Subgroups — #15829624

Order 3328.

1026 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719175	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
3	#13113292	C₂	1	4	yes	maximal, complemented
4	#13113266	C₂	1	4	yes	maximal, complemented
5	#13113240	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88180	—	2	1	no	—
9	C₂×#88178	—	2	1	no	—
10	C₂×#88178	C₄	1	2	yes	—
11	C₂²×#6099	—	2	1	no	—
12	#11719175	—	2	1	no	—
13	#11719175	—	2	1	no	—
14	#11719175	—	2	1	no	—
15	#11719175	—	2	1	no	—
16	#11719175	C₄	1	2	yes	—
17	#11719175	C₄	1	2	yes	—
18	#11719175	C₂²	1	2	yes	—
19	#11719175	C₂²	1	2	yes	—
20	C₂×#88124	—	2	1	no	—
21	C₂×#88123	C₄	1	1	yes	characteristic
22	C₂×#88123	C₄	1	1	yes	characteristic
23	C₂×C₄×Dic₂₆	—	2	1	no	—
24	C₂×C₄×Dic₂₆	C₂²	1	2	yes	—
25	C₁₃×#431	—	2	1	no	—
26	C₁₃×#431	—	2	1	no	—
27	C₁₃×#431	C₂²	1	2	yes	—
28	C₁₃×#431	C₂²	1	2	yes	—
29	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
30	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
32	#11718585	—	2	1	no	—
33	#11718585	—	2	1	no	—
34	#11718585	C₂²	1	2	yes	—
35	#11718585	C₂²	1	2	yes	—
36	C₂×C₄⋊#1055	—	2	1	no	—
37	C₂×C₄⋊#1055	C₂²	1	2	yes	—
38	#11718048	C₂²	1	16	yes	complemented
39	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
42	C₂²×Dic₂₆	—	2	1	no	—
43	C₂²×Dic₂₆	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₃	—	2	2	no	—
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
58	#88180	—	2	2	no	—
59	#88180	—	2	2	no	—
60	#88180	—	2	2	no	—
61	#88180	—	2	2	no	—
62	C₂×C₄⋊Dic₁₃	—	2	1	no	—
63	C₂×C₄⋊Dic₁₃	—	2	1	no	—
64	C₂×C₄⋊Dic₁₃	—	2	1	no	—
65	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
66	#88178	—	2	2	no	—
67	#88178	—	2	2	no	—
68	#88178	—	2	2	no	—
69	#88178	—	2	2	no	—
70	#88178	—	2	2	no	—
71	#88178	—	2	2	no	—
72	#88178	C₂×C₄	1	4	yes	—
73	#88178	C₂×C₄	1	4	yes	—
74	C₂×#6101	—	2	2	no	—
75	C₂×#6101	—	2	2	no	—
76	C₂×C₄×Dic₁₃	—	2	2	no	—
77	C₂×#6099	—	2	2	no	—
78	C₂×#6099	—	2	2	no	—
79	C₂×#6099	—	4	4	no	—
80	C₂²×#1055	—	2	2	no	—
81	#88124	—	2	2	no	—
82	#88124	—	2	2	no	—
83	#88124	—	2	2	no	—
84	#88124	—	2	2	no	—
85	#88123	—	2	1	no	—
86	#88123	—	2	1	no	—
87	#88123	—	2	1	no	—
88	#88123	—	2	1	no	—
89	#88123	C₂×C₄	1	2	yes	—
90	#88123	C₂×C₄	1	2	yes	—
91	#88123	C₂×C₄	1	2	yes	—
92	#88123	C₂×C₄	1	2	yes	—
93	C₄×Dic₂₆	—	2	2	no	—
94	C₄×Dic₂₆	—	2	2	no	—
95	C₄×Dic₂₆	—	2	2	no	—
96	C₄×Dic₂₆	—	2	2	no	—
97	C₄×Dic₂₆	—	2	2	no	—
98	C₄×Dic₂₆	—	2	2	no	—
99	C₄×Dic₂₆	C₂×C₄	1	4	yes	—
100	C₄×Dic₂₆	C₂³	1	4	yes	—
101	C₁₃×C₄⋊C₈	—	2	2	no	—
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×C₂²⋊C₈	—	2	2	no	—
104	C₁₃×C₂²⋊C₈	—	2	2	no	—
105	C₄×C₈×C₁₃	—	2	2	no	—
106	C₄×C₈×C₁₃	C₂³	1	4	yes	—
107	C₄⋊#1055	—	2	2	no	—
