Subgroups — C₁₃×#33533 #15719872

Order 3328.

1102 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3414	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2191	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2190	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#360	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2115	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#585	—	2	1	no	—
9	C₁₃×#578	—	2	2	no	—
10	C₁₃×#577	—	2	4	no	—
11	C₁₃×#576	—	2	2	no	—
12	C₁₃×#575	—	2	1	no	—
13	C₁₃×#575	C₂²	1	4	yes	—
14	C₂×C₁₃×#135	—	2	2	no	—
15	C₂×C₁₃×#135	C₂²	1	2	yes	—
16	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₁₃×#537	—	2	1	no	—
19	C₁₃×#510	—	2	2	no	—
20	C₁₃×#510	C₂²	1	4	yes	complemented
21	C₁₃×#509	—	2	2	no	—
22	C₁₃×#509	C₂²	1	4	yes	complemented
23	C₁₃×#508	—	2	4	no	—
24	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
25	C₁₃×#470	C₂²	1	2	yes	complemented
26	C₁₃×#469	C₂²	1	2	yes	complemented
27	C₁₃×#465	—	2	2	no	—
28	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#417	—	2	1	no	—
30	C₁₃×#360	C₂²	1	8	yes	complemented
31	C₁₃×#349	C₂²	1	4	yes	complemented
32	C₁₃×2₋¹⁺⁴	—	2	4	no	—
33	C₁₃×2₋¹⁺⁴	—	4	1	no	—
34	C₁₃×H(5,𝔽₂)	—	2	4	no	—
35	C₁₃×H(5,𝔽₂)	—	4	2	no	—
36	C₁₃×H(5,𝔽₂)	—	4	1	no	—
37	C₂×C₁₃×#41	—	2	4	no	—
38	C₂×C₁₃×#41	—	2	2	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	—	4	4	no	—
41	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
42	C₁₃×#137	—	2	4	no	—
43	C₁₃×#137	—	2	8	no	—
44	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
45	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
46	C₁₃×#135	—	2	4	no	—
47	C₁₃×#135	—	2	4	no	—
48	C₁₃×#135	—	2	2	no	—
49	C₁₃×#135	—	2	4	no	—
50	C₁₃×#135	—	2	2	no	—
51	C₁₃×#135	—	2	2	no	—
52	C₁₃×#135	—	2	2	no	—
53	C₁₃×#135	D₄	1	4	yes	complemented
54	C₁₃×#135	C₂³	1	4	yes	—
55	C₂×C₁₃×Q₁₆	—	2	2	no	—
56	C₂×C₁₃×Q₁₆	D₄	1	2	yes	complemented
57	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×SD₁₆	—	2	4	no	—
59	C₂×C₁₃×SD₁₆	—	2	2	no	—
60	C₂×C₁₃×SD₁₆	—	2	1	no	—
61	C₂×C₁₃×D₈	—	2	2	no	—
62	C₂×C₁₃×D₈	D₄	1	2	yes	complemented
63	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
64	C₁₃×#131	—	2	2	no	—
65	C₁₃×#131	—	2	2	no	—
66	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₃	D₄	1	2	yes	—
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×C₂²⋊Q₈	—	2	2	no	—
71	C₁₃×C₂²⋊Q₈	—	4	1	no	—
72	C₁₃×#121	—	2	2	no	—
73	C₁₃×#121	—	4	1	no	—
74	C₁₃×#121	—	4	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₁₃×Q₃₂	—	2	4	no	—
77	C₁₃×SD₃₂	—	2	4	no	—
78	C₁₃×SD₃₂	—	2	4	no	—
79	C₁₃×D₁₆	—	2	4	no	—
80	C₁₃×M₃₂	—	2	2	no	—
81	C₁₃×M₃₂	C₂³	1	4	yes	—
82	C₂×C₁₃×C₁₆	—	2	2	no	—
83	C₁₃×#106	—	2	1	no	—
84	C₁₃×#106	C₂³	1	2	yes	—
85	C₁₃×#103	—	2	2	no	—
86	C₁₃×#102	—	2	2	no	—
87	#33533	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₁₃×#41	—	2	2	no	—
89	C₁₃×#41	—	2	2	no	—
90	C₁₃×#41	—	2	8	no	—
91	C₁₃×#41	—	2	4	no	—
92	C₁₃×#41	—	2	4	no	—
93	C₁₃×#41	—	4	4	no	—
94	C₁₃×#41	—	4	8	no	—
95	C₁₃×#41	—	4	4	no	—
96	C₁₃×#41	—	4	4	no	—
97	C₁₃×#41	—	4	4	no	—
98	C₁₃×#41	—	4	2	no	—
99	C₁₃×#41	—	4	2	no	—
100	C₁₃×#41	—	4	2	no	—
101	C₁₃×#41	—	4	2	no	—
