Subgroups — #15870378

Order 3328.

898 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718685	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#88043	C₂	1	1	yes	maximal, characteristic
3	#13115777	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115560	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115402	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115402	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115016	C₂	1	1	yes	maximal, characteristic
8	#13115016	C₂	1	1	yes	maximal, characteristic
9	#13114816	C₂	1	1	yes	maximal, characteristic
10	#13114711	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114711	C₂	1	1	yes	maximal, characteristic, complemented
12	#13114705	C₂	1	1	yes	maximal, characteristic, complemented
13	#13114614	C₂	1	1	yes	maximal, characteristic
14	C₂²⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₂³×#1055	C₂²	1	1	yes	characteristic
20	C₂³×#1055	C₂²	1	1	yes	characteristic
21	C₁₃×#391	C₄	1	1	yes	characteristic
22	C₁₃×#389	C₄	1	1	yes	characteristic
23	C₁₃×#387	C₄	1	1	yes	characteristic
24	C₁₃×#387	C₄	1	1	yes	characteristic
25	C₁₃×#385	C₄	1	1	yes	characteristic
26	C₁₃×#385	C₄	1	1	yes	characteristic
27	C₁₃×#380	C₄	1	1	yes	characteristic
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
35	#11718685	—	2	4	no	—
36	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
42	C₂×#88043	—	2	4	no	—
43	C₂×#88043	C₂²	1	1	yes	characteristic
44	C₂×#88043	C₂²	1	1	yes	characteristic
45	C₂×#88043	C₂²	1	1	yes	characteristic
46	C₂×#88043	C₂²	1	1	yes	characteristic
47	C₂×#88043	C₂²	1	1	yes	characteristic
48	C₂×#88043	C₂²	1	1	yes	characteristic
49	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
50	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
51	#11718116	C₂²	1	1	yes	characteristic
52	#11718116	C₂²	1	1	yes	characteristic
53	#11718116	C₂²	1	1	yes	characteristic
54	#11718116	C₂²	1	1	yes	characteristic
55	#11718116	C₂²	1	1	yes	characteristic
56	#11718116	C₂²	1	1	yes	characteristic
57	#11718116	C₂²	1	1	yes	characteristic
58	#11718116	C₂²	1	1	yes	characteristic
59	#11718116	C₂²	1	1	yes	characteristic
60	#11718116	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×C₂²⋊Q₈	—	2	4	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×#1055	—	2	2	no	—
92	C₂²×#1055	—	2	2	no	—
93	C₂²×#1055	—	2	2	no	—
94	C₂²×#1055	—	2	2	no	—
95	C₂²×#1055	—	2	2	no	—
96	C₂²×#1055	Q₈	1	4	yes	complemented
97	C₂²×#1055	C₂³	1	1	yes	characteristic
98	C₂²×#1055	C₂³	1	1	yes	characteristic
99	C₂²×#1055	C₂³	1	1	yes	characteristic
100	C₂²×#1055	C₂³	1	1	yes	characteristic
101	C₂²×#1055	C₂³	1	1	yes	characteristic
102	C₂²×#1055	C₂³	1	1	yes	characteristic
103	C₂²×#1055	C₂³	1	1	yes	characteristic
104	C₂²×#1055	C₂³	1	1	yes	characteristic
105	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
106	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
107	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
108	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
109	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
110	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
111	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
112	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
113	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
114	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊#1055	—	2	2	no	—
116	C₂²⋊#1055	—	2	2	no	—
117	C₄⋊#1055	—	2	2	no	—
118	C₄⋊#1055	—	2	2	no	—
119	C₄⋊#1055	—	2	2	no	—
120	C₄⋊#1055	—	2	2	no	—
121	C₄⋊#1055	—	2	2	no	—
122	C₄⋊#1055	—	2	2	no	—
123	#88043	—	2	2	no	—
124	#88043	—	2	2	no	—
125	#88043	—	2	2	no	—
126	#88043	—	2	2	no	—
127	#88043	—	2	2	no	—
128	#88043	D₄	1	4	yes	—
129	C₄×#1055	—	2	2	no	—
130	C₄×#1055	—	2	2	no	—
131	#21599	—	13	1	no	maximal, Sylow
