Subgroups — #15867652

Order 3328.

746 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×Dic₂₆	C₂	1	1	yes	maximal, characteristic
2	#13115770	C₂	1	2	yes	maximal
3	#13115551	C₂	1	2	yes	maximal
4	#13115401	C₂	1	2	yes	maximal
5	#13115397	C₂	1	2	yes	maximal
6	#13114690	C₂	1	1	yes	maximal, characteristic
7	#13114690	C₂	1	1	yes	maximal, characteristic
8	#13114585	C₂	1	1	yes	maximal, characteristic
9	#13114584	C₂	1	1	yes	maximal, characteristic
10	#97×Dic₁₃	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₂₆	C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₂₆	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×#97	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
18	C₄³×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×#88055	C₂²	1	2	yes	—
20	C₂×#88054	C₂²	1	2	yes	—
21	C₂×#88054	C₂²	1	2	yes	—
22	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
23	C₄×C₄⋊Dic₁₃	C₄	1	1	yes	characteristic
24	C₄×C₄⋊Dic₁₃	C₄	1	1	yes	characteristic
25	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
26	C₄×#6101	C₄	1	1	yes	characteristic
27	C₄×#6101	C₄	1	1	yes	characteristic
28	C₄×#6101	C₄	1	1	yes	characteristic
29	C₄×#6101	C₄	1	1	yes	characteristic
30	C₄×#6101	C₂²	1	1	yes	characteristic
31	C₄×#6101	C₂²	1	1	yes	characteristic
32	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
33	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
34	C₂×#88043	C₂²	1	1	yes	characteristic
35	C₂×#88043	C₂²	1	1	yes	characteristic
36	C₁₃×#336	C₂²	1	2	yes	—
37	#11718142	C₂²	1	2	yes	—
38	#11718142	C₂²	1	2	yes	—
39	#11718142	C₂²	1	2	yes	—
40	#11718142	C₂²	1	2	yes	—
41	#11718116	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	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×#6101	C₂×C₄	1	1	yes	characteristic
57	C₂×#6101	C₂×C₄	1	1	yes	characteristic
58	C₂×#6101	C₂×C₄	1	1	yes	characteristic
59	C₂×#6101	C₂×C₄	1	1	yes	characteristic
60	C₂×#6101	C₂×C₄	1	1	yes	characteristic
61	C₂×#6101	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
74	C₂²×#1055	C₂³	1	2	yes	—
75	C₂²×#1055	C₂³	1	2	yes	—
76	C₄×Dic₂₆	—	2	4	no	—
77	C₄×Dic₂₆	—	2	4	no	—
78	C₄×Dic₂₆	—	2	4	no	—
79	C₁₃×C₄⋊C₈	—	2	4	no	—
80	C₁₃×#97	—	2	2	no	—
81	C₁₃×#97	—	2	2	no	—
82	#88071	C₂×C₄	1	1	yes	characteristic
83	#88071	C₂×C₄	1	1	yes	characteristic
84	#88071	C₂×C₄	1	1	yes	characteristic
85	#88071	C₂×C₄	1	1	yes	characteristic
86	#88071	C₂×C₄	1	1	yes	characteristic
87	#88071	C₂×C₄	1	1	yes	characteristic
88	#88055	—	2	4	no	—
89	#88054	—	2	4	no	—
90	#88054	—	2	4	no	—
91	C₈×Dic₁₃	—	2	4	no	—
92	#88043	—	2	2	no	—
93	#88043	Q₈	1	4	yes	complemented
94	#21345	—	13	1	no	maximal, Sylow
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×Dic₂₆	—	2	2	no	—
111	C₂×Dic₂₆	—	2	2	no	—
112	C₂×Dic₂₆	M₁₆	1	4	yes	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	#41	1	4	yes	—
119	C₄²×C₁₃	—	2	2	no	—
120	C₄²×C₁₃	—	2	2	no	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₄²×C₁₃	—	4	1	no	—
124	C₄²×C₁₃	—	4	1	no	—
125	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
