Subgroups — #15881823

Order 3328.

876 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₂₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718491	C₂	1	1	yes	maximal, characteristic
3	C₄×#88141	C₂	1	1	yes	maximal, characteristic
4	#13115555	C₂	1	1	yes	maximal, characteristic
5	#13115553	C₂	1	2	yes	maximal
6	#13115551	C₂	1	2	yes	maximal
7	#13114952	C₂	1	1	yes	maximal, characteristic
8	#13114951	C₂	1	2	yes	maximal
9	C₄⋊C₈×Dic₁₃	C₂	1	2	yes	maximal
10	C₄×#88054	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
12	C₂×#88141	C₄	1	1	yes	characteristic
13	C₂×#88141	C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×#88054	C₂²	1	1	yes	characteristic
20	C₂×#88054	C₂²	1	1	yes	characteristic
21	C₂×#88054	C₂²	1	2	yes	—
22	C₂×#88054	C₂²	1	2	yes	—
23	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
24	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
25	C₄⋊C₄×Dic₁₃	C₄	1	1	yes	characteristic
26	C₄⋊C₄×Dic₁₃	C₄	1	1	yes	characteristic
27	C₄×#6101	C₂²	1	2	yes	—
28	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
29	C₄²×Dic₁₃	C₂²	1	2	yes	—
30	C₂×C₄⋊#1055	C₂²	1	2	yes	—
31	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
32	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
33	#11718491	—	2	4	no	—
34	C₈×Dic₂₆	—	2	4	no	—
35	#11718310	C₄	1	2	yes	—
36	#11718310	C₄	1	2	yes	—
37	C₁₃×#336	C₂²	1	2	yes	—
38	#11718142	C₂²	1	1	yes	characteristic
39	#11718142	C₂²	1	1	yes	characteristic
40	#11718142	C₂²	1	2	yes	—
41	#11718142	C₂²	1	2	yes	—
42	#11718116	C₂²	1	2	yes	—
43	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×#6101	C₂×C₄	1	2	yes	—
53	C₂×#6101	C₂×C₄	1	2	yes	—
54	C₂×#6101	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
61	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
62	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
66	C₂²×#1055	C₂³	1	2	yes	—
67	C₂²×#1055	C₂³	1	1	yes	characteristic
68	C₂²×#1055	C₂³	1	1	yes	characteristic
69	#88141	—	2	4	no	—
70	#88141	C₈	1	8	yes	complemented
71	C₄×Dic₂₆	D₄	1	4	yes	—
72	C₄×Dic₂₆	Q₈	1	4	yes	—
73	C₁₃×C₄⋊C₈	—	2	4	no	—
74	C₁₃×C₄⋊C₈	—	2	2	no	—
75	C₄×C₈×C₁₃	—	2	2	no	—
76	C₁₃×#95	C₂×C₄	1	2	yes	—
77	#88071	C₂×C₄	1	2	yes	—
78	#88071	C₂×C₄	1	2	yes	—
79	#88054	—	2	2	no	—
80	#88054	—	2	4	no	—
81	#88054	—	2	4	no	—
82	#88054	—	2	2	no	—
83	C₈×Dic₁₃	—	2	4	no	—
84	C₈×Dic₁₃	—	2	4	no	—
85	C₄⋊#1055	—	2	2	no	—
86	C₄⋊#1055	—	2	4	no	—
87	C₄×#1055	—	2	2	no	—
88	#22734	—	13	1	no	maximal, Sylow
89	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
96	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
100	C₂×Dic₂₆	C₄⋊C₄	1	4	yes	—
101	C₂×Dic₂₆	C₂×C₈	1	4	yes	—
102	C₂×Dic₂₆	M₁₆	1	4	yes	—
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	1	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	#41	1	2	yes	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	—
114	C₄²×C₁₃	—	2	2	no	—
115	C₄²×C₁₃	—	2	2	no	—
116	C₄²×C₁₃	C₂×D₄	1	2	yes	—
117	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
118	C₄⋊Dic₁₃	C₄⋊C₄	1	4	yes	—
