Subgroups — #15768871

Order 3328.

1006 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6101	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718116	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718142	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718142	C₂	1	1	yes	maximal, characteristic
6	C₂×#11718142	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×#6101	C₄	1	2	yes	—
12	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂³×#1055	C₂²	1	1	yes	characteristic
15	C₂³×#1055	C₂²	1	1	yes	characteristic
16	C₂×#88071	C₄	1	2	yes	—
17	C₂×C₈×Dic₁₃	—	2	2	no	—
18	C₂×C₈×Dic₁₃	—	2	2	no	—
19	C₂×C₈×Dic₁₃	—	2	2	no	—
20	C₄×#6101	—	2	2	no	—
21	C₄×#6101	—	2	2	no	—
22	C₁₃×#336	—	2	2	no	—
23	#11718142	—	2	2	no	—
24	#11718142	C₄	1	4	yes	complemented
25	#11718142	C₄	1	4	yes	complemented
26	#11718116	—	2	2	no	—
27	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
29	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×Dic₁₃	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₃	—	2	1	no	—
33	C₂²×C₈×C₁₃	—	2	1	no	—
34	C₂²×C₈×C₁₃	—	2	1	no	—
35	C₂²×C₈×C₁₃	—	2	1	no	—
36	C₂²×C₈×C₁₃	—	2	1	no	—
37	C₂²×C₈×C₁₃	—	2	1	no	—
38	C₂²×C₈×C₁₃	—	2	1	no	—
39	C₂²×C₈×C₁₃	—	2	1	no	—
40	C₂²×C₈×C₁₃	—	2	1	no	—
41	C₂²×C₈×C₁₃	—	2	1	no	—
42	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₃	D₄	1	2	yes	—
45	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
46	C₂×C₄²×C₁₃	—	2	1	no	—
47	C₂×C₄²×C₁₃	—	2	1	no	—
48	C₂×C₄²×C₁₃	—	2	1	no	—
49	C₂×C₄²×C₁₃	—	2	1	no	—
50	C₂×C₄²×C₁₃	—	2	1	no	—
51	C₂×C₄²×C₁₃	—	2	1	no	—
52	C₂×#6101	—	2	4	no	—
53	C₂×#6101	—	2	4	no	—
54	C₂×#6101	C₈	1	8	yes	complemented
55	C₂×C₄×Dic₁₃	—	2	1	no	—
56	C₂×C₄×Dic₁₃	—	2	1	no	—
57	C₂×C₄×Dic₁₃	—	2	1	no	—
58	C₂×C₄×Dic₁₃	—	2	1	no	—
59	C₂×C₄×Dic₁₃	—	2	1	no	—
60	C₂×C₄×Dic₁₃	—	2	1	no	—
61	C₂×C₄×Dic₁₃	—	2	1	no	—
62	C₂×C₄×Dic₁₃	—	2	1	no	—
63	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
64	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
65	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
66	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
67	C₂²×#1055	—	2	1	no	—
68	C₂²×#1055	—	2	1	no	—
69	C₂²×#1055	—	2	1	no	—
70	C₂²×#1055	—	2	1	no	—
71	C₂²×#1055	—	2	1	no	—
72	C₂²×#1055	—	2	1	no	—
73	C₂²×#1055	—	2	1	no	—
74	C₂²×#1055	—	2	1	no	—
75	C₂²×#1055	—	2	1	no	—
76	C₂²×#1055	—	2	1	no	—
77	C₂²×#1055	C₂×C₄	1	2	yes	—
78	C₂²×#1055	C₂×C₄	1	2	yes	—
79	C₂²×#1055	D₄	1	2	yes	—
80	C₂²×#1055	Q₈	1	2	yes	—
81	#88071	—	2	4	no	—
82	C₈×Dic₁₃	—	2	8	no	—
83	#10874	—	13	1	no	maximal, Sylow
84	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
