Subgroups — C₁₃×#33579 #15719918

Order 3328.

718 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#508	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2211	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2210	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2207	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2138	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#135	—	2	1	no	—
13	C₂×C₁₃×#135	C₂²	1	2	yes	—
14	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
15	C₁₃×#532	—	2	1	no	—
16	C₄×C₁₃×#41	—	2	1	no	—
17	C₁₃×#508	—	2	8	no	—
18	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
21	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
23	C₁₃×#495	—	2	1	no	—
24	C₁₃×#495	C₂²	1	2	yes	—
25	C₁₃×#494	C₂²	1	1	yes	characteristic
26	C₁₃×#493	C₂²	1	1	yes	characteristic
27	C₁₃×#492	—	2	1	no	—
28	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×SD₁₆	—	2	1	no	—
31	C₄×C₁₃×SD₁₆	—	2	1	no	—
32	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
34	C₁₃×#427	C₂²	1	1	yes	characteristic
35	C₁₃×#416	—	2	1	no	—
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
40	C₁₃×#358	C₂²	1	2	yes	—
41	C₁₃×#358	C₂²	1	2	yes	—
42	C₁₃×#357	C₂²	1	2	yes	—
43	C₁₃×#357	C₂²	1	2	yes	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×C₁₃×#41	—	2	2	no	—
46	C₁₃×#135	—	2	4	no	—
47	C₁₃×#135	—	2	2	no	—
48	C₁₃×#135	—	2	4	no	—
49	C₁₃×#135	—	4	4	no	—
50	C₁₃×#135	D₄	1	4	yes	complemented
51	C₂×C₁₃×Q₁₆	—	2	1	no	—
52	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
53	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×SD₁₆	—	2	1	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂×C₁₃×SD₁₆	—	2	2	no	—
57	C₂×C₁₃×D₈	—	2	1	no	—
58	C₂×C₁₃×D₈	C₂³	1	2	yes	—
59	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×#127	—	2	1	no	—
64	C₁₃×#124	—	2	2	no	—
65	C₁₃×#121	—	4	1	no	—
66	C₁₃×#121	—	4	1	no	—
67	C₄×Q₈×C₁₃	—	2	1	no	—
68	C₄×Q₈×C₁₃	—	2	1	no	—
69	C₄×D₄×C₁₃	—	2	1	no	—
70	C₄×D₄×C₁₃	—	2	1	no	—
71	C₄×D₄×C₁₃	—	4	1	no	—
72	C₄×D₄×C₁₃	—	4	1	no	—
73	C₄×D₄×C₁₃	—	4	1	no	—
74	C₄×D₄×C₁₃	—	4	1	no	—
75	C₁₃×#117	—	2	1	no	—
76	C₁₃×#117	—	4	1	no	—
77	C₂×C₄²×C₁₃	—	4	1	no	—
78	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
79	C₁₃×Q₃₂	—	2	4	no	—
80	C₁₃×SD₃₂	—	2	4	no	—
81	C₁₃×SD₃₂	—	2	4	no	—
82	C₁₃×D₁₆	—	2	4	no	—
83	C₂×C₁₃×C₁₆	—	2	4	no	—
84	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
85	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
86	C₁₃×#107	C₂³	1	1	yes	characteristic
87	C₁₃×#107	C₂³	1	1	yes	characteristic
88	C₁₃×#106	—	2	1	no	—
89	C₁₃×#103	—	2	1	no	—
90	C₁₃×#103	—	2	1	no	—
91	C₁₃×#102	—	2	1	no	—
92	C₁₃×#102	—	2	1	no	—
93	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
94	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
95	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	#33579	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₁₃×#41	—	2	4	no	—
99	C₁₃×#41	—	4	2	no	—
100	C₁₃×#41	—	4	4	no	—
101	C₁₃×#41	—	4	4	no	—
102	C₂×Q₈×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	4	1	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	—	4	1	no	—
109	C₂×D₄×C₁₃	—	4	1	no	—
110	C₂²×C₄×C₁₃	—	4	1	no	—
111	C₂²×C₄×C₁₃	—	4	1	no	—
112	C₂²×C₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	—	4	2	no	—
114	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₁₃×Q₁₆	—	2	2	no	—
118	C₁₃×Q₁₆	—	2	1	no	—
119	C₁₃×Q₁₆	—	2	2	no	—
120	C₁₃×Q₁₆	—	4	2	no	—
121	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
122	C₁₃×SD₁₆	—	2	4	no	—
123	C₁₃×SD₁₆	—	4	4	no	—
124	C₁₃×SD₁₆	—	4	4	no	—
125	C₁₃×D₈	—	2	2	no	—
126	C₁₃×D₈	—	2	1	no	—
127	C₁₃×D₈	—	2	2	no	—
128	C₁₃×D₈	—	4	2	no	—
129	C₁₃×D₈	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₃	#41	1	2	yes	—
136	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	4	1	no	—
140	C₁₃×C₄⋊C₄	—	4	1	no	—
141	C₁₃×C₄⋊C₄	—	4	1	no	—
142	C₁₃×C₄⋊C₄	—	4	1	no	—
143	C₁₃×C₂²⋊C₄	—	4	1	no	—
144	C₁₃×C₂²⋊C₄	—	4	1	no	—
145	C₁₃×C₂²⋊C₄	—	4	1	no	—
146	C₁₃×C₂²⋊C₄	—	4	2	no	—
147	C₁₃×C₂²⋊C₄	—	4	2	no	—
148	C₄²×C₁₃	—	4	1	no	—
149	C₄²×C₁₃	—	4	1	no	—
150	C₄²×C₁₃	—	4	1	no	—
151	C₄²×C₁₃	D₈	1	1	yes	characteristic
152	C₄²×C₁₃	D₈	1	1	yes	characteristic
