃×#124	—	4	1	no	—
77	C₁₃×#121	—	2	4	no	—
78	C₁₃×#120	—	4	2	no	—
79	C₁₃×#117	—	2	1	no	—
80	C₁₃×SD₃₂	—	2	4	no	—
81	C₁₃×D₁₆	—	2	8	no	—
82	C₁₃×D₁₆	—	2	4	no	—
83	C₁₃×M₃₂	—	2	2	no	—
84	C₂×C₁₃×C₁₆	—	2	2	no	—
85	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
86	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
87	C₁₃×#107	C₂³	1	2	yes	—
88	C₁₃×#106	—	2	1	no	—
89	C₁₃×#102	—	2	4	no	—
90	#33522	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	—	4	2	no	—
92	C₂⁴×C₁₃	—	4	1	no	—
93	C₂⁴×C₁₃	—	4	1	no	—
94	C₁₃×#41	—	2	2	no	—
95	C₁₃×#41	—	2	2	no	—
96	C₁₃×#41	—	2	8	no	—
97	C₁₃×#41	—	2	4	no	—
98	C₁₃×#41	—	4	4	no	—
99	C₁₃×#41	—	4	8	no	—
100	C₁₃×#41	—	4	2	no	—
101	C₂×Q₈×C₁₃	—	2	1	no	—
102	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
103	C₂×D₄×C₁₃	—	2	8	no	—
104	C₂×D₄×C₁₃	—	2	4	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	4	4	no	—
109	C₂×D₄×C₁₃	—	4	16	no	—
110	C₂×D₄×C₁₃	—	4	8	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	—	4	1	no	—
113	C₂×D₄×C₁₃	—	4	4	no	—
114	C₂×D₄×C₁₃	—	4	2	no	—
115	C₂×D₄×C₁₃	—	4	2	no	—
116	C₂×D₄×C₁₃	—	4	1	no	—
117	C₂×D₄×C₁₃	—	4	1	no	—
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	—	4	2	no	—
120	C₂×D₄×C₁₃	D₈	1	2	yes	—
121	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	—	4	1	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₁₃×Q₁₆	—	2	1	no	—
127	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
128	C₁₃×SD₁₆	—	2	8	no	—
129	C₁₃×SD₁₆	—	2	4	no	—
130	C₁₃×D₈	—	2	8	no	—
131	C₁₃×D₈	—	2	4	no	—
132	C₁₃×D₈	—	2	2	no	—
133	C₁₃×D₈	—	2	1	no	—
134	C₁₃×D₈	—	2	2	no	—
135	C₁₃×D₈	—	2	2	no	—
136	C₁₃×D₈	—	4	2	no	—
137	C₁₃×D₈	C₂×D₄	1	2	yes	—
138	C₁₃×D₈	C₂×D₄	1	4	yes	—
139	C₁₃×M₁₆	—	2	2	no	—
140	C₁₃×M₁₆	—	2	4	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₂²⋊C₄	—	4	1	no	—
150	C₁₃×C₂²⋊C₄	—	4	4	no	—
151	C₄²×C₁₃	—	4	1	no	—
152	C₁₃×C₁₆	—	2	2	no	—
153	C₁₃×C₁₆	—	2	2	no	—
154	C₂×#576	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂²×D₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#3058	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2186	C₂×C₁₃	1	4	yes	complemented
159	#2184	C₂×C₁₃	1	4	yes	complemented
160	#2140	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#2138	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#2113	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	4	8	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	—	4	4	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	8	2	no	—
169	C₂³×C₁₃	—	16	2	no	—
170	C₂³×C₁₃	—	16	2	no	—
171	C₂³×C₁₃	—	16	4	no	—
172	C₂³×C₁₃	C₂×D₈	1	2	yes	—
173	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
174	Q₈×C₁₃	—	2	2	no	—
175	Q₈×C₁₃	—	2	2	no	—
176	Q₈×C₁₃	—	4	1	no	—
177	D₄×C₁₃	—	2	4	no	—
178	D₄×C₁₃	—	2	2	no	—
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	2	2	no	—
181	D₄×C₁₃	—	4	8	no	—
182	D₄×C₁₃	—	4	8	no	—
183	D₄×C₁₃	—	4	4	no	—
184	D₄×C₁₃	—	4	2	no	—
185	D₄×C₁₃	—	4	1	no	—
186	D₄×C₁₃	—	4	2	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	4	4	no	—
189	D₄×C₁₃	—	8	2	no	—
190	D₄×C₁₃	—	16	4	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	4	8	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	4	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	#120	1	2	yes	—
198	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
199	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
200	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	#120	1	2	yes	—
204	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×H(5,𝔽₂)	—	2	1	no	—
207	#576	—	2	4	no	—
208	#576	—	2	4	no	—
209	C₂×AGL(1,ℤ/8)	—	2	1	no	—
210	C₂×AGL(1,ℤ/8)	—	2	2	no	—
211	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
213	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
215	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
216	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
217	#535	—	2	1	no	—
218	#509	—	2	4	no	—
219	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
