Subgroups — C₁₃×#17984 #15704323

Order 3328.

578 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3172	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1587	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1585	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1584	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1583	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1569	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1497	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1495	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₁₃×#529	C₂²	1	1	yes	characteristic
14	C₁₃×#501	C₄	1	1	yes	characteristic
15	C₁₃×#497	C₄	1	1	yes	characteristic
16	C₁₃×#491	C₄	1	1	yes	characteristic
17	C₁₃×#489	C₄	1	1	yes	characteristic
18	C₁₃×#470	C₄	1	2	yes	—
19	C₁₃×#468	C₄	1	2	yes	—
20	C₁₃×#446	—	2	1	no	—
21	C₁₃×#446	C₂²	1	1	yes	characteristic
22	C₁₃×#446	C₂²	1	2	yes	—
23	C₈×Q₈×C₁₃	—	2	1	no	—
24	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
27	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
28	C₁₃×#436	C₂²	1	1	yes	characteristic
29	C₁₃×#435	—	2	1	no	—
30	C₈×D₄×C₁₃	—	2	1	no	—
31	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#433	—	2	1	no	—
33	C₁₃×#432	C₂²	1	1	yes	characteristic
34	C₁₃×#431	C₂²	1	1	yes	characteristic
35	C₁₃×#424	—	2	1	no	—
36	C₁₃×#423	C₂²	1	1	yes	characteristic
37	C₁₃×#405	—	2	1	no	—
38	C₁₃×#405	—	2	1	no	—
39	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#335	C₂²	1	2	yes	—
42	C₁₃×#334	C₂²	1	2	yes	—
43	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
47	C₁₃×#322	C₂²	1	2	yes	—
48	C₁₃×#322	C₂²	1	2	yes	—
49	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₁₃	—	2	1	no	—
55	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
57	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
59	C₁₃×#126	—	2	1	no	—
60	C₁₃×#125	—	2	1	no	—
61	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
62	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
63	C₁₃×#123	—	2	1	no	—
64	C₁₃×C₂²⋊Q₈	—	2	1	no	—
65	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
66	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
67	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₃	—	2	1	no	—
69	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
70	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₁₃	—	2	1	no	—
72	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#117	—	2	1	no	—
74	C₁₃×#117	—	2	1	no	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#107	C₂×C₄	1	2	yes	—
77	C₁₃×#106	C₂×C₄	1	2	yes	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×C₄⋊C₈	—	2	1	no	—
81	C₁₃×C₄⋊C₈	—	2	1	no	—
82	C₁₃×C₄⋊C₈	—	2	1	no	—
83	C₁₃×C₄⋊C₈	—	2	1	no	—
84	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
85	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₃×#103	C₂×C₄	1	2	yes	—
88	C₁₃×#103	C₂×C₄	1	2	yes	—
89	C₁₃×#103	C₂×C₄	1	2	yes	—
90	C₁₃×#102	C₂×C₄	1	2	yes	—
91	C₁₃×C₂²⋊C₈	—	2	1	no	—
92	C₁₃×C₂²⋊C₈	—	2	1	no	—
93	C₁₃×C₂²⋊C₈	—	2	1	no	—
94	C₁₃×C₂²⋊C₈	—	2	1	no	—
95	C₁₃×#97	—	2	1	no	—
96	C₁₃×#97	—	2	2	no	—
97	C₁₃×#97	—	2	1	no	—
98	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
99	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
100	C₄×C₈×C₁₃	—	2	1	no	—
101	C₄×C₈×C₁₃	—	2	2	no	—
102	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
103	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
104	C₄×C₈×C₁₃	C₂³	1	2	yes	—
105	C₄×C₈×C₁₃	C₂³	1	2	yes	—
106	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	#17984	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₁₃×Q₁₆	—	4	2	no	—
119	C₁₃×SD₁₆	—	4	2	no	—
120	C₁₃×M₁₆	—	4	2	no	—
121	C₁₃×M₁₆	—	4	2	no	—
122	C₁₃×M₁₆	—	4	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	4	1	no	—
