Subgroups — C₂×#13128169 #16769758

Order 3328.

11662 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6127	C₂	1	2	yes	maximal, complemented
2	#13128169	C₂	1	32	yes	maximal, direct product factor
3	C₂×#11719215	C₂	1	4	yes	maximal, complemented
4	C₂×#11719231	C₂	1	4	yes	maximal, complemented
5	C₂×#11719230	C₂	1	4	yes	maximal, complemented
6	C₂×#11719198	C₂	1	4	yes	maximal, complemented
7	C₂×#11719182	C₂	1	4	yes	maximal, complemented
8	C₂×#11719229	C₂	1	8	yes	maximal, complemented
9	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×C₂²⋊D₁₃	C₂²	1	4	yes	—
12	C₂²×#6127	—	2	32	no	—
13	C₂²×#6127	C₂²	1	4	yes	—
14	C₂²×#6127	C₂²	1	4	yes	—
15	C₂²×#6127	C₂²	1	4	yes	complemented
16	C₂²×#6127	C₂²	1	4	yes	complemented
17	C₂²×#6127	C₂²	1	32	yes	complemented
18	C₂³×D₅₂	C₂²	1	2	yes	complemented
19	C₂³×C₄×D₁₃	C₂²	1	4	yes	complemented
20	C₂³×Dic₂₆	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
22	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
23	C₂×C₁₃×#117	C₂²	1	16	yes	complemented
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
27	C₂×#88184	C₂²	1	16	yes	complemented
28	#11719231	C₂²	1	64	yes	complemented
29	#11719230	C₂²	1	64	yes	complemented
30	#11719229	C₂²	1	128	yes	complemented
31	#11719215	C₂²	1	64	yes	complemented
32	C₂×#88151	C₂²	1	16	yes	complemented
33	C₂×#88149	C₂²	1	16	yes	complemented
34	#11719198	C₂²	1	64	yes	complemented
35	C₂×#88140	C₂²	1	16	yes	complemented
36	C₂×#88136	C₂²	1	16	yes	complemented
37	#11719182	C₂²	1	64	yes	complemented
38	C₂×#88129	C₂²	1	8	yes	complemented
39	C₂×#88128	C₂²	1	4	yes	complemented
40	C₂×C₄×D₅₂	C₂²	1	16	yes	complemented
41	C₂×#88123	C₂²	1	4	yes	complemented
42	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
43	C₂⁴×D₁₃	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₃	D₄	1	16	yes	complemented
45	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
51	C₂²×C₂²⋊D₁₃	—	2	32	no	—
52	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
53	C₂²×C₂²⋊D₁₃	C₂³	1	32	yes	—
54	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
55	C₂³×Dic₁₃	C₂³	1	4	yes	—
56	C₂×#6127	—	2	32	no	—
57	C₂×#6127	—	2	32	no	—
58	C₂×#6127	—	2	32	no	—
59	C₂×#6127	—	2	32	no	—
60	C₂×#6127	—	2	256	no	—
61	C₂×#6127	C₂³	1	32	yes	—
62	C₂×#6127	C₂³	1	32	yes	—
63	C₂×#6127	C₂³	1	32	yes	complemented
64	C₂×#6127	C₂³	1	32	yes	complemented
65	C₂²×D₅₂	—	2	16	no	—
66	C₂²×D₅₂	C₂³	1	4	yes	—
67	C₂²×D₅₂	C₂³	1	4	yes	—
68	C₂²×D₅₂	C₂³	1	16	yes	—
69	C₂²×D₅₂	C₂³	1	16	yes	complemented
70	C₂²×C₄×D₁₃	—	2	32	no	—
71	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
72	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
73	C₂²×C₄×D₁₃	C₂³	1	32	yes	complemented
74	C₂²×Dic₂₆	—	2	16	no	—
75	C₂²×Dic₂₆	C₂³	1	4	yes	—
