Subgroups — C₂×C₁₃×#2398 #15720884

Order 3328.

3246 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2398	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#400	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#397	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#394	C₂	1	2	yes	maximal
7	C₂×C₁₃×#393	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
15	C₂×C₄×D₄×C₁₃	—	2	8	no	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#400	C₂²	1	16	yes	complemented
27	C₁₃×#397	C₂²	1	16	yes	complemented
28	C₁₃×#394	C₂²	1	16	yes	—
29	C₁₃×#393	C₂²	1	16	yes	complemented
30	C₄×C₁₃×C₂²⋊C₄	C₂²	1	32	yes	complemented
31	C₁₃×#376	C₂²	1	8	yes	complemented
32	C₂×C₁₃×#95	C₂²	1	2	yes	—
33	C₂×C₁₃×#95	C₂²	1	2	yes	—
34	C₂×C₁₃×#95	C₂²	1	4	yes	—
35	C₂×C₁₃×#95	C₂²	1	4	yes	—
36	C₂⁵×C₁₃	C₂³	1	2	yes	—
37	C₂²×Q₈×C₁₃	—	2	4	no	—
38	C₂²×Q₈×C₁₃	—	2	8	no	—
39	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
40	C₂²×D₄×C₁₃	—	2	8	no	—
41	C₂²×D₄×C₁₃	—	2	4	no	—
42	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₃	—	2	8	no	—
44	C₂³×C₄×C₁₃	—	2	16	no	—
45	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
46	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₄×Q₈×C₁₃	—	2	32	no	—
54	C₄×D₄×C₁₃	—	2	32	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
64	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
65	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
66	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
67	C₂×C₄²×C₁₃	—	2	8	no	—
68	C₂×C₄²×C₁₃	—	2	8	no	—
69	C₂×C₄²×C₁₃	D₄	1	8	yes	—
70	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
71	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
72	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
73	C₁₃×#95	C₂³	1	16	yes	—
74	C₁₃×#95	C₂³	1	16	yes	—
75	C₁₃×#95	C₂³	1	8	yes	—
76	C₁₃×#95	C₂³	1	8	yes	—
77	C₂×#2398	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁴×C₁₃	—	2	4	no	—
79	C₂⁴×C₁₃	—	2	8	no	—
80	C₂⁴×C₁₃	—	2	8	no	—
81	C₂⁴×C₁₃	—	2	4	no	—
82	C₂⁴×C₁₃	#41	1	8	yes	—
83	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
84	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
85	C₂×Q₈×C₁₃	—	2	32	no	—
86	C₂×Q₈×C₁₃	—	2	8	no	—
87	C₂×Q₈×C₁₃	—	2	16	no	—
88	C₂×D₄×C₁₃	—	2	32	no	—
89	C₂×D₄×C₁₃	—	2	16	no	—
90	C₂×D₄×C₁₃	—	2	8	no	—
91	C₂²×C₄×C₁₃	—	2	4	no	—
92	C₂²×C₄×C₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₃	—	2	4	no	—
95	C₂²×C₄×C₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₃	—	2	8	no	—
98	C₂²×C₄×C₁₃	—	2	8	no	—
99	C₂²×C₄×C₁₃	—	2	8	no	—
100	C₂²×C₄×C₁₃	—	2	8	no	—
101	C₂²×C₄×C₁₃	—	2	8	no	—
102	C₂²×C₄×C₁₃	—	2	16	no	—
103	C₂²×C₄×C₁₃	—	2	32	no	—
104	C₂²×C₄×C₁₃	—	4	32	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₁₃	#41	1	8	yes	—
109	C₂²×C₄×C₁₃	#41	1	8	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
111	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
117	C₁₃×C₄⋊C₄	—	2	8	no	—
118	C₁₃×C₄⋊C₄	—	2	16	no	—
119	C₁₃×C₄⋊C₄	—	2	8	no	—
120	C₁₃×C₂²⋊C₄	—	2	32	no	—
121	C₁₃×C₂²⋊C₄	—	2	16	no	—
122	C₁₃×C₂²⋊C₄	—	2	32	no	—
123	C₄²×C₁₃	—	2	16	no	—
124	C₄²×C₁₃	—	2	16	no	—
125	C₄²×C₁₃	C₂×D₄	1	16	yes	—
126	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
127	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
