Subgroups — C₁₃×#61888 #15748227

Order 3328.

1970 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3397	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3367	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3213	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3206	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3112	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3100	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
11	C₁₃×#556	—	2	4	no	—
12	C₁₃×#556	C₂²	1	8	yes	—
13	C₁₃×#550	C₂²	1	4	yes	complemented
14	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
15	C₁₃×#548	—	2	4	no	—
16	C₁₃×#537	—	2	1	no	—
17	C₁₃×#537	—	2	2	no	—
18	C₁₃×#532	C₂²	1	2	yes	—
19	C₁₃×#532	C₂²	1	4	yes	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#126	—	2	2	no	—
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#117	—	2	1	no	—
28	C₁₃×#496	C₂²	1	8	yes	—
29	C₁₃×#492	C₂²	1	4	yes	complemented
30	C₁₃×#489	C₂²	1	8	yes	—
31	C₁₃×#487	C₂²	1	4	yes	complemented
32	C₁₃×#480	C₂²	1	4	yes	—
33	C₁₃×#477	C₂²	1	8	yes	complemented
34	C₁₃×#474	C₂²	1	4	yes	—
35	C₁₃×#463	C₂²	1	16	yes	—
36	C₁₃×#461	C₂²	1	8	yes	complemented
37	C₁₃×#460	C₂²	1	8	yes	complemented
38	C₁₃×#459	C₂²	1	4	yes	—
39	C₁₃×#448	C₂²	1	8	yes	—
40	C₁₃×#447	C₂²	1	4	yes	—
41	C₁₃×#446	C₂²	1	8	yes	complemented
42	C₁₃×#440	C₂²	1	16	yes	complemented
43	C₄×C₁₃×D₈	C₂²	1	8	yes	—
44	C₁₃×#432	C₂²	1	4	yes	—
45	C₁₃×#431	C₂²	1	2	yes	—
46	C₁₃×2₋¹⁺⁴	—	4	8	no	—
47	C₂×C₁₃×#41	—	2	4	no	—
48	C₂×C₁₃×#41	—	2	4	no	—
49	C₂×C₁₃×#41	—	2	2	no	—
50	C₂²×Q₈×C₁₃	—	2	4	no	—
51	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
56	C₂×C₁₃×D₈	C₂³	1	8	yes	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
59	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
61	C₁₃×#127	C₂³	1	2	yes	—
62	C₁₃×#127	C₂³	1	4	yes	—
63	C₁₃×#126	—	2	16	no	—
64	C₁₃×#124	—	2	4	no	—
65	C₁₃×#124	—	2	2	no	—
66	C₁₃×#124	—	2	4	no	—
67	C₁₃×#124	C₂³	1	8	yes	—
68	C₁₃×C₂²⋊Q₈	—	2	8	no	—
69	C₁₃×C₂²⋊Q₈	—	2	4	no	—
70	C₁₃×C₂²⋊Q₈	—	2	8	no	—
71	C₁₃×#121	—	2	4	no	—
72	C₁₃×#121	—	2	2	no	—
73	C₁₃×#121	—	2	4	no	—
74	C₁₃×#121	—	2	8	no	—
75	C₁₃×#121	C₂³	1	4	yes	—
76	C₄×Q₈×C₁₃	—	2	4	no	—
77	C₄×Q₈×C₁₃	D₄	1	4	yes	—
78	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
79	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
80	C₄×D₄×C₁₃	—	2	2	no	—
81	C₄×D₄×C₁₃	—	2	2	no	—
82	C₄×D₄×C₁₃	—	2	4	no	—
83	C₄×D₄×C₁₃	C₂³	1	4	yes	—
84	C₄×D₄×C₁₃	C₂³	1	4	yes	—
85	C₄×D₄×C₁₃	C₂³	1	8	yes	—
86	C₁₃×#117	—	2	8	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₄²×C₁₃	—	2	2	no	—
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
99	C₁₃×#107	C₂³	1	8	yes	—
100	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
101	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
102	C₁₃×#103	C₂³	1	16	yes	—
103	C₁₃×#102	C₂³	1	8	yes	—
104	C₁₃×#102	C₂³	1	8	yes	—
105	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
106	C₁₃×#97	C₂³	1	8	yes	—
107	C₄×C₈×C₁₃	C₂³	1	4	yes	—
108	#61888	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	1	no	—
110	C₁₃×#41	—	4	16	no	—
111	C₁₃×#41	—	4	16	no	—
112	C₁₃×#41	—	4	8	no	—
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	4	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	4	4	no	—
118	C₂×Q₈×C₁₃	—	4	16	no	—
119	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
120	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
121	C₂×D₄×C₁₃	—	2	4	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	2	2	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	4	2	no	—
128	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
129	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	4	4	no	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₁₃×SD₁₆	—	4	16	no	—
142	C₁₃×D₈	—	4	8	no	—
143	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
151	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
152	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
154	C₁₃×C₂²⋊C₄	—	2	8	no	—
155	C₁₃×C₂²⋊C₄	—	2	4	no	—
156	C₁₃×C₂²⋊C₄	—	2	8	no	—
