Subgroups — C₁₃×#61292 #15747631

Order 3328.

1746 conjugacy classes of subgroups.

The subgroup lattice has 444 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
2	C₁₃×#3349	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3344	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3097	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3078	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3059	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2932	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#2912	C₂	1	2	yes	maximal, complemented
11	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#131	C₂²	1	2	yes	—
13	C₁₃×#559	—	2	2	no	—
14	C₁₃×#557	—	2	2	no	—
15	C₁₃×#556	—	2	4	no	—
16	C₁₃×#556	C₂²	1	4	yes	—
17	C₁₃×#554	C₂²	1	4	yes	—
18	C₁₃×#552	C₂²	1	8	yes	—
19	C₁₃×#539	—	2	4	no	—
20	C₁₃×#536	C₂²	1	4	yes	—
21	C₁₃×#533	C₂²	1	2	yes	—
22	C₁₃×#532	C₂²	1	1	yes	characteristic
23	C₁₃×#529	—	2	4	no	—
24	C₁₃×#520	C₂²	1	4	yes	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#501	C₂²	1	4	yes	—
27	C₁₃×#501	C₂²	1	4	yes	—
28	C₁₃×#485	C₂²	1	8	yes	—
29	C₁₃×#485	C₂²	1	8	yes	—
30	C₁₃×#484	C₂²	1	8	yes	—
31	C₁₃×#483	C₂²	1	8	yes	—
32	C₁₃×#479	C₂²	1	8	yes	—
33	C₁₃×#477	C₂²	1	4	yes	—
34	C₁₃×#475	C₂²	1	4	yes	—
35	C₁₃×#470	C₂²	1	4	yes	—
36	C₁₃×#470	C₂²	1	4	yes	—
37	C₁₃×#467	C₂²	1	8	yes	—
38	C₁₃×#441	C₂²	1	8	yes	—
39	C₁₃×#435	C₂²	1	8	yes	—
40	C₁₃×#428	C₂²	1	4	yes	—
41	C₁₃×#428	C₂²	1	8	yes	—
42	C₁₃×#427	C₂²	1	2	yes	—
43	C₁₃×#427	C₂²	1	4	yes	—
44	C₁₃×#427	C₂²	1	2	yes	—
45	C₂×C₁₃×#106	C₂²	1	4	yes	—
46	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
47	C₁₃×#423	C₂²	1	1	yes	characteristic
48	C₁₃×#419	C₂²	1	4	yes	—
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₁₃×#408	C₂²	1	2	yes	—
51	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#41	C₂³	1	2	yes	—
53	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
54	C₂×C₁₃×Q₁₆	—	2	4	no	—
55	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
56	C₁₃×#131	—	2	8	no	—
57	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
58	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	—	2	4	no	—
63	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₁₃×#127	D₄	1	1	yes	characteristic
67	C₁₃×#126	—	2	8	no	—
68	C₁₃×#126	—	2	8	no	—
69	C₁₃×#125	—	2	4	no	—
70	C₁₃×#125	—	2	8	no	—
71	C₁₃×#125	C₂³	1	4	yes	—
72	C₁₃×#124	—	2	4	no	—
73	C₁₃×#124	—	2	4	no	—
74	C₁₃×#124	D₄	1	2	yes	—
75	C₁₃×#123	—	2	8	no	—
76	C₁₃×#123	—	2	8	no	—
77	C₁₃×C₂²⋊Q₈	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	—	2	8	no	—
80	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
81	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
82	C₁₃×#121	D₄	1	4	yes	—
83	C₄×Q₈×C₁₃	—	2	4	no	—
84	C₄×Q₈×C₁₃	—	2	4	no	—
85	C₄×Q₈×C₁₃	—	2	2	no	—
86	C₄×Q₈×C₁₃	—	2	2	no	—
87	C₄×Q₈×C₁₃	—	2	2	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
90	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
91	C₄×D₄×C₁₃	—	2	8	no	—
92	C₄×D₄×C₁₃	—	2	4	no	—
93	C₄×D₄×C₁₃	—	2	4	no	—
94	C₄×D₄×C₁₃	C₂³	1	4	yes	—
95	C₁₃×#117	—	2	8	no	—
96	C₁₃×#117	C₂³	1	4	yes	—
97	C₁₃×#117	C₂³	1	8	yes	—
98	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
101	C₂×C₄²×C₁₃	—	2	2	no	—
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×#107	C₂³	1	4	yes	—
