Subgroups — C₁₃×#23716 #15710055

Order 3328.

816 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2089	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2078	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2063	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2051	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2018	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#100	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#442	—	2	2	no	—
17	C₁₃×#440	—	2	2	no	—
18	C₄×C₁₃×SD₁₆	—	2	2	no	—
19	C₄×C₁₃×D₈	—	2	2	no	—
20	C₄×C₁₃×D₈	—	2	2	no	—
21	C₄×C₁₃×D₈	—	2	2	no	—
22	C₁₃×#433	—	2	2	no	—
23	C₁₃×#431	—	2	2	no	—
24	C₂×C₁₃×#108	C₂²	1	2	yes	—
25	C₁₃×#428	C₂²	1	2	yes	—
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₁₃×#424	C₂²	1	1	yes	characteristic
28	C₁₃×#424	C₂²	1	1	yes	characteristic
29	C₁₃×#418	C₂²	1	2	yes	—
30	C₁₃×#417	C₂²	1	2	yes	—
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#100	C₂²	1	2	yes	—
33	C₂×C₁₃×#100	C₂²	1	2	yes	—
34	C₁₃×#408	C₂²	1	1	yes	characteristic
35	C₁₃×#408	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#343	C₂²	1	2	yes	—
40	C₁₃×#343	C₂²	1	2	yes	—
41	C₁₃×#341	C₂²	1	1	yes	characteristic
42	C₁₃×#341	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
47	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×D₈	—	2	2	no	—
50	C₂×C₁₃×D₈	—	2	4	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
55	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
59	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	—	2	1	no	—
62	C₄×D₄×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	—	2	2	no	—
64	C₄×D₄×C₁₃	—	2	2	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
67	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
68	C₁₃×#117	—	2	1	no	—
69	C₁₃×#117	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#108	—	2	4	no	—
75	C₁₃×#107	—	2	2	no	—
76	C₁₃×#107	—	2	2	no	—
77	C₁₃×#106	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×#103	—	2	2	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#102	—	2	2	no	—
84	C₁₃×#102	—	2	2	no	—
85	C₁₃×#100	—	2	4	no	—
86	C₁₃×#100	—	2	4	no	—
87	C₁₃×C₂²⋊C₈	—	2	2	no	—
88	C₁₃×C₂²⋊C₈	—	2	2	no	—
89	C₁₃×#97	—	2	1	no	—
90	C₁₃×#97	—	2	2	no	—
91	C₄×C₈×C₁₃	—	2	1	no	—
92	C₄×C₈×C₁₃	—	2	2	no	—
93	C₄×C₈×C₁₃	D₄	1	2	yes	—
94	C₄×C₈×C₁₃	D₄	1	2	yes	—
95	#23716	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₃	—	2	2	no	—
97	C₁₃×#41	—	2	2	no	—
98	C₁₃×#41	—	2	2	no	—
99	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂×D₄×C₁₃	#41	1	4	yes	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	—	4	2	no	—
114	C₂²×C₄×C₁₃	—	8	4	no	—
115	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×SD₁₆	—	2	8	no	—
119	C₁₃×D₈	—	2	8	no	—
120	C₁₃×D₈	—	2	8	no	—
121	C₁₃×M₁₆	—	2	2	no	—
122	C₁₃×M₁₆	—	2	2	no	—
123	C₁₃×M₁₆	—	2	2	no	—
124	C₁₃×M₁₆	—	2	2	no	—
125	C₁₃×M₁₆	—	2	2	no	—
126	C₁₃×M₁₆	#41	1	4	yes	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	1	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
140	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
141	C₁₃×C₂²⋊C₄	—	2	1	no	—
142	C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₁₃×C₂²⋊C₄	—	2	1	no	—
144	C₁₃×C₂²⋊C₄	—	4	2	no	—
145	C₁₃×C₂²⋊C₄	—	4	2	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
154	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2089	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2078	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2063	C₂×C₁₃	1	2	yes	complemented