129	C₂×C₈×C₁₃	—	4	2	no	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
146	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
147	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
148	C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₁₃×C₂²⋊C₄	—	2	1	no	—
150	C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₄²×C₁₃	—	2	1	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₃	#41	1	1	yes	characteristic
159	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
160	#3172	C₂×C₁₃	1	1	yes	characteristic
161	#2966	C₂×C₁₃	1	1	yes	characteristic
162	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1587	C₂×C₁₃	1	2	yes	complemented
164	#1585	C₂×C₁₃	1	2	yes	complemented
165	#1584	C₂×C₁₃	1	2	yes	complemented
166	#1583	C₂×C₁₃	1	2	yes	complemented
167	#1569	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1497	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1495	C₂×C₁₃	1	1	yes	characteristic
170	#1451	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂³×C₁₃	—	2	1	no	—
172	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
173	Q₈×C₁₃	—	2	2	no	—
174	Q₈×C₁₃	—	2	2	no	—
175	Q₈×C₁₃	—	2	2	no	—
176	Q₈×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₈×C₁₃	—	2	2	no	—
197	C₈×C₁₃	—	2	2	no	—
198	C₈×C₁₃	—	2	1	no	—
199	C₈×C₁₃	—	2	1	no	—
200	C₈×C₁₃	—	2	1	no	—
201	C₈×C₁₃	—	4	2	no	—
202	C₈×C₁₃	—	4	1	no	—
203	C₈×C₁₃	—	4	1	no	—
204	C₈×C₁₃	—	4	2	no	—
205	C₈×C₁₃	#137	1	2	yes	—
206	#533	C₂²×C₁₃	1	1	yes	characteristic
207	#529	C₂²×C₁₃	1	1	yes	characteristic
208	#501	C₄×C₁₃	1	1	yes	characteristic
209	#497	C₄×C₁₃	1	1	yes	characteristic
210	#491	C₄×C₁₃	1	1	yes	characteristic
211	#489	C₄×C₁₃	1	1	yes	characteristic
212	#470	C₄×C₁₃	1	2	yes	—
213	#468	C₄×C₁₃	1	2	yes	—
214	#446	—	2	1	no	—
215	#446	C₂²×C₁₃	1	1	yes	characteristic
216	#446	C₂²×C₁₃	1	2	yes	—
217	C₈×Q₈	—	2	1	no	—
218	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
219	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
221	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
222	#436	C₂²×C₁₃	1	1	yes	characteristic
223	#435	—	2	1	no	—
224	C₈×D₄	—	2	1	no	—
225	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
226	#433	—	2	1	no	—
227	#432	C₂²×C₁₃	1	1	yes	characteristic
228	#431	C₂²×C₁₃	1	1	yes	characteristic
229	#424	—	2	1	no	—
230	#423	C₂²×C₁₃	1	1	yes	characteristic
231	#405	—	2	1	no	—
232	#405	—	2	1	no	—
233	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
235	#335	C₂²×C₁₃	1	2	yes	—
236	#334	C₂²×C₁₃	1	2	yes	—
237	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
238	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
239	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
240	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
241	#322	C₂²×C₁₃	1	2	yes	—
242	#322	C₂²×C₁₃	1	2	yes	—
243	C₂²×C₁₃	—	2	1	no	—
244	C₂²×C₁₃	—	2	1	no	—
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	—	4	1	no	—
247	C₂²×C₁₃	—	4	1	no	—
248	C₂²×C₁₃	—	4	1	no	—
249	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	—	2	1	no	—
254	C₄×C₁₃	—	4	1	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	—	4	1	no	—
257	C₄×C₁₃	—	4	1	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	#568	1	2	yes	—
260	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
261	C₄×C₁₃	#575	1	1	yes	characteristic
262	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
263	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
269	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
270	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
271	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
272	#126	—	2	1	no	—
273	#125	—	2	1	no	—
274	#125	C₂×C₄×C₁₃	1	1	yes	characteristic
275	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
