Subgroups — C₁₃×#62000 #15748339

Order 3328.

1818 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3482	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3395	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3359	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3328	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3276	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3255	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3209	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3107	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3039	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	6	yes	—
13	Q₈²×C₁₃	—	2	1	no	—
14	C₁₃×#557	C₂²	1	2	yes	—
15	C₁₃×#557	C₂²	1	1	yes	characteristic
16	C₁₃×#556	C₂²	1	3	yes	—
17	C₁₃×#554	—	2	3	no	—
18	C₁₃×#552	—	2	3	no	—
19	D₄×Q₈×C₁₃	C₂²	1	6	yes	—
20	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#548	—	2	1	no	—
22	C₁₃×#547	C₂²	1	3	yes	—
23	C₁₃×#544	—	2	3	no	—
24	C₁₃×#533	C₂²	1	3	yes	—
25	C₁₃×#533	C₂²	1	3	yes	—
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
27	C₁₃×#529	—	2	3	no	—
28	C₁₃×#520	—	2	1	no	—
29	C₄×C₁₃×#41	C₂²	1	3	yes	—
30	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
32	C₁₃×#494	C₂²	1	6	yes	—
33	C₁₃×#487	C₂²	1	6	yes	—
34	C₁₃×#485	C₂²	1	6	yes	—
35	C₁₃×#475	C₂²	1	6	yes	—
36	C₁₃×#475	C₂²	1	3	yes	—
37	C₁₃×#474	C₂²	1	1	yes	characteristic
38	C₁₃×#470	C₂²	1	12	yes	—
39	C₁₃×#462	C₂²	1	6	yes	—
40	C₁₃×#462	C₂²	1	6	yes	—
41	C₁₃×#462	C₂²	1	6	yes	—
42	C₁₃×#462	C₂²	1	3	yes	—
43	C₁₃×#461	C₂²	1	6	yes	—
44	C₁₃×#461	C₂²	1	3	yes	—
45	C₁₃×#452	C₂²	1	6	yes	—
46	C₁₃×#451	C₂²	1	12	yes	—
47	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
48	C₄×C₁₃×Q₁₆	C₂²	1	6	yes	—
49	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
50	C₁₃×#436	C₂²	1	6	yes	—
51	C₁₃×#431	C₂²	1	3	yes	—
52	C₁₃×#423	C₂²	1	3	yes	—
53	C₁₃×#419	C₂²	1	6	yes	—
54	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
55	C₂×C₁₃×#41	C₂³	1	3	yes	—
56	C₂²×Q₈×C₁₃	—	2	1	no	—
57	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
58	C₁₃×#137	—	4	12	no	—
59	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
60	C₂×C₁₃×Q₁₆	C₂³	1	12	yes	—
61	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
62	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
63	C₁₃×C₄⋊Q₈	—	2	6	no	—
64	C₁₃×C₄⋊Q₈	—	2	3	no	—
65	C₁₃×C₄⋊Q₈	—	2	3	no	—
66	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
67	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
71	C₁₃×#126	—	2	6	no	—
72	C₁₃×#125	—	2	3	no	—
73	C₁₃×#125	—	2	6	no	—
74	C₁₃×#125	—	2	3	no	—
75	C₁₃×#125	—	2	3	no	—
76	C₁₃×#124	—	2	3	no	—
77	C₁₃×#123	—	2	6	no	—
78	C₁₃×C₂²⋊Q₈	—	2	3	no	—
79	C₁₃×C₂²⋊Q₈	—	2	3	no	—
80	C₁₃×C₂²⋊Q₈	—	2	3	no	—
81	C₁₃×C₂²⋊Q₈	—	2	12	no	—
82	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
83	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
84	C₁₃×#121	—	2	3	no	—
85	C₄×Q₈×C₁₃	—	2	1	no	—
86	C₄×Q₈×C₁₃	—	2	2	no	—
87	C₄×Q₈×C₁₃	—	2	3	no	—
88	C₄×Q₈×C₁₃	—	2	3	no	—
89	C₄×Q₈×C₁₃	—	2	3	no	—
90	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
92	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₁₃	—	2	6	no	—
96	C₄×D₄×C₁₃	—	2	3	no	—
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	D₄	1	3	yes	—
