Subgroups — #15768850

Order 3328.

774 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88057	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718762	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718146	C₂	1	2	yes	maximal
4	#13114556	C₂	1	2	yes	maximal
5	C₂²×C₁₃×#108	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88180	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
10	C₂²×#6099	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#108	—	2	2	no	—
12	C₂×C₁₃×#108	—	2	2	no	—
13	C₂×C₁₃×#108	C₄	1	4	yes	complemented
14	C₂×#88057	—	2	1	no	—
15	C₂×#88057	—	2	1	no	—
16	C₂×#88057	—	2	2	no	—
17	C₂×#88057	C₄	1	4	yes	complemented
18	#11718762	—	2	2	no	—
19	#11718762	C₄	1	4	yes	complemented
20	C₂×#88055	—	2	1	no	—
21	C₂×C₈×Dic₁₃	—	2	1	no	—
22	#11718146	—	2	4	no	—
23	#11718143	—	2	4	no	—
24	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₂³×Dic₁₃	—	2	2	no	—
26	C₂×C₁₃×M₁₆	—	2	2	no	—
27	C₂×C₁₃×M₁₆	—	2	2	no	—
28	C₂×C₁₃×M₁₆	—	2	2	no	—
29	C₂×C₁₃×M₁₆	—	2	2	no	—
30	C₂×C₁₃×M₁₆	—	2	2	no	—
31	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₁₃	—	2	2	no	—
33	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₃	D₄	1	2	yes	—
39	C₂²×C₈×C₁₃	D₄	1	2	yes	—
40	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
41	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
42	#88180	—	2	1	no	—
43	#88180	—	2	1	no	—
44	#88180	C₂×C₄	1	2	yes	—
45	#88180	Q₈	1	2	yes	—
46	C₂×C₄⋊Dic₁₃	—	2	2	no	—
47	C₂×C₄⋊Dic₁₃	—	2	2	no	—
48	C₂×C₄⋊Dic₁₃	—	2	2	no	—
49	C₂×C₄⋊Dic₁₃	—	2	2	no	—
50	C₂×C₄⋊Dic₁₃	—	2	2	no	—
51	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
53	C₂×C₄×Dic₁₃	—	2	1	no	—
54	C₂×#6099	—	2	1	no	—
55	C₂×#6099	—	2	1	no	—
56	C₂×#6099	—	2	1	no	—
57	C₂×#6099	C₂×C₄	1	2	yes	—
58	C₂×#6099	D₄	1	2	yes	—
59	C₂×#6099	Q₈	1	2	yes	—
60	C₂²×#1055	—	2	1	no	—
61	C₁₃×#108	—	2	8	no	—
62	#88057	—	2	4	no	—
63	#88057	—	2	4	no	—
64	#88055	—	2	4	no	—
65	C₈×Dic₁₃	—	2	4	no	—
66	#10869	—	13	1	no	maximal, Sylow
67	C₂⁴×C₁₃	#41	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
82	C₂²×Dic₁₃	—	2	2	no	—
83	C₂²×Dic₁₃	—	2	4	no	—
84	C₂²×Dic₁₃	—	4	2	no	—
85	C₂²×Dic₁₃	—	4	2	no	—
86	C₂²×Dic₁₃	—	8	4	no	—
87	C₁₃×M₁₆	—	2	4	no	—
88	C₁₃×M₁₆	—	2	4	no	—
89	C₁₃×M₁₆	—	4	2	no	—
90	C₁₃×M₁₆	—	4	2	no	—
91	C₂×C₈×C₁₃	—	2	4	no	—
92	C₂×C₈×C₁₃	—	4	2	no	—
93	C₂×C₈×C₁₃	—	4	2	no	—
94	C₂×C₈×C₁₃	C₄²	1	4	yes	—
95	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
96	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
97	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
98	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
99	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
100	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
101	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
102	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
103	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
104	C₂²⋊Dic₁₃	—	2	2	no	—