220	C₂×D₁₆	—	2	4	no	—
221	C₂×D₁₆	C₂²×C₁₃	1	4	yes	complemented
222	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
223	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
224	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
225	#469	—	2	2	no	—
226	#466	C₂²×C₁₃	1	4	yes	complemented
227	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
228	#418	—	2	1	no	—
229	#358	C₂²×C₁₃	1	2	yes	complemented
230	#357	C₂²×C₁₃	1	2	yes	complemented
231	#357	C₂²×C₁₃	1	4	yes	complemented
232	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
233	C₂²×C₁₃	—	2	2	no	—
234	C₂²×C₁₃	—	2	4	no	—
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	4	4	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	—	8	4	no	—
239	C₂²×C₁₃	—	8	2	no	—
240	C₂²×C₁₃	—	8	4	no	—
241	C₂²×C₁₃	—	8	2	no	—
242	C₂²×C₁₃	—	16	4	no	—
243	C₂²×C₁₃	—	16	4	no	—
244	C₂²×C₁₃	—	16	8	no	—
245	C₂²×C₁₃	#447	1	2	yes	—
246	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	8	2	no	—
250	C₄×C₁₃	#447	1	2	yes	—
251	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
252	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	H(5,𝔽₂)	—	2	8	no	—
254	H(5,𝔽₂)	—	4	4	no	—
255	C₂×#41	—	2	1	no	—
256	C₂×#41	—	2	2	no	—
257	C₂×#41	—	4	1	no	—
258	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	2	no	—
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	4	2	no	—
263	C₂²×D₄	—	4	1	no	—
264	AGL(1,ℤ/8)	—	2	8	no	—
265	AGL(1,ℤ/8)	—	2	16	no	—
266	#135	—	2	4	no	—
267	#135	—	2	4	no	—
268	#135	—	2	2	no	—
269	#135	D₄×C₁₃	1	4	yes	complemented
270	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×SD₁₆	—	2	1	no	—
272	C₂×SD₁₆	—	2	2	no	—
273	C₂×D₈	—	2	4	no	—
274	C₂×D₈	—	2	4	no	—
275	C₂×D₈	—	2	1	no	—
276	C₂×D₈	—	2	2	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×D₈	—	2	2	no	—
279	C₂×D₈	—	2	2	no	—
280	C₂×D₈	—	2	1	no	—
281	C₂×D₈	D₄×C₁₃	1	4	yes	complemented
282	C₂×D₈	C₂³×C₁₃	1	2	yes	—
283	C₂×D₈	C₂³×C₁₃	1	2	yes	—
284	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
285	#131	—	2	2	no	—
286	#131	—	2	2	no	—
287	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
288	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
289	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
290	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
291	#127	—	4	1	no	—
292	#124	—	4	1	no	—
293	#121	—	2	4	no	—
294	#120	—	4	2	no	—
295	#117	—	2	1	no	—
296	SD₃₂	—	2	4	no	—
297	D₁₆	—	2	8	no	—
298	D₁₆	—	2	4	no	—
299	M₃₂	—	2	2	no	—
300	C₂×C₁₆	—	2	2	no	—
301	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
302	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
303	#107	C₂³×C₁₃	1	2	yes	—
304	#106	—	2	1	no	—
305	#102	—	2	4	no	—
306	C₂×C₁₃	—	2	2	no	—
307	C₂×C₁₃	—	4	2	no	—
308	C₂×C₁₃	—	8	4	no	—
309	C₂×C₁₃	—	8	2	no	—
310	C₂×C₁₃	—	16	2	no	—
311	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
312	C₂×C₁₃	#3415	1	2	yes	—
313	C₂⁴	—	4	2	no	—
314	C₂⁴	—	4	1	no	—
315	C₂⁴	—	4	1	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	—	2	8	no	—
319	#41	—	2	4	no	—
320	#41	—	4	4	no	—
321	#41	—	4	8	no	—
322	#41	—	4	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
325	C₂×D₄	—	2	8	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	—	4	16	no	—
332	C₂×D₄	—	4	8	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	4	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	C₁₃×D₈	1	2	yes	—
343	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	Q₁₆	—	2	1	no	—
349	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
350	SD₁₆	—	2	8	no	—
351	SD₁₆	—	2	4	no	—
352	D₈	—	2	8	no	—
353	D₈	—	2	4	no	—
354	D₈	—	2	2	no	—
355	D₈	—	2	1	no	—
356	D₈	—	2	2	no	—
357	D₈	—	2	2	no	—
358	D₈	—	4	2	no	—
359	D₈	C₂×D₄×C₁₃	1	2	yes	—
360	D₈	C₂×D₄×C₁₃	1	4	yes	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	4	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
366	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
