Subgroups — #15770814

Order 3328.

778 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718122	C₂	1	2	yes	maximal
3	C₂×#11718122	C₂	1	2	yes	maximal
4	#13114530	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
7	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
8	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×#6099	C₂²	1	2	yes	—
11	C₂²×#6099	C₂²	1	2	yes	—
12	C₁₃×#389	—	2	1	no	—
13	C₁₃×#389	—	2	1	no	—
14	C₁₃×#389	—	2	1	no	—
15	C₁₃×#389	—	2	1	no	—
16	C₂×C₁₃×#95	C₄	1	2	yes	—
17	#11718585	—	2	4	no	—
18	C₂×C₄⋊#1055	—	2	1	no	—
19	C₂×C₄⋊#1055	—	2	1	no	—
20	#11718122	—	2	4	no	—
21	#11718122	—	2	4	no	—
22	#11718116	—	2	1	no	—
23	#11718116	—	2	1	no	—
24	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
32	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
35	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
36	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
37	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
38	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
39	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
40	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
41	C₂×C₁₃×C₄⋊C₄	Q₈	1	2	yes	—
42	C₂×C₄²×C₁₃	—	2	2	no	—
43	C₂×C₄²×C₁₃	—	2	2	no	—
44	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
48	C₂×#6099	—	2	2	no	—
49	C₂×#6099	—	2	2	no	—
50	C₂×#6099	—	2	2	no	—
51	C₂×#6099	—	2	2	no	—
52	C₂×#6099	—	2	2	no	—
53	C₂×#6099	—	2	2	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	D₄	1	4	yes	—
59	C₂×#6099	Q₈	1	4	yes	—
60	C₂²×#1055	—	2	2	no	—
61	C₂²×#1055	—	2	2	no	—
62	C₁₃×#95	—	2	2	no	—
63	C₁₃×#95	—	2	2	no	—
64	C₄⋊#1055	—	2	4	no	—
65	C₄⋊#1055	—	2	4	no	—
66	#11204	—	13	1	no	maximal, Sylow
67	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₃	—	2	2	no	—
72	C₂²×C₄×C₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	4	no	—
76	C₂²×C₄×C₁₃	—	4	1	no	—
77	C₂²×C₄×C₁₃	—	4	1	no	—
78	C₂²×C₄×C₁₃	—	4	2	no	—
79	C₂²×C₄×C₁₃	—	4	2	no	—
80	C₂²×C₄×C₁₃	—	4	2	no	—
81	C₂²×C₄×C₁₃	—	4	2	no	—
82	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
87	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	#41	1	2	yes	—
96	C₂²×C₄×C₁₃	#41	1	2	yes	—
97	C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₁₃×C₄⋊C₄	—	2	2	no	—
101	C₁₃×C₄⋊C₄	—	4	4	no	—
102	C₁₃×C₄⋊C₄	—	4	4	no	—
103	C₁₃×C₄⋊C₄	—	4	1	no	—
104	C₁₃×C₄⋊C₄	—	4	2	no	—
105	C₁₃×C₄⋊C₄	—	4	1	no	—
106	C₄²×C₁₃	—	2	1	no	—
107	C₄²×C₁₃	—	2	1	no	—
108	C₄²×C₁₃	—	2	2	no	—
109	C₄²×C₁₃	—	2	2	no	—
110	C₄²×C₁₃	—	2	1	no	—
111	C₄²×C₁₃	—	2	1	no	—
112	#6099	—	2	4	no	—
113	#6099	—	2	4	no	—
114	#6099	—	2	4	no	—
115	#6099	—	2	4	no	—
116	#6099	—	4	2	no	—
117	#6099	—	4	2	no	—
118	#6099	—	4	2	no	—
119	#6099	—	4	2	no	—
120	C₂×#1055	—	2	4	no	—
121	C₂×#1055	—	2	4	no	—
122	C₂×#1055	—	4	2	no	—
123	C₂×#1055	—	4	2	no	—
124	C₂×#1055	—	4	2	no	—
125	C₂×#1055	—	4	2	no	—
126	C₂×#423	—	13	1	no	—
127	C₂×#389	D₁₃	1	1	yes	characteristic
128	C₂×#343	—	13	2	no	—
129	C₂×#343	—	13	2	no	—
130	#1728	—	13	1	no	—
131	C₂³×C₁₃	—	2	1	no	—
132	C₂³×C₁₃	—	2	1	no	—
133	C₂³×C₁₃	—	2	1	no	—
134	C₂³×C₁₃	—	2	1	no	—
135	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂³×C₁₃	#117	1	1	yes	characteristic
138	C₂³×C₁₃	C₄×D₄	1	2	yes	—
139	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	1	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	4	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	4	4	no	—
152	C₂×C₄×C₁₃	—	4	4	no	—
153	C₂×C₄×C₁₃	—	4	4	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	4	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	8	4	no	—