104	C₁₃×#107	C₂³	1	8	yes	—
105	C₁₃×#107	C₂³	1	4	yes	—
106	C₁₃×#106	C₂³	1	4	yes	—
107	C₁₃×#106	C₂³	1	2	yes	—
108	C₁₃×#106	C₂³	1	8	yes	—
109	C₁₃×#106	C₂³	1	2	yes	—
110	C₁₃×#106	C₂³	1	2	yes	—
111	C₁₃×#106	C₂³	1	2	yes	—
112	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
113	C₁₃×#103	C₂³	1	8	yes	—
114	C₁₃×#103	C₂³	1	8	yes	—
115	C₁₃×#103	C₂³	1	8	yes	—
116	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
117	C₁₃×#97	C₂³	1	4	yes	—
118	#61292	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₁₃×#41	—	2	4	no	—
120	C₁₃×#41	—	2	4	no	—
121	C₂×Q₈×C₁₃	—	2	2	no	—
122	C₂×Q₈×C₁₃	—	2	2	no	—
123	C₂×Q₈×C₁₃	—	2	2	no	—
124	C₂×Q₈×C₁₃	—	2	4	no	—
125	C₂×Q₈×C₁₃	—	2	4	no	—
126	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
128	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
129	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×Q₁₆	—	2	8	no	—
138	C₁₃×M₁₆	—	2	4	no	—
139	C₁₃×M₁₆	—	2	8	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	8	no	—
142	C₂×C₈×C₁₃	#41	1	4	yes	—
143	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
144	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
145	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	8	no	—
156	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
157	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
158	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
159	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
160	C₁₃×C₂²⋊C₄	—	2	8	no	—
161	C₁₃×C₂²⋊C₄	—	2	4	no	—
162	C₁₃×C₂²⋊C₄	—	2	8	no	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
165	C₄²×C₁₃	—	2	4	no	—
166	C₄²×C₁₃	—	2	4	no	—
167	C₄²×C₁₃	—	2	8	no	—
168	C₄²×C₁₃	—	2	4	no	—
169	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂⁴	1	2	yes	—
172	#3507	C₂×C₁₃	1	2	yes	—
173	#3349	C₂×C₁₃	1	8	yes	complemented
174	#3344	C₂×C₁₃	1	8	yes	complemented
175	#3162	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#3097	C₂×C₁₃	1	4	yes	complemented
177	#3078	C₂×C₁₃	1	2	yes	complemented
178	#3059	C₂×C₁₃	1	2	yes	complemented
179	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#2932	C₂×C₁₃	1	1	yes	characteristic
181	#2912	C₂×C₁₃	1	2	yes	complemented
182	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
183	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₁₃	—	2	4	no	—
185	Q₈×C₁₃	—	2	4	no	—
186	Q₈×C₁₃	—	2	4	no	—
187	Q₈×C₁₃	—	4	4	no	—
188	Q₈×C₁₃	—	4	4	no	—
189	Q₈×C₁₃	—	8	2	no	—
190	D₄×C₁₃	—	2	8	no	—
191	D₄×C₁₃	—	2	4	no	—
192	D₄×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	4	no	—
201	C₂×C₄×C₁₃	—	8	2	no	—
202	C₂×C₄×C₁₃	—	8	8	no	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
208	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
209	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
210	C₈×C₁₃	—	2	4	no	—
211	C₈×C₁₃	—	2	2	no	—
212	C₈×C₁₃	C₂×#41	1	4	yes	—
213	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#131	C₂²×C₁₃	1	2	yes	—
215	#559	—	2	2	no	—
216	#557	—	2	2	no	—
217	#556	—	2	4	no	—
218	#556	C₂²×C₁₃	1	4	yes	—
219	#554	C₂²×C₁₃	1	4	yes	—
220	#552	C₂²×C₁₃	1	8	yes	—
221	#539	—	2	4	no	—
222	#536	C₂²×C₁₃	1	4	yes	—
223	#533	C₂²×C₁₃	1	2	yes	—
224	#532	C₂²×C₁₃	1	1	yes	characteristic
225	#529	—	2	4	no	—
226	#520	C₂²×C₁₃	1	4	yes	—
