Subgroups — C₁₃×#61416 #15747755

Order 3328.

1850 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3401	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3398	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3156	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3150	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#3046	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3037	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2952	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#137	C₂²	1	4	yes	—
12	C₂×C₁₃×#135	C₂²	1	2	yes	—
13	C₂×C₁₃×#135	C₂²	1	2	yes	—
14	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
15	C₁₃×#559	C₂²	1	4	yes	—
16	C₁₃×#557	C₂²	1	4	yes	—
17	C₁₃×#556	—	2	2	no	—
18	C₁₃×#556	C₂²	1	8	yes	—
19	C₁₃×#554	—	2	2	no	—
20	C₁₃×#552	—	2	4	no	—
21	C₁₃×#539	—	2	4	no	—
22	C₁₃×#536	C₂²	1	4	yes	—
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₁₃×#532	C₂²	1	2	yes	—
25	C₁₃×#529	—	2	4	no	—
26	C₁₃×#520	C₂²	1	4	yes	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#497	C₂²	1	4	yes	—
29	C₁₃×#497	C₂²	1	8	yes	—
30	C₁₃×#496	C₂²	1	4	yes	—
31	C₁₃×#495	C₂²	1	4	yes	—
32	C₁₃×#494	C₂²	1	4	yes	—
33	C₁₃×#464	C₂²	1	8	yes	—
34	C₁₃×#464	C₂²	1	8	yes	—
35	C₁₃×#463	C₂²	1	8	yes	—
36	C₁₃×#462	C₂²	1	4	yes	—
37	C₁₃×#462	C₂²	1	8	yes	—
38	C₁₃×#461	C₂²	1	8	yes	—
39	C₁₃×#460	C₂²	1	4	yes	—
40	C₁₃×#446	C₂²	1	8	yes	—
41	C₁₃×#442	C₂²	1	4	yes	—
42	C₁₃×#441	C₂²	1	4	yes	—
43	C₁₃×#441	C₂²	1	8	yes	—
44	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	—
45	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
46	C₁₃×#424	C₂²	1	2	yes	—
47	C₁₃×#423	C₂²	1	1	yes	characteristic
48	C₁₃×#417	C₂²	1	4	yes	—
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₁₃×#405	C₂²	1	2	yes	—
51	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#41	C₂³	1	4	yes	—
53	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
54	C₁₃×#137	—	4	8	no	—
55	C₁₃×#135	—	2	8	no	—
56	C₁₃×#135	—	4	4	no	—
57	C₂×C₁₃×Q₁₆	—	2	4	no	—
58	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
59	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
60	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
61	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
62	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
63	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
64	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
65	C₂×C₁₃×D₈	C₂³	1	2	yes	—
66	C₂×C₁₃×D₈	C₂³	1	2	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
71	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
72	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
73	C₁₃×#127	C₂³	1	2	yes	—
74	C₁₃×#126	—	2	8	no	—
75	C₁₃×#126	—	2	8	no	—
76	C₁₃×#125	—	2	4	no	—
77	C₁₃×#125	—	2	8	no	—
78	C₁₃×#125	D₄	1	2	yes	—
79	C₁₃×#124	—	2	4	no	—
80	C₁₃×#124	C₂³	1	8	yes	—
81	C₁₃×#124	C₂³	1	4	yes	—
82	C₁₃×#123	—	2	8	no	—
83	C₁₃×#123	—	2	8	no	—
84	C₁₃×C₂²⋊Q₈	—	2	8	no	—
85	C₁₃×C₂²⋊Q₈	—	2	4	no	—
86	C₁₃×C₂²⋊Q₈	—	2	4	no	—
87	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
88	C₁₃×#121	—	2	2	no	—
89	C₁₃×#121	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	2	4	no	—
91	C₄×Q₈×C₁₃	—	2	2	no	—
92	C₄×Q₈×C₁₃	—	2	2	no	—
93	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
96	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
97	C₄×D₄×C₁₃	—	2	4	no	—
98	C₄×D₄×C₁₃	—	2	8	no	—
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	C₂³	1	8	yes	—
102	C₁₃×#117	—	2	4	no	—
