Subgroups — C₁₃×#61411 #15747750

Order 3328.

1838 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3398	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3395	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3393	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3156	C₂	1	2	yes	maximal
6	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3044	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3039	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2950	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#137	C₂²	1	4	yes	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
16	C₁₃×#557	C₂²	1	8	yes	—
17	C₁₃×#556	C₂²	1	8	yes	—
18	C₁₃×#552	—	2	8	no	—
19	C₁₃×#541	—	2	4	no	—
20	C₁₃×#536	C₂²	1	4	yes	—
21	C₁₃×#533	—	2	4	no	—
22	C₁₃×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₁₃×#519	C₂²	1	4	yes	—
25	C₄×C₁₃×#41	C₂²	1	2	yes	—
26	C₁₃×#497	C₂²	1	8	yes	—
27	C₁₃×#495	C₂²	1	4	yes	—
28	C₁₃×#494	C₂²	1	4	yes	—
29	C₁₃×#494	C₂²	1	4	yes	—
30	C₁₃×#494	C₂²	1	4	yes	—
31	C₁₃×#464	C₂²	1	16	yes	—
32	C₁₃×#462	C₂²	1	8	yes	—
33	C₁₃×#462	C₂²	1	16	yes	—
34	C₁₃×#461	C₂²	1	8	yes	—
35	C₁₃×#446	C₂²	1	4	yes	—
36	C₈×Q₈×C₁₃	C₂²	1	4	yes	—
37	C₁₃×#441	C₂²	1	8	yes	—
38	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	—
39	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
40	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
41	C₄×C₁₃×D₈	C₂²	1	2	yes	—
42	C₁₃×#427	C₂²	1	1	yes	characteristic
43	C₁₃×#424	C₂²	1	2	yes	—
44	C₁₃×#423	C₂²	1	1	yes	characteristic
45	C₁₃×#419	C₂²	1	4	yes	—
46	C₁₃×#416	C₂²	1	2	yes	—
47	C₁₃×#405	C₂²	1	2	yes	—
48	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#41	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
51	C₁₃×#137	—	4	8	no	—
52	C₁₃×#135	—	2	4	no	—
53	C₂×C₁₃×Q₁₆	—	2	8	no	—
54	C₂×C₁₃×Q₁₆	—	4	4	no	—
55	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
57	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
58	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
59	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
60	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
61	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
62	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₁₃×C₄⋊Q₈	—	2	2	no	—
68	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
71	C₁₃×#126	—	2	16	no	—
72	C₁₃×#125	—	2	8	no	—
73	C₁₃×#125	—	2	16	no	—
74	C₁₃×#125	D₄	1	2	yes	—
75	C₁₃×#124	C₂³	1	8	yes	—
76	C₁₃×#123	—	2	8	no	—
77	C₁₃×C₂²⋊Q₈	—	2	8	no	—
78	C₁₃×C₂²⋊Q₈	—	2	8	no	—
79	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
80	C₄×Q₈×C₁₃	—	2	8	no	—
81	C₄×Q₈×C₁₃	—	2	8	no	—
82	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
83	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
84	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
85	C₄×D₄×C₁₃	—	2	4	no	—
86	C₄×D₄×C₁₃	C₂³	1	4	yes	—
87	C₁₃×#117	—	2	8	no	—
88	C₁₃×#117	—	2	8	no	—
89	C₁₃×#117	—	2	2	no	—
90	C₁₃×#117	C₂³	1	2	yes	—
91	C₁₃×#117	C₂³	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
93	C₂×C₄²×C₁₃	—	2	2	no	—
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×#107	C₂³	1	2	yes	—
96	C₁₃×#106	C₂³	1	2	yes	—
97	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
98	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
99	C₁₃×#103	C₂³	1	4	yes	—
100	C₁₃×#103	C₂³	1	16	yes	—
101	C₁₃×#102	C₂³	1	4	yes	—
102	C₁₃×#97	C₂³	1	4	yes	—
103	C₄×C₈×C₁₃	C₂³	1	2	yes	—
104	C₄×C₈×C₁₃	C₂³	1	2	yes	—
105	C₄×C₈×C₁₃	C₂³	1	4	yes	—
106	#61411	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₁₃×#41	—	2	4	no	—
108	C₁₃×#41	—	2	4	no	—
109	C₂×Q₈×C₁₃	—	2	4	no	—
110	C₂×Q₈×C₁₃	—	2	8	no	—
111	C₂×Q₈×C₁₃	—	2	8	no	—
112	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
113	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
114	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₁₃×Q₁₆	—	2	8	no	—
123	C₁₃×Q₁₆	—	2	8	no	—
124	C₁₃×Q₁₆	—	2	2	no	—
125	C₁₃×Q₁₆	—	4	8	no	—
126	C₁₃×Q₁₆	—	4	8	no	—
127	C₁₃×SD₁₆	—	2	4	no	—
128	C₁₃×SD₁₆	—	4	8	no	—
129	C₁₃×D₈	—	2	2	no	—
130	C₁₃×M₁₆	—	2	4	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	#41	1	4	yes	—
133	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
134	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
135	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×C₄⋊C₄	—	2	8	no	—
138	C₁₃×C₄⋊C₄	—	2	8	no	—
139	C₁₃×C₄⋊C₄	—	2	4	no	—
140	C₁₃×C₄⋊C₄	—	2	16	no	—
141	C₁₃×C₄⋊C₄	—	2	16	no	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
143	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