227	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
228	#501	C₂²×C₁₃	1	4	yes	—
229	#501	C₂²×C₁₃	1	4	yes	—
230	#485	C₂²×C₁₃	1	8	yes	—
231	#485	C₂²×C₁₃	1	8	yes	—
232	#484	C₂²×C₁₃	1	8	yes	—
233	#483	C₂²×C₁₃	1	8	yes	—
234	#479	C₂²×C₁₃	1	8	yes	—
235	#477	C₂²×C₁₃	1	4	yes	—
236	#475	C₂²×C₁₃	1	4	yes	—
237	#470	C₂²×C₁₃	1	4	yes	—
238	#470	C₂²×C₁₃	1	4	yes	—
239	#467	C₂²×C₁₃	1	8	yes	—
240	#441	C₂²×C₁₃	1	8	yes	—
241	#435	C₂²×C₁₃	1	8	yes	—
242	#428	C₂²×C₁₃	1	4	yes	—
243	#428	C₂²×C₁₃	1	8	yes	—
244	#427	C₂²×C₁₃	1	4	yes	—
245	#427	C₂²×C₁₃	1	2	yes	—
246	#427	C₂²×C₁₃	1	2	yes	—
247	C₂×#106	C₂²×C₁₃	1	4	yes	—
248	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
249	#423	C₂²×C₁₃	1	1	yes	characteristic
250	#419	C₂²×C₁₃	1	4	yes	—
251	C₂×#103	C₂²×C₁₃	1	2	yes	—
252	#408	C₂²×C₁₃	1	2	yes	—
253	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	—	2	8	no	—
256	C₂²×C₁₃	—	2	4	no	—
257	C₂²×C₁₃	#547	1	2	yes	—
258	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	2	4	no	—
262	C₄×C₁₃	—	4	4	no	—
263	C₄×C₁₃	—	4	4	no	—
264	C₄×C₁₃	—	4	4	no	—
265	C₄×C₁₃	—	4	4	no	—
266	C₄×C₁₃	#547	1	2	yes	—
267	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
268	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
269	C₂×#41	C₂³×C₁₃	1	2	yes	—
270	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
271	C₂×Q₁₆	—	2	4	no	—
272	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
273	#131	—	2	8	no	—
274	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
275	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
276	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
277	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
279	C₄⋊Q₈	—	2	4	no	—
280	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
281	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
282	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
283	#127	D₄×C₁₃	1	1	yes	characteristic
284	#126	—	2	8	no	—
285	#126	—	2	8	no	—
286	#125	—	2	4	no	—
287	#125	—	2	8	no	—
288	#125	C₂³×C₁₃	1	4	yes	—
289	#124	—	2	4	no	—
290	#124	—	2	4	no	—
291	#124	D₄×C₁₃	1	2	yes	—
292	#123	—	2	8	no	—
293	#123	—	2	8	no	—
294	C₂²⋊Q₈	—	2	2	no	—
295	C₂²⋊Q₈	—	2	2	no	—
296	C₂²⋊Q₈	—	2	8	no	—
297	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
298	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
299	#121	D₄×C₁₃	1	4	yes	—
300	C₄×Q₈	—	2	4	no	—
301	C₄×Q₈	—	2	4	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
307	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
308	C₄×D₄	—	2	8	no	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	2	4	no	—
311	C₄×D₄	C₂³×C₁₃	1	4	yes	—
312	#117	—	2	8	no	—
313	#117	C₂³×C₁₃	1	4	yes	—
314	#117	C₂³×C₁₃	1	8	yes	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
320	#107	C₂³×C₁₃	1	4	yes	—
321	#107	C₂³×C₁₃	1	8	yes	—
322	#107	C₂³×C₁₃	1	4	yes	—
323	#106	C₂³×C₁₃	1	4	yes	—
324	#106	C₂³×C₁₃	1	2	yes	—
325	#106	C₂³×C₁₃	1	8	yes	—
326	#106	C₂³×C₁₃	1	2	yes	—
327	#106	C₂³×C₁₃	1	2	yes	—
328	#106	C₂³×C₁₃	1	2	yes	—
329	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
330	#103	C₂³×C₁₃	1	8	yes	—
331	#103	C₂³×C₁₃	1	8	yes	—
332	#103	C₂³×C₁₃	1	8	yes	—
333	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
334	#97	C₂³×C₁₃	1	4	yes	—
