Subgroups — C₁₃×#23774 #15710113

Order 3328.

820 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2086	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2067	C₂	1	2	yes	maximal
7	C₁₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₃×#107	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#102	C₂	1	2	yes	maximal
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	—	2	1	no	—
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#391	—	2	1	no	—
23	C₁₃×#390	C₂²	1	1	yes	characteristic
24	C₁₃×#390	C₂²	1	1	yes	characteristic
25	C₁₃×#389	—	2	1	no	—
26	C₁₃×#389	C₂²	1	1	yes	characteristic
27	C₁₃×#389	C₂²	1	1	yes	characteristic
28	C₁₃×#389	C₂²	1	2	yes	—
29	C₁₃×#388	—	2	1	no	—
30	C₁₃×#388	—	2	1	no	—
31	C₁₃×#384	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
36	C₄³×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₁₃×C₄⋊Q₈	—	2	4	no	—
49	C₄×Q₈×C₁₃	—	4	4	no	—
50	C₄×D₄×C₁₃	—	2	2	no	—
51	C₄×D₄×C₁₃	Q₈	1	4	yes	complemented
52	C₁₃×#117	—	4	4	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₃	—	2	2	no	—
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#107	—	2	4	no	—
79	C₁₃×#107	—	2	4	no	—
80	C₁₃×C₄⋊C₈	—	2	4	no	—
81	C₁₃×#102	—	2	4	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₄×C₈×C₁₃	—	2	4	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	2	no	—
89	#23774	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	4	no	—
92	C₂×Q₈×C₁₃	—	4	2	no	—
93	C₂×Q₈×C₁₃	—	4	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	4	2	no	—
105	C₂²×C₄×C₁₃	—	4	2	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	#41	1	4	yes	—
119	C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	4	2	no	—
127	C₁₃×C₄⋊C₄	—	4	2	no	—
128	C₁₃×C₄⋊C₄	—	4	4	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	—	4	2	no	—
131	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
132	C₁₃×C₄⋊C₄	#41	1	4	yes	—
133	C₁₃×C₂²⋊C₄	—	2	4	no	—
134	C₁₃×C₂²⋊C₄	—	4	2	no	—
135	C₁₃×C₂²⋊C₄	—	4	2	no	—
136	C₁₃×C₂²⋊C₄	—	4	2	no	—
137	C₁₃×C₂²⋊C₄	—	4	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	4	1	no	—
143	C₄²×C₁₃	—	4	2	no	—
144	C₄²×C₁₃	—	4	4	no	—
145	C₄²×C₁₃	D₈	1	4	yes	—
146	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
147	C₄²×C₁₃	#41	1	2	yes	—
148	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2293	C₂×C₁₃	1	1	yes	characteristic
150	#2099	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2093	C₂×C₁₃	1	1	yes	characteristic
152	#2086	C₂×C₁₃	1	2	yes	complemented
153	#2067	C₂×C₁₃	1	2	yes	—
154	#2057	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2023	C₂×C₁₃	1	1	yes	characteristic
156	C₄×#107	C₂×C₁₃	1	2	yes	complemented
157	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
158	C₄×#102	C₂×C₁₃	1	2	yes	—
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₃	—	4	8	no	—
168	D₄×C₁₃	—	2	4	no	—
169	D₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	4	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	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	8	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
199	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
200	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
201	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
202	C₂×C₄×C₁₃	#135	1	2	yes	—
203	C₂×C₄×C₁₃	#137	1	2	yes	—
204	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
207	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
208	C₈×C₁₃	—	2	4	no	—
209	C₈×C₁₃	—	4	2	no	—
210	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×C₄×Q₈	—	2	1	no	—
212	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×#117	—	2	1	no	—
214	C₂×#107	C₂²×C₁₃	1	2	yes	—
215	C₂×#107	C₂²×C₁₃	1	2	yes	—
216	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
217	C₂×#102	C₂²×C₁₃	1	2	yes	—
218	C₂×#102	C₂²×C₁₃	1	2	yes	—
219	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
220	#391	—	2	1	no	—
221	#390	C₂²×C₁₃	1	1	yes	characteristic
222	#390	C₂²×C₁₃	1	1	yes	characteristic
223	#389	—	2	1	no	—
224	#389	C₂²×C₁₃	1	2	yes	—
225	#389	C₂²×C₁₃	1	1	yes	characteristic
226	#389	C₂²×C₁₃	1	1	yes	characteristic
227	#388	—	2	1	no	—
228	#388	—	2	1	no	—
229	#384	C₂²×C₁₃	1	1	yes	characteristic
230	C₄×C₄⋊C₄	—	2	1	no	—
231	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
232	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₄×C₂²⋊C₄	—	2	1	no	—
234	C₄³	C₂²×C₁₃	1	1	yes	characteristic
235	#340	C₂²×C₁₃	1	2	yes	—
236	#340	C₂²×C₁₃	1	2	yes	—
237	#340	C₂²×C₁₃	1	2	yes	—
238	#340	C₂²×C₁₃	1	2	yes	—
239	#336	C₂²×C₁₃	1	1	yes	characteristic
240	#336	C₂²×C₁₃	1	1	yes	characteristic
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	2	no	—
244	C₂²×C₁₃	—	8	1	no	—
245	C₂²×C₁₃	—	8	1	no	—