105	C₂²⋊Dic₁₃	—	2	2	no	—
106	C₄⋊Dic₁₃	—	2	2	no	—
107	C₄⋊Dic₁₃	—	2	4	no	—
108	C₄⋊Dic₁₃	—	2	4	no	—
109	C₄⋊Dic₁₃	—	4	2	no	—
110	C₄⋊Dic₁₃	—	4	2	no	—
111	C₄⋊Dic₁₃	C₄⋊C₄	1	4	yes	—
112	C₄×Dic₁₃	—	2	2	no	—
113	C₄×Dic₁₃	—	2	2	no	—
114	#6099	—	2	2	no	—
115	#6099	—	2	2	no	—
116	#6099	—	2	2	no	—
117	#6099	C₄⋊C₄	1	4	yes	—
118	C₂×#1055	—	2	2	no	—
119	C₂×#1055	—	2	2	no	—
120	C₂×#1055	—	2	2	no	—
121	C₂²×#108	D₁₃	1	1	yes	characteristic
122	C₂²×#106	—	13	1	no	—
123	C₂×#405	—	13	1	no	—
124	C₂×#343	—	13	2	no	—
125	#1736	—	13	2	no	—
126	C₂³×C₁₃	—	2	4	no	—
127	C₂³×C₁₃	#117	1	1	yes	characteristic
128	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
129	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
130	C₂³×C₁₃	#121	1	1	yes	characteristic
131	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
132	C₂³×C₁₃	#124	1	1	yes	characteristic
133	C₂³×C₁₃	#125	1	1	yes	characteristic
134	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
135	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
157	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
162	C₂×Dic₁₃	—	2	4	no	—
163	C₂×Dic₁₃	—	4	4	no	—
164	C₂×Dic₁₃	—	4	4	no	—
165	C₂×Dic₁₃	—	8	4	no	—
166	C₂×Dic₁₃	—	8	4	no	—
167	C₂×Dic₁₃	—	8	4	no	—
168	C₈×C₁₃	—	4	4	no	—
169	C₈×C₁₃	#95	1	4	yes	—
170	C₈×C₁₃	#95	1	4	yes	—
171	#1055	—	2	4	no	—
172	C₂²×M₁₆	—	13	1	no	—
173	C₂²×M₁₆	C₂×D₁₃	1	2	yes	—
174	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
175	C₂×#117	—	13	1	no	—
176	C₂²×C₄⋊C₄	—	13	2	no	—
177	C₂×#108	—	2	2	no	—
178	C₂×#108	—	2	2	no	—
179	C₂×#108	Dic₁₃	1	4	yes	complemented
180	C₂×#106	—	13	4	no	—
181	C₂×#106	—	26	1	no	—
182	C₂×#106	—	26	1	no	—
183	C₂×#106	—	26	2	no	—
184	#405	—	13	4	no	—
185	#405	—	26	2	no	—
186	C₂×#97	—	26	1	no	—
187	C₂×C₄×C₈	—	26	1	no	—
188	#343	—	26	4	no	—
189	#340	—	26	4	no	—
190	C₂²×C₁₃	—	2	2	no	—
191	C₂²×C₁₃	—	2	2	no	—
192	C₂²×C₁₃	—	2	2	no	—
193	C₂²×C₁₃	—	2	2	no	—
194	C₂²×C₁₃	—	2	2	no	—
195	C₂²×C₁₃	—	2	2	no	—
196	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
197	C₂²×C₁₃	#380	1	1	yes	characteristic
198	C₂²×C₁₃	#382	1	1	yes	characteristic
199	C₂²×C₁₃	#389	1	1	yes	characteristic
200	C₂²×C₁₃	#389	1	1	yes	characteristic
201	C₂²×C₁₃	#390	1	1	yes	characteristic
202	C₂²×C₁₃	#391	1	1	yes	characteristic
203	C₂²×C₁₃	#471	1	4	yes	—
204	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
205	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
206	C₄×C₁₃	#380	1	1	yes	characteristic
207	C₄×C₁₃	#384	1	1	yes	characteristic
208	C₄×C₁₃	#389	1	1	yes	characteristic
209	C₄×C₁₃	#389	1	1	yes	characteristic
210	C₄×C₁₃	#390	1	1	yes	characteristic
211	C₄×C₁₃	#391	1	1	yes	characteristic
212	Dic₁₃	—	4	4	no	—
213	Dic₁₃	—	8	4	no	—
214	C₂³×C₄	—	26	2	no	—
215	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	13	2	no	—
222	C₂×M₁₆	—	13	2	no	—
223	C₂×M₁₆	—	13	2	no	—
224	C₂×M₁₆	—	26	1	no	—
225	C₂×M₁₆	—	26	1	no	—
226	C₂×M₁₆	—	26	1	no	—
