Subgroups — #15880715

Order 3328.

744 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117243	C₂	1	1	yes	maximal, characteristic
2	#13115554	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115554	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115399	C₂	1	2	yes	maximal, complemented
5	#13115392	C₂	1	2	yes	maximal, complemented
6	#13114818	C₂	1	2	yes	maximal
7	#13114816	C₂	1	1	yes	maximal, characteristic
8	#13114703	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114604	C₂	1	2	yes	maximal
11	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88180	C₂²	1	2	yes	—
14	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	#11718873	C₄	1	1	yes	characteristic
19	#11718873	C₄	1	1	yes	characteristic
20	#11718873	C₄	1	2	yes	—
21	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
22	C₂×#88055	C₂²	1	2	yes	—
23	C₂×#88054	C₂²	1	2	yes	—
24	C₂×#88054	C₂²	1	2	yes	—
25	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
26	#11718597	C₄	1	2	yes	—
27	#11718596	C₄	1	1	yes	characteristic
28	#11718596	C₄	1	1	yes	characteristic
29	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
30	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
34	C₁₃×#336	C₂²	1	1	yes	characteristic
35	C₁₃×#336	C₂²	1	1	yes	characteristic
36	#11718142	C₂²	1	2	yes	—
37	#11718142	C₂²	1	2	yes	—
38	#11718142	C₂²	1	2	yes	—
39	#11718142	C₂²	1	2	yes	—
40	#11718116	C₂²	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	—	2	2	no	—
49	C₂×C₄²×C₁₃	—	2	2	no	—
50	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
56	#88180	—	4	2	no	—
57	#88180	—	4	2	no	—
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	1	yes	characteristic
61	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
66	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
67	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
68	C₂²×#1055	C₂³	1	2	yes	—
69	C₂²×#1055	C₂³	1	2	yes	—
70	C₁₃×C₂²⋊C₈	—	2	2	no	—
71	C₁₃×C₂²⋊C₈	Q₈	1	4	yes	—
72	C₄×C₈×C₁₃	—	2	2	no	—
73	C₄×C₈×C₁₃	—	2	2	no	—
74	#88071	C₂×C₄	1	2	yes	—
75	#88071	C₂×C₄	1	2	yes	—
76	#88071	C₂×C₄	1	2	yes	—
77	#88071	C₂×C₄	1	2	yes	—
78	C₂²⋊#1055	—	2	4	no	—
79	#88055	—	4	2	no	—
80	#88054	—	4	2	no	—
81	#88054	—	4	2	no	—
82	C₈×Dic₁₃	—	4	2	no	—
83	C₄⋊#1055	—	2	2	no	—
84	C₄⋊#1055	—	2	2	no	—
85	#22626	—	13	1	no	maximal, Sylow
86	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	—	2	1	no	—
88	C₂²×C₄×C₁₃	—	2	1	no	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	4	1	no	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₁₃	#41	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
106	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
107	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
108	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
120	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₄²×C₁₃	—	2	1	no	—
124	C₄²×C₁₃	—	2	1	no	—
125	C₄²×C₁₃	#41	1	2	yes	—
