Subgroups — C₂×#13129733 #16780090

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719052	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊#261	C₂	1	1	yes	maximal, characteristic
3	#13129733	C₂	1	4	yes	maximal, direct product factor
4	C₂×#11718494	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊#261	—	2	1	no	—
6	C₂²×C₄×#261	—	2	1	no	—
7	C₂²×#6118	—	2	1	no	—
8	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×(C₂×#261)⋊C₄	C₄	1	2	yes	—
10	C₂×C₄⋊#1057	—	2	1	no	—
11	C₂×C₄⋊#1057	C₄	1	2	yes	complemented
12	C₄×C₄⋊#261	—	2	1	no	—
13	C₄×C₄⋊#261	—	2	1	no	—
14	C₄×C₄⋊#261	C₄	1	2	yes	—
15	C₄×C₄⋊#261	C₂²	1	2	yes	—
16	#11719052	—	2	1	no	—
17	#11719052	—	2	1	no	—
18	#11719052	C₄	1	2	yes	complemented
19	#11719052	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic, complemented
21	C₂×#88060	—	2	1	no	—
22	C₂×C₈×Dic₁₃	—	2	1	no	—
23	C₂×C₄⋊#1055	C₄	1	1	yes	characteristic, complemented
24	#11718494	—	2	1	no	—
25	#11718494	—	2	1	no	—
26	#11718494	C₄	1	2	yes	complemented
27	#11718494	C₂²	1	2	yes	—
28	C₂³×#261	—	2	2	no	—
29	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
32	C₂²×#1057	—	2	2	no	—
33	C₂×C₄⋊#261	—	2	4	no	—
34	C₂×C₄⋊#261	—	2	4	no	—
35	C₂×C₄⋊#261	—	2	2	no	—
36	C₂×C₄⋊#261	—	2	2	no	—
37	C₂×C₄×#261	—	2	2	no	—
38	C₂×C₄×#261	—	2	2	no	—
39	C₂×C₄×#261	—	4	2	no	—
40	C₂×C₄×#261	—	4	2	no	—
41	C₂×#6118	—	2	2	no	—
42	C₂×#6118	—	2	2	no	—
43	C₂×#6118	—	4	2	no	—
44	C₂×#6118	—	4	2	no	—
45	C₂²×C₈×C₁₃	—	2	1	no	—
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
50	C₂²×#1055	—	2	1	no	—
51	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₁₃	D₄	1	1	yes	characteristic
55	C₄²×D₁₃	D₄	1	1	yes	characteristic
56	C₄²×D₁₃	D₄	1	1	yes	characteristic
57	C₄²×D₁₃	Q₈	1	1	yes	characteristic
58	C₄²×D₁₃	C₂³	1	1	yes	characteristic
59	(C₂×#261)⋊C₄	—	2	2	no	—
60	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
61	C₄⋊#1057	—	2	2	no	—
62	C₄⋊#1057	—	2	2	no	—
63	C₄⋊#1057	—	2	2	no	—
64	C₄⋊#1057	C₂×C₄	1	4	yes	complemented
65	C₁₃×C₄⋊C₈	—	2	1	no	—
66	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
67	#88060	—	2	2	no	—
68	#88060	—	2	2	no	—
69	C₈×Dic₁₃	—	2	2	no	—
70	C₈×Dic₁₃	—	2	2	no	—
71	C₄⋊#1055	—	2	1	no	—
72	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
73	C₂×#1303	—	13	1	no	maximal, Sylow
74	C₂³×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×#261	—	2	8	no	—
76	C₂²×#261	—	2	4	no	—
77	C₂²×#261	—	4	4	no	—
78	C₂²×#261	—	4	4	no	—
79	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₃	—	2	2	no	—
