Subgroups — #15768842

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88059	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718762	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718125	C₂	1	2	yes	maximal
4	C₂×#11718123	C₂	1	2	yes	maximal
5	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#117	C₂²	1	2	yes	—
8	C₂×#88180	C₂²	1	1	yes	characteristic
9	C₂²×#6099	C₂²	1	2	yes	—
10	C₂²×#6099	C₂²	1	1	yes	characteristic
11	C₁₃×#427	—	2	2	no	—
12	C₁₃×#427	C₄	1	4	yes	complemented
13	C₂×C₁₃×#107	—	2	1	no	—
14	C₂×C₁₃×#106	—	2	1	no	—
15	C₂×#88059	—	2	2	no	—
16	C₂×#88059	—	2	1	no	—
17	C₂×#88059	—	2	1	no	—
18	C₂×#88059	C₄	1	4	yes	complemented
19	#11718762	—	2	2	no	—
20	#11718762	—	2	2	no	—
21	C₂×#88055	C₄	1	2	yes	complemented
22	C₂×C₈×Dic₁₃	C₄	1	2	yes	complemented
23	#11718125	—	2	4	no	—
24	#11718123	—	2	4	no	—
25	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
30	C₂²×C₈×C₁₃	D₄	1	2	yes	—
31	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₃	D₄	1	2	yes	—
34	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
35	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
36	C₁₃×#117	—	2	2	no	—
37	C₁₃×#117	—	2	2	no	—
38	C₁₃×#117	—	2	2	no	—
39	C₁₃×#117	C₂×C₄	1	4	yes	—
40	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
41	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
42	C₂×C₄²×C₁₃	—	2	2	no	—
43	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
44	#88180	—	2	1	no	—
45	#88180	—	2	1	no	—
46	#88180	D₄	1	2	yes	—
47	#88180	Q₈	1	2	yes	—
48	C₂×C₄⋊Dic₁₃	—	2	1	no	—
49	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
50	C₂×#6099	—	2	1	no	—
51	C₂×#6099	—	2	1	no	—
52	C₂×#6099	—	2	1	no	—
53	C₂×#6099	—	2	1	no	—
54	C₂×#6099	—	2	2	no	—
55	C₂×#6099	—	2	2	no	—
56	C₂×#6099	—	2	2	no	—
57	C₂×#6099	—	2	2	no	—
58	C₂×#6099	—	2	2	no	—
59	C₂×#6099	C₂×C₄	1	4	yes	—
60	C₂×#6099	D₄	1	2	yes	—
61	C₂×#6099	Q₈	1	2	yes	—
62	C₂²×#1055	—	2	2	no	—
63	C₂²×#1055	C₂×C₄	1	2	yes	—
64	C₁₃×#107	—	2	4	no	—
65	C₁₃×#106	—	2	4	no	—
66	#88059	—	2	4	no	—
67	#88059	—	2	4	no	—
68	#88055	—	2	4	no	—
69	C₈×Dic₁₃	—	2	4	no	—
70	#10868	—	13	1	no	maximal, Sylow
71	C₂⁴×C₁₃	#41	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	—	4	2	no	—
73	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
87	C₂²×Dic₁₃	—	2	2	no	—
88	C₂×C₈×C₁₃	C₄²	1	2	yes	—
89	C₂×C₈×C₁₃	C₄²	1	2	yes	—
90	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
91	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
92	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
93	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
94	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
95	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
96	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
101	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
102	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
103	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
104	C₁₃×C₄⋊C₄	—	2	4	no	—
105	C₁₃×C₄⋊C₄	—	4	2	no	—
106	C₁₃×C₂²⋊C₄	—	2	4	no	—
107	C₁₃×C₂²⋊C₄	—	4	2	no	—
108	C₄²×C₁₃	—	2	4	no	—
109	C₄²×C₁₃	—	4	2	no	—
110	C₂²⋊Dic₁₃	—	2	2	no	—
111	C₂²⋊Dic₁₃	—	2	2	no	—
112	C₄⋊Dic₁₃	—	2	2	no	—