103	C₁₃×#117	—	2	8	no	—
104	C₁₃×#117	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₄²×C₁₃	—	2	2	no	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#106	C₂³	1	4	yes	—
111	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
112	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
113	C₁₃×#103	C₂³	1	8	yes	—
114	C₁₃×#103	C₂³	1	8	yes	—
115	C₁₃×#102	C₂³	1	8	yes	—
116	C₁₃×#97	C₂³	1	4	yes	—
117	C₁₃×#97	C₂³	1	4	yes	—
118	C₄×C₈×C₁₃	C₂³	1	4	yes	—
119	#61416	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₁₃×#41	—	2	8	no	—
121	C₁₃×#41	—	2	8	no	—
122	C₂×Q₈×C₁₃	—	2	2	no	—
123	C₂×Q₈×C₁₃	—	2	4	no	—
124	C₂×Q₈×C₁₃	—	2	4	no	—
125	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
126	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
127	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	8	no	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₁₃×Q₁₆	—	2	8	no	—
139	C₁₃×Q₁₆	—	2	4	no	—
140	C₁₃×Q₁₆	—	4	2	no	—
141	C₁₃×Q₁₆	—	4	8	no	—
142	C₁₃×SD₁₆	—	2	8	no	—
143	C₁₃×SD₁₆	—	4	4	no	—
144	C₁₃×SD₁₆	—	4	8	no	—
145	C₁₃×D₈	—	2	4	no	—
146	C₁₃×D₈	—	4	2	no	—
147	C₁₃×M₁₆	—	2	4	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	#41	1	4	yes	—
150	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
151	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
152	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	8	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	8	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
164	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
165	C₁₃×C₂²⋊C₄	—	2	4	no	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	—	2	8	no	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
171	C₄²×C₁₃	—	2	4	no	—
172	C₄²×C₁₃	—	2	4	no	—
173	C₄²×C₁₃	—	2	8	no	—
174	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂⁴	1	4	yes	—
177	C₄²×C₁₃	C₂⁴	1	2	yes	—
178	#3507	C₂×C₁₃	1	2	yes	complemented
179	#3401	C₂×C₁₃	1	8	yes	complemented
180	#3398	C₂×C₁₃	1	8	yes	complemented
181	#3156	C₂×C₁₃	1	2	yes	complemented
182	#3150	C₂×C₁₃	1	1	yes	characteristic
183	#3046	C₂×C₁₃	1	4	yes	complemented
184	#3037	C₂×C₁₃	1	2	yes	complemented
185	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#2952	C₂×C₁₃	1	2	yes	complemented
187	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂³×C₁₃	—	2	4	no	—
189	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₁₃	—	2	4	no	—
191	Q₈×C₁₃	—	2	4	no	—
192	Q₈×C₁₃	—	2	4	no	—
193	Q₈×C₁₃	—	2	4	no	—
194	Q₈×C₁₃	—	4	4	no	—
195	Q₈×C₁₃	—	4	4	no	—
196	D₄×C₁₃	—	2	4	no	—
197	D₄×C₁₃	—	2	4	no	—
198	D₄×C₁₃	—	4	4	no	—
199	D₄×C₁₃	—	4	8	no	—
200	D₄×C₁₃	—	8	2	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	4	no	—
206	C₂×C₄×C₁₃	—	4	8	no	—
207	C₂×C₄×C₁₃	—	8	8	no	—
208	C₂×C₄×C₁₃	—	8	2	no	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
214	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
215	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
216	C₈×C₁₃	—	2	2	no	—
217	C₈×C₁₃	—	2	4	no	—
218	C₈×C₁₃	C₂×#41	1	4	yes	—
219	C₂×#137	C₂²×C₁₃	1	4	yes	—
220	C₂×#135	C₂²×C₁₃	1	2	yes	—
221	C₂×#135	C₂²×C₁₃	1	2	yes	—
222	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
223	#559	C₂²×C₁₃	1	4	yes	—
224	#557	C₂²×C₁₃	1	4	yes	—
225	#556	—	2	2	no	—
226	#556	C₂²×C₁₃	1	8	yes	—
227	#554	—	2	2	no	—
228	#552	—	2	4	no	—
229	#539	—	2	4	no	—
230	#536	C₂²×C₁₃	1	4	yes	—
231	#533	C₂²×C₁₃	1	1	yes	characteristic
232	#532	C₂²×C₁₃	1	2	yes	—
233	#529	—	2	4	no	—
