Subgroups — #16806750

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719089	C₂	1	1	yes	maximal, characteristic
3	#13131056	C₂	1	4	yes	maximal, complemented
4	#13131055	C₂	1	4	yes	maximal, complemented
5	#13131051	C₂	1	4	yes	maximal, complemented
6	C₂×D₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
7	C₂×#88237	C₄	1	1	yes	characteristic
8	C₂×D₁₃⋊M₁₆	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88106	C₄	1	2	yes	complemented
11	#11719089	C₄	1	2	yes	—
12	#11719089	C₄	1	2	yes	—
13	#11719089	C₂²	1	2	yes	—
14	#11719089	C₂²	1	2	yes	—
15	C₂×#88100	C₂²	1	2	yes	—
16	C₂×C₈×#261	C₄	1	2	yes	—
17	D₁₃⋊M₃₂	C₄	1	2	yes	complemented
18	D₁₃⋊M₃₂	C₄	1	2	yes	complemented
19	D₁₃⋊M₃₂	C₂²	1	2	yes	—
20	D₁₃⋊M₃₂	C₂²	1	2	yes	—
21	C₂×#88098	C₂²	1	2	yes	—
22	C₂×D₁₃⋊C₁₆	C₄	1	2	yes	complemented
23	C₂×C₁₃×M₃₂	C₄	1	1	yes	characteristic, complemented
24	C₂×#88052	C₄	1	1	yes	characteristic, complemented
25	D₁₃×M₃₂	C₄	1	2	yes	complemented
26	D₁₃×M₃₂	C₄	1	2	yes	complemented
27	D₁₃×M₃₂	C₂²	1	2	yes	—
28	D₁₃×M₃₂	C₂²	1	2	yes	—
29	C₂×#88038	C₂²	1	2	yes	—
30	C₂×C₁₆×D₁₃	C₄	1	2	yes	complemented
31	#11718218	C₂²	1	8	yes	complemented
32	#11718217	C₂²	1	8	yes	complemented
33	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₂²⋊#261	—	2	1	no	—
35	C₂×#6122	—	2	1	no	—
36	#88237	—	2	1	no	—
37	#88237	—	2	1	no	—
38	#88237	C₂×C₄	1	2	yes	—
39	#88237	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊#261	—	2	1	no	—
41	C₂×C₄×#261	C₂×C₄	1	2	yes	—
42	D₁₃⋊M₁₆	—	2	1	no	—
43	D₁₃⋊M₁₆	—	2	1	no	—
44	D₁₃⋊M₁₆	C₂×C₄	1	2	yes	—
45	D₁₃⋊M₁₆	C₂×C₄	1	2	yes	—
46	C₂×#6118	—	2	1	no	—
47	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
62	#88106	C₂×C₄	1	4	yes	—
63	#88106	C₂×C₄	1	4	yes	complemented
64	C₂×#6092	C₂×C₄	1	4	yes	complemented
65	#88100	C₂×C₄	1	4	yes	—
66	#88100	C₂³	1	4	yes	—
67	C₈×#261	C₂×C₄	1	4	yes	—
68	C₈×#261	C₂×C₄	1	4	yes	—
69	#88098	C₂×C₄	1	4	yes	complemented
70	#88098	C₂³	1	4	yes	—
71	D₁₃⋊C₁₆	C₂×C₄	1	4	yes	—
72	D₁₃⋊C₁₆	C₂×C₄	1	4	yes	complemented
73	C₁₃×M₃₂	C₂×C₄	1	2	yes	—
74	C₁₃×M₃₂	C₂×C₄	1	2	yes	complemented
75	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	complemented
76	#88052	C₂×C₄	1	2	yes	—
77	#88052	C₂×C₄	1	2	yes	complemented
78	C₂×#6090	C₂×C₄	1	2	yes	complemented
79	#88038	C₂×C₄	1	4	yes	complemented
80	#88038	C₂³	1	4	yes	—
81	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
82	C₁₆×D₁₃	C₂×C₄	1	4	yes	complemented
83	C₂×#2110	—	13	1	no	maximal, Sylow
84	C₂³×D₁₃	M₁₆	1	1	yes	characteristic
85	C₂²×#261	—	2	2	no	—
86	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
87	C₂²×Dic₁₃	M₁₆	1	1	yes	characteristic
88	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
91	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
92	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