108	C₄⋊#1055	—	2	2	no	—
109	C₄⋊#1055	—	2	2	no	—
110	C₄⋊#1055	C₂³	1	4	yes	—
111	#17486	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	—	4	2	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
125	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×Dic₁₃	—	2	2	no	—
136	C₂²×Dic₁₃	—	2	2	no	—
137	C₂×Dic₂₆	—	2	2	no	—
138	C₂×Dic₂₆	—	2	2	no	—
139	C₂×Dic₂₆	—	2	2	no	—
140	C₂×Dic₂₆	—	4	4	no	—
141	C₂×Dic₂₆	—	4	4	no	—
142	C₂×Dic₂₆	C₂²×C₄	1	4	yes	—
143	C₂×C₈×C₁₃	—	2	4	no	—
144	C₂×C₈×C₁₃	—	4	4	no	—
145	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
146	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
147	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
148	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
149	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂²⋊Dic₁₃	—	2	4	no	—
162	C₂²⋊Dic₁₃	—	2	4	no	—
163	C₄⋊Dic₁₃	—	2	2	no	—
164	C₄⋊Dic₁₃	—	2	2	no	—
165	C₄⋊Dic₁₃	—	2	2	no	—
166	C₄⋊Dic₁₃	—	2	2	no	—
167	C₄⋊Dic₁₃	—	2	2	no	—
168	C₄⋊Dic₁₃	—	2	2	no	—
169	C₄⋊Dic₁₃	—	2	2	no	—
170	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
171	#6101	—	2	4	no	—
172	#6101	—	2	4	no	—
173	#6101	—	2	4	no	—
174	#6101	—	2	4	no	—
175	C₄×Dic₁₃	—	2	4	no	—
176	C₄×Dic₁₃	—	2	4	no	—
177	#6099	—	4	4	no	—
178	#6099	—	4	4	no	—
179	C₂×#1055	—	2	4	no	—
180	C₂×#1055	—	4	4	no	—
181	C₂×#533	—	13	1	no	—
182	C₂×#431	D₁₃	1	1	yes	characteristic
183	C₂×#423	—	13	1	no	—
184	#1493	—	13	4	no	—
185	#1487	—	13	4	no	—
186	#1481	—	13	4	no	—
187	C₂³×C₁₃	—	4	1	no	—
188	C₂³×C₁₃	—	4	1	no	—
189	C₂³×C₁₃	#103	1	4	yes	—
190	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	#103	1	4	yes	—
206	C₂×C₄×C₁₃	#103	1	4	yes	—
207	C₂×C₄×C₁₃	#103	1	4	yes	—
208	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
218	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
219	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
220	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
221	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
222	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
223	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×Dic₁₃	—	2	4	no	—
227	C₂×Dic₁₃	—	2	4	no	—
228	C₂×Dic₁₃	—	4	4	no	—
229	C₂×Dic₁₃	—	4	4	no	—
230	Dic₂₆	—	2	8	no	—
231	Dic₂₆	—	4	4	no	—
232	Dic₂₆	—	4	4	no	—
233	Dic₂₆	—	4	4	no	—
234	C₈×C₁₃	—	4	4	no	—
235	#1055	—	4	4	no	—
236	C₂²×M₁₆	—	26	1	no	—
237	#533	—	13	2	no	—
238	#533	—	13	2	no	—
239	#533	—	13	2	no	—
240	#533	—	13	2	no	—
241	#533	—	26	1	no	—
242	#533	—	26	1	no	—
243	#533	—	26	1	no	—
244	#533	—	26	1	no	—
245	C₂×C₄⋊Q₈	—	13	1	no	—
246	C₂×C₄⋊Q₈	—	13	1	no	—
247	C₂×#125	—	26	1	no	—
248	C₂×C₂²⋊Q₈	—	13	2	no	—
249	C₂×C₂²⋊Q₈	—	26	1	no	—
250	C₂×C₄×Q₈	—	13	2	no	—