76	C₂²×Dic₂₆	C₂³	1	4	yes	—
77	C₂²×Dic₂₆	C₂³	1	16	yes	complemented
78	C₁₃×#117	C₂³	1	32	yes	complemented
79	C₁₃×#117	C₂³	1	32	yes	complemented
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
84	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
85	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	16	yes	complemented
87	#88184	C₂³	1	128	yes	complemented
88	C₂×#6103	C₂³	1	32	yes	—
89	C₂×C₄⋊Dic₁₃	C₂³	1	16	yes	—
90	#88151	C₂³	1	128	yes	complemented
91	#88149	C₂³	1	128	yes	complemented
92	#88140	C₂³	1	128	yes	complemented
93	#88136	C₂³	1	128	yes	complemented
94	#88129	C₂³	1	64	yes	complemented
95	#88128	C₂³	1	32	yes	complemented
96	C₄×D₅₂	C₂³	1	128	yes	complemented
97	#88123	C₂³	1	32	yes	complemented
98	C₂×#3449	—	13	1	no	maximal, Sylow
99	C₂⁴×C₁₃	—	4	4	no	—
100	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
101	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
102	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
104	C₂³×D₁₃	—	2	16	no	—
105	C₂³×D₁₃	—	4	16	no	—
106	C₂³×D₁₃	C₂⁴	1	8	yes	—
107	C₂³×D₁₃	C₂⁴	1	16	yes	—
108	C₂²×C₄×C₁₃	—	4	8	no	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	64	yes	complemented
114	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
116	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂×C₂²⋊D₁₃	—	2	32	no	—
124	C₂×C₂²⋊D₁₃	—	2	32	no	—
125	C₂×C₂²⋊D₁₃	—	2	128	no	—
126	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
127	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
128	C₂²×Dic₁₃	—	2	16	no	—
129	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
130	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
131	#6127	—	2	128	no	—
132	#6127	—	2	128	no	—
133	#6127	—	2	128	no	—
134	#6127	—	2	128	no	—
135	C₂×D₅₂	—	2	16	no	—
136	C₂×D₅₂	—	2	16	no	—
137	C₂×D₅₂	—	2	64	no	—
138	C₂×D₅₂	—	4	32	no	—
139	C₂×D₅₂	C₂⁴	1	16	yes	—
140	C₂×D₅₂	C₂⁴	1	16	yes	—
141	C₂×D₅₂	C₂⁴	1	64	yes	—
142	C₂×C₄×D₁₃	—	2	32	no	—
143	C₂×C₄×D₁₃	—	2	32	no	—
144	C₂×C₄×D₁₃	—	2	128	no	—
145	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
146	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
147	C₂×Dic₂₆	—	2	16	no	—
148	C₂×Dic₂₆	—	2	16	no	—
149	C₂×Dic₂₆	—	2	64	no	—
150	C₂×Dic₂₆	C₂⁴	1	16	yes	—
151	C₂×Dic₂₆	C₂⁴	1	16	yes	—
152	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
153	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
154	C₄²×C₁₃	C₂⁴	1	16	yes	—
155	C₄²×C₁₃	C₂⁴	1	16	yes	—
156	#6103	C₂⁴	1	128	yes	—
157	C₄⋊Dic₁₃	C₂⁴	1	64	yes	—
158	C₂³×#41	—	13	2	no	—
159	#3449	—	13	32	no	—
160	C₂×#537	—	13	4	no	—
161	C₂×#536	—	13	4	no	—
162	C₂×#535	—	13	4	no	—
163	C₂×#534	—	13	4	no	—
164	C₂×#532	—	13	4	no	—
165	C₂×#525	—	13	8	no	—
166	C₂²×#117	D₁₃	1	1	yes	characteristic, complemented