128	#2398	C₂×C₁₃	1	16	yes	direct product factor
129	C₂×#400	C₂×C₁₃	1	2	yes	complemented
130	C₂×#397	C₂×C₁₃	1	2	yes	complemented
131	C₂×#394	C₂×C₁₃	1	2	yes	—
132	C₂×#393	C₂×C₁₃	1	2	yes	complemented
133	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	4	yes	complemented
134	C₂×#376	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂³×C₁₃	—	2	16	no	—
136	C₂³×C₁₃	—	2	32	no	—
137	C₂³×C₁₃	—	2	4	no	—
138	C₂³×C₁₃	—	2	8	no	—
139	C₂³×C₁₃	—	2	8	no	—
140	C₂³×C₁₃	—	2	4	no	—
141	C₂³×C₁₃	—	4	8	no	—
142	C₂³×C₁₃	—	4	8	no	—
143	C₂³×C₁₃	—	4	16	no	—
144	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
145	C₂³×C₁₃	C₂×#41	1	8	yes	—
146	C₂³×C₁₃	C₂×#41	1	4	yes	—
147	C₂³×C₁₃	C₂×#41	1	4	yes	—
148	C₂³×C₁₃	C₂×#41	1	4	yes	—
149	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
150	Q₈×C₁₃	—	2	32	no	—
151	D₄×C₁₃	—	2	32	no	—
152	C₂×C₄×C₁₃	—	2	8	no	—
153	C₂×C₄×C₁₃	—	2	8	no	—
154	C₂×C₄×C₁₃	—	2	16	no	—
155	C₂×C₄×C₁₃	—	2	4	no	—
156	C₂×C₄×C₁₃	—	2	4	no	—
157	C₂×C₄×C₁₃	—	2	4	no	—
158	C₂×C₄×C₁₃	—	2	4	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	4	no	—
161	C₂×C₄×C₁₃	—	2	8	no	—
162	C₂×C₄×C₁₃	—	2	8	no	—
163	C₂×C₄×C₁₃	—	2	8	no	—
164	C₂×C₄×C₁₃	—	2	8	no	—
165	C₂×C₄×C₁₃	—	2	8	no	—
166	C₂×C₄×C₁₃	—	4	8	no	—
167	C₂×C₄×C₁₃	—	4	8	no	—
168	C₂×C₄×C₁₃	—	4	16	no	—
169	C₂×C₄×C₁₃	—	4	32	no	—
170	C₂×C₄×C₁₃	#124	1	16	yes	—
171	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
172	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
173	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
174	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
175	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
176	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
177	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
178	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
179	C₂×C₄×Q₈	—	2	8	no	—
180	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
181	C₂×C₄×D₄	—	2	8	no	—
182	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
183	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
184	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
185	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
186	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
187	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
188	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
189	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
190	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
191	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
192	#400	C₂²×C₁₃	1	16	yes	complemented
193	#397	C₂²×C₁₃	1	16	yes	complemented
194	#394	C₂²×C₁₃	1	16	yes	—
195	#393	C₂²×C₁₃	1	16	yes	complemented
196	C₄×C₂²⋊C₄	C₂²×C₁₃	1	32	yes	complemented
197	#376	C₂²×C₁₃	1	8	yes	complemented
198	C₂×#95	C₂²×C₁₃	1	2	yes	—
199	C₂×#95	C₂²×C₁₃	1	4	yes	—
200	C₂×#95	C₂²×C₁₃	1	2	yes	—
201	C₂×#95	C₂²×C₁₃	1	4	yes	—
202	C₂²×C₁₃	—	2	8	no	—
203	C₂²×C₁₃	—	2	16	no	—
204	C₂²×C₁₃	—	4	32	no	—
205	C₂²×C₁₃	—	4	4	no	—
206	C₂²×C₁₃	—	4	4	no	—
207	C₂²×C₁₃	—	4	8	no	—
208	C₂²×C₁₃	#525	1	4	yes	—
209	C₂²×C₁₃	#525	1	4	yes	—
210	C₂²×C₁₃	C₂×#124	1	4	yes	—
211	C₂²×C₁₃	#529	1	16	yes	—
212	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
213	C₂²×C₁₃	C₂²×#41	1	2	yes	—
214	C₂²×C₁₃	C₂²×#41	1	2	yes	—
