Subgroups — C₂×C₁₃×#2097 #15710068

Order 3328.

1150 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	C₂²×C₁₃×#107	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×#103	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×#103	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2097	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#107	—	2	4	no	—
17	C₂×C₁₃×#107	C₂²	1	4	yes	—
18	C₂×C₁₃×#106	—	2	4	no	—
19	C₂×C₁₃×#106	C₂²	1	4	yes	—
20	C₂×C₁₃×#103	—	2	4	no	—
21	C₂×C₁₃×#103	—	2	4	no	—
22	C₂×C₁₃×#103	C₂²	1	4	yes	—
23	C₂×C₁₃×#103	C₂²	1	4	yes	—
24	C₁₃×#391	—	2	2	no	—
25	C₁₃×#391	C₂²	1	4	yes	—
26	C₁₃×#382	—	2	2	no	—
27	C₁₃×#382	C₂²	1	4	yes	—
28	C₂×C₁₃×#95	—	2	2	no	—
29	C₂×C₁₃×#95	—	2	2	no	—
30	C₁₃×#336	C₂²	1	4	yes	—
31	C₂²×Q₈×C₁₃	—	2	1	no	—
32	C₂²×Q₈×C₁₃	—	2	2	no	—
33	C₂²×Q₈×C₁₃	—	2	2	no	—
34	C₂²×Q₈×C₁₃	—	2	2	no	—
35	C₂²×Q₈×C₁₃	—	2	2	no	—
36	C₂²×Q₈×C₁₃	—	2	2	no	—
37	C₂²×Q₈×C₁₃	Q₈	1	4	yes	—
38	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃	—	2	1	no	—
40	C₂³×C₄×C₁₃	—	2	1	no	—
41	C₂³×C₄×C₁₃	—	2	1	no	—
42	C₂³×C₄×C₁₃	—	2	1	no	—
43	C₂³×C₄×C₁₃	D₄	1	2	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	—	2	2	no	—
46	C₂²×C₈×C₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	D₄	1	4	yes	—
50	C₂²×C₈×C₁₃	D₄	1	4	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₄²×C₁₃	—	2	2	no	—
66	C₂×C₄²×C₁₃	—	2	2	no	—
67	C₂×C₄²×C₁₃	D₄	1	2	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
69	C₁₃×#107	—	2	8	no	—
70	C₁₃×#106	—	2	8	no	—
71	C₁₃×#103	—	2	8	no	—
72	C₁₃×#103	—	2	8	no	—
73	C₁₃×#95	—	2	8	no	—
74	C₁₃×#95	—	2	8	no	—
75	C₂×#2097	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₁₃	—	2	4	no	—
78	C₂×Q₈×C₁₃	—	2	2	no	—
79	C₂×Q₈×C₁₃	—	2	8	no	—
80	C₂×Q₈×C₁₃	—	2	8	no	—
81	C₂×Q₈×C₁₃	—	2	2	no	—
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×Q₈×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₃	—	4	2	no	—
86	C₂×Q₈×C₁₃	—	4	4	no	—
87	C₂×Q₈×C₁₃	—	4	4	no	—
88	C₂×Q₈×C₁₃	—	4	2	no	—
89	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
90	C₂²×C₄×C₁₃	—	2	4	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	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	—	4	2	no	—
100	C₂²×C₄×C₁₃	—	4	2	no	—
101	C₂²×C₄×C₁₃	—	4	2	no	—
102	C₂²×C₄×C₁₃	—	4	2	no	—
103	C₂²×C₄×C₁₃	—	4	4	no	—
104	C₂²×C₄×C₁₃	—	4	4	no	—
105	C₂²×C₄×C₁₃	—	4	4	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₁₃	#41	1	2	yes	—
112	C₂²×C₄×C₁₃	#41	1	2	yes	—
113	C₂²×C₄×C₁₃	#41	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₁₃	—	2	8	no	—
116	C₂×C₈×C₁₃	—	2	8	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
122	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
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	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	—	4	2	no	—
131	C₁₃×C₄⋊C₄	—	4	2	no	—
132	C₄²×C₁₃	—	2	4	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₂²×#107	C₂×C₁₃	1	1	yes	characteristic
136	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic
137	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic
138	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic
139	C₂×#391	C₂×C₁₃	1	1	yes	characteristic
140	C₂×#382	C₂×C₁₃	1	1	yes	characteristic
141	#2097	C₂×C₁₃	1	8	yes	direct product factor
142	C₂×#336	C₂×C₁₃	1	1	yes	characteristic