132	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	—	4	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	4	1	no	—
145	C₂²×C₄×C₁₃	—	4	1	no	—
146	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
160	C₂²×C₄×C₁₃	#41	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	4	1	no	—
169	C₁₃×C₄⋊C₄	—	4	1	no	—
170	C₁₃×C₄⋊C₄	—	4	1	no	—
171	C₁₃×C₂²⋊C₄	—	2	2	no	—
172	C₁₃×C₂²⋊C₄	—	2	2	no	—
173	C₁₃×C₂²⋊C₄	—	2	2	no	—
174	C₁₃×C₂²⋊C₄	M₁₆	1	4	yes	—
175	C₄²×C₁₃	—	2	2	no	—
176	C₄²×C₁₃	—	2	2	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	—	2	1	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₄²×C₁₃	—	2	1	no	—
182	C₄²×C₁₃	—	2	1	no	—
183	C₄²×C₁₃	—	2	1	no	—
184	C₄²×C₁₃	—	2	1	no	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	—	2	1	no	—
187	C₄²×C₁₃	C₂×D₄	1	2	yes	—
188	C₄²×C₁₃	#41	1	2	yes	—
189	C₂×#1055	—	2	8	no	—
190	C₂×#1055	—	2	1	no	—
191	C₂×#1055	—	2	1	no	—
192	C₂×#1055	—	2	1	no	—
193	C₂×#1055	—	2	1	no	—
194	C₂×#1055	—	2	1	no	—
195	C₂×#1055	—	2	1	no	—
196	C₂×#1055	—	2	8	no	—
197	C₂×#1055	—	2	1	no	—
198	C₂×#1055	—	2	1	no	—
199	C₂×#1055	—	2	1	no	—
200	C₂×#1055	—	2	1	no	—
201	C₂×#1055	—	2	1	no	—
202	C₂×#1055	—	2	1	no	—
203	C₂×#1055	—	2	1	no	—
204	C₂×#1055	—	2	1	no	—
205	C₂×#1055	—	2	1	no	—
206	C₂×#1055	—	2	1	no	—
207	C₂×#1055	—	2	1	no	—
208	C₂×#1055	—	2	1	no	—
209	C₂×#1055	C₂×D₄	1	2	yes	—
210	C₂×#1055	C₂×D₄	1	2	yes	—
211	C₂×#1055	C₂×Q₈	1	2	yes	—
212	C₂×#1055	C₂×Q₈	1	2	yes	—
213	C₂×#1055	#41	1	2	yes	—
214	C₂×#1055	#41	1	2	yes	—
215	C₂×#446	—	13	1	no	—
216	C₂²×#97	—	13	1	no	—
217	C₄×C₂²⋊Q₈	D₁₃	1	1	yes	characteristic
218	#1985	—	13	1	no	—
219	#1940	—	13	1	no	—
220	#1917	—	13	1	no	—
221	#1917	—	13	1	no	—
222	#1850	—	13	1	no	—
223	#1850	—	13	1	no	—
224	#1797	—	13	1	no	—
225	#1771	—	13	1	no	—
226	#1771	—	13	1	no	—
227	#1770	—	13	1	no	—
228	#1752	—	13	1	no	—
229	C₈×C₂²⋊C₄	—	13	1	no	—
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
235	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
236	C₂³×C₁₃	#131	1	2	yes	—
237	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
238	Q₈×C₁₃	—	4	4	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	4	4	no	—
278	C₂×C₄×C₁₃	—	4	4	no	—
279	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
280	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
281	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
282	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
283	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
284	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
290	#1055	—	2	2	no	—
291	#1055	—	2	2	no	—
292	#1055	—	2	2	no	—
293	#1055	—	4	1	no	—
294	#1055	—	4	1	no	—
295	#1055	—	4	1	no	—
296	#1055	—	4	1	no	—
297	#1055	C₂²⋊Q₈	1	4	yes	complemented
298	C₂³×C₈	—	13	1	no	—
299	C₂³×C₈	—	13	1	no	—
300	C₂×C₂²⋊Q₈	Dic₁₃	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
302	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
303	#446	—	26	4	no	—
304	C₂×C₄⋊C₈	—	13	1	no	—
305	C₂×C₄⋊C₈	—	13	1	no	—
306	C₂×C₄⋊C₈	—	13	1	no	—
307	C₂×C₄⋊C₈	—	13	1	no	—
308	C₂×C₄⋊C₈	—	13	1	no	—
309	C₂×C₄⋊C₈	—	13	1	no	—
310	C₂×C₂²⋊C₈	—	13	1	no	—
311	C₂×C₂²⋊C₈	—	13	1	no	—
312	C₂×#97	—	13	1	no	—
313	C₂×#97	—	13	1	no	—
314	C₂×#97	—	13	1	no	—
315	C₂×#97	—	13	1	no	—
316	C₂×#97	—	13	1	no	—
317	C₂×#97	—	13	1	no	—
318	C₂×#97	—	26	4	no	—
319	C₂×C₄×C₈	—	13	1	no	—
320	C₂×C₄×C₈	—	13	1	no	—
321	#391	Dic₁₃	1	1	yes	characteristic
322	#389	Dic₁₃	1	1	yes	characteristic
323	#387	Dic₁₃	1	1	yes	characteristic
324	#387	Dic₁₃	1	1	yes	characteristic
325	#385	Dic₁₃	1	1	yes	characteristic
326	#385	Dic₁₃	1	1	yes	characteristic
327	#380	Dic₁₃	1	1	yes	characteristic
328	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
329	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