234	#520	C₂²×C₁₃	1	4	yes	—
235	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
236	#497	C₂²×C₁₃	1	4	yes	—
237	#497	C₂²×C₁₃	1	8	yes	—
238	#496	C₂²×C₁₃	1	4	yes	—
239	#495	C₂²×C₁₃	1	4	yes	—
240	#494	C₂²×C₁₃	1	4	yes	—
241	#464	C₂²×C₁₃	1	8	yes	—
242	#464	C₂²×C₁₃	1	8	yes	—
243	#463	C₂²×C₁₃	1	8	yes	—
244	#462	C₂²×C₁₃	1	4	yes	—
245	#462	C₂²×C₁₃	1	8	yes	—
246	#461	C₂²×C₁₃	1	8	yes	—
247	#460	C₂²×C₁₃	1	4	yes	—
248	#446	C₂²×C₁₃	1	8	yes	—
249	#442	C₂²×C₁₃	1	4	yes	—
250	#441	C₂²×C₁₃	1	4	yes	—
251	#441	C₂²×C₁₃	1	8	yes	—
252	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	—
253	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
254	#424	C₂²×C₁₃	1	2	yes	—
255	#423	C₂²×C₁₃	1	1	yes	characteristic
256	#417	C₂²×C₁₃	1	4	yes	—
257	C₂×#103	C₂²×C₁₃	1	2	yes	—
258	#405	C₂²×C₁₃	1	2	yes	—
259	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
260	C₂²×C₁₃	—	2	2	no	—
261	C₂²×C₁₃	—	4	4	no	—
262	C₂²×C₁₃	—	4	4	no	—
263	C₂²×C₁₃	—	4	4	no	—
264	C₂²×C₁₃	#550	1	2	yes	—
265	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
266	C₄×C₁₃	—	2	2	no	—
267	C₄×C₁₃	—	2	2	no	—
268	C₄×C₁₃	—	2	8	no	—
269	C₄×C₁₃	—	4	4	no	—
270	C₄×C₁₃	—	4	4	no	—
271	C₄×C₁₃	—	4	4	no	—
272	C₄×C₁₃	#550	1	2	yes	—
273	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
274	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
275	C₂×#41	C₂³×C₁₃	1	4	yes	—
276	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
277	#137	—	4	8	no	—
278	#135	—	2	8	no	—
279	#135	—	4	4	no	—
280	C₂×Q₁₆	—	2	4	no	—
281	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
282	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
283	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
284	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
285	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
286	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
287	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
288	C₂×D₈	C₂³×C₁₃	1	2	yes	—
289	C₂×D₈	C₂³×C₁₃	1	2	yes	—
290	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
293	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
294	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
295	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
296	#127	C₂³×C₁₃	1	2	yes	—
297	#126	—	2	8	no	—
298	#126	—	2	8	no	—
299	#125	—	2	4	no	—
300	#125	—	2	8	no	—
301	#125	D₄×C₁₃	1	2	yes	—
302	#124	—	2	4	no	—
303	#124	C₂³×C₁₃	1	4	yes	—
304	#124	C₂³×C₁₃	1	8	yes	—
305	#123	—	2	8	no	—
306	#123	—	2	8	no	—
307	C₂²⋊Q₈	—	2	8	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₂²⋊Q₈	—	2	4	no	—
310	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
311	#121	—	2	2	no	—
312	#121	—	2	2	no	—
313	C₄×Q₈	—	2	4	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
317	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
318	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
319	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	8	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	C₂³×C₁₃	1	8	yes	—
325	#117	—	2	4	no	—
326	#117	—	2	8	no	—
327	#117	C₂³×C₁₃	1	2	yes	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	4	no	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
333	#106	C₂³×C₁₃	1	4	yes	—
334	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
335	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
336	#103	C₂³×C₁₃	1	8	yes	—
337	#103	C₂³×C₁₃	1	8	yes	—
338	#102	C₂³×C₁₃	1	8	yes	—
339	#97	C₂³×C₁₃	1	4	yes	—
340	#97	C₂³×C₁₃	1	4	yes	—