144	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
145	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
146	C₁₃×C₂²⋊C₄	—	2	2	no	—
147	C₁₃×C₂²⋊C₄	—	2	4	no	—
148	C₁₃×C₂²⋊C₄	—	2	16	no	—
149	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
150	C₄²×C₁₃	—	2	2	no	—
151	C₄²×C₁₃	—	2	4	no	—
152	C₄²×C₁₃	—	2	16	no	—
153	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂⁴	1	2	yes	—
156	C₄²×C₁₃	C₂⁴	1	4	yes	—
157	#3509	C₂×C₁₃	1	2	yes	complemented
158	#3398	C₂×C₁₃	1	8	yes	complemented
159	#3395	C₂×C₁₃	1	4	yes	complemented
160	#3393	C₂×C₁₃	1	4	yes	complemented
161	#3156	C₂×C₁₃	1	2	yes	—
162	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#3044	C₂×C₁₃	1	4	yes	complemented
164	#3039	C₂×C₁₃	1	2	yes	complemented
165	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#2950	C₂×C₁₃	1	2	yes	complemented
167	C₄×#135	C₂×C₁₃	1	1	yes	characteristic
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	8	no	—
171	Q₈×C₁₃	—	2	2	no	—
172	Q₈×C₁₃	—	2	8	no	—
173	Q₈×C₁₃	—	2	8	no	—
174	Q₈×C₁₃	—	2	2	no	—
175	Q₈×C₁₃	—	4	8	no	—
176	D₄×C₁₃	—	2	2	no	—
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	4	4	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	8	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	4	8	no	—
184	C₂×C₄×C₁₃	—	4	4	no	—
185	C₂×C₄×C₁₃	—	4	8	no	—
186	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
191	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
192	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
193	C₈×C₁₃	—	2	2	no	—
194	C₈×C₁₃	—	2	4	no	—
195	C₈×C₁₃	C₂×#41	1	2	yes	—
196	C₈×C₁₃	C₂×#41	1	2	yes	—
197	C₂×#137	C₂²×C₁₃	1	4	yes	—
198	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
199	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
200	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
201	#557	C₂²×C₁₃	1	8	yes	—
202	#556	C₂²×C₁₃	1	8	yes	—
203	#552	—	2	8	no	—
204	#541	—	2	4	no	—
205	#536	C₂²×C₁₃	1	4	yes	—
206	#533	—	2	4	no	—
207	#533	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
209	#519	C₂²×C₁₃	1	4	yes	—
210	C₄×#41	C₂²×C₁₃	1	2	yes	—
211	#497	C₂²×C₁₃	1	8	yes	—
212	#495	C₂²×C₁₃	1	4	yes	—
213	#494	C₂²×C₁₃	1	4	yes	—
214	#494	C₂²×C₁₃	1	4	yes	—
215	#494	C₂²×C₁₃	1	4	yes	—
216	#464	C₂²×C₁₃	1	16	yes	—
217	#462	C₂²×C₁₃	1	8	yes	—
218	#462	C₂²×C₁₃	1	16	yes	—
219	#461	C₂²×C₁₃	1	8	yes	—
220	#446	C₂²×C₁₃	1	4	yes	—
221	C₈×Q₈	C₂²×C₁₃	1	4	yes	—
222	#441	C₂²×C₁₃	1	8	yes	—
223	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	—
224	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
225	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
226	C₄×D₈	C₂²×C₁₃	1	2	yes	—
227	#427	C₂²×C₁₃	1	1	yes	characteristic
228	#424	C₂²×C₁₃	1	2	yes	—
229	#423	C₂²×C₁₃	1	1	yes	characteristic
230	#419	C₂²×C₁₃	1	4	yes	—
231	#416	C₂²×C₁₃	1	2	yes	—
232	#405	C₂²×C₁₃	1	2	yes	—
233	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂²×C₁₃	—	2	2	no	—
235	C₂²×C₁₃	—	4	2	no	—
236	C₂²×C₁₃	—	4	4	no	—
237	C₂²×C₁₃	#550	1	2	yes	—
238	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
239	C₄×C₁₃	—	2	2	no	—
240	C₄×C₁₃	—	2	8	no	—
241	C₄×C₁₃	—	4	2	no	—
242	C₄×C₁₃	—	4	8	no	—
243	C₄×C₁₃	—	4	4	no	—
244	C₄×C₁₃	#550	1	2	yes	—
245	C₄×C₁₃	#578	1	4	yes	—
246	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
247	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
248	C₂×#41	C₂³×C₁₃	1	2	yes	—
249	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
250	#137	—	4	8	no	—
251	#135	—	2	4	no	—
252	C₂×Q₁₆	—	2	8	no	—
253	C₂×Q₁₆	—	4	4	no	—
254	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
255	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
256	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
257	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
258	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
259	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
260	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
261	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
263	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
268	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
269	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
270	#126	—	2	16	no	—
271	#125	—	2	8	no	—
272	#125	—	2	16	no	—
273	#125	D₄×C₁₃	1	2	yes	—
274	#124	C₂³×C₁₃	1	8	yes	—
275	#123	—	2	8	no	—
276	C₂²⋊Q₈	—	2	8	no	—
277	C₂²⋊Q₈	—	2	8	no	—
278	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
279	C₄×Q₈	—	2	8	no	—
280	C₄×Q₈	—	2	8	no	—