215	C₂²×C₁₃	C₂²×#41	1	2	yes	—
216	C₄×C₁₃	—	2	4	no	—
217	C₄×C₁₃	—	2	4	no	—
218	C₄×C₁₃	—	2	8	no	—
219	C₄×C₁₃	—	4	4	no	—
220	C₄×C₁₃	—	4	4	no	—
221	C₄×C₁₃	—	4	8	no	—
222	C₄×C₁₃	C₂×#124	1	8	yes	—
223	C₂⁵	C₂³×C₁₃	1	2	yes	—
224	C₂²×Q₈	—	2	4	no	—
225	C₂²×Q₈	—	2	8	no	—
226	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
227	C₂²×D₄	—	2	8	no	—
228	C₂²×D₄	—	2	4	no	—
229	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
230	C₂³×C₄	—	2	8	no	—
231	C₂³×C₄	—	2	16	no	—
232	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
233	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
234	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
235	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
236	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
239	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
240	C₄×Q₈	—	2	32	no	—
241	C₄×D₄	—	2	32	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	8	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
247	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
248	C₂×C₂²⋊C₄	—	2	16	no	—
249	C₂×C₂²⋊C₄	—	2	8	no	—
250	C₂×C₂²⋊C₄	—	2	16	no	—
251	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
252	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
253	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
254	C₂×C₄²	—	2	8	no	—
255	C₂×C₄²	—	2	8	no	—
256	C₂×C₄²	D₄×C₁₃	1	8	yes	—
257	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
258	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
259	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
260	#95	C₂³×C₁₃	1	8	yes	—
261	#95	C₂³×C₁₃	1	8	yes	—
262	#95	C₂³×C₁₃	1	16	yes	—
263	#95	C₂³×C₁₃	1	16	yes	—
264	C₂×C₁₃	—	4	8	no	—
265	C₂×C₁₃	#2398	1	8	yes	direct product factor
266	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
267	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
268	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
269	C₂×C₁₃	C₂×#529	1	4	yes	—
270	C₂⁴	—	2	4	no	—
271	C₂⁴	—	2	8	no	—
272	C₂⁴	—	2	8	no	—
273	C₂⁴	—	2	4	no	—
274	C₂⁴	C₁₃×#41	1	8	yes	—
275	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
276	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
277	C₂×Q₈	—	2	32	no	—
278	C₂×Q₈	—	2	8	no	—
279	C₂×Q₈	—	2	16	no	—
280	C₂×D₄	—	2	32	no	—
281	C₂×D₄	—	2	16	no	—
282	C₂×D₄	—	2	8	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	2	16	no	—
295	C₂²×C₄	—	2	32	no	—
296	C₂²×C₄	—	4	32	no	—
297	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
298	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
299	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
300	C₂²×C₄	C₁₃×#41	1	8	yes	—
301	C₂²×C₄	C₁₃×#41	1	8	yes	—
302	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
303	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
304	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
305	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
308	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	16	no	—
311	C₄⋊C₄	—	2	8	no	—
312	C₂²⋊C₄	—	2	32	no	—
313	C₂²⋊C₄	—	2	16	no	—
314	C₂²⋊C₄	—	2	32	no	—
315	C₄²	—	2	16	no	—
316	C₄²	—	2	16	no	—
317	C₄²	C₂×D₄×C₁₃	1	16	yes	—
318	C₁₃	C₂×#2398	1	1	yes	characteristic, direct product factor, Sylow
319	C₂³	—	2	16	no	—