143	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
144	C₂³×C₁₃	#123	1	2	yes	—
145	C₂³×C₁₃	#127	1	2	yes	—
146	C₂³×C₁₃	#135	1	4	yes	—
147	C₂³×C₁₃	#137	1	4	yes	—
148	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₁₃	—	2	4	no	—
150	Q₈×C₁₃	—	2	4	no	—
151	Q₈×C₁₃	—	4	2	no	—
152	Q₈×C₁₃	—	4	2	no	—
153	Q₈×C₁₃	—	4	8	no	—
154	C₂×C₄×C₁₃	—	2	4	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	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	8	no	—
161	C₂×C₄×C₁₃	—	4	8	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	—	4	4	no	—
167	C₂×C₄×C₁₃	—	4	4	no	—
168	C₂×C₄×C₁₃	—	8	4	no	—
169	C₂×C₄×C₁₃	—	8	4	no	—
170	C₂×C₄×C₁₃	—	8	4	no	—
171	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
172	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
173	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₁₃	#123	1	4	yes	—
175	C₂×C₄×C₁₃	#123	1	4	yes	—
176	C₂×C₄×C₁₃	#123	1	2	yes	—
177	C₂×C₄×C₁₃	#127	1	2	yes	—
178	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
184	C₈×C₁₃	—	2	4	no	—
185	C₈×C₁₃	—	2	4	no	—
186	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
188	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
189	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
190	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
191	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
192	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×#107	—	2	4	no	—
194	C₂×#107	C₂²×C₁₃	1	4	yes	—
195	C₂×#106	—	2	4	no	—
196	C₂×#106	C₂²×C₁₃	1	4	yes	—
197	C₂×#103	—	2	4	no	—
198	C₂×#103	—	2	4	no	—
199	C₂×#103	C₂²×C₁₃	1	4	yes	—
200	C₂×#103	C₂²×C₁₃	1	4	yes	—
201	#391	—	2	2	no	—
202	#391	C₂²×C₁₃	1	4	yes	—
203	#382	—	2	2	no	—
204	#382	C₂²×C₁₃	1	4	yes	—
205	C₂×#95	—	2	2	no	—
206	C₂×#95	—	2	2	no	—
207	#336	C₂²×C₁₃	1	4	yes	—
208	C₂²×C₁₃	#399	1	4	yes	—
209	C₂²×C₁₃	#479	1	8	yes	—
210	C₂²×C₁₃	#485	1	8	yes	—
211	C₂²×C₁₃	#495	1	4	yes	—
212	C₂²×C₁₃	#497	1	4	yes	—
213	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
214	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
216	C₂²×C₁₃	C₂×#135	1	2	yes	—
217	C₂²×C₁₃	C₂×#137	1	2	yes	—
218	C₄×C₁₃	—	4	4	no	—
219	C₄×C₁₃	—	4	4	no	—
220	C₄×C₁₃	—	8	2	no	—
221	C₄×C₁₃	—	8	2	no	—
222	C₄×C₁₃	—	8	2	no	—
223	C₄×C₁₃	#399	1	4	yes	—
224	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
225	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
226	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
227	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×Q₈	—	2	2	no	—
230	C₂²×Q₈	—	2	2	no	—
231	C₂²×Q₈	—	2	2	no	—
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	Q₈×C₁₃	1	4	yes	—
235	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
236	C₂³×C₄	—	2	1	no	—
237	C₂³×C₄	—	2	1	no	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	D₄×C₁₃	1	2	yes	—
241	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	D₄×C₁₃	1	4	yes	—
247	C₂²×C₈	D₄×C₁₃	1	4	yes	—
248	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
249	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	D₄×C₁₃	1	2	yes	—
265	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
266	#107	—	2	8	no	—
267	#106	—	2	8	no	—
268	#103	—	2	8	no	—
269	#103	—	2	8	no	—
270	#95	—	2	8	no	—
271	#95	—	2	8	no	—
272	C₂×C₁₃	#2097	1	8	yes	direct product factor
273	C₂×C₁₃	C₂×#399	1	1	yes	characteristic