246	C₂²×C₁₃	—	8	1	no	—
247	C₂²×C₁₃	—	8	1	no	—
248	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
249	C₂²×C₁₃	#525	1	1	yes	characteristic
250	C₂²×C₁₃	#532	1	1	yes	characteristic
251	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
252	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
253	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
254	C₂²×C₁₃	#575	1	1	yes	characteristic
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	4	4	no	—
260	C₄×C₁₃	—	4	1	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	8	1	no	—
263	C₄×C₁₃	—	8	1	no	—
264	C₄×C₁₃	—	8	2	no	—
265	C₄×C₁₃	#474	1	4	yes	—
266	C₄×C₁₃	#529	1	2	yes	—
267	C₄×C₁₃	#533	1	2	yes	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₂³×C₄	—	2	1	no	—
271	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
272	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
273	C₄⋊Q₈	—	2	4	no	—
274	C₄×Q₈	—	4	4	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	Q₈×C₁₃	1	4	yes	complemented
277	#117	—	4	4	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
297	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
298	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
299	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
303	#107	—	2	4	no	—
304	#107	—	2	4	no	—
305	C₄⋊C₈	—	2	4	no	—
306	#102	—	2	4	no	—
307	#102	—	2	4	no	—
308	C₄×C₈	—	2	4	no	—
309	#95	—	2	1	no	—
310	#95	—	2	1	no	—
311	#95	—	2	2	no	—
312	#95	—	2	1	no	—
313	#95	—	2	2	no	—
314	C₂×C₁₃	—	8	2	no	—
315	C₂×C₁₃	#2396	1	1	yes	characteristic
316	C₂×C₁₃	C₂×#474	1	1	yes	characteristic
317	C₂×C₁₃	#3076	1	1	yes	characteristic
318	C₂×C₁₃	#3100	1	1	yes	characteristic
319	C₂×C₁₃	#3108	1	1	yes	characteristic
320	C₂×C₁₃	#3169	1	1	yes	characteristic
321	C₂×C₁₃	#3172	1	1	yes	characteristic
322	C₂⁴	—	2	1	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	C₁₃×#41	1	4	yes	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
364	C₄⋊C₄	C₁₃×#41	1	4	yes	—
365	C₂²⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	4	1	no	—
375	C₄²	—	4	2	no	—
376	C₄²	—	4	4	no	—
377	C₄²	C₁₃×D₈	1	4	yes	—
378	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
379	C₄²	C₁₃×#41	1	2	yes	—
380	C₁₃	#23774	1	1	yes	characteristic, direct product factor, Sylow
381	C₂³	—	2	2	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
389	Q₈	—	4	8	no	—
390	D₄	—	2	4	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
420	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
421	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
422	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
423	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
424	C₂×C₄	C₁₃×#135	1	2	yes	—
425	C₂×C₄	C₁₃×#137	1	2	yes	—
426	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
427	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
428	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
429	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
430	C₈	—	2	4	no	—
431	C₈	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
440	C₂²	C₁₃×#525	1	1	yes	characteristic
441	C₂²	C₁₃×#532	1	1	yes	characteristic
442	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
443	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
444	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
445	C₂²	C₁₃×#575	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	1	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	2	no	—
456	C₄	C₁₃×#474	1	4	yes	—
457	C₄	C₁₃×#529	1	2	yes	—
458	C₄	C₁₃×#533	1	2	yes	—
459	C₂	—	8	2	no	—
460	C₂	C₁₃×#2396	1	1	yes	characteristic
461	C₂	C₂×C₁₃×#474	1	1	yes	characteristic
462	C₂	C₁₃×#3076	1	1	yes	characteristic
463	C₂	C₁₃×#3100	1	1	yes	characteristic
464	C₂	C₁₃×#3108	1	1	yes	characteristic
465	C₂	C₁₃×#3169	1	1	yes	characteristic
466	C₂	C₁₃×#3172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#2099	C₂	semidirect
5. C₁₃×#2086	C₂	semidirect
7. C₁₃×#2057	C₂	semidirect
9. C₄×C₁₃×#107	C₂	semidirect
10. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
51. C₄×D₄×C₁₃	Q₈	semidirect
89. #23774	C₁₃	direct (N × H)
148. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
150. #2099	C₂×C₁₃	semidirect
152. #2086	C₂×C₁₃	semidirect
154. #2057	C₂×C₁₃	semidirect
156. C₄×#107	C₂×C₁₃	semidirect
157. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
276. C₄×D₄	Q₈×C₁₃	semidirect
380. C₁₃	#23774	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₃×C₄⋊Q₈	2
C₁₃×#2293	2
C₁₃×#2099	2
C₁₃×#2093	2
C₁₃×#2086	2
C₁₃×#2067	2
C₁₃×#2057	2
C₁₃×#2023	2
C₄×C₁₃×#107	2
C₄×C₁₃×C₄⋊C₈	2
C₄×C₁₃×#102	2
#23774	13

Subgroups — C13×#23774 #15710113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23774 #15710113