126	C₄²×C₁₃	#41	1	2	yes	—
127	C₂²⋊Dic₁₃	—	4	2	no	—
128	C₂²⋊Dic₁₃	—	4	2	no	—
129	C₄⋊Dic₁₃	—	2	4	no	—
130	C₄⋊Dic₁₃	—	2	2	no	—
131	C₄⋊Dic₁₃	—	2	2	no	—
132	C₄⋊Dic₁₃	—	2	2	no	—
133	C₄⋊Dic₁₃	—	2	2	no	—
134	C₄⋊Dic₁₃	—	4	2	no	—
135	C₄⋊Dic₁₃	—	4	2	no	—
136	C₄⋊Dic₁₃	—	4	2	no	—
137	C₄×Dic₁₃	—	2	2	no	—
138	C₄×Dic₁₃	—	2	2	no	—
139	C₄×Dic₁₃	—	2	2	no	—
140	C₄×Dic₁₃	—	2	2	no	—
141	C₂×#1055	—	2	2	no	—
142	C₂×#1055	—	2	2	no	—
143	C₂×#1055	—	2	2	no	—
144	C₂×#1055	—	2	2	no	—
145	C₂×#1055	—	2	2	no	—
146	C₂×#1055	—	2	2	no	—
147	#2285	—	13	1	no	—
148	#1939	—	13	1	no	—
149	#1939	—	13	1	no	—
150	#1917	—	13	2	no	—
151	#1916	—	13	2	no	—
152	#1798	—	13	2	no	—
153	#1797	—	13	1	no	—
154	#1770	—	13	1	no	—
155	C₈×C₄⋊C₄	—	13	1	no	—
156	#1750	—	13	2	no	—
157	C₄×C₂²⋊C₈	D₁₃	1	1	yes	characteristic
158	C₂³×C₁₃	—	2	1	no	—
159	C₂³×C₁₃	—	2	1	no	—
160	C₂³×C₁₃	—	2	1	no	—
161	C₂³×C₁₃	—	2	1	no	—
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	—	2	1	no	—
164	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
165	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	4	4	no	—
180	C₂×C₄×C₁₃	—	4	4	no	—
181	C₂×C₄×C₁₃	#117	1	2	yes	—
182	C₂×C₄×C₁₃	#117	1	2	yes	—
183	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
184	C₂×C₄×C₁₃	#131	1	2	yes	—
185	C₂×C₄×C₁₃	#131	1	2	yes	—
186	C₂×C₄×C₁₃	#131	1	2	yes	—
187	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×Dic₁₃	—	2	2	no	—
194	C₂×Dic₁₃	—	2	2	no	—
195	C₂×Dic₁₃	—	2	2	no	—
196	C₂×Dic₁₃	—	2	2	no	—
197	C₂×Dic₁₃	—	2	2	no	—
198	C₂×Dic₁₃	—	2	2	no	—
199	C₂×Dic₁₃	—	2	2	no	—
200	C₂×Dic₁₃	—	2	2	no	—
201	C₂×Dic₁₃	—	2	2	no	—
202	C₂×Dic₁₃	—	2	2	no	—
203	C₂×Dic₁₃	—	2	2	no	—
204	C₂×Dic₁₃	—	2	2	no	—
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	2	2	no	—
207	C₈×C₁₃	—	4	1	no	—
208	C₈×C₁₃	—	4	1	no	—
209	#1055	—	4	2	no	—
210	#1055	—	4	2	no	—
211	C₂×#117	—	13	2	no	—
212	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
213	C₂×C₄⋊C₈	—	13	1	no	—
214	C₂×C₄⋊C₈	—	13	1	no	—
215	C₂×C₄⋊C₈	—	13	2	no	—
216	C₂×C₄⋊C₈	—	13	2	no	—
217	C₂×C₂²⋊C₈	—	13	2	no	—
218	C₂×C₂²⋊C₈	C₂×D₁₃	1	1	yes	characteristic
219	C₂×C₂²⋊C₈	C₂×D₁₃	1	1	yes	characteristic
220	C₂×#97	—	13	2	no	—
221	C₂×C₄×C₈	—	13	2	no	—
222	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
224	#384	—	13	1	no	—
225	#384	—	13	1	no	—
226	#382	—	13	2	no	—
227	#380	—	13	1	no	—
228	#380	—	13	1	no	—
229	#380	—	13	2	no	—
230	C₄×C₄⋊C₄	—	13	2	no	—
231	C₄×C₄⋊C₄	—	13	1	no	—
232	C₄×C₄⋊C₄	—	13	1	no	—
233	#336	—	13	2	no	—
234	#336	—	13	2	no	—
235	#336	—	13	2	no	—
236	#336	—	13	2	no	—
237	#336	—	13	2	no	—
238	#336	C₂×D₁₃	1	1	yes	characteristic
239	#336	C₂×D₁₃	1	1	yes	characteristic
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	4	1	no	—
244	C₂²×C₁₃	—	4	1	no	—
245	C₂²×C₁₃	—	4	1	no	—
246	C₂²×C₁₃	—	4	1	no	—
247	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
249	C₂²×C₁₃	#518	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