106	C₂²×Dic₁₃	—	2	1	no	—
107	C₂²×Dic₁₃	—	2	1	no	—
108	C₂²×Dic₁₃	—	2	2	no	—
109	C₂²×Dic₁₃	—	2	2	no	—
110	C₂²×Dic₁₃	—	2	2	no	—
111	C₂²×Dic₁₃	—	2	2	no	—
112	C₂²×Dic₁₃	—	2	2	no	—
113	C₂²×Dic₁₃	—	2	1	no	—
114	C₂²×Dic₁₃	—	2	1	no	—
115	C₂²×Dic₁₃	—	2	2	no	—
116	C₂²×Dic₁₃	—	2	2	no	—
117	C₂²×Dic₁₃	C₄²	1	2	yes	—
118	C₂²×Dic₁₃	C₄²	1	2	yes	—
119	C₂²×Dic₁₃	C₂²⋊C₄	1	4	yes	—
120	C₂²×Dic₁₃	C₂×C₈	1	4	yes	—
121	C₂²×Dic₁₃	C₂×C₈	1	4	yes	—
122	C₂²×Dic₁₃	M₁₆	1	4	yes	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	4	1	no	—
133	C₂×C₈×C₁₃	—	4	1	no	—
134	C₂×C₈×C₁₃	—	4	1	no	—
135	C₂×C₈×C₁₃	—	4	1	no	—
136	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	complemented
137	C₄²×C₁₃	—	4	1	no	—
138	C₄²×C₁₃	—	4	1	no	—
139	C₄²×C₁₃	—	4	1	no	—
140	C₄²×C₁₃	—	4	1	no	—
141	#6101	—	2	16	no	—
142	C₄×Dic₁₃	—	2	2	no	—
143	C₄×Dic₁₃	—	2	2	no	—
144	C₄×Dic₁₃	—	2	2	no	—
145	C₄×Dic₁₃	—	2	2	no	—
146	C₄×Dic₁₃	—	2	2	no	—
147	C₄×Dic₁₃	—	2	2	no	—
148	C₄×Dic₁₃	—	2	2	no	—
149	C₄×Dic₁₃	—	2	2	no	—
150	C₂×#1055	—	2	2	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	—	2	2	no	—
154	C₂×#1055	—	2	2	no	—
155	C₂×#1055	—	2	2	no	—
156	C₂×#1055	—	2	2	no	—
157	C₂×#1055	—	2	2	no	—
158	C₂×#1055	—	2	2	no	—
159	C₂×#1055	—	4	1	no	—
160	C₂×#1055	—	4	1	no	—
161	C₂×#1055	—	4	1	no	—
162	C₂×#1055	—	4	1	no	—
163	C₂×#1055	C₄⋊C₄	1	4	yes	complemented
164	C₂²×C₄×C₈	—	13	1	no	—
165	C₂×C₄×C₄⋊C₄	—	13	1	no	—
166	C₂×#336	—	13	1	no	—
167	C₂×#336	—	13	1	no	—
168	C₂×#336	—	13	1	no	—
169	C₂×#336	—	13	1	no	—
170	C₂×#336	D₁₃	1	1	yes	characteristic
171	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
172	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂³×C₁₃	#117	1	1	yes	characteristic
174	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
176	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
177	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
178	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
179	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
180	C₂³×C₁₃	#131	1	2	yes	—
181	C₂³×C₁₃	#131	1	2	yes	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
192	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
201	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
202	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
203	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
208	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
209	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
210	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
211	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