251	C₂×C₄×Q₈	—	26	1	no	—
252	C₂×#117	—	26	1	no	—
253	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
254	#431	—	2	1	no	—
255	#431	—	2	1	no	—
256	#431	C₂×D₁₃	1	2	yes	—
257	#431	C₂×D₁₃	1	2	yes	—
258	#423	—	13	2	no	—
259	#423	—	13	2	no	—
260	#423	—	26	1	no	—
261	#423	—	26	1	no	—
262	C₂×C₄⋊C₈	—	2	1	no	—
263	C₂×C₄⋊C₈	—	13	2	no	—
264	C₂×C₄⋊C₈	—	26	1	no	—
265	C₂×C₂²⋊C₈	—	2	1	no	—
266	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
267	Q₈⋊C₈	—	13	16	no	—
268	C₂²×C₁₃	—	2	1	no	—
269	C₂²×C₁₃	—	2	1	no	—
270	C₂²×C₁₃	—	2	1	no	—
271	C₂²×C₁₃	—	2	1	no	—
272	C₂²×C₁₃	—	2	1	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	4	4	no	—
275	C₂²×C₁₃	C₂×#103	1	2	yes	—
276	C₂²×C₁₃	C₂×#103	1	2	yes	—
277	C₂²×C₁₃	C₂×#103	1	2	yes	—
278	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	2	1	no	—
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	—	2	1	no	—
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	C₂×#103	1	2	yes	—
286	C₄×C₁₃	C₂×#103	1	2	yes	—
287	C₄×C₁₃	C₂×#103	1	2	yes	—
288	C₄×C₁₃	#421	1	2	yes	—
289	C₄×C₁₃	#568	1	2	yes	—
290	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
291	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
292	Dic₁₃	—	4	4	no	—
293	Dic₁₃	—	4	4	no	—
294	C₂²×Q₈	—	13	2	no	—
295	C₂²×Q₈	—	26	1	no	—
296	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
297	C₂³×C₄	D₅₂	1	1	yes	characteristic
298	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
299	C₂×M₁₆	—	26	2	no	—
300	C₂×M₁₆	—	26	2	no	—
301	C₂×M₁₆	—	52	4	no	—
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	—	26	2	no	—
304	C₄⋊Q₈	—	13	2	no	—
305	C₄⋊Q₈	—	13	2	no	—
306	C₄⋊Q₈	—	13	2	no	—
307	C₄⋊Q₈	—	13	2	no	—
308	C₄⋊Q₈	—	26	1	no	—
309	C₄⋊Q₈	—	26	1	no	—
310	C₄⋊Q₈	—	26	1	no	—
311	C₄⋊Q₈	—	26	1	no	—
312	#125	—	26	2	no	—
313	#125	—	26	2	no	—
314	#125	—	26	2	no	—
315	#125	—	26	2	no	—
316	C₂²⋊Q₈	—	13	4	no	—
317	C₂²⋊Q₈	—	13	4	no	—
318	C₂²⋊Q₈	—	26	2	no	—
319	C₂²⋊Q₈	—	26	2	no	—
320	C₂²⋊Q₈	—	26	2	no	—
321	C₂²⋊Q₈	—	26	2	no	—
322	C₂²⋊Q₈	—	26	2	no	—
323	C₂²⋊Q₈	—	26	2	no	—
324	C₄×Q₈	—	13	4	no	—
325	C₄×Q₈	—	13	4	no	—
326	C₄×Q₈	—	26	2	no	—
327	C₄×Q₈	—	26	2	no	—
328	C₄×Q₈	—	26	2	no	—
329	C₄×Q₈	—	26	2	no	—
330	C₄×Q₈	—	26	2	no	—
331	C₄×Q₈	—	26	2	no	—
332	#117	—	26	2	no	—
333	#117	—	26	2	no	—
334	#117	—	26	2	no	—
335	#117	—	26	2	no	—
336	C₂×C₄⋊C₄	—	13	2	no	—
337	C₂×C₄⋊C₄	—	26	1	no	—
338	C₂×C₄⋊C₄	—	26	1	no	—
339	C₂×C₄⋊C₄	—	26	2	no	—
340	C₂×C₄⋊C₄	—	26	1	no	—
341	C₂×C₄⋊C₄	—	26	2	no	—
342	C₂×C₂²⋊C₄	—	26	2	no	—
343	C₂×C₄²	—	26	2	no	—
344	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
345	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
346	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