281	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
282	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
283	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
284	C₄×D₄	—	2	4	no	—
285	C₄×D₄	C₂³×C₁₃	1	4	yes	—
286	#117	—	2	8	no	—
287	#117	—	2	8	no	—
288	#117	—	2	2	no	—
289	#117	C₂³×C₁₃	1	2	yes	—
290	#117	C₂³×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
294	#107	C₂³×C₁₃	1	2	yes	—
295	#106	C₂³×C₁₃	1	2	yes	—
296	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
297	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
298	#103	C₂³×C₁₃	1	4	yes	—
299	#103	C₂³×C₁₃	1	16	yes	—
300	#102	C₂³×C₁₃	1	4	yes	—
301	#97	C₂³×C₁₃	1	4	yes	—
302	C₄×C₈	C₂³×C₁₃	1	2	yes	—
303	C₄×C₈	C₂³×C₁₃	1	2	yes	—
304	C₄×C₈	C₂³×C₁₃	1	4	yes	—
305	C₂×C₁₃	—	2	2	no	—
306	C₂×C₁₃	—	8	2	no	—
307	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
308	C₂×C₁₃	C₂×#578	1	2	yes	—
309	#41	—	2	4	no	—
310	#41	—	2	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	8	no	—
313	C₂×Q₈	—	2	8	no	—
314	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
315	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
316	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
324	Q₁₆	—	2	8	no	—
325	Q₁₆	—	2	8	no	—
326	Q₁₆	—	2	2	no	—
327	Q₁₆	—	4	8	no	—
328	Q₁₆	—	4	8	no	—
329	SD₁₆	—	2	4	no	—
330	SD₁₆	—	4	8	no	—
331	D₈	—	2	2	no	—
332	M₁₆	—	2	4	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	C₁₃×#41	1	4	yes	—
335	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
336	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
337	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
338	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	16	no	—
343	C₄⋊C₄	—	2	16	no	—
344	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
345	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
346	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
347	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	2	16	no	—
351	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	2	16	no	—
355	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
356	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₄²	C₂⁴×C₁₃	1	2	yes	—
358	C₄²	C₂⁴×C₁₃	1	4	yes	—
359	C₁₃	#61411	1	1	yes	characteristic, direct product factor, Sylow
360	C₂³	—	2	2	no	—
361	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
362	Q₈	—	2	8	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	2	8	no	—
365	Q₈	—	2	8	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	4	8	no	—
368	D₄	—	2	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	8	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
379	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
380	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
382	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
383	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
384	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	2	4	no	—
387	C₈	C₂×C₁₃×#41	1	2	yes	—
388	C₈	C₂×C₁₃×#41	1	2	yes	—
389	C₂²	—	2	2	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	2	no	—
392	C₂²	C₁₃×#550	1	2	yes	—
393	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	2	8	no	—
396	C₄	—	4	4	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	8	no	—
399	C₄	C₁₃×#550	1	2	yes	—
400	C₄	C₁₃×#578	1	4	yes	—
401	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
402	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂	—	2	2	no	—
404	C₂	—	8	2	no	—
405	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
406	C₂	C₂×C₁₃×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#135	C₂²
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×#3509	C₂	semidirect
2. C₁₃×#3398	C₂	semidirect
3. C₁₃×#3395	C₂	semidirect
4. C₁₃×#3393	C₂	semidirect
6. C₂×C₁₃×#494	C₂	semidirect
7. C₁₃×#3044	C₂	semidirect
8. C₁₃×#3039	C₂	semidirect
9. C₁₃×#2960	C₂	semidirect
10. C₁₃×#2950	C₂	semidirect
106. #61411	C₁₃	direct (N × H)
157. #3509	C₂×C₁₃	semidirect
158. #3398	C₂×C₁₃	semidirect
159. #3395	C₂×C₁₃	semidirect
160. #3393	C₂×C₁₃	semidirect
162. C₂×#494	C₂×C₁₃	semidirect
163. #3044	C₂×C₁₃	semidirect
164. #3039	C₂×C₁₃	semidirect
165. #2960	C₂×C₁₃	semidirect
166. #2950	C₂×C₁₃	semidirect
359. C₁₃	#61411	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×#3509	2
C₁₃×#3398	2
C₁₃×#3395	2
C₁₃×#3393	2
C₁₃×#3156	2
C₂×C₁₃×#494	2
C₁₃×#3044	2
C₁₃×#3039	2
C₁₃×#2960	2
C₁₃×#2950	2
C₄×C₁₃×#135	2
#61411	13

Subgroups — C13×#61411 #15747750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61411 #15747750