212	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
213	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
214	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
215	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
217	C₂×Dic₁₃	—	2	2	no	—
218	C₂×Dic₁₃	—	2	4	no	—
219	C₂×Dic₁₃	—	2	2	no	—
220	C₂×Dic₁₃	—	2	4	no	—
221	C₂×Dic₁₃	—	2	4	no	—
222	C₂×Dic₁₃	—	2	4	no	—
223	C₂×Dic₁₃	—	2	4	no	—
224	C₂×Dic₁₃	—	2	4	no	—
225	C₂×Dic₁₃	—	2	4	no	—
226	C₂×Dic₁₃	—	2	4	no	—
227	C₂×Dic₁₃	—	2	2	no	—
228	C₂×Dic₁₃	—	2	2	no	—
229	C₂×Dic₁₃	—	2	2	no	—
230	C₂×Dic₁₃	—	4	2	no	—
231	C₂×Dic₁₃	—	4	2	no	—
232	C₂×Dic₁₃	C₄×C₈	1	4	yes	complemented
233	C₂×Dic₁₃	C₂²⋊C₈	1	8	yes	—
234	C₈×C₁₃	—	2	4	no	—
235	C₈×C₁₃	—	4	2	no	—
236	#1055	—	2	4	no	—
237	#1055	—	4	2	no	—
238	C₂³×C₈	—	13	1	no	—
239	C₂³×C₈	—	13	1	no	—
240	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
241	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	—	13	2	no	—
243	C₂²×C₄²	—	13	1	no	—
244	C₂²×C₄²	—	13	1	no	—
245	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
246	C₂×C₄×C₈	—	26	2	no	—
247	C₂×C₄×C₈	—	26	2	no	—
248	C₂×C₄×C₈	—	26	2	no	—
249	C₄×C₄⋊C₄	—	26	2	no	—
250	C₄×C₄⋊C₄	—	26	2	no	—
251	C₂×#95	—	13	2	no	—
252	#336	—	2	2	no	—
253	#336	—	13	4	no	—
254	#336	—	13	4	no	—
255	#336	—	26	2	no	—
256	#336	—	26	2	no	—
257	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
258	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
259	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
260	C₂²×C₁₃	#386	1	1	yes	characteristic
261	C₂²×C₁₃	#387	1	1	yes	characteristic
262	C₂²×C₁₃	#387	1	1	yes	characteristic
263	C₂²×C₁₃	#391	1	1	yes	characteristic
264	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
265	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
266	C₂²×C₁₃	#405	1	1	yes	characteristic
267	C₂²×C₁₃	#405	1	1	yes	characteristic
268	C₂²×C₁₃	C₂×C₂²⋊C₈	1	2	yes	—
269	C₂²×C₁₃	#408	1	2	yes	—
270	C₂²×C₁₃	#431	1	2	yes	—
271	C₂²×C₁₃	#433	1	2	yes	—
272	C₂²×C₁₃	C₈×D₄	1	2	yes	—
273	C₂²×C₁₃	C₈×D₄	1	2	yes	—
274	C₂²×C₁₃	#435	1	2	yes	—
275	C₂²×C₁₃	#435	1	2	yes	—
276	C₂²×C₁₃	C₈×Q₈	1	2	yes	—
277	C₂²×C₁₃	C₈×Q₈	1	2	yes	—
278	C₂²×C₁₃	#446	1	2	yes	—
279	C₂²×C₁₃	#446	1	2	yes	—
280	C₄×C₁₃	—	4	4	no	—
281	C₄×C₁₃	#385	1	1	yes	characteristic
282	C₄×C₁₃	#385	1	1	yes	characteristic
283	C₄×C₁₃	#387	1	1	yes	characteristic
284	C₄×C₁₃	#387	1	1	yes	characteristic
285	C₄×C₁₃	#388	1	1	yes	characteristic
286	C₄×C₁₃	#388	1	1	yes	characteristic
287	C₄×C₁₃	#389	1	1	yes	characteristic
288	C₄×C₁₃	#389	1	1	yes	characteristic