93	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
94	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
95	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
96	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²⋊#261	—	2	2	no	—
101	C₂²⋊#261	—	2	2	no	—
102	#6122	—	2	2	no	—
103	#6122	—	2	2	no	—
104	C₂×#1057	—	2	2	no	—
105	C₄⋊#261	—	2	2	no	—
106	C₄⋊#261	—	2	2	no	—
107	C₄×#261	—	2	2	no	—
108	C₄×#261	C₂²×C₄	1	4	yes	—
109	#6118	—	2	2	no	—
110	#6118	—	2	2	no	—
111	D₁₃⋊C₈	—	2	2	no	—
112	D₁₃⋊C₈	C₂²×C₄	1	4	yes	—
113	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×#1055	C₄²	1	1	yes	characteristic
120	C₂×#1055	C₄²	1	1	yes	characteristic
121	C₂×#1055	C₄²	1	1	yes	characteristic
122	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
123	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
124	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
125	C₈×D₁₃	C₄²	1	1	yes	characteristic
126	C₈×D₁₃	C₄²	1	1	yes	characteristic
127	C₈×D₁₃	C₄²	1	1	yes	characteristic
128	C₈×D₁₃	C₄²	1	1	yes	characteristic
129	C₈×D₁₃	C₄²	1	1	yes	characteristic
130	C₈×D₁₃	C₄²	1	1	yes	characteristic
131	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₈×D₁₃	C₂⁴	1	1	yes	characteristic
141	#6092	C₂²×C₄	1	8	yes	—
142	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
143	#6090	C₂²×C₄	1	4	yes	—
144	C₂²×M₃₂	—	13	1	no	—
145	C₂²×M₃₂	—	13	1	no	—
146	C₂×#405	—	13	1	no	—
147	#2110	—	13	4	no	—
148	#2110	—	13	4	no	—
149	C₂×#347	—	13	4	no	—
150	C₂³×C₁₃	#97	1	1	yes	characteristic
151	C₂²×D₁₃	—	4	2	no	—
152	C₂²×D₁₃	#97	1	1	yes	characteristic
153	C₂²×D₁₃	#97	1	1	yes	characteristic
154	C₂²×D₁₃	#97	1	1	yes	characteristic
155	C₂²×D₁₃	C₂×M₁₆	1	1	yes	characteristic
156	C₂²×D₁₃	C₂×M₁₆	1	1	yes	characteristic
157	C₂²×D₁₃	C₂×M₁₆	1	1	yes	characteristic
158	C₂×#261	—	2	4	no	—
159	C₂×#261	—	4	4	no	—
160	C₂×C₄×C₁₃	#97	1	1	yes	characteristic
161	C₂×C₄×C₁₃	#97	1	1	yes	characteristic
162	C₂×C₄×C₁₃	#97	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×Dic₁₃	#97	1	1	yes	characteristic
167	C₂×Dic₁₃	#97	1	1	yes	characteristic
168	C₂×Dic₁₃	#97	1	1	yes	characteristic
169	C₂×Dic₁₃	C₂×M₁₆	1	1	yes	characteristic
170	C₂×Dic₁₃	C₂×M₁₆	1	1	yes	characteristic
171	C₂×Dic₁₃	C₂×M₁₆	1	1	yes	characteristic
172	C₄×D₁₃	#97	1	1	yes	characteristic
173	C₄×D₁₃	#97	1	1	yes	characteristic
174	C₄×D₁₃	#97	1	1	yes	characteristic
175	C₄×D₁₃	#97	1	1	yes	characteristic
176	C₄×D₁₃	#97	1	1	yes	characteristic
177	C₄×D₁₃	#97	1	1	yes	characteristic
178	C₄×D₁₃	C₂×C₄²	1	1	yes	characteristic
179	C₄×D₁₃	C₂×C₄²	1	1	yes	characteristic
180	C₄×D₁₃	C₂×C₄²	1	1	yes	characteristic
181	C₄×D₁₃	C₂×M₁₆	1	1	yes	characteristic
182	C₄×D₁₃	C₂×M₁₆	1	1	yes	characteristic
183	C₄×D₁₃	C₂×M₁₆	1	1	yes	characteristic