119	#6101	—	2	4	no	—
120	#6101	C₄⋊C₄	1	8	yes	—
121	#6101	C₂×C₈	1	8	yes	—
122	C₄×Dic₁₃	—	2	2	no	—
123	C₄×Dic₁₃	—	2	1	no	—
124	C₄×Dic₁₃	—	2	1	no	—
125	C₄×Dic₁₃	—	2	1	no	—
126	C₄×Dic₁₃	—	2	1	no	—
127	C₄×Dic₁₃	—	2	4	no	—
128	C₄×Dic₁₃	—	2	2	no	—
129	C₄×Dic₁₃	—	2	4	no	—
130	C₄×Dic₁₃	—	4	2	no	—
131	C₄×Dic₁₃	—	4	1	no	—
132	C₄×Dic₁₃	C₂×C₈	1	4	yes	—
133	C₄×Dic₁₃	C₂×C₈	1	8	yes	—
134	C₄×Dic₁₃	C₂×D₄	1	4	yes	—
135	C₄×Dic₁₃	C₂×Q₈	1	4	yes	—
136	C₂×#1055	—	2	1	no	—
137	C₂×#1055	—	2	1	no	—
138	C₂×#1055	—	2	1	no	—
139	C₂×#1055	—	2	2	no	—
140	C₂×#1055	—	2	2	no	—
141	C₂×#1055	—	2	1	no	—
142	C₂×#1055	—	2	2	no	—
143	C₂×#1055	—	2	1	no	—
144	C₂×#1055	#41	1	2	yes	—
145	C₂×C₈×Q₈	—	13	1	no	—
146	C₂×C₈×Q₈	—	13	1	no	—
147	C₄²×Q₈	—	13	1	no	—
148	#1939	—	13	2	no	—
149	#1939	—	13	1	no	—
150	#1939	—	13	2	no	—
151	#1939	D₁₃	1	1	yes	characteristic
152	#1831	—	13	1	no	—
153	#1831	—	13	2	no	—
154	C₄×C₄⋊C₈	—	13	2	no	—
155	C₄×C₄⋊C₈	—	13	1	no	—
156	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
167	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
168	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
169	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
175	C₂×Dic₁₃	—	2	1	no	—
176	C₂×Dic₁₃	—	2	1	no	—
177	C₂×Dic₁₃	—	2	1	no	—
178	C₂×Dic₁₃	—	2	1	no	—
179	C₂×Dic₁₃	—	2	2	no	—
180	C₂×Dic₁₃	—	2	1	no	—
181	C₂×Dic₁₃	—	2	1	no	—
182	C₂×Dic₁₃	—	2	2	no	—
183	C₂×Dic₁₃	—	2	1	no	—
184	C₂×Dic₁₃	—	2	1	no	—
185	C₂×Dic₁₃	—	2	1	no	—
186	C₂×Dic₁₃	C₂×C₄⋊C₄	1	4	yes	—
187	C₂×Dic₁₃	C₂×C₄⋊C₄	1	4	yes	—
188	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
189	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
190	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
191	C₂×Dic₁₃	C₂×M₁₆	1	4	yes	—
192	C₂×Dic₁₃	#131	1	2	yes	—
193	Dic₂₆	C₄⋊C₈	1	16	yes	complemented
194	C₈×C₁₃	—	2	2	no	—
195	C₈×C₁₃	—	4	2	no	—
196	C₈×C₁₃	—	4	1	no	—
197	#1055	—	2	2	no	—
198	#1055	—	4	1	no	—
199	#1055	—	4	2	no	—
200	C₂×C₄×Q₈	—	13	1	no	—
201	C₂×C₄×Q₈	—	13	1	no	—
202	C₂×C₄×Q₈	—	13	1	no	—
203	C₈×Q₈	—	26	4	no	—
204	C₈×Q₈	—	26	4	no	—
205	C₂×C₄⋊C₈	—	13	2	no	—
206	C₂×C₄⋊C₈	—	13	2	no	—
207	C₂×C₄⋊C₈	—	13	1	no	—
208	C₂×C₄⋊C₈	—	13	1	no	—
209	C₂×C₄⋊C₈	—	13	1	no	—
210	C₂×C₄⋊C₈	—	13	2	no	—
211	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
213	C₂×C₄×C₈	—	13	2	no	—
214	C₂×C₄×C₈	—	13	2	no	—
215	C₂×C₄×C₈	—	13	1	no	—
216	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
217	C₄×C₄⋊C₄	—	13	1	no	—
218	C₄×C₄⋊C₄	—	13	1	no	—
219	C₄×C₄⋊C₄	—	13	2	no	—
220	C₄×C₄⋊C₄	—	13	2	no	—
221	C₄×C₄⋊C₄	—	13	2	no	—
222	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
223	C₄³	—	13	2	no	—
224	C₄³	—	13	1	no	—
225	#336	—	13	2	no	—
226	#336	—	13	1	no	—
227	#336	—	13	2	no	—
228	#336	—	13	1	no	—
229	#336	—	13	2	no	—
230	#336	C₂×D₁₃	1	2	yes	—
231	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
232	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
233	C₂²×C₁₃	#519	1	1	yes	characteristic
234	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
235	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