289	Dic₁₃	—	2	8	no	—
290	Dic₁₃	—	2	4	no	—
291	Dic₁₃	—	4	2	no	—
292	C₂³×C₄	—	13	1	no	—
293	C₂³×C₄	—	13	2	no	—
294	C₂³×C₄	—	13	1	no	—
295	C₂³×C₄	C₄×D₁₃	1	2	yes	—
296	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
297	C₂²×C₈	—	2	1	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	13	2	no	—
308	C₂²×C₈	—	13	2	no	—
309	C₂²×C₈	—	13	2	no	—
310	C₂²×C₈	—	13	2	no	—
311	C₂²×C₈	—	26	1	no	—
312	C₂²×C₈	—	26	1	no	—
313	C₂²×C₈	—	26	1	no	—
314	C₂²×C₈	—	26	1	no	—
315	C₂²×C₈	—	26	1	no	—
316	C₂²×C₈	—	26	1	no	—
317	C₂²×C₈	—	26	1	no	—
318	C₂²×C₈	—	26	1	no	—
319	C₂²×C₈	—	26	1	no	—
320	C₂²×C₈	—	26	1	no	—
321	C₂²×C₈	Dic₂₆	1	2	yes	—
322	C₂²×C₈	C₄×D₁₃	1	2	yes	—
323	C₂²×C₈	C₄×D₁₃	1	2	yes	—
324	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
325	C₂×C₄⋊C₄	—	13	8	no	—
326	C₂×C₄⋊C₄	—	26	4	no	—
327	C₂×C₄⋊C₄	—	26	4	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	13	2	no	—
335	C₂×C₄²	—	13	2	no	—
336	C₂×C₄²	—	13	2	no	—
337	C₂×C₄²	—	13	2	no	—
338	C₂×C₄²	—	26	1	no	—
339	C₂×C₄²	—	26	1	no	—
340	C₂×C₄²	—	26	1	no	—
341	C₂×C₄²	—	26	1	no	—
342	C₂×C₄²	—	26	1	no	—
343	C₂×C₄²	—	26	1	no	—
344	C₂×C₄²	—	26	1	no	—
345	C₂×C₄²	—	26	1	no	—
346	C₄×C₈	—	26	8	no	—
347	#95	—	26	4	no	—
348	C₂×C₁₃	#1436	1	1	yes	characteristic
349	C₂×C₁₃	C₄×C₂²⋊C₈	1	1	yes	characteristic
350	C₂×C₁₃	#1750	1	1	yes	characteristic
351	C₂×C₁₃	C₈×C₄⋊C₄	1	1	yes	characteristic
352	C₂×C₁₃	C₈×C₄⋊C₄	1	1	yes	characteristic
353	C₂×C₁₃	#1771	1	1	yes	characteristic
354	C₂×C₁₃	#1771	1	1	yes	characteristic
355	C₂×C₁₃	#1869	1	2	yes	—
356	C₂×C₁₃	#1916	1	2	yes	—
357	C₂×C₁₃	#1916	1	2	yes	—
358	C₂×C₁₃	#1984	1	2	yes	—
359	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	13	2	no	—
367	C₂²×C₄	—	13	4	no	—
368	C₂²×C₄	—	13	4	no	—
369	C₂²×C₄	—	13	4	no	—
370	C₂²×C₄	—	13	4	no	—
371	C₂²×C₄	—	13	2	no	—
372	C₂²×C₄	—	26	1	no	—
373	C₂²×C₄	—	26	2	no	—
374	C₂²×C₄	—	26	1	no	—
375	C₂²×C₄	—	26	2	no	—
376	C₂²×C₄	—	26	2	no	—
377	C₂²×C₄	—	26	2	no	—
378	C₂²×C₄	—	26	2	no	—
379	C₂²×C₄	—	26	1	no	—
380	C₂²×C₄	—	26	1	no	—
381	C₂²×C₄	—	26	2	no	—
382	C₂²×C₄	—	26	2	no	—
383	C₂²×C₄	C₈×D₁₃	1	4	yes	—
384	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
387	C₂²×C₄	#6127	1	1	yes	characteristic
388	C₂²×C₄	#6127	1	1	yes	characteristic
389	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
390	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
391	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
392	C₂²×C₄	#6129	1	1	yes	characteristic
393	C₂²×C₄	#6129	1	1	yes	characteristic
394	C₂²×C₄	#6129	1	1	yes	characteristic
395	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