159	#2051	C₂×C₁₃	1	2	yes	complemented
160	#2045	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#2018	C₂×C₁₃	1	1	yes	characteristic
162	C₄×#108	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₄×#100	C₂×C₁₃	1	2	yes	complemented
164	C₂³×C₁₃	—	2	1	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	8	2	no	—
169	C₂³×C₁₃	—	8	2	no	—
170	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
171	Q₈×C₁₃	—	2	2	no	—
172	D₄×C₁₃	—	2	4	no	—
173	D₄×C₁₃	—	2	2	no	—
174	D₄×C₁₃	—	2	4	no	—
175	D₄×C₁₃	—	4	2	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	8	4	no	—
189	C₂×C₄×C₁₃	—	8	4	no	—
190	C₂×C₄×C₁₃	—	8	2	no	—
191	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
192	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
198	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
199	C₈×C₁₃	—	2	2	no	—
200	C₈×C₁₃	—	2	4	no	—
201	C₈×C₁₃	—	2	2	no	—
202	C₈×C₁₃	—	4	1	no	—
203	C₈×C₁₃	—	4	2	no	—
204	C₈×C₁₃	—	4	1	no	—
205	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
206	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
209	#442	—	2	2	no	—
210	#440	—	2	2	no	—
211	C₄×SD₁₆	—	2	2	no	—
212	C₄×D₈	—	2	2	no	—
213	C₄×D₈	—	2	2	no	—
214	C₄×D₈	—	2	2	no	—
215	#433	—	2	2	no	—
216	#431	—	2	2	no	—
217	C₂×#108	C₂²×C₁₃	1	2	yes	—
218	#428	C₂²×C₁₃	1	2	yes	—
219	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
220	#424	C₂²×C₁₃	1	1	yes	characteristic
221	#424	C₂²×C₁₃	1	1	yes	characteristic
222	#418	C₂²×C₁₃	1	2	yes	—
223	#417	C₂²×C₁₃	1	2	yes	—
224	C₂×#102	C₂²×C₁₃	1	2	yes	—
225	C₂×#100	C₂²×C₁₃	1	2	yes	—
226	C₂×#100	C₂²×C₁₃	1	2	yes	—
227	#408	C₂²×C₁₃	1	1	yes	characteristic
228	#408	C₂²×C₁₃	1	1	yes	characteristic
229	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
230	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
231	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
232	#343	C₂²×C₁₃	1	2	yes	—
233	#343	C₂²×C₁₃	1	2	yes	—
234	#341	C₂²×C₁₃	1	1	yes	characteristic
235	#341	C₂²×C₁₃	1	1	yes	characteristic
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	4	1	no	—
239	C₂²×C₁₃	—	4	4	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	—	8	4	no	—
243	C₂²×C₁₃	—	8	4	no	—
244	C₂²×C₁₃	—	8	2	no	—
245	C₂²×C₁₃	—	8	2	no	—
246	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
247	C₂²×C₁₃	#529	1	2	yes	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	4	1	no	—
252	C₄×C₁₃	—	4	1	no	—
253	C₄×C₁₃	—	4	1	no	—
254	C₄×C₁₃	—	8	2	no	—
255	C₄×C₁₃	#472	1	2	yes	—
256	C₄×C₁₃	#525	1	1	yes	characteristic
257	C₄×C₁₃	#525	1	2	yes	—
258	C₄×C₁₃	#532	1	1	yes	characteristic
259	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
260	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
261	C₂³×C₄	—	2	2	no	—
262	AGL(1,ℤ/8)	—	2	4	no	—
263	AGL(1,ℤ/8)	—	2	4	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×D₈	—	2	2	no	—
266	C₂×D₈	—	2	4	no	—
267	C₂×D₈	—	2	2	no	—
268	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
269	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
270	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
272	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
275	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
283	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
284	#117	—	2	1	no	—
285	#117	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
290	#108	—	2	4	no	—
291	#107	—	2	2	no	—
292	#107	—	2	2	no	—