347	C₂×C₄²	D₅₂	1	1	yes	characteristic
348	C₂×C₄²	D₅₂	1	1	yes	characteristic
349	C₂×C₄²	D₅₂	1	1	yes	characteristic
350	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
351	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
352	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
353	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
354	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
355	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
356	C₄⋊C₈	—	2	2	no	—
357	C₄⋊C₈	—	2	2	no	—
358	C₄⋊C₈	—	13	4	no	—
359	C₄⋊C₈	—	26	2	no	—
360	C₄⋊C₈	—	26	2	no	—
361	C₄⋊C₈	—	26	2	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	C₂²⋊C₈	—	2	2	no	—
364	C₄×C₈	—	2	2	no	—
365	C₄×C₈	C₂²×D₁₃	1	4	yes	—
366	C₂×C₁₃	—	2	2	no	—
367	C₂×C₁₃	—	2	2	no	—
368	C₂×C₁₃	—	2	2	no	—
369	C₂×C₁₃	#2879	1	1	yes	characteristic
370	C₂×C₁₃	C₂²×#103	1	1	yes	characteristic
371	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
372	C₂⁴	#6103	1	1	yes	characteristic
373	C₂×Q₈	—	13	4	no	—
374	C₂×Q₈	—	26	2	no	—
375	C₂×Q₈	—	26	2	no	—
376	C₂×Q₈	—	26	2	no	—
377	C₂×Q₈	—	52	4	no	—
378	C₂×Q₈	—	52	4	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	26	2	no	—
382	C₂²×C₄	—	26	2	no	—
383	C₂²×C₄	#6095	1	4	yes	—
384	C₂²×C₄	Dic₅₂	1	4	yes	—
385	C₂²×C₄	#6103	1	1	yes	characteristic
386	C₂²×C₄	#6103	1	1	yes	characteristic
387	C₂²×C₄	#6103	1	1	yes	characteristic
388	C₂²×C₄	#6103	1	1	yes	characteristic
389	C₂²×C₄	#6103	1	1	yes	characteristic
390	C₂²×C₄	#6103	1	1	yes	characteristic
391	C₂²×C₄	#6103	1	1	yes	characteristic
392	C₂²×C₄	#6103	1	1	yes	characteristic
393	C₂²×C₄	#6103	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
400	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
403	M₁₆	—	52	4	no	—
404	M₁₆	—	52	4	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	—	4	4	no	—
407	C₂×C₈	—	26	4	no	—
408	C₂×C₈	—	52	4	no	—
409	C₄⋊C₄	—	13	4	no	—
410	C₄⋊C₄	—	26	2	no	—
411	C₄⋊C₄	—	26	2	no	—
412	C₄⋊C₄	—	26	2	no	—
413	C₄⋊C₄	—	26	2	no	—
414	C₄⋊C₄	—	26	2	no	—
415	C₄⋊C₄	—	26	4	no	—
416	C₄⋊C₄	—	26	4	no	—
417	C₄⋊C₄	—	26	4	no	—
418	C₄⋊C₄	—	26	2	no	—
419	C₄⋊C₄	—	26	2	no	—
420	C₄⋊C₄	—	26	4	no	—
421	C₂²⋊C₄	—	26	4	no	—
422	C₂²⋊C₄	—	26	4	no	—
423	C₄²	—	26	4	no	—
424	C₄²	—	26	4	no	—
425	C₄²	#6103	1	1	yes	characteristic
426	C₄²	#6103	1	1	yes	characteristic
427	C₄²	#6103	1	1	yes	characteristic
428	C₄²	#6103	1	1	yes	characteristic
429	C₄²	#6103	1	1	yes	characteristic
430	C₄²	#6103	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
432	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
433	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
434	C₄²	C₂×D₅₂	1	1	yes	characteristic
435	C₄²	C₂×D₅₂	1	1	yes	characteristic