86	C₂×C₄×D₁₃	—	2	2	no	—
87	C₂×C₄×D₁₃	—	4	2	no	—
88	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	D₈	1	2	yes	—
98	C₂×C₄×D₁₃	SD₁₆	1	2	yes	—
99	C₂×C₄×D₁₃	SD₁₆	1	2	yes	—
100	C₂×C₄×D₁₃	Q₁₆	1	2	yes	—
101	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×#1057	—	2	4	no	—
105	C₂×#1057	—	4	4	no	—
106	C₄⋊#261	—	2	8	no	—
107	C₄⋊#261	—	2	4	no	—
108	C₄⋊#261	—	2	4	no	—
109	C₄×#261	—	4	4	no	—
110	C₄×#261	—	4	2	no	—
111	C₄×#261	—	4	2	no	—
112	#6118	—	4	4	no	—
113	#6118	—	4	2	no	—
114	#6118	—	4	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	4	2	no	—
117	C₄²×C₁₃	C₄²	1	1	yes	characteristic
118	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
122	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
133	C₂×#1055	—	2	2	no	—
134	C₂×#1055	—	4	2	no	—
135	C₂×#431	—	13	1	no	—
136	C₂×#423	—	13	1	no	—
137	C₂×C₄×C₄⋊C₄	—	13	1	no	—
138	#1303	—	13	4	no	—
139	C₂³×C₁₃	#95	1	1	yes	characteristic
140	C₂²×D₁₃	—	2	2	no	—
141	C₂²×D₁₃	—	2	2	no	—
142	C₂²×D₁₃	#95	1	1	yes	characteristic
143	C₂²×D₁₃	#102	1	2	yes	—
144	C₂²×D₁₃	#103	1	2	yes	—
145	C₂²×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×#261	—	2	8	no	—
147	C₂×#261	—	4	16	no	—
148	C₂×#261	—	4	4	no	—
149	C₂×#261	—	4	4	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
152	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
153	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
154	C₂×C₄×C₁₃	#104	1	2	yes	—
155	C₂×C₄×C₁₃	#104	1	2	yes	—
156	C₂×C₄×C₁₃	#106	1	2	yes	—
157	C₂×C₄×C₁₃	#107	1	2	yes	—
158	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×Dic₁₃	—	2	2	no	—
162	C₂×Dic₁₃	—	2	2	no	—
163	C₂×Dic₁₃	#95	1	1	yes	characteristic
164	C₂×Dic₁₃	#95	1	1	yes	characteristic
165	C₂×Dic₁₃	#95	1	1	yes	characteristic
166	C₂×Dic₁₃	#102	1	2	yes	—
167	C₂×Dic₁₃	#103	1	2	yes	—
168	C₂×Dic₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₄×D₁₃	—	2	2	no	—
172	C₄×D₁₃	—	2	2	no	—
173	C₄×D₁₃	—	2	1	no	—
174	C₄×D₁₃	—	2	1	no	—
175	C₄×D₁₃	—	2	1	no	—
176	C₄×D₁₃	—	2	1	no	—
177	C₄×D₁₃	—	4	1	no	—
178	C₄×D₁₃	—	4	1	no	—
179	C₄×D₁₃	—	4	1	no	—
180	C₄×D₁₃	—	4	1	no	—
181	C₄×D₁₃	#102	1	2	yes	—
182	C₄×D₁₃	#102	1	2	yes	—
183	C₄×D₁₃	#103	1	2	yes	—
184	C₄×D₁₃	#103	1	2	yes	—
185	C₄×D₁₃	#106	1	2	yes	—
186	C₄×D₁₃	#107	1	2	yes	—
187	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
188	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
189	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
190	C₄×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
191	#1057	—	4	4	no	—
192	C₈×C₁₃	—	4	2	no	—