102	C₂×Q₈×C₁₃	—	2	4	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	4	4	no	—
106	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
107	C₂×D₄×C₁₃	—	2	4	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	—	4	8	no	—
111	C₂×D₄×C₁₃	—	4	4	no	—
112	C₂×D₄×C₁₃	—	4	4	no	—
113	C₂×D₄×C₁₃	—	4	2	no	—
114	C₂×D₄×C₁₃	—	4	1	no	—
115	C₂×D₄×C₁₃	—	4	2	no	—
116	C₂×D₄×C₁₃	D₈	1	2	yes	—
117	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	—	4	4	no	—
119	C₂²×C₄×C₁₃	—	4	2	no	—
120	C₂²×C₄×C₁₃	—	4	1	no	—
121	C₂²×C₄×C₁₃	—	4	1	no	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₁₃×Q₁₆	—	2	4	no	—
125	C₁₃×Q₁₆	—	2	2	no	—
126	C₁₃×Q₁₆	—	2	2	no	—
127	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
128	C₁₃×SD₁₆	—	2	8	no	—
129	C₁₃×SD₁₆	—	2	4	no	—
130	C₁₃×SD₁₆	—	2	4	no	—
131	C₁₃×SD₁₆	—	4	1	no	—
132	C₁₃×SD₁₆	—	4	1	no	—
133	C₁₃×D₈	—	2	4	no	—
134	C₁₃×D₈	—	2	2	no	—
135	C₁₃×D₈	—	2	2	no	—
136	C₁₃×D₈	C₂×D₄	1	4	yes	—
137	C₁₃×M₁₆	—	2	2	no	—
138	C₁₃×M₁₆	—	2	4	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	4	1	no	—
148	C₁₃×C₄⋊C₄	—	4	2	no	—
149	C₁₃×C₂²⋊C₄	—	4	2	no	—
150	C₁₃×C₂²⋊C₄	—	4	2	no	—
151	C₁₃×C₁₆	—	2	4	no	—
152	#3584	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#3414	C₂×C₁₃	1	2	yes	complemented
154	#3060	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2191	C₂×C₁₃	1	4	yes	complemented
156	#2190	C₂×C₁₃	1	4	yes	complemented
157	C₂×#360	C₂×C₁₃	1	2	yes	complemented
158	#2115	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₂³×C₁₃	—	4	4	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	C₂×D₈	1	2	yes	—
163	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
164	Q₈×C₁₃	—	2	2	no	—
165	Q₈×C₁₃	—	2	4	no	—
166	Q₈×C₁₃	—	4	4	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	4	1	no	—
169	Q₈×C₁₃	—	4	1	no	—
170	D₄×C₁₃	—	2	4	no	—
171	D₄×C₁₃	—	2	4	no	—
172	D₄×C₁₃	—	2	2	no	—
173	D₄×C₁₃	—	4	4	no	—
174	D₄×C₁₃	—	4	8	no	—
175	D₄×C₁₃	—	4	4	no	—
176	D₄×C₁₃	—	4	4	no	—
177	D₄×C₁₃	—	4	1	no	—
178	D₄×C₁₃	—	4	1	no	—
179	D₄×C₁₃	—	4	2	no	—
180	D₄×C₁₃	—	8	2	no	—
181	D₄×C₁₃	—	16	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	4	8	no	—
185	C₂×C₄×C₁₃	—	4	4	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	4	no	—
188	C₂×C₄×C₁₃	—	4	4	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	8	2	no	—
192	C₂×C₄×C₁₃	—	16	1	no	—
193	C₂×C₄×C₁₃	#120	1	2	yes	—
194	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
195	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₈×C₁₃	—	2	2	no	—
199	C₈×C₁₃	#120	1	1	yes	characteristic
200	C₈×C₁₃	#120	1	1	yes	characteristic
201	C₈×C₁₃	C₂²×D₄	1	2	yes	—
202	#585	—	2	1	no	—
203	#578	—	2	2	no	—
204	#577	—	2	4	no	—
205	#576	—	2	2	no	—
206	#575	—	2	1	no	—
207	#575	C₂²×C₁₃	1	4	yes	—
208	C₂×#135	—	2	2	no	—
209	C₂×#135	C₂²×C₁₃	1	2	yes	—
210	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
211	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
212	#537	—	2	1	no	—
213	#510	—	2	2	no	—
214	#510	C₂²×C₁₃	1	4	yes	complemented
215	#509	—	2	2	no	—
216	#509	C₂²×C₁₃	1	4	yes	complemented
217	#508	—	2	4	no	—
218	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
219	#470	C₂²×C₁₃	1	2	yes	complemented
220	#469	C₂²×C₁₃	1	2	yes	complemented