251	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
252	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
253	C₂²×C₁₃	#568	1	1	yes	characteristic
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	4	1	no	—
258	C₄×C₁₃	#433	1	4	yes	—
259	C₄×C₁₃	#553	1	1	yes	characteristic
260	C₄×C₁₃	#553	1	1	yes	characteristic
261	C₄×C₁₃	#554	1	1	yes	characteristic
262	C₄×C₁₃	#554	1	1	yes	characteristic
263	Dic₁₃	—	4	2	no	—
264	Dic₁₃	—	4	2	no	—
265	Dic₁₃	—	4	2	no	—
266	Dic₁₃	—	4	2	no	—
267	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
268	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
269	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
270	C₂²×C₈	—	13	2	no	—
271	C₂²×C₈	—	13	2	no	—
272	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
273	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
274	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
276	#117	—	52	2	no	—
277	#117	—	52	2	no	—
278	C₂×C₄⋊C₄	—	13	2	no	—
279	C₂×C₄⋊C₄	—	13	1	no	—
280	C₂×C₄⋊C₄	—	13	1	no	—
281	C₂×C₄⋊C₄	—	13	1	no	—
282	C₂×C₄⋊C₄	—	13	1	no	—
283	C₂×C₄⋊C₄	—	13	2	no	—
284	C₂×C₄⋊C₄	—	13	2	no	—
285	C₂×C₄⋊C₄	—	13	2	no	—
286	C₂×C₂²⋊C₄	—	13	2	no	—
287	C₂×C₂²⋊C₄	—	13	2	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	—	13	2	no	—
291	C₂×C₄²	—	13	2	no	—
292	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
293	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
294	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
295	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
296	C₄⋊C₈	—	26	2	no	—
297	C₄⋊C₈	—	26	2	no	—
298	C₄⋊C₈	—	52	2	no	—
299	C₄⋊C₈	—	52	2	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₂²⋊C₈	—	26	4	no	—
302	C₂²⋊C₈	Dic₂₆	1	4	yes	—
303	#97	—	52	2	no	—
304	C₄×C₈	—	2	2	no	—
305	C₄×C₈	—	2	2	no	—
306	C₄×C₈	—	52	2	no	—
307	#95	—	13	2	no	—
308	#95	—	13	2	no	—
309	#95	—	13	2	no	—
310	#95	—	13	2	no	—
311	C₂×C₁₃	—	4	2	no	—
312	C₂×C₁₃	#2345	1	1	yes	characteristic
313	C₂×C₁₃	C₂×#433	1	1	yes	characteristic
314	C₂×C₁₃	#2924	1	1	yes	characteristic
315	C₂×C₁₃	#2960	1	1	yes	characteristic
316	C₂×C₁₃	#2962	1	1	yes	characteristic
317	C₂×C₁₃	#2979	1	1	yes	characteristic
318	C₂×C₁₃	#2981	1	1	yes	characteristic
319	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	13	2	no	—
331	C₂²×C₄	—	13	2	no	—
332	C₂²×C₄	—	13	2	no	—
333	C₂²×C₄	—	13	2	no	—
334	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
335	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
340	C₂²×C₄	#6127	1	2	yes	—
341	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	26	2	no	—
353	C₂×C₈	—	26	2	no	—
354	C₂×C₈	—	26	2	no	—
355	C₂×C₈	—	26	2	no	—
356	C₂×C₈	—	26	2	no	—
357	C₂×C₈	—	26	2	no	—
358	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
359	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
360	C₄⋊C₄	—	26	4	no	—
361	C₄⋊C₄	—	26	2	no	—
362	C₄⋊C₄	—	26	2	no	—