167	C₂³×C₁₃	—	2	4	no	—
168	C₂³×C₁₃	—	2	8	no	—
169	C₂³×C₁₃	—	4	16	no	—
170	C₂³×C₁₃	—	4	8	no	—
171	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
172	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
173	C₂³×C₁₃	C₂²×D₄	1	16	yes	—
174	C₂³×C₁₃	C₂⁵	1	4	yes	—
175	C₂³×C₁₃	C₂⁵	1	2	yes	—
176	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
177	C₂²×D₁₃	—	2	32	no	—
178	C₂²×D₁₃	—	2	16	no	—
179	C₂²×D₁₃	—	2	32	no	—
180	C₂²×D₁₃	—	4	32	no	—
181	C₂²×D₁₃	—	4	64	no	—
182	C₂²×D₁₃	C₂⁵	1	16	yes	—
183	C₂×C₄×C₁₃	—	2	16	no	—
184	C₂×C₄×C₁₃	—	4	16	no	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
186	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	32	yes	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	32	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	—
192	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
193	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
194	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
195	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
196	C₂²⋊D₁₃	—	2	64	no	—
197	C₂²⋊D₁₃	—	2	64	no	—
198	C₂×Dic₁₃	—	2	32	no	—
199	C₂×Dic₁₃	—	2	16	no	—
200	C₂×Dic₁₃	C₂⁵	1	16	yes	—
201	D₅₂	—	2	32	no	—
202	D₅₂	—	2	32	no	—
203	D₅₂	—	4	64	no	—
204	C₄×D₁₃	—	2	64	no	—
205	C₄×D₁₃	—	2	64	no	—
206	Dic₂₆	—	2	32	no	—
207	Dic₂₆	—	2	32	no	—
208	C₂²×#41	—	13	4	no	—
209	C₂²×#41	—	13	4	no	—
210	C₂²×#41	—	13	4	no	—
211	C₂²×#41	—	13	4	no	—
212	C₂²×#41	—	13	32	no	—
213	C₂²×#41	—	26	32	no	—
214	C₂³×Q₈	—	13	2	no	—
215	C₂³×D₄	—	13	4	no	—
216	C₂³×D₄	—	13	2	no	—
217	C₂⁴×C₄	—	13	4	no	—
218	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
219	#537	—	13	64	no	—
220	#536	—	13	64	no	—
221	#535	—	13	64	no	—
222	#534	—	13	64	no	—
223	#532	—	13	64	no	—
224	C₂×C₄⋊Q₈	—	13	4	no	—
225	C₂×#127	—	13	4	no	—
226	C₂×#124	—	13	8	no	—
227	#525	—	13	128	no	—
228	C₂×#123	—	13	16	no	—
229	C₂×C₂²⋊Q₈	—	13	16	no	—
230	C₂×#121	—	13	16	no	—
231	C₂×#121	—	13	16	no	—
232	C₂×#120	—	13	16	no	—
233	C₂×C₄×D₄	—	13	16	no	—
234	C₂×#117	C₂×D₁₃	1	4	yes	complemented
235	C₂×#117	C₂×D₁₃	1	4	yes	complemented
236	C₂×#117	C₂×D₁₃	1	16	yes	complemented
237	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
238	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
239	C₂²×C₄²	C₂×D₁₃	1	2	yes	complemented
240	C₂²×C₁₃	—	2	4	no	—
241	C₂²×C₁₃	—	2	8	no	—
242	C₂²×C₁₃	—	2	16	no	—
243	C₂²×C₁₃	—	2	8	no	—
244	C₂²×C₁₃	—	4	16	no	—
245	C₂²×C₁₃	C₂³×D₄	1	8	yes	—
246	C₂²×C₁₃	C₂³×D₄	1	4	yes	—
247	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
248	C₂²×C₁₃	#585	1	4	yes	—
249	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
250	C₂×D₁₃	—	2	16	no	—
251	C₂×D₁₃	—	2	32	no	—
252	C₂×D₁₃	—	4	64	no	—
253	C₂×D₁₃	—	4	32	no	—