274	C₂×C₁₃	C₂×#479	1	2	yes	—
275	C₂×C₁₃	C₂×#485	1	2	yes	—
276	C₂×C₁₃	C₂×#495	1	1	yes	characteristic
277	C₂×C₁₃	C₂×#497	1	1	yes	characteristic
278	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	8	no	—
282	C₂×Q₈	—	2	8	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	4	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
309	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
312	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
313	C₂²×C₄	C₁₃×#41	1	2	yes	—
314	C₂²×C₄	C₁₃×#41	1	2	yes	—
315	C₂²×C₄	C₁₃×#41	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
317	C₂×C₈	—	2	8	no	—
318	C₂×C₈	—	2	8	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
324	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄²	—	2	4	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₁₃	C₂×#2097	1	1	yes	characteristic, direct product factor, Sylow
338	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
339	C₂³	C₁₃×#123	1	2	yes	—
340	C₂³	C₁₃×#127	1	2	yes	—
341	C₂³	C₁₃×#135	1	4	yes	—
342	C₂³	C₁₃×#137	1	4	yes	—
343	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	2	4	no	—
346	Q₈	—	4	8	no	—
347	Q₈	—	4	2	no	—
348	Q₈	—	4	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	—	8	4	no	—
365	C₂×C₄	—	8	4	no	—
366	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
367	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
368	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
369	C₂×C₄	C₁₃×#123	1	2	yes	—
370	C₂×C₄	C₁₃×#123	1	4	yes	—
371	C₂×C₄	C₁₃×#123	1	4	yes	—
372	C₂×C₄	C₁₃×#127	1	2	yes	—
373	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
376	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
377	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
378	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	2	4	no	—
381	C₂²	C₁₃×#399	1	4	yes	—
382	C₂²	C₁₃×#479	1	8	yes	—
383	C₂²	C₁₃×#485	1	8	yes	—
384	C₂²	C₁₃×#495	1	4	yes	—
385	C₂²	C₁₃×#497	1	4	yes	—
386	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
387	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
388	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
389	C₂²	C₂×C₁₃×#135	1	2	yes	—
390	C₂²	C₂×C₁₃×#137	1	2	yes	—
391	C₄	—	4	4	no	—
392	C₄	—	4	4	no	—
393	C₄	—	8	2	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	2	no	—
396	C₄	C₁₃×#399	1	4	yes	—
397	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
398	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
399	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
400	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
401	C₂	C₁₃×#2097	1	8	yes	direct product factor
402	C₂	C₂×C₁₃×#399	1	1	yes	characteristic
403	C₂	C₂×C₁₃×#479	1	2	yes	—
404	C₂	C₂×C₁₃×#485	1	2	yes	—
405	C₂	C₂×C₁₃×#495	1	1	yes	characteristic
406	C₂	C₂×C₁₃×#497	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
7. C₁₃×#2097	C₂	direct (N × H)
75. C₂×#2097	C₁₃	direct (N × H)
141. #2097	C₂×C₁₃	direct (N × H)
272. C₂×C₁₃	#2097	direct (N × H)
337. C₁₃	C₂×#2097	direct (N × H)
401. C₂	C₁₃×#2097	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×C₁₃×#107	2
C₂²×C₁₃×#106	2
C₂²×C₁₃×#103	2
C₂×C₁₃×#391	2
C₂×C₁₃×#382	2
C₁₃×#2097	2
C₂×C₁₃×#336	2
C₂×#2097	13

Subgroups — C2×C13×#2097 #15710068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2097 #15710068