126	C₄²×C₁₃	#41	1	2	yes	—
127	C₄⋊Dic₁₃	—	2	2	no	—
128	C₄⋊Dic₁₃	—	2	2	no	—
129	C₄⋊Dic₁₃	—	2	2	no	—
130	#6101	—	2	2	no	—
131	#6101	—	2	2	no	—
132	#6101	—	2	2	no	—
133	#6101	—	2	2	no	—
134	#6101	—	2	2	no	—
135	#6101	M₁₆	1	4	yes	—
136	C₄×Dic₁₃	—	2	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	C₄×Dic₁₃	—	2	2	no	—
142	C₄×Dic₁₃	—	2	2	no	—
143	C₄×Dic₁₃	—	4	1	no	—
144	C₄×Dic₁₃	—	4	1	no	—
145	C₄×Dic₁₃	—	4	1	no	—
146	C₄×Dic₁₃	—	4	1	no	—
147	C₄×Dic₁₃	#41	1	4	yes	—
148	C₂×#1055	—	2	2	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	2	2	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	C₂×Q₈	1	4	yes	—
154	C₄²×Q₈	—	13	1	no	—
155	#1984	—	13	2	no	—
156	#1939	—	13	2	no	—
157	#1917	—	13	2	no	—
158	#1917	—	13	2	no	—
159	#1767	—	13	1	no	—
160	#1767	—	13	1	no	—
161	#1767	D₁₃	1	1	yes	characteristic
162	#1745	—	13	1	no	—
163	#1745	—	13	1	no	—
164	C₄×#97	—	13	1	no	—
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	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	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	—	2	1	no	—
180	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
181	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
182	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
184	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
188	C₂×Dic₁₃	—	2	1	no	—
189	C₂×Dic₁₃	—	2	1	no	—
190	C₂×Dic₁₃	—	2	1	no	—
191	C₂×Dic₁₃	—	2	1	no	—
192	C₂×Dic₁₃	—	2	1	no	—
193	C₂×Dic₁₃	—	2	1	no	—
194	C₂×Dic₁₃	—	2	1	no	—
195	C₂×Dic₁₃	—	2	1	no	—
196	C₂×Dic₁₃	—	2	1	no	—
197	C₂×Dic₁₃	—	2	1	no	—
198	C₂×Dic₁₃	—	2	1	no	—
199	C₂×Dic₁₃	—	2	1	no	—
200	C₂×Dic₁₃	—	2	1	no	—
201	C₂×Dic₁₃	—	2	1	no	—
202	C₂×Dic₁₃	—	2	1	no	—
203	C₂×Dic₁₃	—	2	1	no	—
204	C₂×Dic₁₃	—	2	1	no	—
205	C₂×Dic₁₃	—	2	1	no	—
206	C₂×Dic₁₃	#117	1	2	yes	—
207	C₂×Dic₁₃	#117	1	2	yes	—
208	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
209	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
210	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
211	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
212	Dic₂₆	—	2	8	no	—
213	C₈×C₁₃	—	2	4	no	—
214	C₈×C₁₃	—	4	2	no	—
215	#1055	—	2	4	no	—
216	#1055	—	4	2	no	—
217	C₂×C₄×Q₈	—	13	1	no	—
218	C₂×C₄×Q₈	—	13	1	no	—
219	C₂×C₄×Q₈	—	13	1	no	—
220	C₂×C₄⋊C₈	—	13	2	no	—
221	C₂×C₄⋊C₈	—	13	2	no	—
222	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
223	C₂×#97	—	13	1	no	—
224	C₂×#97	—	13	2	no	—
225	C₂×#97	—	13	1	no	—
226	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
227	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
228	C₂×C₄×C₈	—	13	2	no	—
229	C₄×C₄⋊C₄	—	13	1	no	—
230	C₄×C₄⋊C₄	—	13	1	no	—
231	C₄×C₄⋊C₄	—	13	1	no	—
232	C₄×C₄⋊C₄	—	13	1	no	—
233	C₄×C₄⋊C₄	—	13	1	no	—
234	C₄×C₄⋊C₄	—	13	1	no	—
235	C₄×C₄⋊C₄	—	13	1	no	—
236	C₄×C₄⋊C₄	—	13	1	no	—
237	C₄×C₄⋊C₄	—	13	1	no	—
238	C₄³	—	13	1	no	—
239	C₄³	—	13	1	no	—
240	C₄³	C₂×D₁₃	1	1	yes	characteristic
241	#336	—	13	2	no	—
242	#336	—	13	2	no	—
243	#336	—	13	2	no	—
244	#336	—	13	2	no	—
245	#336	—	13	2	no	—
246	#336	—	13	2	no	—