184	C₄×D₁₃	C₂×M₁₆	1	1	yes	characteristic
185	C₄×D₁₃	C₂×M₁₆	1	1	yes	characteristic
186	C₄×D₁₃	C₂×M₁₆	1	1	yes	characteristic
187	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
188	#1057	—	2	4	no	—
189	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
190	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
191	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
192	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
193	#1055	C₂×C₄²	1	1	yes	characteristic
194	#1055	C₂×C₄²	1	1	yes	characteristic
195	#1055	C₂×C₄²	1	1	yes	characteristic
196	#1055	C₂³×C₄	1	1	yes	characteristic
197	C₂²×M₁₆	—	13	1	no	—
198	C₂³×C₈	—	13	1	no	—
199	C₂×#117	—	13	1	no	—
200	C₂×M₃₂	—	13	2	no	—
201	C₂×M₃₂	—	13	2	no	—
202	C₂×M₃₂	—	13	2	no	—
203	C₂×M₃₂	—	13	2	no	—
204	C₂×M₃₂	—	13	2	no	—
205	C₂×M₃₂	—	13	2	no	—
206	C₂×M₃₂	—	13	1	no	—
207	C₂×M₃₂	—	13	2	no	—
208	C₂×M₃₂	—	13	2	no	—
209	C₂×M₃₂	—	13	2	no	—
210	C₂×M₃₂	—	13	2	no	—
211	C₂×M₃₂	—	13	2	no	—
212	C₂×M₃₂	#261	1	1	yes	characteristic, complemented
213	C₂²×C₁₆	—	13	2	no	—
214	C₂²×C₁₆	—	13	2	no	—
215	#405	—	13	2	no	—
216	#405	—	13	2	no	—
217	#405	—	13	2	no	—
218	#405	—	13	2	no	—
219	C₂×#97	—	13	2	no	—
220	C₂×C₄×C₈	—	13	2	no	—
221	#347	—	13	8	no	—
222	#347	—	13	8	no	—
223	C₂²×C₁₃	—	4	1	no	—
224	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
225	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
226	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
227	C₂×D₁₃	—	2	2	no	—
228	C₂×D₁₃	—	2	2	no	—
229	C₂×D₁₃	—	2	2	no	—
230	C₂×D₁₃	—	4	1	no	—
231	C₂×D₁₃	—	4	1	no	—
232	C₂×D₁₃	—	4	1	no	—
233	C₂×D₁₃	C₂×#97	1	1	yes	characteristic
234	C₂×D₁₃	C₂×#97	1	1	yes	characteristic
235	C₂×D₁₃	C₂×#97	1	1	yes	characteristic
236	C₂×D₁₃	C₂²×M₁₆	1	1	yes	characteristic
237	#261	—	4	4	no	—
238	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
239	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
240	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
241	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
242	Dic₁₃	C₂×#97	1	1	yes	characteristic
243	Dic₁₃	C₂×#97	1	1	yes	characteristic
244	Dic₁₃	C₂×#97	1	1	yes	characteristic
245	Dic₁₃	C₂²×M₁₆	1	1	yes	characteristic
246	C₂³×C₄	—	13	1	no	—
247	C₂×M₁₆	—	13	2	no	—
248	C₂×M₁₆	—	13	2	no	—
249	C₂×M₁₆	—	26	1	no	—
250	C₂×M₁₆	—	26	1	no	—
251	C₂×M₁₆	—	26	1	no	—
252	C₂×M₁₆	—	26	1	no	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	—	13	1	no	—
255	C₂²×C₈	—	13	1	no	—
256	C₂²×C₈	—	13	1	no	—
257	C₂²×C₈	—	13	1	no	—
258	C₂²×C₈	—	13	1	no	—
259	C₂²×C₈	—	13	1	no	—
260	C₂²×C₈	—	13	1	no	—
261	C₂²×C₈	—	13	1	no	—
262	C₂²×C₈	—	13	1	no	—
263	C₂²×C₈	—	13	1	no	—
264	C₂²×C₈	—	13	1	no	—
265	C₂²×C₈	—	13	1	no	—
266	C₂²×C₈	—	13	2	no	—
267	C₂²×C₈	C₂×#261	1	1	yes	characteristic
268	#117	—	13	2	no	—