157	C₁₃×C₂²⋊C₄	—	2	4	no	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₄²×C₁₃	—	2	8	no	—
161	C₄²×C₁₃	C₂×D₄	1	2	yes	—
162	C₄²×C₁₃	C₂×D₄	1	4	yes	—
163	C₄²×C₁₃	C₂⁴	1	2	yes	—
164	C₄²×C₁₃	C₂⁴	1	4	yes	—
165	#3497	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#3397	C₂×C₁₃	1	8	yes	complemented
168	#3367	C₂×C₁₃	1	8	yes	complemented
169	#3213	C₂×C₁₃	1	4	yes	complemented
170	#3206	C₂×C₁₃	1	2	yes	complemented
171	#3112	C₂×C₁₃	1	4	yes	complemented
172	#3100	C₂×C₁₃	1	2	yes	complemented
173	#2983	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	4	no	—
176	C₂³×C₁₃	—	4	2	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	—	4	2	no	—
179	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₃	—	2	8	no	—
181	Q₈×C₁₃	—	2	8	no	—
182	Q₈×C₁₃	—	4	4	no	—
183	Q₈×C₁₃	—	4	8	no	—
184	Q₈×C₁₃	—	4	4	no	—
185	D₄×C₁₃	—	2	4	no	—
186	D₄×C₁₃	—	2	8	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	4	8	no	—
189	D₄×C₁₃	—	4	8	no	—
190	D₄×C₁₃	—	4	4	no	—
191	D₄×C₁₃	—	8	4	no	—
192	D₄×C₁₃	—	8	2	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	16	no	—
201	C₂×C₄×C₁₃	—	4	4	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	8	no	—
204	C₂×C₄×C₁₃	—	4	8	no	—
205	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
212	C₈×C₁₃	—	2	8	no	—
213	C₂×2₋¹⁺⁴	—	2	1	no	—
214	#556	—	2	4	no	—
215	#556	C₂²×C₁₃	1	8	yes	—
216	#550	C₂²×C₁₃	1	4	yes	complemented
217	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
218	#548	—	2	4	no	—
219	#537	—	2	1	no	—
220	#537	—	2	2	no	—
221	#532	C₂²×C₁₃	1	2	yes	—
222	#532	C₂²×C₁₃	1	4	yes	—
223	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#126	—	2	2	no	—
225	C₂×#124	C₂²×C₁₃	1	2	yes	—
226	C₂×C₂²⋊Q₈	—	2	1	no	—
227	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
228	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×#117	—	2	1	no	—
231	#496	C₂²×C₁₃	1	8	yes	—
232	#492	C₂²×C₁₃	1	4	yes	complemented
233	#489	C₂²×C₁₃	1	8	yes	—
234	#487	C₂²×C₁₃	1	4	yes	complemented
235	#480	C₂²×C₁₃	1	4	yes	—
236	#477	C₂²×C₁₃	1	8	yes	complemented
237	#474	C₂²×C₁₃	1	4	yes	—
238	#463	C₂²×C₁₃	1	16	yes	—
239	#461	C₂²×C₁₃	1	8	yes	complemented
240	#460	C₂²×C₁₃	1	8	yes	complemented
241	#459	C₂²×C₁₃	1	4	yes	—
242	#448	C₂²×C₁₃	1	8	yes	—
243	#447	C₂²×C₁₃	1	4	yes	—
244	#446	C₂²×C₁₃	1	8	yes	complemented
245	#440	C₂²×C₁₃	1	16	yes	complemented
246	C₄×D₈	C₂²×C₁₃	1	8	yes	—
247	#432	C₂²×C₁₃	1	4	yes	—
248	#431	C₂²×C₁₃	1	2	yes	—
249	C₂²×C₁₃	—	2	1	no	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	—	4	4	no	—
252	C₂²×C₁₃	—	4	2	no	—
253	C₂²×C₁₃	—	4	2	no	—
254	C₂²×C₁₃	—	4	4	no	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	—	8	4	no	—
258	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
259	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
260	C₄×C₁₃	—	2	4	no	—
261	C₄×C₁₃	—	2	2	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	2	4	no	—
264	C₄×C₁₃	—	4	4	no	—
265	C₄×C₁₃	—	4	2	no	—
266	C₄×C₁₃	—	4	4	no	—
267	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
268	C₄×C₁₃	#585	1	2	yes	—
269	2₋¹⁺⁴	—	4	8	no	—
270	C₂×#41	—	2	4	no	—
271	C₂×#41	—	2	4	no	—
272	C₂×#41	—	2	2	no	—
273	C₂²×Q₈	—	2	4	no	—
274	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
275	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
276	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
277	C₂³×C₄	—	2	1	no	—
278	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
279	C₂×D₈	C₂³×C₁₃	1	8	yes	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
282	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
283	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
284	#127	C₂³×C₁₃	1	2	yes	—
285	#127	C₂³×C₁₃	1	4	yes	—
286	#126	—	2	16	no	—
287	#124	—	2	4	no	—
288	#124	—	2	2	no	—
289	#124	—	2	4	no	—
290	#124	C₂³×C₁₃	1	8	yes	—
291	C₂²⋊Q₈	—	2	8	no	—
292	C₂²⋊Q₈	—	2	4	no	—
293	C₂²⋊Q₈	—	2	8	no	—
294	#121	—	2	4	no	—
295	#121	—	2	2	no	—
296	#121	—	2	4	no	—
297	#121	—	2	8	no	—
298	#121	C₂³×C₁₃	1	4	yes	—
299	C₄×Q₈	—	2	4	no	—
300	C₄×Q₈	D₄×C₁₃	1	4	yes	—
301	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