153	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₁₃×C₁₆	—	2	2	no	—
156	C₁₃×C₁₆	—	2	2	no	—
157	C₂×#508	C₂×C₁₃	1	2	yes	complemented
158	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#2211	C₂×C₁₃	1	2	yes	complemented
161	#2210	C₂×C₁₃	1	2	yes	complemented
162	#2209	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#2208	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#2207	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#2206	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₂×C₄⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#2138	C₂×C₁₃	1	2	yes	complemented
168	C₂³×C₁₃	—	4	1	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
171	Q₈×C₁₃	—	2	2	no	—
172	Q₈×C₁₃	—	4	1	no	—
173	Q₈×C₁₃	—	4	2	no	—
174	Q₈×C₁₃	—	4	2	no	—
175	D₄×C₁₃	—	2	2	no	—
176	D₄×C₁₃	—	4	4	no	—
177	D₄×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	4	1	no	—
179	D₄×C₁₃	—	4	2	no	—
180	D₄×C₁₃	—	8	2	no	—
181	D₄×C₁₃	—	8	4	no	—
182	D₄×C₁₃	—	8	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	4	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	8	2	no	—
191	C₂×C₄×C₁₃	—	8	4	no	—
192	C₂×C₄×C₁₃	—	8	2	no	—
193	C₂×C₄×C₁₃	#121	1	2	yes	—
194	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
199	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₈×C₁₃	—	2	1	no	—
202	C₈×C₁₃	—	2	1	no	—
203	C₈×C₁₃	#121	1	2	yes	—
204	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₂×#135	—	2	1	no	—
207	C₂×#135	C₂²×C₁₃	1	2	yes	—
208	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
209	#532	—	2	1	no	—
210	C₄×#41	—	2	1	no	—
211	#508	—	2	8	no	—
212	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
213	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
214	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
215	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
216	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
217	#495	—	2	1	no	—
218	#495	C₂²×C₁₃	1	2	yes	—
219	#494	C₂²×C₁₃	1	1	yes	characteristic
220	#493	C₂²×C₁₃	1	1	yes	characteristic
221	#492	—	2	1	no	—
222	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
223	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
224	C₄×SD₁₆	—	2	1	no	—
225	C₄×SD₁₆	—	2	1	no	—
226	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
228	#427	C₂²×C₁₃	1	1	yes	characteristic
229	#416	—	2	1	no	—
230	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
231	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
232	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
233	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
234	#358	C₂²×C₁₃	1	2	yes	—
235	#358	C₂²×C₁₃	1	2	yes	—
236	#357	C₂²×C₁₃	1	2	yes	—
237	#357	C₂²×C₁₃	1	2	yes	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	8	1	no	—
242	C₂²×C₁₃	—	8	1	no	—
243	C₂²×C₁₃	—	8	2	no	—
244	C₂²×C₁₃	—	8	2	no	—
245	C₂²×C₁₃	—	8	2	no	—
246	C₂²×C₁₃	#459	1	2	yes	—
247	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	—	8	1	no	—
253	C₄×C₁₃	—	8	1	no	—
254	C₄×C₁₃	—	8	2	no	—
255	C₄×C₁₃	#459	1	2	yes	—
256	C₄×C₁₃	#508	1	2	yes	complemented
257	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
258	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₂×#41	—	2	1	no	—
260	C₂×#41	—	2	2	no	—
261	#135	—	2	4	no	—
262	#135	—	2	2	no	—
263	#135	—	2	4	no	—
264	#135	—	4	4	no	—
265	#135	D₄×C₁₃	1	4	yes	complemented
266	C₂×Q₁₆	—	2	1	no	—
267	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
268	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
269	C₂×SD₁₆	—	2	1	no	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×D₈	—	2	1	no	—
273	C₂×D₈	C₂³×C₁₃	1	2	yes	—
274	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₄⋊Q₈	—	2	1	no	—
278	#127	—	2	1	no	—
279	#124	—	2	2	no	—
280	#121	—	4	1	no	—
281	#121	—	4	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	4	1	no	—
287	C₄×D₄	—	4	1	no	—
288	C₄×D₄	—	4	1	no	—
289	C₄×D₄	—	4	1	no	—
290	#117	—	2	1	no	—
291	#117	—	4	1	no	—
292	C₂×C₄²	—	4	1	no	—
293	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
294	Q₃₂	—	2	4	no	—
295	SD₃₂	—	2	4	no	—
296	SD₃₂	—	2	4	no	—
297	D₁₆	—	2	4	no	—
298	C₂×C₁₆	—	2	4	no	—