320	C₂³	—	2	32	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	8	no	—
323	C₂³	—	2	8	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	4	8	no	—
326	C₂³	—	4	8	no	—
327	C₂³	—	4	16	no	—
328	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
329	C₂³	C₂×C₁₃×#41	1	8	yes	—
330	C₂³	C₂×C₁₃×#41	1	4	yes	—
331	C₂³	C₂×C₁₃×#41	1	4	yes	—
332	C₂³	C₂×C₁₃×#41	1	4	yes	—
333	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
334	Q₈	—	2	32	no	—
335	D₄	—	2	32	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	16	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	—	4	8	no	—
352	C₂×C₄	—	4	16	no	—
353	C₂×C₄	—	4	32	no	—
354	C₂×C₄	C₁₃×#124	1	16	yes	—
355	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
356	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
357	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
358	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
359	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
360	C₂²	—	2	8	no	—
361	C₂²	—	2	16	no	—
362	C₂²	—	4	32	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	8	no	—
366	C₂²	C₁₃×#525	1	4	yes	—
367	C₂²	C₁₃×#525	1	4	yes	—
368	C₂²	C₂×C₁₃×#124	1	4	yes	—
369	C₂²	C₁₃×#529	1	16	yes	—
370	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
371	C₂²	C₂²×C₁₃×#41	1	2	yes	—
372	C₂²	C₂²×C₁₃×#41	1	2	yes	—
373	C₂²	C₂²×C₁₃×#41	1	2	yes	—
374	C₄	—	2	4	no	—
375	C₄	—	2	4	no	—
376	C₄	—	2	8	no	—
377	C₄	—	4	4	no	—
378	C₄	—	4	4	no	—
379	C₄	—	4	8	no	—
380	C₄	C₂×C₁₃×#124	1	8	yes	—
381	C₂	—	4	8	no	—
382	C₂	C₁₃×#2398	1	8	yes	direct product factor
383	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
384	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
385	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
386	C₂	C₂×C₁₃×#529	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#2398	C₂	direct (N × H)
4. C₂×C₁₃×#400	C₂	semidirect
5. C₂×C₁₃×#397	C₂	semidirect
7. C₂×C₁₃×#393	C₂	semidirect
8. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
9. C₂×C₁₃×#376	C₂	semidirect
14. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
26. C₁₃×#400	C₂²	semidirect
27. C₁₃×#397	C₂²	semidirect
29. C₁₃×#393	C₂²	semidirect
30. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
31. C₁₃×#376	C₂²	semidirect
77. C₂×#2398	C₁₃	direct (N × H)
126. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
128. #2398	C₂×C₁₃	direct (N × H)
129. C₂×#400	C₂×C₁₃	semidirect
130. C₂×#397	C₂×C₁₃	semidirect
132. C₂×#393	C₂×C₁₃	semidirect
133. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
134. C₂×#376	C₂×C₁₃	semidirect
180. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
192. #400	C₂²×C₁₃	semidirect
193. #397	C₂²×C₁₃	semidirect
195. #393	C₂²×C₁₃	semidirect
196. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
197. #376	C₂²×C₁₃	semidirect
265. C₂×C₁₃	#2398	direct (N × H)
318. C₁₃	C₂×#2398	direct (N × H)
382. C₂	C₁₃×#2398	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₃	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2398	2
C₂×C₁₃×#400	2
C₂×C₁₃×#397	2
C₂×C₁₃×#394	2
C₂×C₁₃×#393	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×C₁₃×#376	2
C₂×#2398	13

Subgroups — C2×C13×#2398 #15720884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2398 #15720884