396	C₂²×C₄	#6131	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	4	1	no	—
408	C₂×C₈	—	4	1	no	—
409	C₂×C₈	—	4	1	no	—
410	C₂×C₈	—	4	1	no	—
411	C₂×C₈	—	13	4	no	—
412	C₂×C₈	—	26	2	no	—
413	C₂×C₈	—	26	2	no	—
414	C₂×C₈	—	26	2	no	—
415	C₂×C₈	—	26	2	no	—
416	C₂×C₈	—	26	2	no	—
417	C₂×C₈	—	26	2	no	—
418	C₂×C₈	—	26	2	no	—
419	C₂×C₈	—	26	2	no	—
420	C₂×C₈	—	26	2	no	—
421	C₂×C₈	—	52	1	no	—
422	C₂×C₈	—	52	1	no	—
423	C₂×C₈	—	52	1	no	—
424	C₂×C₈	—	52	1	no	—
425	C₂×C₈	#6101	1	4	yes	complemented
426	C₄⋊C₄	—	26	16	no	—
427	C₄²	—	4	1	no	—
428	C₄²	—	4	1	no	—
429	C₄²	—	4	1	no	—
430	C₄²	—	4	1	no	—
431	C₄²	—	26	2	no	—
432	C₄²	—	26	2	no	—
433	C₄²	—	26	2	no	—
434	C₄²	—	26	2	no	—
435	C₄²	—	26	2	no	—
436	C₄²	—	26	2	no	—
437	C₄²	—	26	2	no	—
438	C₄²	—	26	2	no	—
439	C₁₃	#10874	1	1	yes	characteristic, complemented, Sylow
440	C₂³	C₄×Dic₂₆	1	1	yes	characteristic
441	C₂³	C₄²×D₁₃	1	1	yes	characteristic
442	C₂³	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
443	C₂³	#88135	1	1	yes	characteristic
444	C₂³	#88141	1	1	yes	characteristic
445	C₂³	#88146	1	1	yes	characteristic
446	C₂³	C₂×C₈×D₁₃	1	2	yes	—
447	C₂³	#88155	1	2	yes	—
448	C₂³	M₁₆×D₁₃	1	2	yes	—
449	C₂³	#88161	1	2	yes	—
450	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	13	4	no	—
459	C₂×C₄	—	13	8	no	—
460	C₂×C₄	—	26	4	no	—
461	C₂×C₄	—	26	4	no	—
462	C₂×C₄	—	26	4	no	—
463	C₂×C₄	—	26	2	no	—
464	C₂×C₄	—	26	4	no	—
465	C₂×C₄	—	26	2	no	—
466	C₂×C₄	—	26	4	no	—
467	C₂×C₄	—	26	4	no	—
468	C₂×C₄	—	26	4	no	—
469	C₂×C₄	—	26	4	no	—
470	C₂×C₄	—	26	2	no	—
471	C₂×C₄	—	26	2	no	—
472	C₂×C₄	—	26	2	no	—
473	C₂×C₄	—	52	2	no	—
474	C₂×C₄	—	52	2	no	—
475	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
476	C₂×C₄	#88126	1	1	yes	characteristic
477	C₂×C₄	#88131	1	1	yes	characteristic
478	C₂×C₄	#88132	1	1	yes	characteristic
479	C₂×C₄	#88132	1	1	yes	characteristic
480	C₂×C₄	#88133	1	1	yes	characteristic
481	C₂×C₄	#88135	1	1	yes	characteristic
482	C₂×C₄	#88135	1	1	yes	characteristic
483	C₂×C₄	#88135	1	1	yes	characteristic
484	C₂×C₄	#88137	1	1	yes	characteristic
485	C₂×C₄	#88138	1	1	yes	characteristic
486	C₂×C₄	#88139	1	1	yes	characteristic
487	C₂×C₄	#88141	1	1	yes	characteristic
488	C₂×C₄	#88142	1	1	yes	characteristic
489	C₂×C₄	#88143	1	1	yes	characteristic
490	C₂×C₄	#88144	1	1	yes	characteristic
491	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
492	C₂×C₄	#88147	1	1	yes	characteristic
493	C₂×C₄	#88147	1	1	yes	characteristic
494	C₂×C₄	#88148	1	1	yes	characteristic
495	C₂×C₄	#88150	1	1	yes	characteristic