368	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
369	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
370	C₄⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	4	1	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₄²	—	4	1	no	—
374	C₁₆	—	2	2	no	—
375	C₁₆	—	2	2	no	—
376	C₁₃	#33522	1	1	yes	characteristic, direct product factor, Sylow
377	C₂³	—	4	8	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	4	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	8	2	no	—
383	C₂³	—	16	2	no	—
384	C₂³	—	16	2	no	—
385	C₂³	—	16	4	no	—
386	C₂³	C₂×C₁₃×D₈	1	2	yes	—
387	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	4	1	no	—
391	D₄	—	2	4	no	—
392	D₄	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	4	no	—
395	D₄	—	4	8	no	—
396	D₄	—	4	8	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	4	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	1	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	8	2	no	—
404	D₄	—	16	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	C₁₃×#120	1	2	yes	—
412	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
413	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
414	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	C₁₃×#120	1	2	yes	—
418	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
420	C₂²	—	2	2	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	8	4	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	4	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	16	4	no	—
430	C₂²	—	16	4	no	—
431	C₂²	—	16	8	no	—
432	C₂²	C₁₃×#447	1	2	yes	—
433	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	2	no	—
437	C₄	C₁₃×#447	1	2	yes	—
438	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
439	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₂	—	2	2	no	—
441	C₂	—	4	2	no	—
442	C₂	—	8	4	no	—
443	C₂	—	8	2	no	—
444	C₂	—	16	2	no	—
445	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
446	C₂	C₁₃×#3415	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#41 ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#576	C₂	semidirect
2. C₂×C₁₃×#509	C₂	semidirect
3. C₂²×C₁₃×D₁₆	C₂	semidirect
4. C₁₃×#3058	C₂	semidirect
5. C₁₃×#2186	C₂	semidirect
6. C₁₃×#2184	C₂	semidirect
7. C₁₃×#2140	C₂	semidirect
8. C₁₃×#2138	C₂	semidirect
9. C₁₃×#2113	C₂	semidirect
16. C₂×C₁₃×#135	C₂²	semidirect
18. C₂²×C₁₃×D₈	C₂²	semidirect
19. C₂²×C₁₃×D₈	C₂²	semidirect
23. C₂×C₁₃×SD₃₂	C₂²	semidirect
25. C₂×C₁₃×D₁₆	C₂²	semidirect
26. C₂×C₁₃×D₁₆	C₂²	semidirect
27. C₂×C₁₃×M₃₂	C₂²	semidirect
28. C₂²×C₁₃×C₁₆	C₂²	semidirect
30. C₁₃×#466	C₂²	semidirect
31. C₁₃×#427	C₂²	semidirect
33. C₁₃×#358	C₂²	semidirect
34. C₁₃×#357	C₂²	semidirect
35. C₁₃×#357	C₂²	semidirect
36. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
53. C₁₃×#135	D₄	semidirect
65. C₂×C₁₃×D₈	D₄	semidirect
90. #33522	C₁₃	direct (N × H)
154. C₂×#576	C₂×C₁₃	semidirect
155. C₂×#509	C₂×C₁₃	semidirect
156. C₂²×D₁₆	C₂×C₁₃	semidirect
157. #3058	C₂×C₁₃	semidirect
158. #2186	C₂×C₁₃	semidirect
159. #2184	C₂×C₁₃	semidirect
160. #2140	C₂×C₁₃	semidirect
161. #2138	C₂×C₁₃	semidirect
162. #2113	C₂×C₁₃	semidirect
212. C₂×#135	C₂²×C₁₃	semidirect
214. C₂²×D₈	C₂²×C₁₃	semidirect
215. C₂²×D₈	C₂²×C₁₃	semidirect
219. C₂×SD₃₂	C₂²×C₁₃	semidirect
221. C₂×D₁₆	C₂²×C₁₃	semidirect
222. C₂×D₁₆	C₂²×C₁₃	semidirect
223. C₂×M₃₂	C₂²×C₁₃	semidirect
224. C₂²×C₁₆	C₂²×C₁₃	semidirect
226. #466	C₂²×C₁₃	semidirect
227. #427	C₂²×C₁₃	semidirect
229. #358	C₂²×C₁₃	semidirect
230. #357	C₂²×C₁₃	semidirect
231. #357	C₂²×C₁₃	semidirect
232. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
269. #135	D₄×C₁₃	semidirect
281. C₂×D₈	D₄×C₁₃	semidirect
376. C₁₃	#33522	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#576	2
C₂×C₁₃×#509	2
C₂²×C₁₃×D₁₆	2
C₁₃×#3058	2
C₁₃×#2186	2
C₁₃×#2184	2
C₁₃×#2140	2
C₁₃×#2138	2
C₁₃×#2113	2
#33522	13

Subgroups — C13×#33522 #15719861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33522 #15719861