193	#1055	—	4	2	no	—
194	C₂²×M₁₆	—	26	1	no	—
195	C₂²×C₄⋊C₄	—	26	1	no	—
196	C₂²×C₄²	—	13	1	no	—
197	C₂²×C₄²	—	26	1	no	—
198	#431	—	13	2	no	—
199	#431	—	13	2	no	—
200	#431	—	26	1	no	—
201	#431	—	26	1	no	—
202	#423	—	13	2	no	—
203	#423	—	13	2	no	—
204	#423	—	26	1	no	—
205	#423	—	26	1	no	—
206	C₂×C₄⋊C₈	—	13	2	no	—
207	C₂×C₄⋊C₈	—	13	1	no	—
208	C₂×C₄⋊C₈	—	26	1	no	—
209	C₂×C₄⋊C₈	#261	1	1	yes	characteristic, complemented
210	C₂×C₂²⋊C₈	—	26	1	no	—
211	C₂×C₄×C₈	—	26	1	no	—
212	C₄×C₄⋊C₄	—	13	2	no	—
213	C₄×C₄⋊C₄	—	13	2	no	—
214	C₄×C₄⋊C₄	—	26	1	no	—
215	C₄×C₄⋊C₄	—	26	1	no	—
216	C₂×#95	—	13	2	no	—
217	C₂²×C₁₃	#339	1	2	yes	—
218	C₂²×C₁₃	#340	1	2	yes	—
219	C₂²×C₁₃	#344	1	2	yes	—
220	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
221	C₂×D₁₃	—	2	4	no	—
222	C₂×D₁₃	—	2	4	no	—
223	C₂×D₁₃	—	2	1	no	—
224	C₂×D₁₃	—	2	1	no	—
225	C₂×D₁₃	—	2	1	no	—
226	C₂×D₁₃	—	2	1	no	—
227	C₂×D₁₃	#340	1	2	yes	—
228	C₂×D₁₃	C₂×#102	1	1	yes	characteristic
229	C₂×D₁₃	C₂×#103	1	1	yes	characteristic
230	#261	—	4	8	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	2	1	no	—
233	C₄×C₁₃	#339	1	2	yes	—
234	C₄×C₁₃	#340	1	2	yes	—
235	C₄×C₁₃	C₂×#104	1	1	yes	characteristic
236	C₄×C₁₃	C₂×#104	1	1	yes	characteristic
237	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
238	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
239	Dic₁₃	—	2	1	no	—
240	Dic₁₃	—	2	1	no	—
241	Dic₁₃	—	2	1	no	—
242	Dic₁₃	—	2	1	no	—
243	Dic₁₃	#340	1	2	yes	—
244	Dic₁₃	C₂×#102	1	1	yes	characteristic
245	Dic₁₃	C₂×#103	1	1	yes	characteristic
246	C₂³×C₄	—	13	1	no	—
247	C₂³×C₄	—	13	1	no	—
248	C₂³×C₄	—	13	1	no	—
249	C₂³×C₄	—	26	2	no	—
250	C₂×M₁₆	—	26	2	no	—
251	C₂×M₁₆	—	26	2	no	—
252	C₂×M₁₆	—	52	2	no	—
253	C₂×M₁₆	—	52	2	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	26	2	no	—
256	C₂²×C₈	—	26	1	no	—
257	C₂×C₄⋊C₄	—	26	2	no	—
258	C₂×C₄⋊C₄	—	26	2	no	—
259	C₂×C₄⋊C₄	—	26	4	no	—
260	C₂×C₄⋊C₄	—	26	4	no	—
261	C₂×C₄²	—	13	1	no	—
262	C₂×C₄²	—	13	1	no	—
263	C₂×C₄²	—	13	1	no	—
264	C₂×C₄²	—	13	1	no	—
265	C₂×C₄²	—	13	1	no	—
266	C₂×C₄²	—	13	1	no	—
267	C₂×C₄²	—	13	1	no	—
268	C₂×C₄²	—	13	1	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	—	13	1	no	—
271	C₂×C₄²	—	13	1	no	—
272	C₂×C₄²	—	26	2	no	—
273	C₂×C₄²	—	26	2	no	—
274	C₂×C₄²	—	52	2	no	—
275	C₂×C₄²	—	52	2	no	—
276	C₂×C₄²	C₂×#261	1	1	yes	characteristic
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	13	4	no	—
279	C₄⋊C₈	—	13	2	no	—
280	C₄⋊C₈	—	26	2	no	—
281	C₄⋊C₈	—	26	2	no	—
282	C₄⋊C₈	—	26	2	no	—
283	C₄⋊C₈	—	26	1	no	—