247	#336	C₂×D₁₃	1	2	yes	—
248	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
249	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
250	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
251	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
252	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
253	C₂²×C₁₃	#568	1	1	yes	characteristic
254	C₂²×C₁₃	#568	1	1	yes	characteristic
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	4	1	no	—
260	C₄×C₁₃	—	4	1	no	—
261	C₄×C₁₃	#529	1	2	yes	—
262	C₄×C₁₃	#533	1	2	yes	—
263	Dic₁₃	—	2	2	no	—
264	Dic₁₃	—	2	2	no	—
265	Dic₁₃	—	2	2	no	—
266	Dic₁₃	—	4	1	no	—
267	Dic₁₃	—	4	1	no	—
268	Dic₁₃	—	4	1	no	—
269	Dic₁₃	—	4	1	no	—
270	Dic₁₃	#432	1	4	yes	—
271	C₂²×Q₈	—	13	1	no	—
272	C₂²×C₈	—	13	2	no	—
273	C₂²×C₈	—	13	2	no	—
274	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
275	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
276	C₄×Q₈	—	26	4	no	—
277	C₄×Q₈	—	26	4	no	—
278	C₄×Q₈	—	26	4	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	1	no	—
284	C₂×C₄⋊C₄	—	13	1	no	—
285	C₂×C₄⋊C₄	—	13	1	no	—
286	C₂×C₄⋊C₄	—	13	1	no	—
287	C₂×C₄⋊C₄	—	13	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₂×C₄²	—	13	1	no	—
290	C₂×C₄²	—	13	1	no	—
291	C₂×C₄²	—	13	1	no	—
292	C₂×C₄²	—	13	1	no	—
293	C₂×C₄²	—	13	1	no	—
294	C₂×C₄²	—	13	1	no	—
295	C₂×C₄²	—	13	1	no	—
296	C₂×C₄²	—	13	1	no	—
297	C₂×C₄²	—	13	1	no	—
298	C₂×C₄²	—	13	1	no	—
299	C₂×C₄²	—	13	1	no	—
300	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
301	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
302	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
303	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
304	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
305	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
306	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
307	C₄⋊C₈	—	2	4	no	—
308	C₄⋊C₈	—	26	4	no	—
309	C₄⋊C₈	—	26	4	no	—
310	#97	—	2	2	no	—
311	#97	—	2	2	no	—
312	#97	—	13	4	no	—
313	#97	—	26	4	no	—
314	#97	—	26	2	no	—
315	C₄×C₈	—	26	4	no	—
316	#95	—	13	1	no	—
317	#95	—	13	1	no	—
318	#95	—	13	1	no	—
319	#95	—	13	1	no	—
320	#95	—	13	1	no	—
321	#95	—	13	1	no	—
322	C₂×C₁₃	#2295	1	1	yes	characteristic
323	C₂×C₁₃	C₂×#432	1	1	yes	characteristic
324	C₂×C₁₃	#2923	1	1	yes	characteristic
325	C₂×C₁₃	Q₈×M₁₆	1	1	yes	characteristic
326	C₂×C₁₃	Q₈×M₁₆	1	1	yes	characteristic
327	C₂×C₁₃	#2970	1	1	yes	characteristic
328	C₂×C₁₃	#2971	1	1	yes	characteristic
329	C₂×Q₈	—	13	4	no	—
330	C₂×Q₈	—	26	2	no	—
331	C₂×Q₈	—	26	2	no	—
332	C₂²×C₄	—	13	1	no	—
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	13	1	no	—
335	C₂²×C₄	—	13	1	no	—
336	C₂²×C₄	—	13	1	no	—
337	C₂²×C₄	—	13	1	no	—
338	C₂²×C₄	—	13	1	no	—
339	C₂²×C₄	—	13	1	no	—
340	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
346	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	13	4	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	#6127	1	4	yes	—
359	C₄⋊C₄	—	13	4	no	—
360	C₄⋊C₄	—	26	2	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	—	26	2	no	—
