Subgroups — C₁₃×#61404 #15747743

Order 3328.

1900 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	6	yes	maximal, complemented
4	C₁₃×#3398	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3395	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3392	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3152	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3039	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3037	C₂	1	3	yes	maximal, complemented
10	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#137	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₃×#137	C₂²	1	3	yes	—
13	C₂×C₁₃×#137	C₂²	1	6	yes	—
14	C₁₃×#559	C₂²	1	3	yes	—
15	C₁₃×#557	—	2	1	no	—
16	C₁₃×#557	—	2	3	no	—
17	C₁₃×#557	C₂²	1	2	yes	—
18	C₁₃×#557	C₂²	1	1	yes	characteristic
19	C₁₃×#557	C₂²	1	6	yes	—
20	C₁₃×#556	C₂²	1	3	yes	—
21	C₁₃×#553	—	2	3	no	—
22	C₁₃×#550	C₂²	1	1	yes	characteristic
23	C₁₃×#548	—	2	1	no	—
24	C₁₃×#532	C₂²	1	3	yes	—
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
26	C₁₃×#529	—	2	3	no	—
27	C₂×C₁₃×#125	—	2	3	no	—
28	C₄×C₁₃×#41	—	2	1	no	—
29	C₄×C₁₃×#41	C₂²	1	3	yes	—
30	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#497	C₂²	1	12	yes	—
34	C₁₃×#494	C₂²	1	6	yes	—
35	C₁₃×#492	C₂²	1	6	yes	—
36	C₁₃×#464	C₂²	1	12	yes	—
37	C₁₃×#462	C₂²	1	6	yes	—
38	C₁₃×#462	C₂²	1	6	yes	—
39	C₁₃×#462	C₂²	1	6	yes	—
40	C₁₃×#461	C₂²	1	6	yes	—
41	C₁₃×#461	C₂²	1	6	yes	—
42	C₁₃×#460	C₂²	1	6	yes	—
43	C₁₃×#446	C₂²	1	6	yes	—
44	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
45	C₁₃×#441	C₂²	1	6	yes	—
46	C₁₃×#440	C₂²	1	6	yes	—
47	C₄×C₁₃×Q₁₆	C₂²	1	6	yes	—
48	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
49	C₁₃×#428	C₂²	1	1	yes	characteristic
50	C₁₃×#423	C₂²	1	3	yes	—
51	C₁₃×#419	C₂²	1	3	yes	—
52	C₁₃×#417	C₂²	1	3	yes	—
53	C₄×C₁₃×M₁₆	C₂²	1	3	yes	—
54	C₂×C₁₃×#41	—	2	1	no	—
55	C₂×C₁₃×#41	C₂³	1	3	yes	—
56	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
58	C₁₃×#137	—	2	12	no	—
59	C₁₃×#137	—	4	12	no	—
60	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
61	C₂×C₁₃×Q₁₆	C₂³	1	12	yes	—
62	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
63	C₂×C₁₃×SD₁₆	C₂³	1	12	yes	—
64	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
65	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
66	C₁₃×C₄⋊Q₈	—	2	3	no	—
67	C₁₃×C₄⋊Q₈	—	2	3	no	—
68	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
71	C₁₃×#127	C₂³	1	3	yes	—
72	C₁₃×#126	—	2	6	no	—
73	C₁₃×#125	—	2	6	no	—
74	C₁₃×#125	—	2	6	no	—
75	C₁₃×#125	—	2	12	no	—
76	C₁₃×#125	—	2	3	no	—
77	C₁₃×#124	—	2	3	no	—
78	C₁₃×#124	C₂³	1	6	yes	—
79	C₁₃×#123	—	2	6	no	—
80	C₁₃×C₂²⋊Q₈	—	2	3	no	—
81	C₁₃×#121	—	2	3	no	—
82	C₁₃×#121	—	2	3	no	—
83	C₁₃×#121	—	2	3	no	—
84	C₄×Q₈×C₁₃	—	2	6	no	—
85	C₄×Q₈×C₁₃	—	2	2	no	—
86	C₄×Q₈×C₁₃	—	2	1	no	—
87	C₄×Q₈×C₁₃	—	2	3	no	—
88	C₄×Q₈×C₁₃	—	2	3	no	—
89	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₃	D₄	1	3	yes	—
91	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
92	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	—	2	3	no	—
99	C₄×D₄×C₁₃	—	2	3	no	—
100	C₄×D₄×C₁₃	—	2	3	no	—
101	C₄×D₄×C₁₃	—	2	3	no	—
102	C₄×D₄×C₁₃	C₂³	1	3	yes	—
103	C₄×D₄×C₁₃	C₂³	1	3	yes	—
104	C₁₃×#117	—	2	3	no	—
105	C₁₃×#117	—	2	3	no	—
106	C₁₃×#117	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