335	C₂×C₁₃	—	2	2	no	—
336	C₂×C₁₃	—	4	4	no	—
337	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
338	C₂×C₁₃	#3586	1	2	yes	—
339	#41	—	2	4	no	—
340	#41	—	2	4	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
347	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
348	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
349	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
350	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
356	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
357	Q₁₆	—	2	8	no	—
358	M₁₆	—	2	4	no	—
359	M₁₆	—	2	8	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	8	no	—
362	C₂×C₈	C₁₃×#41	1	4	yes	—
363	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
364	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
365	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
377	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
378	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
379	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	8	no	—
388	C₄²	—	2	4	no	—
389	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₄²	C₂⁴×C₁₃	1	2	yes	—
392	C₁₃	#61292	1	1	yes	characteristic, direct product factor, Sylow
393	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
394	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	2	4	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	4	no	—
399	Q₈	—	4	4	no	—
400	Q₈	—	8	2	no	—
401	D₄	—	2	8	no	—
402	D₄	—	2	4	no	—
403	D₄	—	4	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	—	8	8	no	—
414	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
416	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
419	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
420	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
421	C₈	—	2	4	no	—
422	C₈	—	2	2	no	—
423	C₈	C₂×C₁₃×#41	1	4	yes	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	8	no	—
426	C₂²	—	2	4	no	—
427	C₂²	C₁₃×#547	1	2	yes	—
428	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	4	no	—
432	C₄	—	4	4	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	4	no	—
436	C₄	C₁₃×#547	1	2	yes	—
437	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
438	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
439	C₂	—	2	2	no	—
440	C₂	—	4	4	no	—
441	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
442	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×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3349	C₂	semidirect
3. C₁₃×#3344	C₂	semidirect
4. C₁₃×#3162	C₂	semidirect
5. C₁₃×#3097	C₂	semidirect
6. C₁₃×#3078	C₂	semidirect
7. C₁₃×#3059	C₂	semidirect
8. C₂×C₁₃×#441	C₂	semidirect
10. C₁₃×#2912	C₂	semidirect
118. #61292	C₁₃	direct (N × H)
173. #3349	C₂×C₁₃	semidirect
174. #3344	C₂×C₁₃	semidirect
175. #3162	C₂×C₁₃	semidirect
176. #3097	C₂×C₁₃	semidirect
177. #3078	C₂×C₁₃	semidirect
178. #3059	C₂×C₁₃	semidirect
179. C₂×#441	C₂×C₁₃	semidirect
181. #2912	C₂×C₁₃	semidirect
392. C₁₃	#61292	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×#3349	2
C₁₃×#3344	2
C₁₃×#3162	2
C₁₃×#3097	2
C₁₃×#3078	2
C₁₃×#3059	2
C₂×C₁₃×#441	2
C₁₃×#2932	2
C₁₃×#2912	2
#61292	13

Subgroups — C13×#61292 #15747631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61292 #15747631