276	#123	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
279	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
280	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
286	#117	—	2	1	no	—
287	#117	—	2	1	no	—
288	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
289	#107	C₂×C₄×C₁₃	1	2	yes	—
290	#106	C₂×C₄×C₁₃	1	2	yes	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
298	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
299	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
300	#103	C₂×C₄×C₁₃	1	2	yes	—
301	#103	C₂×C₄×C₁₃	1	2	yes	—
302	#103	C₂×C₄×C₁₃	1	2	yes	—
303	#102	C₂×C₄×C₁₃	1	2	yes	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	1	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	#97	—	2	1	no	—
309	#97	—	2	2	no	—
310	#97	—	2	1	no	—
311	#97	C₂×C₄×C₁₃	1	1	yes	characteristic
312	#97	C₂×C₄×C₁₃	1	1	yes	characteristic
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
316	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
317	C₄×C₈	C₂³×C₁₃	1	2	yes	—
318	C₄×C₈	C₂³×C₁₃	1	2	yes	—
319	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
320	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
321	C₂×C₁₃	—	4	1	no	—
322	C₂×C₁₃	—	8	1	no	—
323	C₂×C₁₃	#2932	1	1	yes	characteristic
324	C₂×C₁₃	C₄×#137	1	1	yes	characteristic
325	C₂×C₁₃	#2955	1	1	yes	characteristic
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
328	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
335	Q₁₆	—	4	2	no	—
336	SD₁₆	—	4	2	no	—
337	M₁₆	—	4	2	no	—
338	M₁₆	—	4	2	no	—
339	M₁₆	—	4	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
348	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
349	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
363	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
374	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₄²	C₁₃×#41	1	1	yes	characteristic
376	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
377	C₁₃	#17984	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	2	1	no	—
379	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	2	2	no	—
383	Q₈	—	4	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
398	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
399	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
400	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	2	2	no	—
405	C₈	—	2	1	no	—
406	C₈	—	2	1	no	—
407	C₈	—	2	1	no	—
408	C₈	—	4	2	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	2	no	—
412	C₈	C₁₃×#137	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	2	no	—
429	C₄	C₁₃×#568	1	2	yes	—
430	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
431	C₄	C₁₃×#575	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	8	1	no	—
434	C₂	C₁₃×#2932	1	1	yes	characteristic
435	C₂	C₄×C₁₃×#137	1	1	yes	characteristic
436	C₂	C₁₃×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#121	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2960	C₂	semidirect
4. C₁₃×#1587	C₂	semidirect
5. C₁₃×#1585	C₂	semidirect
6. C₁₃×#1584	C₂	semidirect
7. C₁₃×#1583	C₂	semidirect
8. C₁₃×#1569	C₂	semidirect
9. C₁₃×#1497	C₂	semidirect
11. C₁₃×#1451	C₂	semidirect
108. #17984	C₁₃	direct (N × H)
162. #2960	C₂×C₁₃	semidirect
163. #1587	C₂×C₁₃	semidirect
164. #1585	C₂×C₁₃	semidirect
165. #1584	C₂×C₁₃	semidirect
166. #1583	C₂×C₁₃	semidirect
167. #1569	C₂×C₁₃	semidirect
168. #1497	C₂×C₁₃	semidirect
170. #1451	C₂×C₁₃	semidirect
377. C₁₃	#17984	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×#3172	2
C₁₃×#2966	2
C₁₃×#2960	2
C₁₃×#1587	2
C₁₃×#1585	2
C₁₃×#1584	2
C₁₃×#1583	2
C₁₃×#1569	2
C₁₃×#1497	2
C₁₃×#1495	2
C₁₃×#1451	2
#17984	13

Subgroups — C13×#17984 #15704323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17984 #15704323