363	C₄⋊C₄	—	26	2	no	—
364	C₄⋊C₄	—	26	2	no	—
365	C₄⋊C₄	—	52	2	no	—
366	C₄⋊C₄	—	52	2	no	—
367	C₄⋊C₄	—	52	2	no	—
368	C₂²⋊C₄	—	52	2	no	—
369	C₂²⋊C₄	—	52	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	26	2	no	—
375	C₄²	—	26	2	no	—
376	C₄²	—	26	2	no	—
377	C₄²	—	26	2	no	—
378	C₄²	#6129	1	2	yes	—
379	C₄²	#6129	1	2	yes	—
380	C₁₃	#22626	1	1	yes	characteristic, complemented, Sylow
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	C₄×Dic₂₆	1	2	yes	—
388	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	26	2	no	—
406	C₂×C₄	—	26	2	no	—
407	C₂×C₄	—	26	2	no	—
408	C₂×C₄	—	26	2	no	—
409	C₂×C₄	—	26	2	no	—
410	C₂×C₄	—	26	2	no	—
411	C₂×C₄	—	26	2	no	—
412	C₂×C₄	—	26	2	no	—
413	C₂×C₄	—	26	2	no	—
414	C₂×C₄	—	26	2	no	—
415	C₂×C₄	—	26	2	no	—
416	C₂×C₄	C₄×Dic₂₆	1	2	yes	—
417	C₂×C₄	#88131	1	2	yes	—
418	C₂×C₄	#88131	1	2	yes	—
419	C₂×C₄	#88155	1	2	yes	—
420	C₂×C₄	#88155	1	2	yes	—
421	C₂×C₄	#88161	1	2	yes	—
422	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
423	C₂×C₄	C₂×#6127	1	1	yes	characteristic
424	C₂×C₄	C₂×#6129	1	1	yes	characteristic
425	C₂×C₄	C₂×#6129	1	1	yes	characteristic
426	C₂×C₄	#88256	1	1	yes	characteristic
427	C₂×C₄	#88256	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	2	2	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₈	—	52	2	no	—
433	C₈	—	52	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	C₂×C₄×Dic₂₆	1	1	yes	characteristic
442	C₂²	C₂×#88131	1	1	yes	characteristic
443	C₂²	#11719226	1	1	yes	characteristic
444	C₂²	C₂×#88155	1	1	yes	characteristic
445	C₂²	C₂×#88155	1	1	yes	characteristic
446	C₂²	C₂×#88161	1	1	yes	characteristic
447	C₂²	#11719450	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	52	2	no	—
453	C₄	—	52	2	no	—
454	C₄	—	52	2	no	—
455	C₄	—	52	2	no	—
456	C₄	#11718381	1	4	yes	—
457	C₄	#11719248	1	1	yes	characteristic
458	C₄	#11719248	1	1	yes	characteristic
459	C₄	#11719270	1	1	yes	characteristic
460	C₄	#11719270	1	1	yes	characteristic
461	C₂	—	4	2	no	—
462	C₂	#13117711	1	1	yes	characteristic
463	C₂	C₂×#11718381	1	1	yes	characteristic
464	C₂	#13123490	1	1	yes	characteristic
465	C₂	#13123770	1	1	yes	characteristic
466	C₂	#13123783	1	1	yes	characteristic
467	C₂	#13123902	1	1	yes	characteristic
468	C₂	#13123911	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₄×C₁₃×C₂²⋊C₈	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×C₂²⋊C₈	D₁₃
hypocenter	C₁₃	#22626
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. #13115554	C₂	semidirect
3. #13115554	C₂	semidirect
4. #13115399	C₂	semidirect
5. #13115392	C₂	semidirect
8. #13114703	C₂	semidirect
9. C₈×C₄⋊Dic₁₃	C₂	semidirect
380. C₁₃	#22626	semidirect

Maximal subgroups

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

subgroup	index
#13117243	2
#13115554	2
#13115399	2
#13115392	2
#13114818	2
#13114816	2
#13114703	2
C₈×C₄⋊Dic₁₃	2
#13114604	2
C₄×C₁₃×C₂²⋊C₈	2
#22626	13