366	C₄⋊C₄	—	26	2	no	—
367	C₄⋊C₄	—	26	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	4	1	no	—
373	C₄²	—	4	1	no	—
374	C₄²	—	13	4	no	—
375	C₄²	—	26	2	no	—
376	C₄²	—	26	2	no	—
377	C₄²	—	26	2	no	—
378	C₄²	—	26	2	no	—
379	C₄²	—	26	2	no	—
380	C₄²	—	26	2	no	—
381	C₄²	—	26	2	no	—
382	C₄²	—	52	1	no	—
383	C₄²	—	52	1	no	—
384	C₄²	—	52	1	no	—
385	C₄²	—	52	1	no	—
386	C₄²	#6129	1	2	yes	—
387	C₄²	Q₈×D₁₃	1	2	yes	—
388	C₁₃	#21345	1	1	yes	characteristic, complemented, Sylow
389	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
390	Q₈	—	26	8	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	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	13	2	no	—
406	C₂×C₄	—	13	2	no	—
407	C₂×C₄	—	13	2	no	—
408	C₂×C₄	—	13	2	no	—
409	C₂×C₄	—	13	2	no	—
410	C₂×C₄	—	13	2	no	—
411	C₂×C₄	—	26	1	no	—
412	C₂×C₄	—	26	1	no	—
413	C₂×C₄	—	26	1	no	—
414	C₂×C₄	—	26	1	no	—
415	C₂×C₄	—	26	1	no	—
416	C₂×C₄	—	26	1	no	—
417	C₂×C₄	—	26	1	no	—
418	C₂×C₄	—	26	1	no	—
419	C₂×C₄	—	26	1	no	—
420	C₂×C₄	—	26	1	no	—
421	C₂×C₄	—	26	1	no	—
422	C₂×C₄	—	26	1	no	—
423	C₂×C₄	—	26	1	no	—
424	C₂×C₄	—	26	1	no	—
425	C₂×C₄	—	26	1	no	—
426	C₂×C₄	—	26	1	no	—
427	C₂×C₄	—	26	1	no	—
428	C₂×C₄	—	26	1	no	—
429	C₂×C₄	#88141	1	2	yes	—
430	C₂×C₄	#88141	1	2	yes	—
431	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
432	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
433	C₂×C₄	C₂×#6127	1	2	yes	—
434	C₂×C₄	C₂×#6129	1	1	yes	characteristic
435	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
436	C₂×C₄	#41×D₁₃	1	2	yes	—
437	C₈	—	2	4	no	—
438	C₈	—	4	2	no	—
439	C₈	—	26	4	no	—
440	C₈	—	52	2	no	—
441	C₂²	C₄×#6127	1	1	yes	characteristic
442	C₂²	C₂×#88141	1	1	yes	characteristic
443	C₂²	D₁₃×#117	1	1	yes	characteristic
444	C₂²	C₂×M₁₆×D₁₃	1	1	yes	characteristic
445	C₂²	C₂×M₁₆×D₁₃	1	1	yes	characteristic
446	C₂²	#11719450	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	—	2	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	13	4	no	—
455	C₄	—	26	2	no	—
456	C₄	—	26	2	no	—
457	C₄	—	26	2	no	—
458	C₄	—	52	1	no	—
459	C₄	—	52	1	no	—
460	C₄	—	52	1	no	—
461	C₄	—	52	1	no	—
462	C₄	#11719243	1	2	yes	—
463	C₄	#11719283	1	2	yes	—
464	C₂	#13117312	1	1	yes	characteristic
465	C₂	D₁₃×#432	1	1	yes	characteristic
466	C₂	#13123482	1	1	yes	characteristic
467	C₂	#13123787	1	1	yes	characteristic
468	C₂	#13123787	1	1	yes	characteristic
469	C₂	#13123847	1	1	yes	characteristic
470	C₂	#13123854	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#1767	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1767	D₁₃
hypocenter	C₁₃	#21345
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1767

Complements

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

N	H ≅ G/N	type
93. #88043	Q₈	semidirect
388. C₁₃	#21345	semidirect

Maximal subgroups

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

subgroup	index
C₄²×Dic₂₆	2
#13115770	2
#13115551	2
#13115401	2
#13115397	2
#13114690	2
#13114585	2
#13114584	2
#97×Dic₁₃	2
C₁₃×#1767	2
#21345	13