284	C₄⋊C₈	C₂×#261	1	2	yes	complemented
285	C₂²⋊C₈	—	26	2	no	—
286	C₂²⋊C₈	—	26	2	no	—
287	C₄×C₈	—	26	2	no	—
288	C₄×C₈	—	26	2	no	—
289	#95	—	13	4	no	—
290	#95	—	26	2	no	—
291	C₂×C₁₃	#1303	1	4	yes	complemented
292	C₂×C₁₃	C₂×#339	1	1	yes	characteristic
293	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
294	C₂×C₁₃	C₂×#344	1	1	yes	characteristic
295	D₁₃	—	2	1	no	—
296	D₁₃	—	2	2	no	—
297	D₁₃	—	2	1	no	—
298	C₂⁴	—	13	1	no	—
299	C₂²×C₄	—	13	1	no	—
300	C₂²×C₄	—	13	2	no	—
301	C₂²×C₄	—	13	2	no	—
302	C₂²×C₄	—	13	2	no	—
303	C₂²×C₄	—	13	2	no	—
304	C₂²×C₄	—	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	—	26	2	no	—
320	C₂²×C₄	—	26	4	no	—
321	C₂²×C₄	—	26	8	no	—
322	C₂²×C₄	—	52	2	no	—
323	C₂²×C₄	—	52	4	no	—
324	C₂²×C₄	—	52	4	no	—
325	C₂²×C₄	C₄×#261	1	1	yes	characteristic
326	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
327	C₂²×C₄	C₂²⋊#261	1	1	yes	characteristic
328	M₁₆	—	52	4	no	—
329	M₁₆	—	52	2	no	—
330	M₁₆	—	52	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	2	no	—
333	C₂×C₈	—	26	4	no	—
334	C₂×C₈	—	26	2	no	—
335	C₂×C₈	—	52	4	no	—
336	C₂×C₈	—	52	2	no	—
337	C₄⋊C₄	—	26	8	no	—
338	C₄⋊C₄	—	26	4	no	—
339	C₄⋊C₄	—	26	4	no	—
340	C₄²	—	13	1	no	—
341	C₄²	—	13	1	no	—
342	C₄²	—	13	1	no	—
343	C₄²	—	13	1	no	—
344	C₄²	—	13	1	no	—
345	C₄²	—	13	1	no	—
346	C₄²	—	13	1	no	—
347	C₄²	—	13	1	no	—
348	C₄²	—	13	1	no	—
349	C₄²	—	13	1	no	—
350	C₄²	—	13	1	no	—
351	C₄²	—	13	1	no	—
352	C₄²	—	52	4	no	—
353	C₄²	—	52	2	no	—
354	C₄²	—	52	2	no	—
355	C₄²	C₄×#261	1	1	yes	characteristic
356	C₄²	C₄⋊#261	1	1	yes	characteristic
357	C₄²	C₂²⋊#261	1	1	yes	characteristic
358	C₄²	C₂²×#261	1	1	yes	characteristic
359	C₁₃	C₂×#1303	1	1	yes	characteristic, complemented, Sylow
360	C₂³	—	13	2	no	—
361	C₂³	—	13	2	no	—
362	C₂³	—	13	1	no	—
363	C₂³	—	13	1	no	—
364	C₂³	—	26	2	no	—
365	C₂³	—	26	2	no	—
366	C₂³	(C₂×#261)⋊C₄	1	1	yes	characteristic
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	13	2	no	—
369	C₂×C₄	—	13	2	no	—
370	C₂×C₄	—	13	1	no	—
371	C₂×C₄	—	13	1	no	—
372	C₂×C₄	—	13	2	no	—
373	C₂×C₄	—	13	2	no	—
374	C₂×C₄	—	13	2	no	—
375	C₂×C₄	—	13	2	no	—
376	C₂×C₄	—	13	1	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	2	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	2	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	—	26	2	no	—
387	C₂×C₄	—	26	2	no	—
388	C₂×C₄	—	26	2	no	—
389	C₂×C₄	—	26	2	no	—
390	C₂×C₄	—	26	1	no	—
391	C₂×C₄	—	26	1	no	—
392	C₂×C₄	—	26	1	no	—
393	C₂×C₄	—	26	1	no	—
394	C₂×C₄	—	26	8	no	—
395	C₂×C₄	—	52	1	no	—
396	C₂×C₄	—	52	1	no	—