330	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
331	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
332	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
333	#336	—	13	1	no	—
334	#336	—	13	1	no	—
335	#336	—	13	1	no	—
336	#336	—	13	1	no	—
337	#336	—	13	1	no	—
338	#336	—	13	1	no	—
339	#336	—	13	1	no	—
340	#336	—	13	1	no	—
341	#336	—	13	1	no	—
342	#336	—	13	1	no	—
343	C₂²×C₁₃	—	2	2	no	—
344	C₂²×C₁₃	—	2	2	no	—
345	C₂²×C₁₃	—	2	2	no	—
346	C₂²×C₁₃	—	2	2	no	—
347	C₂²×C₁₃	—	2	2	no	—
348	C₂²×C₁₃	—	2	2	no	—
349	C₂²×C₁₃	#446	1	4	yes	complemented
350	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
351	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
352	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
353	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
354	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
355	C₂²×C₁₃	#568	1	1	yes	characteristic
356	C₂²×C₁₃	#568	1	1	yes	characteristic
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	2	2	no	—
359	C₄×C₁₃	—	2	2	no	—
360	C₄×C₁₃	—	2	2	no	—
361	C₄×C₁₃	—	2	2	no	—
362	C₄×C₁₃	—	4	1	no	—
363	C₄×C₁₃	—	4	1	no	—
364	C₄×C₁₃	—	4	1	no	—
365	C₄×C₁₃	—	4	1	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	—	4	1	no	—
370	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
371	C₄×C₁₃	#525	1	1	yes	characteristic
372	C₄×C₁₃	#529	1	1	yes	characteristic
373	C₄×C₁₃	#533	1	1	yes	characteristic
374	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
375	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
376	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
377	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
378	C₂²×C₈	—	13	1	no	—
379	C₂²×C₈	—	13	4	no	—
380	C₂²×C₈	—	13	1	no	—
381	C₂²×C₈	—	13	1	no	—
382	C₂²×C₈	—	13	1	no	—
383	C₂²×C₈	—	13	1	no	—
384	C₂²×C₈	—	13	1	no	—
385	C₂²×C₈	—	13	1	no	—
386	C₂²×C₈	—	13	1	no	—
387	C₂²×C₈	—	26	2	no	—
388	C₂²×C₈	—	26	2	no	—
389	C₂²×C₈	—	26	2	no	—
390	C₂²×C₈	—	26	2	no	—
391	C₂²×C₈	—	26	2	no	—
392	C₂²⋊Q₈	—	2	4	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
407	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
408	C₂×C₄²	—	2	2	no	—
409	C₂×C₄²	—	2	2	no	—
410	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
411	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
412	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
413	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
414	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
415	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
416	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
417	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
418	C₄⋊C₈	—	26	2	no	—
419	C₄⋊C₈	—	26	2	no	—
420	C₄⋊C₈	—	26	2	no	—
421	C₄⋊C₈	—	26	2	no	—
422	C₄⋊C₈	—	26	2	no	—
423	C₄⋊C₈	—	26	2	no	—
424	C₂²⋊C₈	—	26	2	no	—
425	C₂²⋊C₈	—	26	2	no	—
426	#97	—	13	4	no	—
427	#97	—	26	2	no	—
428	#97	—	26	2	no	—
429	#97	—	26	2	no	—
430	#97	—	26	2	no	—
431	#97	—	26	2	no	—
432	C₄×C₈	—	26	2	no	—
433	C₄×C₈	—	26	2	no	—
434	#95	C₂×Dic₁₃	1	1	yes	characteristic
435	#95	C₂×Dic₁₃	1	1	yes	characteristic
436	#95	C₂×Dic₁₃	1	1	yes	characteristic
437	#95	C₂×Dic₁₃	1	1	yes	characteristic
438	#95	C₂×Dic₁₃	1	1	yes	characteristic
439	#95	C₂×Dic₁₃	1	1	yes	characteristic
440	#95	C₂×Dic₁₃	1	1	yes	characteristic
441	#95	C₂×Dic₁₃	1	1	yes	characteristic
442	#95	C₂×Dic₁₃	1	1	yes	characteristic
443	#95	C₂×Dic₁₃	1	1	yes	characteristic
444	C₂×C₁₃	—	2	4	no	—
445	C₂×C₁₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
446	C₂×C₁₃	#2933	1	1	yes	characteristic
447	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
448	C₂×C₁₃	C₂×#446	1	1	yes	characteristic
449	C₂×C₁₃	#2961	1	1	yes	characteristic
450	C₂×C₁₃	#2968	1	1	yes	characteristic
451	C₂×C₁₃	#2970	1	1	yes	characteristic