113	C₄⋊Dic₁₃	—	2	2	no	—
114	C₄×Dic₁₃	—	2	2	no	—
115	C₄×Dic₁₃	C₄⋊C₄	1	4	yes	—
116	#6099	—	2	2	no	—
117	#6099	—	2	2	no	—
118	#6099	—	2	2	no	—
119	#6099	—	2	2	no	—
120	#6099	—	2	4	no	—
121	#6099	—	2	4	no	—
122	#6099	—	4	2	no	—
123	#6099	—	4	2	no	—
124	C₂×#1055	—	2	2	no	—
125	C₂×#1055	—	2	2	no	—
126	C₂×#1055	—	2	4	no	—
127	C₂×#1055	—	4	2	no	—
128	C₂×#1055	—	4	2	no	—
129	C₂×#1055	C₄⋊C₄	1	4	yes	—
130	C₂²×#108	—	13	1	no	—
131	C₂×#427	D₁₃	1	1	yes	characteristic
132	C₂×#405	—	13	1	no	—
133	C₂×#344	—	13	2	no	—
134	C₂×H(3,ℤ/4)	—	13	2	no	—
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	#117	1	1	yes	characteristic
137	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
138	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
139	C₂³×C₁₃	#121	1	1	yes	characteristic
140	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂³×C₁₃	#124	1	1	yes	characteristic
142	C₂³×C₁₃	#125	1	1	yes	characteristic
143	C₂×C₄×C₁₃	—	4	4	no	—
144	C₂×C₄×C₁₃	—	8	4	no	—
145	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₄×Q₈	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	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
168	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
169	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
173	C₂×Dic₁₃	—	2	4	no	—
174	C₂×Dic₁₃	—	4	4	no	—
175	C₈×C₁₃	#95	1	2	yes	—
176	C₈×C₁₃	#95	1	2	yes	—
177	C₈×C₁₃	#95	1	2	yes	—
178	C₈×C₁₃	#95	1	2	yes	—
179	#1055	—	2	4	no	—
180	#1055	—	4	4	no	—
181	C₂²×M₁₆	—	13	1	no	—
182	C₂²×M₁₆	—	13	2	no	—
183	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
184	C₂×#117	—	13	1	no	—
185	C₂×#117	C₂×D₁₃	1	2	yes	—
186	C₂×#108	—	13	4	no	—
187	C₂×#108	—	26	2	no	—
188	C₂×#108	—	26	1	no	—
189	C₂×#108	—	26	1	no	—
190	#427	—	2	2	no	—
191	#427	Dic₁₃	1	4	yes	complemented
192	C₂×#107	—	2	1	no	—
193	C₂×#106	—	2	1	no	—
194	#405	—	26	2	no	—
195	#405	—	26	2	no	—
196	C₂×#97	—	13	2	no	—
197	C₂×C₄×C₈	—	13	2	no	—
198	#344	—	26	4	no	—
199	H(3,ℤ/4)	—	26	4	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	—	4	1	no	—
204	C₂²×C₁₃	—	4	1	no	—
205	C₂²×C₁₃	—	4	1	no	—
206	C₂²×C₁₃	—	4	1	no	—
207	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
208	C₂²×C₁₃	#380	1	1	yes	characteristic
209	C₂²×C₁₃	#382	1	1	yes	characteristic
210	C₂²×C₁₃	#389	1	1	yes	characteristic
211	C₂²×C₁₃	#389	1	1	yes	characteristic
212	C₂²×C₁₃	#390	1	1	yes	characteristic
213	C₂²×C₁₃	#391	1	1	yes	characteristic
214	C₄×C₁₃	—	8	4	no	—
215	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
216	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
217	C₄×C₁₃	#380	1	1	yes	characteristic
218	C₄×C₁₃	#384	1	1	yes	characteristic
219	C₄×C₁₃	#389	1	1	yes	characteristic
220	C₄×C₁₃	#389	1	1	yes	characteristic
221	C₄×C₁₃	#390	1	1	yes	characteristic
222	C₄×C₁₃	#391	1	1	yes	characteristic
223	Dic₁₃	—	4	4	no	—
224	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
225	C₂×M₁₆	—	13	2	no	—
226	C₂×M₁₆	—	13	2	no	—
227	C₂×M₁₆	—	13	4	no	—
228	C₂×M₁₆	—	26	1	no	—
229	C₂×M₁₆	—	26	1	no	—
230	C₂×M₁₆	—	26	1	no	—
231	C₂×M₁₆	—	26	1	no	—
232	C₂×M₁₆	—	26	2	no	—
233	C₂×M₁₆	—	26	2	no	—
234	C₂×M₁₆	—	26	2	no	—
235	C₂×M₁₆	—	26	2	no	—
236	C₂×M₁₆	—	26	2	no	—