110	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	—	2	3	no	—
113	C₂×C₄²×C₁₃	—	2	3	no	—
114	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
115	C₁₃×#107	C₂³	1	2	yes	—
116	C₁₃×#106	C₂³	1	2	yes	—
117	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
118	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
119	C₁₃×#103	C₂³	1	6	yes	—
120	C₁₃×#103	C₂³	1	6	yes	—
121	C₁₃×#103	C₂³	1	6	yes	—
122	C₁₃×#102	C₂³	1	6	yes	—
123	C₁₃×#97	C₂³	1	6	yes	—
124	C₄×C₈×C₁₃	C₂³	1	6	yes	—
125	#61404	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₁₃×#41	—	2	6	no	—
127	C₁₃×#41	—	2	6	no	—
128	C₁₃×#41	—	4	4	no	—
129	C₂×Q₈×C₁₃	—	2	4	no	—
130	C₂×Q₈×C₁₃	—	2	3	no	—
131	C₂×Q₈×C₁₃	—	2	6	no	—
132	C₂×Q₈×C₁₃	—	2	6	no	—
133	C₂×Q₈×C₁₃	C₂×D₄	1	3	yes	—
134	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
136	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
137	C₂×D₄×C₁₃	—	2	3	no	—
138	C₂×D₄×C₁₃	—	2	3	no	—
139	C₂×D₄×C₁₃	—	2	3	no	—
140	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	3	no	—
143	C₂²×C₄×C₁₃	—	2	3	no	—
144	C₂²×C₄×C₁₃	—	2	3	no	—
145	C₂²×C₄×C₁₃	—	2	3	no	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₁₃×Q₁₆	—	2	12	no	—
150	C₁₃×Q₁₆	—	4	12	no	—
151	C₁₃×SD₁₆	—	2	12	no	—
152	C₁₃×SD₁₆	—	4	12	no	—
153	C₁₃×M₁₆	—	2	6	no	—
154	C₁₃×M₁₆	#41	1	4	yes	complemented
155	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
156	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
157	C₁₃×C₄⋊C₄	—	2	6	no	—
158	C₁₃×C₄⋊C₄	—	2	6	no	—
159	C₁₃×C₄⋊C₄	—	2	6	no	—
160	C₁₃×C₄⋊C₄	—	2	6	no	—
161	C₁₃×C₄⋊C₄	—	2	6	no	—
162	C₁₃×C₄⋊C₄	—	2	6	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	3	no	—
165	C₁₃×C₄⋊C₄	—	2	3	no	—
166	C₁₃×C₄⋊C₄	—	2	3	no	—
167	C₁₃×C₄⋊C₄	—	2	3	no	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
169	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
170	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
171	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
172	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
173	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
174	C₁₃×C₂²⋊C₄	—	2	1	no	—
175	C₁₃×C₂²⋊C₄	—	2	6	no	—
176	C₁₃×C₂²⋊C₄	—	2	3	no	—
177	C₁₃×C₂²⋊C₄	—	2	3	no	—
178	C₁₃×C₂²⋊C₄	—	2	6	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	2	3	no	—
181	C₄²×C₁₃	—	2	3	no	—
182	C₄²×C₁₃	—	2	6	no	—
183	C₄²×C₁₃	—	2	6	no	—
184	C₄²×C₁₃	C₂×D₄	1	3	yes	—
185	C₄²×C₁₃	C₂×D₄	1	3	yes	—
186	C₄²×C₁₃	C₂⁴	1	3	yes	—
187	C₄²×C₁₃	C₂⁴	1	3	yes	—
188	#3480	C₂×C₁₃	1	1	yes	characteristic
189	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#3400	C₂×C₁₃	1	6	yes	complemented
191	#3398	C₂×C₁₃	1	6	yes	complemented
192	#3395	C₂×C₁₃	1	2	yes	complemented
193	#3392	C₂×C₁₃	1	2	yes	complemented
194	#3152	C₂×C₁₃	1	3	yes	complemented
195	#3039	C₂×C₁₃	1	3	yes	complemented
196	#3037	C₂×C₁₃	1	3	yes	complemented
197	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₄×#137	C₂×C₁₃	1	3	yes	complemented
199	C₂³×C₁₃	—	2	3	no	—
200	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₁₃	—	2	6	no	—
202	Q₈×C₁₃	—	2	6	no	—
203	Q₈×C₁₃	—	2	3	no	—
204	Q₈×C₁₃	—	2	6	no	—
205	Q₈×C₁₃	—	2	3	no	—
206	Q₈×C₁₃	—	4	6	no	—
207	Q₈×C₁₃	#137	1	4	yes	complemented
208	D₄×C₁₃	—	2	3	no	—
209	D₄×C₁₃	—	2	3	no	—
210	D₄×C₁₃	—	4	6	no	—
211	D₄×C₁₃	—	4	6	no	—
212	D₄×C₁₃	—	8	3	no	—