236	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
237	C₂²×C₁₃	#568	1	1	yes	characteristic
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	—	2	4	no	—
240	C₄×C₁₃	—	4	2	no	—
241	C₄×C₁₃	C₂×C₄⋊C₈	1	4	yes	—
242	C₄×C₁₃	#548	1	1	yes	characteristic
243	C₄×C₁₃	#548	1	1	yes	characteristic
244	C₄×C₁₃	#557	1	1	yes	characteristic
245	C₄×C₁₃	#557	1	1	yes	characteristic
246	Dic₁₃	—	2	4	no	—
247	Dic₁₃	—	2	2	no	—
248	Dic₁₃	—	2	2	no	—
249	Dic₁₃	—	2	2	no	—
250	Dic₁₃	—	4	1	no	—
251	Dic₁₃	C₂×C₄⋊C₈	1	8	yes	—
252	C₂²×Q₈	—	13	1	no	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	—	13	1	no	—
255	C₂²×C₈	—	13	2	no	—
256	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
257	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
258	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
259	C₄×Q₈	—	13	8	no	—
260	C₄×Q₈	—	13	4	no	—
261	C₄×Q₈	—	13	4	no	—
262	C₄×Q₈	—	26	4	no	—
263	C₂×C₄⋊C₄	—	13	2	no	—
264	C₂×C₄⋊C₄	—	13	2	no	—
265	C₂×C₄⋊C₄	—	13	1	no	—
266	C₂×C₄⋊C₄	—	13	2	no	—
267	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
269	C₂×C₄²	—	13	2	no	—
270	C₂×C₄²	—	13	1	no	—
271	C₂×C₄²	—	13	2	no	—
272	C₂×C₄²	—	13	2	no	—
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	C₂×C₄²	—	13	2	no	—
276	C₂×C₄²	—	13	1	no	—
277	C₂×C₄²	—	13	1	no	—
278	C₂×C₄²	—	13	2	no	—
279	C₂×C₄²	—	13	1	no	—
280	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
281	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
282	C₄⋊C₈	—	2	4	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	26	4	no	—
285	C₄⋊C₈	—	26	4	no	—
286	C₄⋊C₈	—	26	4	no	—
287	C₄⋊C₈	—	26	2	no	—
288	C₄⋊C₈	—	26	2	no	—
289	C₄⋊C₈	—	26	2	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	26	4	no	—
292	C₄×C₈	—	26	4	no	—
293	C₄×C₈	—	26	2	no	—
294	#95	—	13	2	no	—
295	#95	—	13	2	no	—
296	#95	C₄×D₁₃	1	2	yes	—
297	C₂×C₁₃	#2351	1	1	yes	characteristic
298	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
299	C₂×C₁₃	#2906	1	1	yes	characteristic
300	C₂×C₁₃	C₈×#41	1	1	yes	characteristic
301	C₂×C₁₃	#2971	1	1	yes	characteristic
302	C₂×C₁₃	#2982	1	1	yes	characteristic
303	C₂×C₁₃	#2984	1	1	yes	characteristic
304	C₂×Q₈	—	13	4	no	—
305	C₂×Q₈	—	13	4	no	—
306	C₂×Q₈	—	13	4	no	—
307	C₂²×C₄	—	13	2	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	2	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
314	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
316	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	13	2	no	—
327	C₂×C₈	—	26	1	no	—
328	C₂×C₈	—	26	1	no	—
329	C₂×C₈	—	26	1	no	—
330	C₂×C₈	—	26	2	no	—
331	C₂×C₈	—	26	1	no	—
332	C₂×C₈	—	26	2	no	—
333	C₂×C₈	—	26	2	no	—
334	C₂×C₈	—	26	1	no	—
335	C₂×C₈	#6129	1	2	yes	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	13	8	no	—
338	C₄⋊C₄	—	13	4	no	—
339	C₄⋊C₄	—	13	8	no	—
340	C₄⋊C₄	—	26	4	no	—
341	C₄⋊C₄	C₈×D₁₃	1	4	yes	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	13	8	no	—
345	C₄²	—	13	4	no	—
346	C₄²	—	13	4	no	—
347	C₄²	—	13	4	no	—
348	C₄²	—	26	4	no	—
349	C₄²	—	26	2	no	—