99	C₄×D₄×C₁₃	C₂³	1	3	yes	—
100	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₃	C₂³	1	3	yes	—
102	C₁₃×#117	—	2	3	no	—
103	C₁₃×#117	—	2	3	no	—
104	C₁₃×#117	—	2	3	no	—
105	C₁₃×#117	D₄	1	3	yes	—
106	C₁₃×#117	C₂³	1	3	yes	—
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×C₄²×C₁₃	—	2	3	no	—
111	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
112	C₁₃×#107	C₂³	1	2	yes	—
113	C₁₃×#106	C₂³	1	6	yes	—
114	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
115	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×#103	C₂³	1	6	yes	—
118	C₁₃×#103	C₂³	1	12	yes	—
119	C₁₃×#103	C₂³	1	6	yes	—
120	C₁₃×#103	C₂³	1	6	yes	—
121	C₁₃×#102	C₂³	1	2	yes	—
122	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
123	C₄×C₈×C₁₃	C₂³	1	6	yes	—
124	#62000	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₁₃×#41	—	2	4	no	—
126	C₁₃×#41	—	2	6	no	—
127	C₁₃×#41	—	4	3	no	—
128	C₂×Q₈×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	3	no	—
130	C₂×Q₈×C₁₃	—	2	6	no	—
131	C₂×Q₈×C₁₃	—	4	6	no	—
132	C₂×Q₈×C₁₃	—	4	6	no	—
133	C₂×Q₈×C₁₃	—	4	4	no	—
134	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
136	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
137	C₂×D₄×C₁₃	—	2	3	no	—
138	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
139	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	—	2	6	no	—
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	C₂×D₄	1	3	yes	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
147	C₁₃×Q₁₆	—	4	6	no	—
148	C₁₃×Q₁₆	—	4	12	no	—
149	C₁₃×SD₁₆	—	2	12	no	—
150	C₁₃×M₁₆	—	4	6	no	—
151	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
152	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
153	C₁₃×C₄⋊C₄	—	2	3	no	—
154	C₁₃×C₄⋊C₄	—	2	3	no	—
155	C₁₃×C₄⋊C₄	—	2	6	no	—
156	C₁₃×C₄⋊C₄	—	2	3	no	—
157	C₁₃×C₄⋊C₄	—	2	6	no	—
158	C₁₃×C₄⋊C₄	—	2	6	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	3	no	—
161	C₁₃×C₄⋊C₄	—	2	3	no	—
162	C₁₃×C₄⋊C₄	—	2	3	no	—
163	C₁₃×C₄⋊C₄	—	2	3	no	—
164	C₁₃×C₄⋊C₄	—	2	6	no	—
165	C₁₃×C₄⋊C₄	—	2	6	no	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
167	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
168	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
169	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
170	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
171	C₁₃×C₂²⋊C₄	—	2	6	no	—
172	C₁₃×C₂²⋊C₄	—	2	6	no	—
173	C₁₃×C₂²⋊C₄	—	2	3	no	—
174	C₁₃×C₂²⋊C₄	—	2	1	no	—
175	C₁₃×C₂²⋊C₄	—	2	3	no	—
176	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
177	C₄²×C₁₃	—	2	3	no	—
178	C₄²×C₁₃	—	2	3	no	—
179	C₄²×C₁₃	—	2	3	no	—
180	C₄²×C₁₃	—	2	6	no	—
181	C₄²×C₁₃	C₂×D₄	1	3	yes	—
182	C₄²×C₁₃	C₂×D₄	1	3	yes	—
183	C₄²×C₁₃	C₂⁴	1	3	yes	—
184	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
185	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#3482	C₂×C₁₃	1	1	yes	characteristic
187	#3395	C₂×C₁₃	1	2	yes	complemented
188	#3359	C₂×C₁₃	1	2	yes	complemented
189	#3328	C₂×C₁₃	1	6	yes	complemented
190	#3276	C₂×C₁₃	1	6	yes	complemented
191	#3255	C₂×C₁₃	1	3	yes	complemented
192	#3209	C₂×C₁₃	1	3	yes	complemented
193	#3107	C₂×C₁₃	1	3	yes	complemented
194	#3039	C₂×C₁₃	1	3	yes	complemented
195	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂³×C₁₃	—	2	1	no	—