452	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	4	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
467	C₂²×C₄	#6131	1	2	yes	—
468	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
478	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
482	C₂×C₈	—	13	2	no	—
483	C₂×C₈	—	13	2	no	—
484	C₂×C₈	—	13	2	no	—
485	C₂×C₈	—	13	2	no	—
486	C₂×C₈	—	13	2	no	—
487	C₂×C₈	—	13	2	no	—
488	C₂×C₈	—	26	8	no	—
489	C₂×C₈	—	26	8	no	—
490	C₂×C₈	—	26	1	no	—
491	C₂×C₈	—	26	1	no	—
492	C₂×C₈	—	26	1	no	—
493	C₂×C₈	—	26	1	no	—
494	C₂×C₈	—	26	1	no	—
495	C₂×C₈	—	26	1	no	—
496	C₂×C₈	—	26	1	no	—
497	C₂×C₈	—	26	1	no	—
498	C₂×C₈	—	26	1	no	—
499	C₂×C₈	—	26	1	no	—
500	C₂×C₈	—	26	1	no	—
501	C₂×C₈	—	26	1	no	—
502	C₂×C₈	—	26	1	no	—
503	C₂×C₈	—	26	1	no	—
504	C₂×C₈	—	26	1	no	—
505	C₂×C₈	—	26	1	no	—
506	C₂×C₈	—	26	1	no	—
507	C₂×C₈	—	26	1	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	—	4	1	no	—
516	C₄⋊C₄	—	4	1	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	#6099	1	4	yes	—
521	C₄²	—	2	2	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	D₄×D₁₃	1	2	yes	—
534	C₄²	#6129	1	2	yes	—
535	C₁₃	#21599	1	1	yes	characteristic, complemented, Sylow
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	C₂×#6099	1	2	yes	—
541	C₂³	Q₈×Dic₁₃	1	2	yes	—
542	C₂³	#88202	1	2	yes	—
543	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
544	Q₈	—	4	4	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	C₂×#6099	1	2	yes	—
586	C₂×C₄	C₂×#6099	1	2	yes	—
587	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
588	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
589	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
590	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
591	C₂×C₄	C₂×#6129	1	1	yes	characteristic
592	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
593	C₂×C₄	C₂×#6131	1	1	yes	characteristic
594	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
595	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
596	C₈	—	13	4	no	—
597	C₈	—	26	2	no	—
598	C₈	—	26	2	no	—
599	C₈	—	26	2	no	—
600	C₈	—	52	1	no	—
601	C₈	—	52	1	no	—
602	C₈	—	52	1	no	—
603	C₈	—	52	1	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	#11718685	1	4	yes	complemented
611	C₂²	C₂²×#6099	1	1	yes	characteristic
612	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
613	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
614	C₂²	C₂×#88202	1	1	yes	characteristic
615	C₂²	#11719524	1	1	yes	characteristic
616	C₂²	#11719524	1	1	yes	characteristic
617	C₂²	#41×Dic₁₃	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	#11719327	1	1	yes	characteristic
632	C₄	#11719329	1	1	yes	characteristic
633	C₄	D₁₃×C₂²⋊Q₈	1	1	yes	characteristic
634	C₄	#11719332	1	1	yes	characteristic
635	C₂	—	2	4	no	—
636	C₂	C₂²⋊Q₈×Dic₁₃	1	1	yes	characteristic
637	C₂	#13123563	1	1	yes	characteristic
638	C₂	D₄×#6099	1	1	yes	characteristic
639	C₂	C₂×#11718685	1	1	yes	characteristic
640	C₂	#13123777	1	1	yes	characteristic
641	C₂	#13123832	1	1	yes	characteristic
642	C₂	#13123850	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₄×C₁₃×C₂²⋊Q₈	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×C₂²⋊Q₈	D₁₃
hypocenter	C₁₃	#21599
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#11718685	C₂	semidirect
3. #13115777	C₂	semidirect
4. #13115560	C₂	semidirect
5. #13115402	C₂	semidirect
6. #13115402	C₂	semidirect
10. #13114711	C₂	semidirect
11. #13114711	C₂	semidirect
12. #13114705	C₂	semidirect
96. C₂²×#1055	Q₈	semidirect
297. #1055	C₂²⋊Q₈	semidirect
349. C₂²×C₁₃	#446	semidirect
535. C₁₃	#21599	semidirect
610. C₂²	#11718685	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718685	2
C₂²×#88043	2
#13115777	2
#13115560	2
#13115402	2
#13115016	2
#13114816	2
#13114711	2
#13114705	2
#13114614	2
C₂²⋊C₄×#1055	2
C₄×C₁₃×C₂²⋊Q₈	2
#21599	13