213	C₂×C₄×C₁₃	—	2	6	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	3	no	—
218	C₂×C₄×C₁₃	—	2	6	no	—
219	C₂×C₄×C₁₃	—	4	3	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	6	no	—
222	C₂×C₄×C₁₃	—	4	6	no	—
223	C₂×C₄×C₁₃	—	4	6	no	—
224	C₂×C₄×C₁₃	—	8	3	no	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
230	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
231	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
232	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
233	C₈×C₁₃	—	2	6	no	—
234	C₈×C₁₃	C₂×#41	1	4	yes	—
235	C₂×#137	C₂²×C₁₃	1	3	yes	—
236	C₂×#137	C₂²×C₁₃	1	6	yes	—
237	#559	C₂²×C₁₃	1	3	yes	—
238	#557	—	2	1	no	—
239	#557	—	2	3	no	—
240	#557	C₂²×C₁₃	1	2	yes	—
241	#557	C₂²×C₁₃	1	1	yes	characteristic
242	#557	C₂²×C₁₃	1	6	yes	—
243	#556	C₂²×C₁₃	1	3	yes	—
244	#553	—	2	3	no	—
245	#550	C₂²×C₁₃	1	1	yes	characteristic
246	#548	—	2	1	no	—
247	#532	C₂²×C₁₃	1	3	yes	—
248	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
249	#529	—	2	3	no	—
250	C₂×#125	—	2	3	no	—
251	C₄×#41	—	2	1	no	—
252	C₄×#41	C₂²×C₁₃	1	3	yes	—
253	C₂×C₄×Q₈	—	2	1	no	—
254	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
255	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
256	#497	C₂²×C₁₃	1	12	yes	—
257	#494	C₂²×C₁₃	1	6	yes	—
258	#492	C₂²×C₁₃	1	6	yes	—
259	#464	C₂²×C₁₃	1	12	yes	—
260	#462	C₂²×C₁₃	1	6	yes	—
261	#462	C₂²×C₁₃	1	6	yes	—
262	#462	C₂²×C₁₃	1	6	yes	—
263	#461	C₂²×C₁₃	1	6	yes	—
264	#461	C₂²×C₁₃	1	6	yes	—
265	#460	C₂²×C₁₃	1	6	yes	—
266	#446	C₂²×C₁₃	1	6	yes	—
267	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
268	#441	C₂²×C₁₃	1	6	yes	—
269	#440	C₂²×C₁₃	1	6	yes	—
270	C₄×Q₁₆	C₂²×C₁₃	1	6	yes	—
271	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
272	#428	C₂²×C₁₃	1	1	yes	characteristic
273	#423	C₂²×C₁₃	1	3	yes	—
274	#419	C₂²×C₁₃	1	3	yes	—
275	#417	C₂²×C₁₃	1	3	yes	—
276	C₄×M₁₆	C₂²×C₁₃	1	3	yes	—
277	C₂²×C₁₃	—	2	1	no	—
278	C₂²×C₁₃	—	2	1	no	—
279	C₂²×C₁₃	—	4	3	no	—
280	C₂²×C₁₃	—	4	3	no	—
281	C₂²×C₁₃	—	4	3	no	—
282	C₂²×C₁₃	#550	1	2	yes	—
283	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
284	C₄×C₁₃	—	2	3	no	—
285	C₄×C₁₃	—	2	3	no	—
286	C₄×C₁₃	—	2	3	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	—	4	1	no	—
289	C₄×C₁₃	—	4	3	no	—
290	C₄×C₁₃	—	4	6	no	—
291	C₄×C₁₃	—	4	1	no	—
292	C₄×C₁₃	#550	1	2	yes	—
293	C₄×C₁₃	C₂×#137	1	6	yes	—
294	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
295	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
296	C₂×#41	—	2	1	no	—
297	C₂×#41	C₂³×C₁₃	1	3	yes	—
298	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
299	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
300	#137	—	2	12	no	—
301	#137	—	4	12	no	—
302	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
303	C₂×Q₁₆	C₂³×C₁₃	1	12	yes	—
304	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
305	C₂×SD₁₆	C₂³×C₁₃	1	12	yes	—
306	C₂×M₁₆	C₂³×C₁₃	1	3	yes	—
307	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
308	C₄⋊Q₈	—	2	3	no	—
309	C₄⋊Q₈	—	2	3	no	—
310	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
311	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
312	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
313	#127	C₂³×C₁₃	1	3	yes	—
314	#126	—	2	6	no	—
315	#125	—	2	6	no	—
316	#125	—	2	6	no	—
317	#125	—	2	12	no	—
318	#125	—	2	3	no	—