197	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
198	Q₈×C₁₃	—	2	6	no	—
199	Q₈×C₁₃	—	2	3	no	—
200	Q₈×C₁₃	—	2	3	no	—
201	Q₈×C₁₃	—	2	6	no	—
202	Q₈×C₁₃	—	4	6	no	—
203	Q₈×C₁₃	—	4	2	no	—
204	Q₈×C₁₃	—	8	6	no	—
205	Q₈×C₁₃	#137	1	4	yes	complemented
206	D₄×C₁₃	—	2	6	no	—
207	D₄×C₁₃	—	2	1	no	—
208	D₄×C₁₃	—	4	6	no	—
209	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
210	C₂×C₄×C₁₃	—	2	6	no	—
211	C₂×C₄×C₁₃	—	2	6	no	—
212	C₂×C₄×C₁₃	—	2	3	no	—
213	C₂×C₄×C₁₃	—	2	3	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	3	no	—
217	C₂×C₄×C₁₃	—	2	3	no	—
218	C₂×C₄×C₁₃	—	2	6	no	—
219	C₂×C₄×C₁₃	—	4	6	no	—
220	C₂×C₄×C₁₃	—	4	6	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	8	6	no	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
229	C₈×C₁₃	—	2	6	no	—
230	C₈×C₁₃	—	2	2	no	—
231	C₂×#137	C₂²×C₁₃	1	6	yes	—
232	Q₈²	—	2	1	no	—
233	#557	C₂²×C₁₃	1	2	yes	—
234	#557	C₂²×C₁₃	1	1	yes	characteristic
235	#556	C₂²×C₁₃	1	3	yes	—
236	#554	—	2	3	no	—
237	#552	—	2	3	no	—
238	D₄×Q₈	C₂²×C₁₃	1	6	yes	—
239	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
240	#548	—	2	1	no	—
241	#547	C₂²×C₁₃	1	3	yes	—
242	#544	—	2	3	no	—
243	#533	C₂²×C₁₃	1	3	yes	—
244	#533	C₂²×C₁₃	1	3	yes	—
245	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
246	#529	—	2	3	no	—
247	#520	—	2	1	no	—
248	C₄×#41	C₂²×C₁₃	1	3	yes	—
249	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₄×Q₈	—	2	1	no	—
251	#494	C₂²×C₁₃	1	6	yes	—
252	#487	C₂²×C₁₃	1	6	yes	—
253	#485	C₂²×C₁₃	1	6	yes	—
254	#475	C₂²×C₁₃	1	6	yes	—
255	#475	C₂²×C₁₃	1	3	yes	—
256	#474	C₂²×C₁₃	1	1	yes	characteristic
257	#470	C₂²×C₁₃	1	12	yes	—
258	#462	C₂²×C₁₃	1	6	yes	—
259	#462	C₂²×C₁₃	1	3	yes	—
260	#462	C₂²×C₁₃	1	6	yes	—
261	#462	C₂²×C₁₃	1	6	yes	—
262	#461	C₂²×C₁₃	1	6	yes	—
263	#461	C₂²×C₁₃	1	3	yes	—
264	#452	C₂²×C₁₃	1	6	yes	—
265	#451	C₂²×C₁₃	1	12	yes	—
266	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
267	C₄×Q₁₆	C₂²×C₁₃	1	6	yes	—
268	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
269	#436	C₂²×C₁₃	1	6	yes	—
270	#431	C₂²×C₁₃	1	3	yes	—
271	#423	C₂²×C₁₃	1	3	yes	—
272	#419	C₂²×C₁₃	1	6	yes	—
273	C₂²×C₁₃	—	2	3	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	3	no	—
276	C₂²×C₁₃	—	2	3	no	—
277	C₂²×C₁₃	—	4	1	no	—
278	C₂²×C₁₃	—	4	1	no	—
279	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
280	C₄×C₁₃	—	2	3	no	—
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	—	2	3	no	—
283	C₄×C₁₃	—	4	3	no	—
284	C₄×C₁₃	—	4	6	no	—
285	C₄×C₁₃	—	4	3	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	C₂×#137	1	6	yes	—
289	C₄×C₁₃	#578	1	2	yes	—
290	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
291	C₄×C₁₃	#585	1	1	yes	characteristic
292	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
293	C₂×#41	C₂³×C₁₃	1	3	yes	—
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
296	#137	—	4	12	no	—
297	C₂×Q₁₆	C₂³×C₁₃	1	12	yes	—
298	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
299	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
300	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
301	C₄⋊Q₈	—	2	6	no	—
302	C₄⋊Q₈	—	2	3	no	—
303	C₄⋊Q₈	—	2	3	no	—
304	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
305	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