227	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	—	26	1	no	—
230	C₂²×C₈	Dic₂₆	1	2	yes	—
231	C₂²×C₈	C₄×D₁₃	1	2	yes	—
232	C₂²×C₈	C₄×D₁₃	1	2	yes	—
233	C₂²×C₈	D₅₂	1	1	yes	characteristic
234	C₂²×C₈	D₅₂	1	1	yes	characteristic
235	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
236	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
237	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
238	#117	—	13	2	no	—
239	#117	—	13	2	no	—
240	#117	—	26	1	no	—
241	#117	—	26	1	no	—
242	C₂×C₄⋊C₄	—	13	2	no	—
243	C₂×C₄⋊C₄	—	13	4	no	—
244	C₂×C₄⋊C₄	—	26	2	no	—
245	C₂×C₄⋊C₄	—	26	2	no	—
246	C₂×C₄⋊C₄	—	26	2	no	—
247	C₂×C₄⋊C₄	—	26	2	no	—
248	C₂×C₄⋊C₄	—	26	2	no	—
249	C₂×C₂²⋊C₄	—	26	1	no	—
250	C₂×C₄²	—	26	1	no	—
251	#108	—	2	8	no	—
252	#106	—	26	4	no	—
253	#106	—	26	4	no	—
254	#97	—	26	4	no	—
255	C₄×C₈	—	26	4	no	—
256	C₂×C₁₃	—	2	1	no	—
257	C₂×C₁₃	—	2	1	no	—
258	C₂×C₁₃	—	2	1	no	—
259	C₂×C₁₃	—	2	1	no	—
260	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
261	C₂×C₁₃	#1815	1	2	yes	—
262	C₂×C₁₃	#1951	1	2	yes	—
263	C₂×C₁₃	#1977	1	2	yes	—
264	C₂⁴	#6131	1	1	yes	characteristic
265	C₂²×C₄	—	26	2	no	—
266	C₂²×C₄	—	26	4	no	—
267	C₂²×C₄	—	52	2	no	—
268	C₂²×C₄	—	52	2	no	—
269	C₂²×C₄	—	104	4	no	—
270	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
274	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
275	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
276	C₂²×C₄	#6129	1	1	yes	characteristic
277	C₂²×C₄	#6129	1	1	yes	characteristic
278	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
279	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
280	C₂²×C₄	#6131	1	1	yes	characteristic
281	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	—	4	2	no	—
287	M₁₆	—	4	2	no	—
288	M₁₆	—	13	4	no	—
289	M₁₆	—	26	2	no	—
290	M₁₆	—	26	2	no	—
291	M₁₆	—	26	2	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₂×C₈	—	26	2	no	—
296	C₂×C₈	—	26	2	no	—
297	C₂×C₈	—	26	2	no	—
298	C₂×C₈	C₄×Dic₁₃	1	4	yes	—
299	C₂×C₈	#6101	1	4	yes	—
300	C₂×C₈	#6101	1	4	yes	—
301	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
302	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
303	C₂×C₈	#6103	1	2	yes	—
304	C₂×C₈	#6103	1	2	yes	—
305	C₂×C₈	#6103	1	2	yes	—
306	C₂×C₈	#6103	1	2	yes	—
307	C₂×C₈	C₂²⋊Dic₁₃	1	4	yes	—
308	C₄⋊C₄	—	13	4	no	—
309	C₄⋊C₄	—	26	2	no	—
310	C₄⋊C₄	—	26	4	no	—
311	C₄⋊C₄	—	26	4	no	—
312	C₄⋊C₄	—	52	2	no	—
313	C₄⋊C₄	—	52	2	no	—
314	C₂²⋊C₄	—	26	2	no	—
315	C₂²⋊C₄	—	26	2	no	—
316	C₄²	—	26	2	no	—
317	C₄²	—	26	2	no	—
318	C₁₃	#10869	1	1	yes	characteristic, complemented, Sylow
319	C₂³	—	2	4	no	—
320	C₂³	#88144	1	1	yes	characteristic
321	C₂³	#88146	1	1	yes	characteristic
322	C₂³	#88147	1	1	yes	characteristic
323	C₂³	#88149	1	1	yes	characteristic
324	C₂³	Q₈×Dic₁₃	1	1	yes	characteristic
325	C₂³	#88200	1	1	yes	characteristic
326	C₂³	#88201	1	1	yes	characteristic
327	C₂×C₄	—	26	4	no	—
328	C₂×C₄	—	52	4	no	—
329	C₂×C₄	—	52	4	no	—