496	C₂×C₄	#88152	1	1	yes	characteristic
497	C₂×C₄	C₂×#6101	1	1	yes	characteristic
498	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
499	C₂×C₄	#88189	1	1	yes	characteristic
500	C₂×C₄	#88191	1	1	yes	characteristic
501	C₂×C₄	#88192	1	1	yes	characteristic
502	C₂×C₄	#88200	1	1	yes	characteristic
503	C₈	—	2	4	no	—
504	C₈	—	4	2	no	—
505	C₈	—	26	4	no	—
506	C₈	—	52	2	no	—
507	C₂²	#11718307	1	1	yes	characteristic
508	C₂²	#11718310	1	1	yes	characteristic
509	C₂²	#11718316	1	1	yes	characteristic
510	C₂²	#11718327	1	1	yes	characteristic
511	C₂²	C₈×Dic₂₆	1	2	yes	—
512	C₂²	C₄×C₈×D₁₃	1	1	yes	characteristic
513	C₂²	#11718350	1	1	yes	characteristic
514	C₂²	#11718362	1	2	yes	—
515	C₂²	#11718368	1	1	yes	characteristic
516	C₂²	#11718369	1	1	yes	characteristic
517	C₂²	D₁₃×C₂²⋊C₈	1	2	yes	—
518	C₂²	#11718386	1	2	yes	—
519	C₂²	#11718388	1	2	yes	—
520	C₂²	#11718389	1	2	yes	—
521	C₂²	#11718489	1	2	yes	—
522	C₂²	#11718491	1	2	yes	—
523	C₂²	#11718494	1	2	yes	—
524	C₂²	#11718501	1	2	yes	—
525	C₂²	C₄×#6101	1	1	yes	characteristic
526	C₂²	#11718617	1	1	yes	characteristic
527	C₂²	#11718639	1	1	yes	characteristic
528	C₂²	C₈×C₂²⋊D₁₃	1	2	yes	—
529	C₂²	#11718788	1	2	yes	—
530	C₄	—	4	4	no	—
531	C₄	—	26	4	no	—
532	C₄	—	26	8	no	—
533	C₄	—	52	2	no	—
534	C₄	#11718308	1	1	yes	characteristic
535	C₄	#11718313	1	1	yes	characteristic
536	C₄	#11718315	1	1	yes	characteristic
537	C₄	#11718330	1	1	yes	characteristic
538	C₄	#11718605	1	1	yes	characteristic
539	C₄	#11718607	1	1	yes	characteristic
540	C₄	#11718634	1	1	yes	characteristic
541	C₄	#11718650	1	1	yes	characteristic
542	C₂	#13113067	1	1	yes	characteristic
543	C₂	#13114593	1	1	yes	characteristic
544	C₂	#13114601	1	1	yes	characteristic
545	C₂	#13114697	1	1	yes	characteristic
546	C₂	C₈×#6101	1	1	yes	characteristic
547	C₂	#13114709	1	1	yes	characteristic
548	C₂	#13114712	1	1	yes	characteristic
549	C₂	#13115125	1	2	yes	—
550	C₂	#13115390	1	2	yes	—
551	C₂	#13115396	1	2	yes	—
552	C₂	#13115770	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂×C₄×C₈
Fitting	C₂×C₁₃×#336	C₂
socle, prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#336	D₁₃
hypocenter	C₁₃	#10874
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
24. #11718142	C₄	semidirect
25. #11718142	C₄	semidirect
54. C₂×#6101	C₈	semidirect
136. C₂×C₈×C₁₃	C₄⋊C₄	semidirect
163. C₂×#1055	C₄⋊C₄	semidirect
232. C₂×Dic₁₃	C₄×C₈	semidirect
425. C₂×C₈	#6101	semidirect
439. C₁₃	#10874	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×Dic₁₃	2
C₂×C₄×#6101	2
C₂×#11718116	2
C₂×#11718142	2
C₂×C₁₃×#336	2
#10874	13