221	#465	—	2	2	no	—
222	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
223	#417	—	2	1	no	—
224	#360	C₂²×C₁₃	1	8	yes	complemented
225	#349	C₂²×C₁₃	1	4	yes	complemented
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	4	1	no	—
228	C₂²×C₁₃	—	4	2	no	—
229	C₂²×C₁₃	—	4	4	no	—
230	C₂²×C₁₃	—	8	1	no	—
231	C₂²×C₁₃	—	8	1	no	—
232	C₂²×C₁₃	—	8	1	no	—
233	C₂²×C₁₃	—	16	2	no	—
234	C₂²×C₁₃	—	16	4	no	—
235	C₂²×C₁₃	#447	1	2	yes	—
236	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	4	4	no	—
239	C₄×C₁₃	—	8	2	no	—
240	C₄×C₁₃	—	8	1	no	—
241	C₄×C₁₃	#447	1	2	yes	—
242	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
243	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
244	2₋¹⁺⁴	—	2	4	no	—
245	2₋¹⁺⁴	—	4	1	no	—
246	H(5,𝔽₂)	—	2	4	no	—
247	H(5,𝔽₂)	—	4	2	no	—
248	H(5,𝔽₂)	—	4	1	no	—
249	C₂×#41	—	2	4	no	—
250	C₂×#41	—	2	2	no	—
251	C₂×#41	—	2	1	no	—
252	C₂×#41	—	4	4	no	—
253	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
254	#137	—	2	4	no	—
255	#137	—	2	8	no	—
256	AGL(1,ℤ/8)	—	2	4	no	—
257	AGL(1,ℤ/8)	—	2	8	no	—
258	#135	—	2	4	no	—
259	#135	—	2	4	no	—
260	#135	—	2	2	no	—
261	#135	—	2	4	no	—
262	#135	—	2	2	no	—
263	#135	—	2	2	no	—
264	#135	—	2	2	no	—
265	#135	D₄×C₁₃	1	4	yes	complemented
266	#135	C₂³×C₁₃	1	4	yes	—
267	C₂×Q₁₆	—	2	2	no	—
268	C₂×Q₁₆	D₄×C₁₃	1	2	yes	complemented
269	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
270	C₂×SD₁₆	—	2	4	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	2	1	no	—
273	C₂×D₈	—	2	2	no	—
274	C₂×D₈	D₄×C₁₃	1	2	yes	complemented
275	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
276	#131	—	2	2	no	—
277	#131	—	2	2	no	—
278	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
279	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
280	C₂²×C₈	D₄×C₁₃	1	2	yes	—
281	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₂²⋊Q₈	—	2	2	no	—
283	C₂²⋊Q₈	—	4	1	no	—
284	#121	—	2	2	no	—
285	#121	—	4	1	no	—
286	#121	—	4	2	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	Q₃₂	—	2	4	no	—
289	SD₃₂	—	2	4	no	—
290	SD₃₂	—	2	4	no	—
291	D₁₆	—	2	4	no	—
292	M₃₂	—	2	2	no	—
293	M₃₂	C₂³×C₁₃	1	4	yes	—
294	C₂×C₁₆	—	2	2	no	—
295	#106	—	2	1	no	—
296	#106	C₂³×C₁₃	1	2	yes	—
297	#103	—	2	2	no	—
298	#102	—	2	2	no	—
299	C₂×C₁₃	—	2	1	no	—
300	C₂×C₁₃	—	2	2	no	—
301	C₂×C₁₃	—	4	2	no	—
302	C₂×C₁₃	—	8	4	no	—
303	C₂×C₁₃	—	16	1	no	—
304	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
305	#41	—	2	2	no	—
306	#41	—	2	2	no	—
307	#41	—	2	8	no	—
308	#41	—	2	4	no	—
309	#41	—	2	4	no	—
310	#41	—	4	4	no	—
311	#41	—	4	8	no	—
312	#41	—	4	4	no	—
313	#41	—	4	4	no	—
314	#41	—	4	4	no	—
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	4	4	no	—
323	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	4	8	no	—
328	C₂×D₄	—	4	4	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	C₁₃×D₈	1	2	yes	—
334	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	Q₁₆	—	2	4	no	—
342	Q₁₆	—	2	2	no	—
343	Q₁₆	—	2	2	no	—
344	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
345	SD₁₆	—	2	8	no	—
346	SD₁₆	—	2	4	no	—
347	SD₁₆	—	2	4	no	—
348	SD₁₆	—	4	1	no	—
349	SD₁₆	—	4	1	no	—
350	D₈	—	2	4	no	—
351	D₈	—	2	2	no	—