299	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
300	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
301	#107	C₂³×C₁₃	1	1	yes	characteristic
302	#107	C₂³×C₁₃	1	1	yes	characteristic
303	#106	—	2	1	no	—
304	#103	—	2	1	no	—
305	#103	—	2	1	no	—
306	#102	—	2	1	no	—
307	#102	—	2	1	no	—
308	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
309	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
310	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
311	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×C₁₃	—	2	2	no	—
313	C₂×C₁₃	—	8	2	no	—
314	C₂×C₁₃	—	16	2	no	—
315	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
316	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
317	C₂×C₁₃	#3414	1	1	yes	characteristic
318	#41	—	2	4	no	—
319	#41	—	4	2	no	—
320	#41	—	4	4	no	—
321	#41	—	4	4	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
335	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	Q₁₆	—	2	2	no	—
338	Q₁₆	—	2	1	no	—
339	Q₁₆	—	2	2	no	—
340	Q₁₆	—	4	2	no	—
341	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
342	SD₁₆	—	2	4	no	—
343	SD₁₆	—	4	4	no	—
344	SD₁₆	—	4	4	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	1	no	—
347	D₈	—	2	2	no	—
348	D₈	—	4	2	no	—
349	D₈	C₂×D₄×C₁₃	1	2	yes	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
355	C₂×C₈	C₁₃×#41	1	2	yes	—
356	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₄²	—	4	1	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	1	no	—
371	C₄²	C₁₃×D₈	1	1	yes	characteristic
372	C₄²	C₁₃×D₈	1	1	yes	characteristic
373	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
374	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₁₆	—	2	2	no	—
376	C₁₆	—	2	2	no	—
377	C₁₃	#33579	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	4	1	no	—
379	C₂³	—	4	2	no	—
380	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	1	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	8	4	no	—
392	D₄	—	8	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	C₁₃×#121	1	2	yes	—
404	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
405	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
406	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
407	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
408	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
409	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
410	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	C₁₃×#121	1	2	yes	—
414	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
415	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	C₁₃×#459	1	2	yes	—
425	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₄	C₁₃×#459	1	2	yes	—
434	C₄	C₁₃×#508	1	2	yes	complemented
435	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
436	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	8	2	no	—
439	C₂	—	16	2	no	—
440	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
441	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
442	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#508	C₂	semidirect
2. C₁₃×#3147	C₂	semidirect
3. C₄×C₁₃×#135	C₂	semidirect
4. C₁₃×#2211	C₂	semidirect
5. C₁₃×#2210	C₂	semidirect
6. C₁₃×#2209	C₂	semidirect
7. C₁₃×#2208	C₂	semidirect
8. C₁₃×#2207	C₂	semidirect
9. C₁₃×#2206	C₂	semidirect
10. C₂×C₁₃×C₄⋊C₁₆	C₂	semidirect
11. C₁₃×#2138	C₂	semidirect
50. C₁₃×#135	D₄	semidirect
97. #33579	C₁₃	direct (N × H)
157. C₂×#508	C₂×C₁₃	semidirect
158. #3147	C₂×C₁₃	semidirect
159. C₄×#135	C₂×C₁₃	semidirect
160. #2211	C₂×C₁₃	semidirect
161. #2210	C₂×C₁₃	semidirect
162. #2209	C₂×C₁₃	semidirect
163. #2208	C₂×C₁₃	semidirect
164. #2207	C₂×C₁₃	semidirect
165. #2206	C₂×C₁₃	semidirect
166. C₂×C₄⋊C₁₆	C₂×C₁₃	semidirect
167. #2138	C₂×C₁₃	semidirect
256. C₄×C₁₃	#508	semidirect
265. #135	D₄×C₁₃	semidirect
377. C₁₃	#33579	direct (N × H)
434. C₄	C₁₃×#508	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#508	2
C₁₃×#3147	2
C₄×C₁₃×#135	2
C₁₃×#2211	2
C₁₃×#2210	2
C₁₃×#2209	2
C₁₃×#2208	2
C₁₃×#2207	2
C₁₃×#2206	2
C₂×C₁₃×C₄⋊C₁₆	2
C₁₃×#2138	2
#33579	13

Subgroups — C13×#33579 #15719918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33579 #15719918