306	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
307	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
308	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
309	#126	—	2	6	no	—
310	#125	—	2	3	no	—
311	#125	—	2	6	no	—
312	#125	—	2	3	no	—
313	#125	—	2	3	no	—
314	#124	—	2	3	no	—
315	#123	—	2	6	no	—
316	C₂²⋊Q₈	—	2	3	no	—
317	C₂²⋊Q₈	—	2	3	no	—
318	C₂²⋊Q₈	—	2	3	no	—
319	C₂²⋊Q₈	—	2	12	no	—
320	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
321	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
322	#121	—	2	3	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	3	no	—
326	C₄×Q₈	—	2	3	no	—
327	C₄×Q₈	—	2	3	no	—
328	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
329	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
330	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
331	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
332	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
333	C₄×D₄	—	2	6	no	—
334	C₄×D₄	—	2	3	no	—
335	C₄×D₄	—	2	3	no	—
336	C₄×D₄	D₄×C₁₃	1	3	yes	—
337	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₄×D₄	C₂³×C₁₃	1	3	yes	—
339	C₄×D₄	C₂³×C₁₃	1	3	yes	—
340	#117	—	2	3	no	—
341	#117	—	2	3	no	—
342	#117	—	2	3	no	—
343	#117	D₄×C₁₃	1	3	yes	—
344	#117	C₂³×C₁₃	1	3	yes	—
345	C₂×C₄⋊C₄	—	2	3	no	—
346	C₂×C₄⋊C₄	—	2	3	no	—
347	C₂×C₄⋊C₄	—	2	3	no	—
348	C₂×C₄²	—	2	3	no	—
349	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
350	#107	C₂³×C₁₃	1	2	yes	—
351	#106	C₂³×C₁₃	1	6	yes	—
352	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
353	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
354	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
355	#103	C₂³×C₁₃	1	6	yes	—
356	#103	C₂³×C₁₃	1	12	yes	—
357	#103	C₂³×C₁₃	1	6	yes	—
358	#103	C₂³×C₁₃	1	6	yes	—
359	#102	C₂³×C₁₃	1	2	yes	—
360	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
361	C₄×C₈	C₂³×C₁₃	1	6	yes	—
362	C₂×C₁₃	—	4	3	no	—
363	C₂×C₁₃	—	4	2	no	—
364	C₂×C₁₃	#3488	1	1	yes	characteristic
365	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
366	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
367	#41	—	2	4	no	—
368	#41	—	2	6	no	—
369	#41	—	4	3	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	3	no	—
372	C₂×Q₈	—	2	6	no	—
373	C₂×Q₈	—	4	6	no	—
374	C₂×Q₈	—	4	6	no	—
375	C₂×Q₈	—	4	4	no	—
376	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
378	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
379	C₂×D₄	—	2	3	no	—
380	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
381	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	—	2	6	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	3	no	—
385	C₂²×C₄	—	2	3	no	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
388	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
389	Q₁₆	—	4	12	no	—
390	Q₁₆	—	4	6	no	—
391	SD₁₆	—	2	12	no	—
392	M₁₆	—	4	6	no	—
393	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
394	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
395	C₄⋊C₄	—	2	3	no	—
396	C₄⋊C₄	—	2	3	no	—
397	C₄⋊C₄	—	2	6	no	—
398	C₄⋊C₄	—	2	3	no	—
399	C₄⋊C₄	—	2	6	no	—
400	C₄⋊C₄	—	2	6	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	3	no	—
403	C₄⋊C₄	—	2	3	no	—
404	C₄⋊C₄	—	2	3	no	—
405	C₄⋊C₄	—	2	3	no	—
406	C₄⋊C₄	—	2	6	no	—
407	C₄⋊C₄	—	2	6	no	—