269	#117	—	13	2	no	—
270	#117	—	26	1	no	—
271	#117	—	26	1	no	—
272	C₂×C₄⋊C₄	—	26	1	no	—
273	C₂×C₂²⋊C₄	—	26	1	no	—
274	C₂×C₄²	—	13	2	no	—
275	M₃₂	—	13	4	no	—
276	M₃₂	—	13	4	no	—
277	M₃₂	—	13	4	no	—
278	M₃₂	—	13	4	no	—
279	M₃₂	—	13	2	no	—
280	M₃₂	—	13	2	no	—
281	M₃₂	—	13	4	no	—
282	M₃₂	—	13	4	no	—
283	M₃₂	C₂×#261	1	2	yes	—
284	M₃₂	C₂×#261	1	2	yes	complemented
285	C₂×C₁₆	—	13	4	no	—
286	C₂×C₁₆	—	13	4	no	—
287	C₂×C₁₆	—	13	4	no	—
288	C₂×C₁₆	—	13	2	no	—
289	C₂×C₁₆	—	13	4	no	—
290	C₂×C₁₆	—	13	4	no	—
291	C₂×C₁₆	C₂×#261	1	2	yes	complemented
292	#97	—	13	4	no	—
293	#97	—	13	4	no	—
294	C₄×C₈	—	13	4	no	—
295	C₄×C₈	—	13	4	no	—
296	C₂×C₁₃	—	2	1	no	—
297	C₂×C₁₃	—	2	1	no	—
298	C₂×C₁₃	—	2	1	no	—
299	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
300	D₁₃	—	2	1	no	—
301	D₁₃	—	2	1	no	—
302	D₁₃	—	2	1	no	—
303	D₁₃	#2110	1	2	yes	complemented
304	C₂⁴	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	1	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	26	2	no	—
319	C₂²×C₄	C₄×#261	1	1	yes	characteristic
320	M₁₆	—	26	2	no	—
321	M₁₆	—	26	2	no	—
322	M₁₆	—	26	2	no	—
323	M₁₆	—	26	2	no	—
324	C₂×C₈	—	13	1	no	—
325	C₂×C₈	—	13	1	no	—
326	C₂×C₈	—	13	1	no	—
327	C₂×C₈	—	13	1	no	—
328	C₂×C₈	—	13	1	no	—
329	C₂×C₈	—	13	1	no	—
330	C₂×C₈	—	13	1	no	—
331	C₂×C₈	—	13	1	no	—
332	C₂×C₈	—	13	1	no	—
333	C₂×C₈	—	13	1	no	—
334	C₂×C₈	—	13	1	no	—
335	C₂×C₈	—	13	1	no	—
336	C₂×C₈	—	13	1	no	—
337	C₂×C₈	—	13	1	no	—
338	C₂×C₈	—	13	1	no	—
339	C₂×C₈	—	13	1	no	—
340	C₂×C₈	—	13	1	no	—
341	C₂×C₈	—	13	1	no	—
342	C₂×C₈	—	13	1	no	—
343	C₂×C₈	—	13	1	no	—
344	C₂×C₈	—	13	1	no	—
345	C₂×C₈	—	13	1	no	—
346	C₂×C₈	—	13	4	no	—
347	C₂×C₈	—	26	2	no	—
348	C₂×C₈	—	26	2	no	—
349	C₂×C₈	C₄×#261	1	1	yes	characteristic
350	C₂×C₈	C₄×#261	1	1	yes	characteristic
351	C₂×C₈	C₄×#261	1	1	yes	characteristic
352	C₂×C₈	C₂²×#261	1	1	yes	characteristic
353	C₂×C₈	C₂²×#261	1	1	yes	characteristic
354	C₂×C₈	C₂²×#261	1	1	yes	characteristic
355	C₄⋊C₄	—	26	2	no	—
356	C₄⋊C₄	—	26	2	no	—
357	C₂²⋊C₄	—	26	2	no	—
358	C₂²⋊C₄	—	26	2	no	—
359	C₄²	—	13	4	no	—
360	C₄²	—	26	2	no	—
361	C₁₆	—	13	8	no	—
362	C₁₆	—	13	4	no	—
363	C₁₆	C₂²×#261	1	4	yes	—
364	C₁₃	C₂×#2110	1	1	yes	characteristic, complemented, Sylow
365	C₂³	—	13	1	no	—
366	C₂³	—	13	1	no	—
367	C₂³	—	13	1	no	—
368	C₂³	—	13	1	no	—
369	C₂³	—	13	1	no	—
370	C₂³	—	13	1	no	—
371	C₂³	—	52	2	no	—
372	C₂³	#88100	1	1	yes	characteristic
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	13	1	no	—
376	C₂×C₄	—	13	1	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	13	1	no	—
382	C₂×C₄	—	13	1	no	—
383	C₂×C₄	—	13	1	no	—
384	C₂×C₄	—	13	1	no	—
385	C₂×C₄	—	13	1	no	—
386	C₂×C₄	—	13	1	no	—
387	C₂×C₄	—	13	1	no	—
388	C₂×C₄	—	13	1	no	—
389	C₂×C₄	—	13	1	no	—
390	C₂×C₄	—	13	1	no	—