319	#124	—	2	3	no	—
320	#124	C₂³×C₁₃	1	6	yes	—
321	#123	—	2	6	no	—
322	C₂²⋊Q₈	—	2	3	no	—
323	#121	—	2	3	no	—
324	#121	—	2	3	no	—
325	#121	—	2	3	no	—
326	C₄×Q₈	—	2	6	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	—	2	3	no	—
330	C₄×Q₈	—	2	3	no	—
331	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
332	C₄×Q₈	D₄×C₁₃	1	3	yes	—
333	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
334	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
335	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
336	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
337	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
338	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
339	C₄×D₄	—	2	3	no	—
340	C₄×D₄	—	2	3	no	—
341	C₄×D₄	—	2	3	no	—
342	C₄×D₄	—	2	3	no	—
343	C₄×D₄	—	2	3	no	—
344	C₄×D₄	C₂³×C₁₃	1	3	yes	—
345	C₄×D₄	C₂³×C₁₃	1	3	yes	—
346	#117	—	2	3	no	—
347	#117	—	2	3	no	—
348	#117	C₂³×C₁₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	—	2	3	no	—
350	C₂×C₄⋊C₄	—	2	3	no	—
351	C₂×C₄⋊C₄	—	2	3	no	—
352	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
354	C₂×C₄²	—	2	3	no	—
355	C₂×C₄²	—	2	3	no	—
356	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
357	#107	C₂³×C₁₃	1	2	yes	—
358	#106	C₂³×C₁₃	1	2	yes	—
359	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
360	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
361	#103	C₂³×C₁₃	1	6	yes	—
362	#103	C₂³×C₁₃	1	6	yes	—
363	#103	C₂³×C₁₃	1	6	yes	—
364	#102	C₂³×C₁₃	1	6	yes	—
365	#97	C₂³×C₁₃	1	6	yes	—
366	C₄×C₈	C₂³×C₁₃	1	6	yes	—
367	C₂×C₁₃	—	2	2	no	—
368	C₂×C₁₃	—	8	3	no	—
369	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
370	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
371	C₂×C₁₃	#3586	1	1	yes	characteristic
372	#41	—	2	6	no	—
373	#41	—	2	6	no	—
374	#41	—	4	4	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	3	no	—
377	C₂×Q₈	—	2	6	no	—
378	C₂×Q₈	—	2	6	no	—
379	C₂×Q₈	C₂×D₄×C₁₃	1	3	yes	—
380	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
382	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
383	C₂×D₄	—	2	3	no	—
384	C₂×D₄	—	2	3	no	—
385	C₂×D₄	—	2	3	no	—
386	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	3	no	—
389	C₂²×C₄	—	2	3	no	—
390	C₂²×C₄	—	2	3	no	—
391	C₂²×C₄	—	2	3	no	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
393	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
394	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
395	Q₁₆	—	2	12	no	—
396	Q₁₆	—	4	12	no	—
397	SD₁₆	—	2	12	no	—
398	SD₁₆	—	4	12	no	—
399	M₁₆	—	2	6	no	—
400	M₁₆	C₁₃×#41	1	4	yes	complemented
401	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
402	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
403	C₄⋊C₄	—	2	6	no	—
404	C₄⋊C₄	—	2	6	no	—
405	C₄⋊C₄	—	2	6	no	—
406	C₄⋊C₄	—	2	6	no	—
407	C₄⋊C₄	—	2	6	no	—
408	C₄⋊C₄	—	2	6	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	3	no	—
411	C₄⋊C₄	—	2	3	no	—
412	C₄⋊C₄	—	2	3	no	—
413	C₄⋊C₄	—	2	3	no	—
414	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
415	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
416	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
417	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
418	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