237	C₂²×C₈	—	13	2	no	—
238	C₂²×C₈	—	26	2	no	—
239	C₂²×C₈	Dic₂₆	1	1	yes	characteristic
240	C₂²×C₈	Dic₂₆	1	1	yes	characteristic
241	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
242	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
243	C₂²×C₈	C₄×D₁₃	1	2	yes	—
244	C₂²×C₈	D₅₂	1	2	yes	—
245	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
246	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
247	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
248	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
249	#117	—	2	2	no	—
250	#117	—	2	2	no	—
251	#117	—	2	2	no	—
252	#117	—	13	2	no	—
253	#117	—	13	2	no	—
254	#117	—	26	1	no	—
255	#117	—	26	1	no	—
256	#117	C₂×Dic₁₃	1	4	yes	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	26	1	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	26	1	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	13	2	no	—
263	#108	—	26	4	no	—
264	#108	—	26	4	no	—
265	#107	—	2	4	no	—
266	#106	—	2	4	no	—
267	#97	—	26	4	no	—
268	C₄×C₈	—	26	4	no	—
269	C₂×C₁₃	—	2	1	no	—
270	C₂×C₁₃	—	2	1	no	—
271	C₂×C₁₃	—	2	1	no	—
272	C₂×C₁₃	—	2	1	no	—
273	C₂×C₁₃	—	2	1	no	—
274	C₂×C₁₃	—	2	1	no	—
275	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
276	C₂×C₁₃	#1833	1	2	yes	—
277	C₂⁴	#6129	1	1	yes	characteristic
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	26	2	no	—
280	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
284	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
285	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
286	C₂²×C₄	#6129	1	1	yes	characteristic
287	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
288	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
289	C₂²×C₄	#6131	1	1	yes	characteristic
290	C₂²×C₄	#6131	1	1	yes	characteristic
291	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
294	M₁₆	—	26	2	no	—
295	M₁₆	—	26	2	no	—
296	M₁₆	—	26	2	no	—
297	M₁₆	—	26	2	no	—
298	M₁₆	—	26	4	no	—
299	M₁₆	—	26	4	no	—
300	M₁₆	—	52	2	no	—
301	M₁₆	—	52	2	no	—
302	C₂×C₈	—	13	4	no	—
303	C₂×C₈	—	26	2	no	—
304	C₂×C₈	—	26	2	no	—
305	C₂×C₈	—	26	4	no	—
306	C₂×C₈	—	52	2	no	—
307	C₂×C₈	—	52	2	no	—
308	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
309	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
310	C₂×C₈	#6101	1	2	yes	—
311	C₂×C₈	#6101	1	2	yes	—
312	C₂×C₈	#6101	1	1	yes	characteristic
313	C₂×C₈	#6101	1	1	yes	characteristic
314	C₂×C₈	#6101	1	1	yes	characteristic
315	C₂×C₈	#6101	1	1	yes	characteristic
316	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
317	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
318	C₂×C₈	#6103	1	2	yes	—
319	C₂×C₈	#6103	1	2	yes	—
320	C₂×C₈	#6103	1	2	yes	—
321	C₂×C₈	#6103	1	2	yes	—
322	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
323	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	26	2	no	—
327	C₄⋊C₄	—	26	2	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	26	2	no	—
331	C₂²⋊C₄	—	26	2	no	—
332	C₄²	—	2	4	no	—
333	C₄²	—	4	2	no	—
334	C₄²	—	13	4	no	—
335	C₄²	—	26	2	no	—
336	C₁₃	#10868	1	1	yes	characteristic, complemented, Sylow
337	C₂³	—	4	2	no	—
338	C₂³	#88141	1	1	yes	characteristic
339	C₂³	#88144	1	1	yes	characteristic