293	#106	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	#103	—	2	2	no	—
297	#102	—	2	2	no	—
298	#102	—	2	4	no	—
299	#102	—	2	2	no	—
300	#102	—	2	2	no	—
301	#100	—	2	4	no	—
302	#100	—	2	4	no	—
303	C₂²⋊C₈	—	2	2	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	#97	—	2	1	no	—
306	#97	—	2	2	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	—	2	2	no	—
309	C₄×C₈	D₄×C₁₃	1	2	yes	—
310	C₄×C₈	D₄×C₁₃	1	2	yes	—
311	C₂×C₁₃	—	2	2	no	—
312	C₂×C₁₃	—	8	1	no	—
313	C₂×C₁₃	—	8	4	no	—
314	C₂×C₁₃	#2392	1	1	yes	characteristic
315	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
316	C₂×C₁₃	#3067	1	1	yes	characteristic
317	C₂⁴	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
328	C₂×D₄	C₁₃×#41	1	4	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	8	4	no	—
336	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
337	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
339	SD₁₆	—	2	8	no	—
340	D₈	—	2	8	no	—
341	D₈	—	2	8	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	C₁₃×#41	1	4	yes	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
355	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
374	C₁₃	#23716	1	1	yes	characteristic, direct product factor, Sylow
375	C₂³	—	2	1	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	D₄	—	2	4	no	—
384	D₄	—	2	2	no	—
385	D₄	—	2	4	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	8	4	no	—
400	C₂×C₄	—	8	4	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
403	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
404	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
405	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
409	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
410	C₈	—	2	2	no	—
411	C₈	—	2	4	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	2	no	—
415	C₈	—	4	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	8	4	no	—
423	C₂²	—	8	4	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
427	C₂²	C₁₃×#529	1	2	yes	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₁₃×#472	1	2	yes	—
436	C₄	C₁₃×#525	1	1	yes	characteristic
437	C₄	C₁₃×#525	1	2	yes	—
438	C₄	C₁₃×#532	1	1	yes	characteristic
439	C₂	—	2	2	no	—
440	C₂	—	8	1	no	—
441	C₂	—	8	4	no	—
442	C₂	C₁₃×#2392	1	1	yes	characteristic
443	C₂	C₂×C₁₃×#472	1	1	yes	characteristic
444	C₂	C₁₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×#121
prime radical	C₁₃×#2018	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₄×C₁₃×D₈	C₂	semidirect
3. C₁₃×#2922	C₂	semidirect
4. C₁₃×#2089	C₂	semidirect
5. C₁₃×#2078	C₂	semidirect
6. C₁₃×#2063	C₂	semidirect
7. C₁₃×#2051	C₂	semidirect
8. C₁₃×#2045	C₂	semidirect
10. C₄×C₁₃×#108	C₂	semidirect
11. C₄×C₁₃×#100	C₂	semidirect
95. #23716	C₁₃	direct (N × H)
153. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
154. C₂×C₄×D₈	C₂×C₁₃	semidirect
155. #2922	C₂×C₁₃	semidirect
156. #2089	C₂×C₁₃	semidirect
157. #2078	C₂×C₁₃	semidirect
158. #2063	C₂×C₁₃	semidirect
159. #2051	C₂×C₁₃	semidirect
160. #2045	C₂×C₁₃	semidirect
162. C₄×#108	C₂×C₁₃	semidirect
163. C₄×#100	C₂×C₁₃	semidirect
374. C₁₃	#23716	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×AGL(1,ℤ/8)	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2922	2
C₁₃×#2089	2
C₁₃×#2078	2
C₁₃×#2063	2
C₁₃×#2051	2
C₁₃×#2045	2
C₁₃×#2018	2
C₄×C₁₃×#108	2
C₄×C₁₃×#100	2
#23716	13

Subgroups — C13×#23716 #15710055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23716 #15710055