419	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	6	no	—
422	C₂²⋊C₄	—	2	3	no	—
423	C₂²⋊C₄	—	2	3	no	—
424	C₂²⋊C₄	—	2	6	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	3	no	—
427	C₄²	—	2	3	no	—
428	C₄²	—	2	6	no	—
429	C₄²	—	2	6	no	—
430	C₄²	C₂×D₄×C₁₃	1	3	yes	—
431	C₄²	C₂×D₄×C₁₃	1	3	yes	—
432	C₄²	C₂⁴×C₁₃	1	3	yes	—
433	C₄²	C₂⁴×C₁₃	1	3	yes	—
434	C₁₃	#61404	1	1	yes	characteristic, direct product factor, Sylow
435	C₂³	—	2	3	no	—
436	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
437	Q₈	—	2	6	no	—
438	Q₈	—	2	6	no	—
439	Q₈	—	2	3	no	—
440	Q₈	—	2	6	no	—
441	Q₈	—	2	3	no	—
442	Q₈	—	4	6	no	—
443	Q₈	C₁₃×#137	1	4	yes	complemented
444	D₄	—	2	3	no	—
445	D₄	—	2	3	no	—
446	D₄	—	4	6	no	—
447	D₄	—	4	6	no	—
448	D₄	—	8	3	no	—
449	C₂×C₄	—	2	6	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	3	no	—
454	C₂×C₄	—	2	6	no	—
455	C₂×C₄	—	4	3	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	6	no	—
458	C₂×C₄	—	4	6	no	—
459	C₂×C₄	—	4	6	no	—
460	C₂×C₄	—	8	3	no	—
461	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
462	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
463	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
464	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
466	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
467	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
468	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
469	C₈	—	2	6	no	—
470	C₈	C₂×C₁₃×#41	1	4	yes	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	4	3	no	—
474	C₂²	—	4	3	no	—
475	C₂²	—	4	3	no	—
476	C₂²	C₁₃×#550	1	2	yes	—
477	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
478	C₄	—	2	3	no	—
479	C₄	—	2	3	no	—
480	C₄	—	2	3	no	—
481	C₄	—	4	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	3	no	—
485	C₄	—	4	6	no	—
486	C₄	C₁₃×#550	1	2	yes	—
487	C₄	C₂×C₁₃×#137	1	6	yes	—
488	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
489	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
490	C₂	—	2	2	no	—
491	C₂	—	8	3	no	—
492	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
493	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
494	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3480	C₂
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
2. C₂×C₁₃×#557	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3398	C₂	semidirect
5. C₁₃×#3395	C₂	semidirect
6. C₁₃×#3392	C₂	semidirect
7. C₁₃×#3152	C₂	semidirect
8. C₁₃×#3039	C₂	semidirect
9. C₁₃×#3037	C₂	semidirect
10. Q₈×C₁₃×M₁₆	C₂	semidirect
11. C₄×C₁₃×#137	C₂	semidirect
125. #61404	C₁₃	direct (N × H)
154. C₁₃×M₁₆	#41	semidirect
189. C₂×#557	C₂×C₁₃	semidirect
190. #3400	C₂×C₁₃	semidirect
191. #3398	C₂×C₁₃	semidirect
192. #3395	C₂×C₁₃	semidirect
193. #3392	C₂×C₁₃	semidirect
194. #3152	C₂×C₁₃	semidirect
195. #3039	C₂×C₁₃	semidirect
196. #3037	C₂×C₁₃	semidirect
197. Q₈×M₁₆	C₂×C₁₃	semidirect
198. C₄×#137	C₂×C₁₃	semidirect
207. Q₈×C₁₃	#137	semidirect
400. M₁₆	C₁₃×#41	semidirect
434. C₁₃	#61404	direct (N × H)
443. Q₈	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3480	2
C₂×C₁₃×#557	2
C₁₃×#3400	2
C₁₃×#3398	2
C₁₃×#3395	2
C₁₃×#3392	2
C₁₃×#3152	2
C₁₃×#3039	2
C₁₃×#3037	2
Q₈×C₁₃×M₁₆	2
C₄×C₁₃×#137	2
#61404	13

Subgroups — C13×#61404 #15747743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61404 #15747743