161	C₂×C₄×C₁₃	#100	1	2	yes	—
162	C₂×C₄×C₁₃	#101	1	2	yes	—
163	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
164	C₂×C₄×C₁₃	#121	1	2	yes	—
165	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
167	C₂×C₄×C₁₃	#121	1	2	yes	—
168	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
169	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
171	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	#123	1	2	yes	—
174	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
175	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
176	C₂×C₄×C₁₃	#125	1	2	yes	—
177	C₂×C₄×C₁₃	#125	1	2	yes	—
178	C₂×C₄×C₁₃	#126	1	2	yes	—
179	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
180	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
181	#1055	—	4	4	no	—
182	#1055	—	4	4	no	—
183	C₂²×M₁₆	—	13	2	no	—
184	C₂²×M₁₆	—	13	2	no	—
185	C₂²×C₄⋊C₄	Dic₁₃	1	2	yes	—
186	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
187	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
188	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
189	#423	—	26	4	no	—
190	C₂×C₄⋊C₈	—	26	1	no	—
191	C₂×C₄⋊C₈	—	26	1	no	—
192	#389	—	2	1	no	—
193	#389	—	2	1	no	—
194	#389	—	2	1	no	—
195	#389	—	2	1	no	—
196	C₂×#95	Dic₁₃	1	2	yes	—
197	#343	—	26	4	no	—
198	#343	—	26	4	no	—
199	#336	—	26	1	no	—
200	#336	—	26	1	no	—
201	C₂²×C₁₃	—	2	1	no	—
202	C₂²×C₁₃	—	2	1	no	—
203	C₂²×C₁₃	—	2	1	no	—
204	C₂²×C₁₃	—	2	1	no	—
205	C₂²×C₁₃	—	2	2	no	—
206	C₂²×C₁₃	—	2	2	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	2	2	no	—
209	C₂²×C₁₃	#380	1	1	yes	characteristic
210	C₂²×C₁₃	#386	1	1	yes	characteristic
211	C₂²×C₁₃	#387	1	2	yes	—
212	C₂²×C₁₃	#389	1	2	yes	—
213	C₂²×C₁₃	#391	1	1	yes	characteristic
214	C₂²×C₁₃	C₂×#100	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×#101	1	1	yes	characteristic
216	C₂²×C₁₃	#413	1	1	yes	characteristic
217	C₂²×C₁₃	#413	1	1	yes	characteristic
218	C₄×C₁₃	—	2	2	no	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	4	4	no	—
221	C₄×C₁₃	—	4	1	no	—
222	C₄×C₁₃	—	4	1	no	—
223	C₄×C₁₃	—	8	2	no	—
224	C₄×C₁₃	#394	1	1	yes	characteristic
225	C₄×C₁₃	#395	1	1	yes	characteristic
226	C₄×C₁₃	#396	1	2	yes	—
227	C₄×C₁₃	#398	1	1	yes	characteristic
228	C₄×C₁₃	#398	1	2	yes	—
229	C₄×C₁₃	#400	1	1	yes	characteristic
230	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
231	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
232	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
233	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
234	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
235	C₂×M₁₆	—	13	4	no	—
236	C₂×M₁₆	—	13	4	no	—
237	C₂×M₁₆	—	26	2	no	—
238	C₂×M₁₆	—	26	2	no	—
239	C₂×M₁₆	—	26	2	no	—
240	C₂×M₁₆	—	26	2	no	—
241	C₂×M₁₆	—	26	2	no	—
242	C₂×M₁₆	—	26	2	no	—
243	C₂×M₁₆	—	26	2	no	—
244	C₂×M₁₆	—	26	2	no	—
245	C₂×M₁₆	—	26	2	no	—
246	C₂×M₁₆	—	26	2	no	—
247	C₂²×C₈	—	26	2	no	—
248	C₂²×C₈	—	26	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	4	4	no	—
260	C₂×C₄⋊C₄	Dic₂₆	1	2	yes	—
261	C₂×C₄⋊C₄	D₅₂	1	2	yes	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
265	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
266	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
267	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
268	C₄⋊C₈	—	26	4	no	—
269	C₄⋊C₈	—	26	4	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	C₂×C₁₃	—	2	2	no	—
273	C₂×C₁₃	—	2	2	no	—
274	C₂×C₁₃	#1441	1	1	yes	characteristic