408	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
409	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
410	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
411	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
412	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
413	C₂²⋊C₄	—	2	6	no	—
414	C₂²⋊C₄	—	2	6	no	—
415	C₂²⋊C₄	—	2	3	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	3	no	—
418	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
419	C₄²	—	2	3	no	—
420	C₄²	—	2	3	no	—
421	C₄²	—	2	3	no	—
422	C₄²	—	2	6	no	—
423	C₄²	C₂×D₄×C₁₃	1	3	yes	—
424	C₄²	C₂×D₄×C₁₃	1	3	yes	—
425	C₄²	C₂⁴×C₁₃	1	3	yes	—
426	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
427	C₁₃	#62000	1	1	yes	characteristic, direct product factor, Sylow
428	C₂³	—	2	1	no	—
429	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
430	Q₈	—	2	6	no	—
431	Q₈	—	2	3	no	—
432	Q₈	—	2	3	no	—
433	Q₈	—	2	6	no	—
434	Q₈	—	4	6	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	8	6	no	—
437	Q₈	C₁₃×#137	1	4	yes	complemented
438	D₄	—	2	6	no	—
439	D₄	—	2	1	no	—
440	D₄	—	4	6	no	—
441	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
442	C₂×C₄	—	2	6	no	—
443	C₂×C₄	—	2	6	no	—
444	C₂×C₄	—	2	3	no	—
445	C₂×C₄	—	2	3	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	3	no	—
449	C₂×C₄	—	2	3	no	—
450	C₂×C₄	—	2	6	no	—
451	C₂×C₄	—	4	6	no	—
452	C₂×C₄	—	4	6	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	8	6	no	—
455	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
456	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
458	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
459	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
461	C₈	—	2	6	no	—
462	C₈	—	2	2	no	—
463	C₂²	—	2	3	no	—
464	C₂²	—	2	3	no	—
465	C₂²	—	2	3	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	3	no	—
472	C₄	—	2	3	no	—
473	C₄	—	4	3	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	3	no	—
477	C₄	—	4	6	no	—
478	C₄	C₂×C₁₃×#137	1	6	yes	—
479	C₄	C₁₃×#578	1	2	yes	—
480	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
481	C₄	C₁₃×#585	1	1	yes	characteristic
482	C₂	—	4	3	no	—
483	C₂	—	4	2	no	—
484	C₂	C₁₃×#3488	1	1	yes	characteristic
485	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
486	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3395	C₂	semidirect
4. C₁₃×#3359	C₂	semidirect
5. C₁₃×#3328	C₂	semidirect
6. C₁₃×#3276	C₂	semidirect
7. C₁₃×#3255	C₂	semidirect
8. C₁₃×#3209	C₂	semidirect
9. C₁₃×#3107	C₂	semidirect
10. C₁₃×#3039	C₂	semidirect
11. C₁₃×#2991	C₂	semidirect
124. #62000	C₁₃	direct (N × H)
185. #3503	C₂×C₁₃	semidirect
187. #3395	C₂×C₁₃	semidirect
188. #3359	C₂×C₁₃	semidirect
189. #3328	C₂×C₁₃	semidirect
190. #3276	C₂×C₁₃	semidirect
191. #3255	C₂×C₁₃	semidirect
192. #3209	C₂×C₁₃	semidirect
193. #3107	C₂×C₁₃	semidirect
194. #3039	C₂×C₁₃	semidirect
195. #2991	C₂×C₁₃	semidirect
205. Q₈×C₁₃	#137	semidirect
427. C₁₃	#62000	direct (N × H)
437. 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×#3503	2
C₁₃×#3482	2
C₁₃×#3395	2
C₁₃×#3359	2
C₁₃×#3328	2
C₁₃×#3276	2
C₁₃×#3255	2
C₁₃×#3209	2
C₁₃×#3107	2
C₁₃×#3039	2
C₁₃×#2991	2
#62000	13

Subgroups — C13×#62000 #15748339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62000 #15748339