350	C₄²	—	26	4	no	—
351	C₄²	—	26	2	no	—
352	C₄²	—	26	1	no	—
353	C₄²	—	26	1	no	—
354	C₄²	—	26	1	no	—
355	C₄²	—	26	1	no	—
356	C₄²	—	52	1	no	—
357	C₄²	—	52	2	no	—
358	C₄²	D₄×D₁₃	1	2	yes	—
359	C₄²	Q₈×D₁₃	1	2	yes	—
360	C₁₃	#22734	1	1	yes	characteristic, complemented, Sylow
361	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
362	Q₈	—	13	16	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	13	4	no	—
371	C₂×C₄	—	13	4	no	—
372	C₂×C₄	—	13	4	no	—
373	C₂×C₄	—	13	2	no	—
374	C₂×C₄	—	13	2	no	—
375	C₂×C₄	—	13	2	no	—
376	C₂×C₄	—	13	4	no	—
377	C₂×C₄	—	26	1	no	—
378	C₂×C₄	—	26	2	no	—
379	C₂×C₄	—	26	1	no	—
380	C₂×C₄	—	26	1	no	—
381	C₂×C₄	—	26	2	no	—
382	C₂×C₄	—	26	1	no	—
383	C₂×C₄	—	26	1	no	—
384	C₂×C₄	—	26	1	no	—
385	C₂×C₄	—	26	1	no	—
386	C₂×C₄	—	26	1	no	—
387	C₂×C₄	—	26	1	no	—
388	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
389	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
390	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
391	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
392	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
393	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂×#6129	1	1	yes	characteristic
395	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
396	C₂×C₄	#88254	1	1	yes	characteristic
397	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
398	C₂×C₄	#88257	1	1	yes	characteristic
399	C₈	—	2	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	1	no	—
402	C₈	—	26	2	no	—
403	C₈	—	52	1	no	—
404	C₈	—	52	2	no	—
405	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
406	C₂²	C₄×#6129	1	1	yes	characteristic
407	C₂²	#11719277	1	1	yes	characteristic
408	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
409	C₂²	C₂×M₁₆×D₁₃	1	1	yes	characteristic
410	C₂²	D₁₃×#131	1	1	yes	characteristic
411	C₂²	#11719455	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	2	4	no	—
414	C₄	—	4	2	no	—
415	C₄	—	13	8	no	—
416	C₄	—	26	4	no	—
417	C₄	—	26	2	no	—
418	C₄	—	26	2	no	—
419	C₄	—	26	2	no	—
420	C₄	—	52	1	no	—
421	C₄	D₁₃×C₄⋊C₈	1	4	yes	—
422	C₄	#11719303	1	1	yes	characteristic
423	C₄	#11719338	1	1	yes	characteristic
424	C₄	#11719390	1	1	yes	characteristic
425	C₄	#11719426	1	1	yes	characteristic
426	C₂	#13117755	1	1	yes	characteristic
427	C₂	C₂×D₁₃×C₄⋊C₈	1	1	yes	characteristic
428	C₂	#13123403	1	1	yes	characteristic
429	C₂	C₈×#6129	1	1	yes	characteristic
430	C₂	#13123852	1	1	yes	characteristic
431	C₂	#13123915	1	1	yes	characteristic
432	C₂	#13123922	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#1939	C₂
socle, prime radical	C₂³×C₁₃	C₂³×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1939	D₁₃
hypocenter	C₁₃	#22734
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
70. #88141	C₈	semidirect
193. Dic₂₆	C₄⋊C₈	semidirect
360. C₁₃	#22734	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Dic₂₆	2
C₂×#11718491	2
C₄×#88141	2
#13115555	2
#13115553	2
#13115551	2
#13114952	2
#13114951	2
C₄⋊C₈×Dic₁₃	2
C₄×#88054	2
C₁₃×#1939	2
#22734	13