391	C₂×C₄	—	13	1	no	—
392	C₂×C₄	—	13	1	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	26	4	no	—
396	C₂×C₄	—	52	4	no	—
397	C₂×C₄	#88100	1	1	yes	characteristic
398	C₂×C₄	#88100	1	1	yes	characteristic
399	C₂×C₄	#88100	1	1	yes	characteristic
400	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
401	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
402	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
403	C₈	—	13	1	no	—
404	C₈	—	13	1	no	—
405	C₈	—	13	1	no	—
406	C₈	—	13	1	no	—
407	C₈	—	26	4	no	—
408	C₈	C₂×C₄×#261	1	1	yes	characteristic
409	C₈	C₂×C₄×#261	1	1	yes	characteristic
410	C₈	C₂×C₄×#261	1	1	yes	characteristic
411	C₈	C₂³×#261	1	1	yes	characteristic
412	C₂²	—	4	1	no	—
413	C₂²	—	13	1	no	—
414	C₂²	—	13	1	no	—
415	C₂²	—	13	1	no	—
416	C₂²	—	13	1	no	—
417	C₂²	—	26	2	no	—
418	C₂²	—	26	2	no	—
419	C₂²	—	26	2	no	—
420	C₂²	—	52	1	no	—
421	C₂²	—	52	1	no	—
422	C₂²	—	52	1	no	—
423	C₂²	C₂×#88100	1	1	yes	characteristic
424	C₂²	C₂×#88100	1	1	yes	characteristic
425	C₂²	C₂×#88100	1	1	yes	characteristic
426	C₄	—	13	1	no	—
427	C₄	—	13	1	no	—
428	C₄	—	13	1	no	—
429	C₄	—	13	1	no	—
430	C₄	—	52	4	no	—
431	C₄	C₂×#88100	1	1	yes	characteristic
432	C₄	C₂×#88100	1	1	yes	characteristic
433	C₄	C₂×#88100	1	1	yes	characteristic
434	C₄	C₂²×C₄×#261	1	1	yes	characteristic
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	13	2	no	—
439	C₂	—	26	1	no	—
440	C₂	—	26	1	no	—
441	C₂	—	26	1	no	—
442	C₂	C₂²×#88100	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×C₄×#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₈	C₂³×#261
Fitting	C₂×C₁₃×M₃₂	C₄
socle	C₂×C₁₃	C₂²×#97
prime radical	C₂³×D₁₃	M₁₆
cosocle	C₈×D₁₃	C₂⁴
hypercenter	C₂×M₃₂	#261
hypocenter	C₁₃	C₂×#2110
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #13131056	C₂	semidirect
4. #13131055	C₂	semidirect
5. #13131051	C₂	semidirect
10. C₂×#88106	C₄	semidirect
17. D₁₃⋊M₃₂	C₄	semidirect
18. D₁₃⋊M₃₂	C₄	semidirect
22. C₂×D₁₃⋊C₁₆	C₄	semidirect
23. C₂×C₁₃×M₃₂	C₄	semidirect
24. C₂×#88052	C₄	semidirect
25. D₁₃×M₃₂	C₄	semidirect
26. D₁₃×M₃₂	C₄	semidirect
30. C₂×C₁₆×D₁₃	C₄	semidirect
31. #11718218	C₂²	semidirect
32. #11718217	C₂²	semidirect
63. #88106	C₂×C₄	semidirect
64. C₂×#6092	C₂×C₄	semidirect
69. #88098	C₂×C₄	semidirect
72. D₁₃⋊C₁₆	C₂×C₄	semidirect
74. C₁₃×M₃₂	C₂×C₄	semidirect
75. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
77. #88052	C₂×C₄	semidirect
78. C₂×#6090	C₂×C₄	semidirect
79. #88038	C₂×C₄	semidirect
82. C₁₆×D₁₃	C₂×C₄	semidirect
212. C₂×M₃₂	#261	semidirect
284. M₃₂	C₂×#261	semidirect
291. C₂×C₁₆	C₂×#261	semidirect
303. D₁₃	#2110	semidirect
364. C₁₃	C₂×#2110	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃⋊M₃₂	2
C₂×#11719089	2
#13131056	2
#13131055	2
#13131051	2
C₂×D₁₃×M₃₂	2
C₂×#2110	13