340	C₂³	#88146	1	1	yes	characteristic
341	C₂³	#88151	1	1	yes	characteristic
342	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
343	C₂³	#88190	1	1	yes	characteristic
344	C₂³	#88192	1	1	yes	characteristic
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	8	4	no	—
347	C₂×C₄	—	26	4	no	—
348	C₂×C₄	—	52	4	no	—
349	C₂×C₄	#88141	1	1	yes	characteristic
350	C₂×C₄	#88142	1	1	yes	characteristic
351	C₂×C₄	#88142	1	1	yes	characteristic
352	C₂×C₄	#88144	1	1	yes	characteristic
353	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
354	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
355	C₂×C₄	#88146	1	1	yes	characteristic
356	C₂×C₄	#88147	1	1	yes	characteristic
357	C₂×C₄	#88147	1	1	yes	characteristic
358	C₂×C₄	#88149	1	1	yes	characteristic
359	C₂×C₄	#88149	1	1	yes	characteristic
360	C₂×C₄	#88151	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
362	C₂×C₄	C₂×#6101	1	1	yes	characteristic
363	C₂×C₄	C₂×#6101	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
365	C₂×C₄	C₂×#6103	1	1	yes	characteristic
366	C₂×C₄	C₂×#6103	1	1	yes	characteristic
367	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
368	C₂×C₄	#88192	1	1	yes	characteristic
369	C₂×C₄	#88194	1	1	yes	characteristic
370	C₂×C₄	#88198	1	1	yes	characteristic
371	C₂×C₄	Q₈×Dic₁₃	1	1	yes	characteristic
372	C₂×C₄	Q₈×Dic₁₃	1	1	yes	characteristic
373	C₂×C₄	#88200	1	1	yes	characteristic
374	C₂×C₄	#88200	1	1	yes	characteristic
375	C₂×C₄	#88201	1	1	yes	characteristic
376	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
377	C₈	—	26	4	no	—
378	C₈	—	52	4	no	—
379	C₈	#88071	1	2	yes	—
380	C₈	#88071	1	2	yes	—
381	C₈	#88071	1	2	yes	—
382	C₈	#88071	1	2	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	#11718634	1	1	yes	characteristic
391	C₂²	#11718635	1	1	yes	characteristic
392	C₂²	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
393	C₂²	#11718638	1	1	yes	characteristic
394	C₂²	#11718646	1	1	yes	characteristic
395	C₂²	#11718648	1	1	yes	characteristic
396	C₂²	#11718882	1	1	yes	characteristic
397	C₄	—	8	4	no	—
398	C₄	—	52	4	no	—
399	C₄	#11718634	1	1	yes	characteristic
400	C₄	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
401	C₄	#11718637	1	1	yes	characteristic
402	C₄	#11718646	1	1	yes	characteristic
403	C₄	#11718648	1	1	yes	characteristic
404	C₄	#11718649	1	1	yes	characteristic
405	C₄	C₂×#88071	1	1	yes	characteristic
406	C₄	#11718891	1	1	yes	characteristic
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	#13113065	1	1	yes	characteristic
414	C₂	#13114959	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#88146
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#427	C₂
socle	C₂²×C₁₃	#382
prime radical	C₂⁴×C₁₃	#41
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#427	D₁₃
hypocenter	C₁₃	#10868
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
12. C₁₃×#427	C₄	semidirect
18. C₂×#88059	C₄	semidirect
21. C₂×#88055	C₄	semidirect
22. C₂×C₈×Dic₁₃	C₄	semidirect
191. #427	Dic₁₃	semidirect
336. C₁₃	#10868	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88059	2
C₂×#11718762	2
C₂×#11718125	2
C₂×#11718123	2
C₂×C₁₃×#427	2
#10868	13