275	C₂×C₁₃	#1800	1	1	yes	characteristic
276	C₂×C₁₃	#1801	1	1	yes	characteristic
277	C₂×C₁₃	#1900	1	1	yes	characteristic
278	C₂×C₁₃	#1901	1	1	yes	characteristic
279	C₂×C₁₃	#1997	1	1	yes	characteristic
280	C₂×C₁₃	#1998	1	1	yes	characteristic
281	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
297	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
303	C₂²×C₄	#6127	1	1	yes	characteristic
304	C₂²×C₄	#6127	1	1	yes	characteristic
305	C₂²×C₄	D₄×D₁₃	1	2	yes	—
306	C₂²×C₄	#6129	1	2	yes	—
307	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
308	C₂²×C₄	#6131	1	2	yes	—
309	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
311	M₁₆	—	26	4	no	—
312	M₁₆	—	26	4	no	—
313	M₁₆	—	26	4	no	—
314	M₁₆	—	26	4	no	—
315	M₁₆	—	52	2	no	—
316	M₁₆	—	52	2	no	—
317	M₁₆	—	52	2	no	—
318	M₁₆	—	52	2	no	—
319	C₂×C₈	—	26	4	no	—
320	C₂×C₈	—	26	4	no	—
321	C₂×C₈	—	52	2	no	—
322	C₂×C₈	—	52	2	no	—
323	C₂×C₈	—	52	2	no	—
324	C₂×C₈	—	52	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₁₃	#11204	1	1	yes	characteristic, complemented, Sylow
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
346	C₂³	#88180	1	1	yes	characteristic
347	C₂³	D₄×Dic₁₃	1	2	yes	—
348	C₂³	Q₈×Dic₁₃	1	2	yes	—
349	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	4	no	—
371	C₂×C₄	#88073	1	2	yes	—
372	C₂×C₄	#88076	1	2	yes	—
373	C₂×C₄	#88142	1	2	yes	—
374	C₂×C₄	#88143	1	2	yes	—
375	C₂×C₄	#88144	1	2	yes	—
376	C₂×C₄	#88148	1	2	yes	—
377	C₂×C₄	#88149	1	2	yes	—
378	C₂×C₄	#88150	1	2	yes	—
379	C₂×C₄	#88151	1	2	yes	—
380	C₂×C₄	#88152	1	2	yes	—
381	C₂×C₄	#88178	1	1	yes	characteristic
382	C₂×C₄	#88178	1	1	yes	characteristic
383	C₂×C₄	#88184	1	1	yes	characteristic
384	C₂×C₄	#88184	1	1	yes	characteristic
385	C₂×C₄	#88189	1	1	yes	characteristic
386	C₂×C₄	#88191	1	1	yes	characteristic
387	C₂×C₄	#88193	1	2	yes	—
388	C₂×C₄	#88198	1	1	yes	characteristic
389	C₂×C₄	#88200	1	2	yes	—
390	C₂×C₄	#88201	1	1	yes	characteristic
391	C₈	—	52	4	no	—
392	C₈	—	52	4	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	#11718642	1	2	yes	—
402	C₂²	#11718646	1	2	yes	—
403	C₂²	#11718873	1	1	yes	characteristic
404	C₂²	C₂×#88073	1	1	yes	characteristic
405	C₂²	#11718881	1	1	yes	characteristic
406	C₂²	C₂×#88076	1	1	yes	characteristic
407	C₂²	#11718891	1	1	yes	characteristic
408	C₂²	#11718898	1	1	yes	characteristic
409	C₂²	#11718898	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	4	no	—
415	C₄	—	8	2	no	—
416	C₄	#11718640	1	1	yes	characteristic
417	C₄	#11718644	1	1	yes	characteristic
418	C₄	#11718645	1	2	yes	—
419	C₄	#11718647	1	1	yes	characteristic
420	C₄	#11718652	1	1	yes	characteristic
421	C₄	#11718655	1	2	yes	—
422	C₂	—	2	2	no	—
423	C₂	—	2	2	no	—
424	C₂	#13113089	1	1	yes	characteristic
425	C₂	#13114828	1	1	yes	characteristic
426	C₂	#13114832	1	1	yes	characteristic
427	C₂	#13115300	1	1	yes	characteristic
428	C₂	#13115305	1	1	yes	characteristic
429	C₂	#13115826	1	1	yes	characteristic
430	C₂	#13115830	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₃
commutator, prime radical	C₂⁴×C₁₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#389	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#389	D₁₃
hypocenter	C₁₃	#11204
LCS	G ▷ C₂⁴×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#389

Complements

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

N	H ≅ G/N	type
340. C₁₃	#11204	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718585	2
C₂×#11718122	2
#13114530	2
C₂×C₁₃×#389	2
#11204	13