397	C₂×C₄	—	52	1	no	—
398	C₂×C₄	—	52	1	no	—
399	C₂×C₄	—	52	4	no	—
400	C₂×C₄	—	52	16	no	—
401	C₂×C₄	—	52	4	no	—
402	C₂×C₄	#88101	1	2	yes	—
403	C₂×C₄	#88102	1	2	yes	—
404	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
405	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
406	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
407	C₂×C₄	#88116	1	2	yes	—
408	C₂×C₄	#88118	1	2	yes	—
409	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
411	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
412	C₈	—	4	2	no	—
413	C₈	—	52	4	no	—
414	C₈	—	52	2	no	—
415	C₂²	—	13	2	no	—
416	C₂²	—	13	1	no	—
417	C₂²	—	13	1	no	—
418	C₂²	—	26	4	no	—
419	C₂²	—	26	4	no	—
420	C₂²	—	26	1	no	—
421	C₂²	—	26	1	no	—
422	C₂²	—	26	1	no	—
423	C₂²	—	26	1	no	—
424	C₂²	#11718247	1	2	yes	—
425	C₂²	#11718265	1	2	yes	—
426	C₂²	#11718274	1	2	yes	—
427	C₂²	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	13	2	no	—
431	C₄	—	13	1	no	—
432	C₄	—	13	1	no	—
433	C₄	—	26	1	no	—
434	C₄	—	26	1	no	—
435	C₄	—	26	1	no	—
436	C₄	—	26	1	no	—
437	C₄	—	52	8	no	—
438	C₄	#11718247	1	2	yes	—
439	C₄	#11718265	1	2	yes	—
440	C₄	C₂×#88101	1	1	yes	characteristic
441	C₄	C₂×#88102	1	1	yes	characteristic
442	C₄	C₂×#88116	1	1	yes	characteristic
443	C₄	C₂×#88118	1	1	yes	characteristic
444	C₂	—	26	1	no	—
445	C₂	—	26	2	no	—
446	C₂	—	26	1	no	—
447	C₂	#13129733	1	4	yes	direct product factor
448	C₂	C₂×#11718247	1	1	yes	characteristic
449	C₂	C₂×#11718265	1	1	yes	characteristic
450	C₂	C₂×#11718274	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	(C₂×#261)⋊C₄
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₄²	C₂²×#261
Fitting	C₂×C₁₃×C₄⋊C₈	C₄
socle	C₂³×C₁₃	#95
prime radical	C₂³×D₁₃	C₂²⋊C₄
cosocle	C₄²×D₁₃	C₂³
hypercenter	C₂×C₄⋊C₈	#261
hypocenter	C₁₃	C₂×#1303
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #13129733	C₂	direct (N × H)
11. C₂×C₄⋊#1057	C₄	semidirect
18. #11719052	C₄	semidirect
20. C₂×C₁₃×C₄⋊C₈	C₄	semidirect
23. C₂×C₄⋊#1055	C₄	semidirect
26. #11718494	C₄	semidirect
64. C₄⋊#1057	C₂×C₄	semidirect
66. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
72. C₄⋊#1055	C₂×C₄	semidirect
209. C₂×C₄⋊C₈	#261	semidirect
284. C₄⋊C₈	C₂×#261	semidirect
291. C₂×C₁₃	#1303	semidirect
359. C₁₃	C₂×#1303	semidirect
447. C₂	#13129733	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11719052	2
C₂×C₄×C₄⋊#261	2
#13129733	2
C₂×#11718494	2
C₂×#1303	13

Subgroups — C2×#13129733 #16780090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129733 #16780090