352	D₈	—	2	2	no	—
353	D₈	C₂×D₄×C₁₃	1	4	yes	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	4	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
362	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	1	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₁₆	—	2	4	no	—
369	C₁₃	#33533	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	—	4	4	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	C₂×C₁₃×D₈	1	2	yes	—
374	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	2	4	no	—
377	Q₈	—	4	4	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	D₄	—	2	4	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	4	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	8	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	1	no	—
390	D₄	—	4	1	no	—
391	D₄	—	8	2	no	—
392	D₄	—	16	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	—	16	1	no	—
404	C₂×C₄	C₁₃×#120	1	2	yes	—
405	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
406	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
407	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	C₁₃×#120	1	1	yes	characteristic
411	C₈	C₁₃×#120	1	1	yes	characteristic
412	C₈	C₂²×D₄×C₁₃	1	2	yes	—
413	C₂²	—	2	2	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	16	2	no	—
421	C₂²	—	16	4	no	—
422	C₂²	C₁₃×#447	1	2	yes	—
423	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	8	2	no	—
427	C₄	—	8	1	no	—
428	C₄	C₁₃×#447	1	2	yes	—
429	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
430	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
431	C₂	—	2	1	no	—
432	C₂	—	2	2	no	—
433	C₂	—	4	2	no	—
434	C₂	—	8	4	no	—
435	C₂	—	16	1	no	—
436	C₂	C₂×C₁₃×#447	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3584	C₂	semidirect
2. C₁₃×#3414	C₂	semidirect
3. C₁₃×#3060	C₂	semidirect
4. C₁₃×#2191	C₂	semidirect
5. C₁₃×#2190	C₂	semidirect
6. C₂×C₁₃×#360	C₂	semidirect
7. C₁₃×#2115	C₂	semidirect
16. C₂×C₁₃×#135	C₂²	semidirect
20. C₁₃×#510	C₂²	semidirect
22. C₁₃×#509	C₂²	semidirect
24. C₂×C₁₃×M₃₂	C₂²	semidirect
25. C₁₃×#470	C₂²	semidirect
26. C₁₃×#469	C₂²	semidirect
28. C₂×C₁₃×#106	C₂²	semidirect
30. C₁₃×#360	C₂²	semidirect
31. C₁₃×#349	C₂²	semidirect
53. C₁₃×#135	D₄	semidirect
56. C₂×C₁₃×Q₁₆	D₄	semidirect
62. C₂×C₁₃×D₈	D₄	semidirect
87. #33533	C₁₃	direct (N × H)
152. #3584	C₂×C₁₃	semidirect
153. #3414	C₂×C₁₃	semidirect
154. #3060	C₂×C₁₃	semidirect
155. #2191	C₂×C₁₃	semidirect
156. #2190	C₂×C₁₃	semidirect
157. C₂×#360	C₂×C₁₃	semidirect
158. #2115	C₂×C₁₃	semidirect
210. C₂×#135	C₂²×C₁₃	semidirect
214. #510	C₂²×C₁₃	semidirect
216. #509	C₂²×C₁₃	semidirect
218. C₂×M₃₂	C₂²×C₁₃	semidirect
219. #470	C₂²×C₁₃	semidirect
220. #469	C₂²×C₁₃	semidirect
222. C₂×#106	C₂²×C₁₃	semidirect
224. #360	C₂²×C₁₃	semidirect
225. #349	C₂²×C₁₃	semidirect
265. #135	D₄×C₁₃	semidirect
268. C₂×Q₁₆	D₄×C₁₃	semidirect
274. C₂×D₈	D₄×C₁₃	semidirect
369. C₁₃	#33533	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×#3584	2
C₁₃×#3414	2
C₁₃×#3060	2
C₁₃×#2191	2
C₁₃×#2190	2
C₂×C₁₃×#360	2
C₁₃×#2115	2
#33533	13

Subgroups — C13×#33533 #15719872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33533 #15719872