436	C₄²	C₂×D₅₂	1	1	yes	characteristic
437	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
438	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
439	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
440	C₄²	C₂³×D₁₃	1	1	yes	characteristic
441	C₁₃	#17486	1	1	yes	characteristic, complemented, Sylow
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	#88056	1	4	yes	—
445	C₂³	C₂×#6103	1	1	yes	characteristic
446	C₂³	C₂×#6103	1	1	yes	characteristic
447	C₂³	C₂×#6103	1	1	yes	characteristic
448	Q₈	—	26	8	no	—
449	Q₈	—	52	4	no	—
450	Q₈	—	52	4	no	—
451	Q₈	—	52	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	26	4	no	—
465	C₂×C₄	—	26	4	no	—
466	C₂×C₄	—	52	4	no	—
467	C₂×C₄	—	52	4	no	—
468	C₂×C₄	#88056	1	4	yes	—
469	C₂×C₄	#88056	1	4	yes	—
470	C₂×C₄	#88056	1	4	yes	—
471	C₂×C₄	C₂×#6095	1	2	yes	—
472	C₂×C₄	C₂×#6095	1	2	yes	—
473	C₂×C₄	C₂×#6095	1	2	yes	—
474	C₂×C₄	C₂×Dic₅₂	1	2	yes	—
475	C₂×C₄	C₂×Dic₅₂	1	2	yes	—
476	C₂×C₄	C₂×Dic₅₂	1	2	yes	—
477	C₂×C₄	C₂×#6103	1	1	yes	characteristic
478	C₂×C₄	C₂×#6103	1	1	yes	characteristic
479	C₂×C₄	C₂×#6103	1	1	yes	characteristic
480	C₂×C₄	C₂×#6103	1	1	yes	characteristic
481	C₂×C₄	C₂×#6103	1	1	yes	characteristic
482	C₂×C₄	C₂×#6103	1	1	yes	characteristic
483	C₂×C₄	C₂×#6103	1	1	yes	characteristic
484	C₂×C₄	C₂×#6103	1	1	yes	characteristic
485	C₂×C₄	C₂×#6103	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
488	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
489	C₈	—	4	4	no	—
490	C₈	—	52	4	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	4	4	no	—
498	C₂²	C₂×#88056	1	2	yes	—
499	C₂²	C₂×#88056	1	2	yes	—
500	C₂²	C₂×#88056	1	2	yes	—
501	C₂²	C₂²×#6103	1	1	yes	characteristic
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	52	4	no	—
509	C₄	—	52	4	no	—
510	C₄	#11718666	1	2	yes	—
511	C₄	C₂×#88056	1	2	yes	—
512	C₄	C₂×#88056	1	2	yes	—
513	C₄	C₂×#88056	1	2	yes	—
514	C₄	C₂²×#6095	1	1	yes	characteristic
515	C₄	C₂²×Dic₅₂	1	1	yes	characteristic
516	C₄	#11719450	1	2	yes	—
517	C₂	—	2	2	no	—
518	C₂	—	2	2	no	—
519	C₂	—	2	2	no	—
520	C₂	#13123280	1	1	yes	characteristic
521	C₂	C₂²×#88056	1	1	yes	characteristic
522	C₂	C₂×#11718666	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#431	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂²⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×#431	D₁₃
hypocenter	C₁₃	#17486
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #13113292	C₂	semidirect
4. #13113266	C₂	semidirect
5. #13113240	C₂	semidirect
38. #11718048	C₂²	semidirect
441. C₁₃	#17486	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719175	2
C₂×#11718585	2
#13113292	2
#13113266	2
#13113240	2
C₂×C₁₃×#431	2
#17486	13