330	C₂×C₄	—	104	4	no	—
331	C₂×C₄	—	104	4	no	—
332	C₂×C₄	—	104	4	no	—
333	C₂×C₄	#88141	1	1	yes	characteristic
334	C₂×C₄	#88141	1	1	yes	characteristic
335	C₂×C₄	#88142	1	1	yes	characteristic
336	C₂×C₄	#88142	1	1	yes	characteristic
337	C₂×C₄	#88144	1	1	yes	characteristic
338	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
339	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
340	C₂×C₄	#88146	1	1	yes	characteristic
341	C₂×C₄	#88147	1	1	yes	characteristic
342	C₂×C₄	#88149	1	1	yes	characteristic
343	C₂×C₄	#88151	1	1	yes	characteristic
344	C₂×C₄	#88151	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
346	C₂×C₄	C₂×#6101	1	1	yes	characteristic
347	C₂×C₄	C₂×#6101	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
349	C₂×C₄	C₂×#6103	1	1	yes	characteristic
350	C₂×C₄	C₂×#6103	1	1	yes	characteristic
351	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
352	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
353	C₂×C₄	#88190	1	1	yes	characteristic
354	C₂×C₄	#88192	1	1	yes	characteristic
355	C₂×C₄	#88192	1	1	yes	characteristic
356	C₂×C₄	#88194	1	1	yes	characteristic
357	C₂×C₄	#88198	1	1	yes	characteristic
358	C₂×C₄	Q₈×Dic₁₃	1	1	yes	characteristic
359	C₂×C₄	#88200	1	1	yes	characteristic
360	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
361	C₈	—	4	4	no	—
362	C₈	—	26	4	no	—
363	C₈	#88071	1	4	yes	—
364	C₈	#88071	1	4	yes	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	#11718559	1	4	yes	—
372	C₂²	#11718634	1	1	yes	characteristic
373	C₂²	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
374	C₂²	#11718638	1	1	yes	characteristic
375	C₂²	#11718646	1	1	yes	characteristic
376	C₂²	#11718648	1	1	yes	characteristic
377	C₂²	#11718649	1	1	yes	characteristic
378	C₂²	#11718891	1	1	yes	characteristic
379	C₄	—	52	4	no	—
380	C₄	—	104	4	no	—
381	C₄	#11718634	1	1	yes	characteristic
382	C₄	#11718635	1	1	yes	characteristic
383	C₄	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
384	C₄	#11718637	1	1	yes	characteristic
385	C₄	#11718646	1	1	yes	characteristic
386	C₄	#11718648	1	1	yes	characteristic
387	C₄	C₂×#88071	1	1	yes	characteristic
388	C₄	#11718882	1	1	yes	characteristic
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	#13113065	1	1	yes	characteristic
394	C₂	#13114892	1	2	yes	—
395	C₂	#13115617	1	2	yes	—
396	C₂	#13115737	1	2	yes	—

	subgroup	G/H
center	C₂³	#88149
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂²×C₁₃×#108	C₂
socle	C₂³×C₁₃	#121
prime radical	C₂⁴×C₁₃	#41
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂²×#108	D₁₃
hypocenter	C₁₃	#10869
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
13. C₂×C₁₃×#108	C₄	semidirect
17. C₂×#88057	C₄	semidirect
19. #11718762	C₄	semidirect
179. C₂×#108	Dic₁₃	semidirect
318. C₁₃	#10869	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88057	2
C₂×#11718762	2
C₂×#11718146	2
#13114556	2
C₂²×C₁₃×#108	2
#10869	13