302	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	C₂³×C₁₃	1	4	yes	—
307	C₄×D₄	C₂³×C₁₃	1	4	yes	—
308	C₄×D₄	C₂³×C₁₃	1	8	yes	—
309	#117	—	2	8	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
314	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
322	#107	C₂³×C₁₃	1	8	yes	—
323	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
324	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
325	#103	C₂³×C₁₃	1	16	yes	—
326	#102	C₂³×C₁₃	1	8	yes	—
327	#102	C₂³×C₁₃	1	8	yes	—
328	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
329	#97	C₂³×C₁₃	1	8	yes	—
330	C₄×C₈	C₂³×C₁₃	1	4	yes	—
331	C₂×C₁₃	—	2	2	no	—
332	C₂×C₁₃	—	8	4	no	—
333	C₂×C₁₃	—	8	2	no	—
334	C₂×C₁₃	#3487	1	1	yes	characteristic
335	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
336	C₂×C₁₃	#3586	1	1	yes	characteristic
337	C₂⁴	—	2	1	no	—
338	#41	—	4	16	no	—
339	#41	—	4	16	no	—
340	#41	—	4	8	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	4	4	no	—
346	C₂×Q₈	—	4	16	no	—
347	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
348	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
357	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
369	SD₁₆	—	4	16	no	—
370	D₈	—	4	8	no	—
371	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
379	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
380	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
381	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₄²	—	2	8	no	—
389	C₄²	C₂×D₄×C₁₃	1	2	yes	—
390	C₄²	C₂×D₄×C₁₃	1	4	yes	—
391	C₄²	C₂⁴×C₁₃	1	2	yes	—
392	C₄²	C₂⁴×C₁₃	1	4	yes	—
393	C₁₃	#61888	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
400	Q₈	—	2	8	no	—
401	Q₈	—	2	8	no	—
402	Q₈	—	4	8	no	—
403	Q₈	—	4	4	no	—
404	Q₈	—	4	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	8	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	4	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	16	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
426	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
430	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
431	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
432	C₈	—	2	8	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	8	4	no	—
442	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
443	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
444	C₄	—	2	4	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
452	C₄	C₁₃×#585	1	2	yes	—
453	C₂	—	2	2	no	—
454	C₂	—	8	2	no	—
455	C₂	—	8	4	no	—
456	C₂	C₁₃×#3487	1	1	yes	characteristic
457	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
458	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3497	C₂	semidirect
2. C₂×C₁₃×#556	C₂	semidirect
3. C₁₃×#3397	C₂	semidirect
4. C₁₃×#3367	C₂	semidirect
5. C₁₃×#3213	C₂	semidirect
6. C₁₃×#3206	C₂	semidirect
7. C₁₃×#3112	C₂	semidirect
8. C₁₃×#3100	C₂	semidirect
9. C₁₃×#2983	C₂	semidirect
13. C₁₃×#550	C₂²	semidirect
14. D₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#492	C₂²	semidirect
31. C₁₃×#487	C₂²	semidirect
33. C₁₃×#477	C₂²	semidirect
36. C₁₃×#461	C₂²	semidirect
37. C₁₃×#460	C₂²	semidirect
41. C₁₃×#446	C₂²	semidirect
42. C₁₃×#440	C₂²	semidirect
108. #61888	C₁₃	direct (N × H)
165. #3497	C₂×C₁₃	semidirect
166. C₂×#556	C₂×C₁₃	semidirect
167. #3397	C₂×C₁₃	semidirect
168. #3367	C₂×C₁₃	semidirect
169. #3213	C₂×C₁₃	semidirect
170. #3206	C₂×C₁₃	semidirect
171. #3112	C₂×C₁₃	semidirect
172. #3100	C₂×C₁₃	semidirect
173. #2983	C₂×C₁₃	semidirect
216. #550	C₂²×C₁₃	semidirect
217. D₄×Q₈	C₂²×C₁₃	semidirect
232. #492	C₂²×C₁₃	semidirect
234. #487	C₂²×C₁₃	semidirect
236. #477	C₂²×C₁₃	semidirect
239. #461	C₂²×C₁₃	semidirect
240. #460	C₂²×C₁₃	semidirect
244. #446	C₂²×C₁₃	semidirect
245. #440	C₂²×C₁₃	semidirect
393. C₁₃	#61888	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×#3497	2
C₂×C₁₃×#556	2
C₁₃×#3397	2
C₁₃×#3367	2
C₁₃×#3213	2
C₁₃×#3206	2
C₁₃×#3112	2
C₁₃×#3100	2
C₁₃×#2983	2
#61888	13

Subgroups — C13×#61888 #15748227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61888 #15748227