341	C₄×C₈	C₂³×C₁₃	1	4	yes	—
342	C₂×C₁₃	—	2	2	no	—
343	C₂×C₁₃	—	8	4	no	—
344	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
345	C₂×C₁₃	#3586	1	2	yes	—
346	#41	—	2	8	no	—
347	#41	—	2	8	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	4	no	—
351	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
352	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
353	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
364	Q₁₆	—	2	8	no	—
365	Q₁₆	—	2	4	no	—
366	Q₁₆	—	4	2	no	—
367	Q₁₆	—	4	8	no	—
368	SD₁₆	—	2	8	no	—
369	SD₁₆	—	4	4	no	—
370	SD₁₆	—	4	8	no	—
371	D₈	—	2	4	no	—
372	D₈	—	4	2	no	—
373	M₁₆	—	2	4	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	C₁₃×#41	1	4	yes	—
376	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
377	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
378	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
388	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
389	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
390	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	8	no	—
396	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
397	C₄²	—	2	4	no	—
398	C₄²	—	2	4	no	—
399	C₄²	—	2	8	no	—
400	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
402	C₄²	C₂⁴×C₁₃	1	4	yes	—
403	C₄²	C₂⁴×C₁₃	1	2	yes	—
404	C₁₃	#61416	1	1	yes	characteristic, direct product factor, Sylow
405	C₂³	—	2	4	no	—
406	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
407	Q₈	—	2	4	no	—
408	Q₈	—	2	4	no	—
409	Q₈	—	2	4	no	—
410	Q₈	—	2	4	no	—
411	Q₈	—	4	4	no	—
412	Q₈	—	4	4	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	4	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	8	no	—
417	D₄	—	8	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	8	8	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
429	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
431	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
432	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	2	4	no	—
435	C₈	C₂×C₁₃×#41	1	4	yes	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	C₁₃×#550	1	2	yes	—
441	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	8	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	4	no	—
448	C₄	C₁₃×#550	1	2	yes	—
449	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
450	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂	—	2	2	no	—
452	C₂	—	8	4	no	—
453	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
454	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3150	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3507	C₂	semidirect
2. C₁₃×#3401	C₂	semidirect
3. C₁₃×#3398	C₂	semidirect
4. C₁₃×#3156	C₂	semidirect
6. C₁₃×#3046	C₂	semidirect
7. C₁₃×#3037	C₂	semidirect
8. C₁₃×#2961	C₂	semidirect
9. C₁₃×#2952	C₂	semidirect
10. C₂×C₁₃×#441	C₂	semidirect
119. #61416	C₁₃	direct (N × H)
178. #3507	C₂×C₁₃	semidirect
179. #3401	C₂×C₁₃	semidirect
180. #3398	C₂×C₁₃	semidirect
181. #3156	C₂×C₁₃	semidirect
183. #3046	C₂×C₁₃	semidirect
184. #3037	C₂×C₁₃	semidirect
185. #2961	C₂×C₁₃	semidirect
186. #2952	C₂×C₁₃	semidirect
187. C₂×#441	C₂×C₁₃	semidirect
404. C₁₃	#61416	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×#3507	2
C₁₃×#3401	2
C₁₃×#3398	2
C₁₃×#3156	2
C₁₃×#3150	2
C₁₃×#3046	2
C₁₃×#3037	2
C₁₃×#2961	2
C₁₃×#2952	2
C₂×C₁₃×#441	2
#61416	13

Subgroups — C13×#61416 #15747755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61416 #15747755