254	C₄×C₁₃	—	2	16	no	—
255	C₄×C₁₃	C₂³×D₄	1	4	yes	—
256	C₄×C₁₃	C₂³×D₄	1	8	yes	—
257	C₄×C₁₃	C₂³×D₄	1	4	yes	—
258	Dic₁₃	—	2	16	no	—
259	C₂⁵	—	13	4	no	—
260	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
261	C₂×#41	—	13	32	no	—
262	C₂×#41	—	13	32	no	—
263	C₂×#41	—	13	32	no	—
264	C₂×#41	—	13	32	no	—
265	C₂×#41	—	26	32	no	—
266	C₂×#41	—	26	32	no	—
267	C₂×#41	—	26	32	no	—
268	C₂×#41	—	26	32	no	—
269	C₂×#41	—	26	256	no	—
270	C₂²×Q₈	—	13	4	no	—
271	C₂²×Q₈	—	13	4	no	—
272	C₂²×Q₈	—	13	16	no	—
273	C₂²×Q₈	—	26	16	no	—
274	C₂²×D₄	—	13	8	no	—
275	C₂²×D₄	—	13	8	no	—
276	C₂²×D₄	—	13	32	no	—
277	C₂²×D₄	—	13	4	no	—
278	C₂²×D₄	—	13	4	no	—
279	C₂²×D₄	—	13	16	no	—
280	C₂²×D₄	—	13	16	no	—
281	C₂²×D₄	—	26	32	no	—
282	C₂²×D₄	—	26	16	no	—
283	C₂³×C₄	—	13	4	no	—
284	C₂³×C₄	—	13	8	no	—
285	C₂³×C₄	—	13	32	no	—
286	C₂³×C₄	—	13	8	no	—
287	C₂³×C₄	—	26	32	no	—
288	C₂³×C₄	D₅₂	1	16	yes	complemented
289	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
290	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
291	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
292	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
293	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
294	C₂³×C₄	C₂²×D₁₃	1	8	yes	—
295	C₄⋊Q₈	—	13	32	no	—
296	#127	—	13	32	no	—
297	#124	—	13	64	no	—
298	#123	—	13	128	no	—
299	C₂²⋊Q₈	—	13	128	no	—
300	#121	—	13	128	no	—
301	#121	—	13	128	no	—
302	#120	—	13	128	no	—
303	C₄×D₄	—	13	128	no	—
304	#117	C₂²×D₁₃	1	32	yes	complemented
305	#117	C₂²×D₁₃	1	32	yes	complemented
306	C₂×C₄⋊C₄	—	13	16	no	—
307	C₂×C₄⋊C₄	C₂²×D₁₃	1	8	yes	—
308	C₂×C₄⋊C₄	C₂²×D₁₃	1	16	yes	complemented
309	C₂×C₂²⋊C₄	—	13	32	no	—
310	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
311	C₂×C₂²⋊C₄	C₂²×D₁₃	1	16	yes	—
312	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
313	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
314	C₂×C₄²	C₂²×D₁₃	1	16	yes	complemented
315	C₂×C₁₃	—	2	8	no	—
316	C₂×C₁₃	—	2	4	no	—
317	C₂×C₁₃	#3449	1	4	yes	complemented
318	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
319	C₂×C₁₃	C₂×#585	1	2	yes	—
320	D₁₃	—	4	16	no	—
321	C₂⁴	—	4	4	no	—
322	C₂⁴	—	13	8	no	—
323	C₂⁴	—	13	16	no	—
324	C₂⁴	—	26	16	no	—
325	C₂⁴	—	52	16	no	—
326	C₂⁴	C₂×D₅₂	1	8	yes	—
327	C₂⁴	C₂³×D₁₃	1	2	yes	—
328	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
329	C₂⁴	C₂³×D₁₃	1	4	yes	—
330	#41	—	26	128	no	—
331	#41	—	26	128	no	—
332	#41	—	26	128	no	—
333	#41	—	26	128	no	—
334	C₂×Q₈	—	13	16	no	—
335	C₂×Q₈	—	13	16	no	—
336	C₂×Q₈	—	26	16	no	—
337	C₂×Q₈	—	26	16	no	—
338	C₂×Q₈	—	26	64	no	—
339	C₂×D₄	—	13	32	no	—
340	C₂×D₄	—	13	32	no	—
341	C₂×D₄	—	13	16	no	—
342	C₂×D₄	—	13	16	no	—
343	C₂×D₄	—	13	64	no	—
344	C₂×D₄	—	26	32	no	—
345	C₂×D₄	—	26	32	no	—
346	C₂×D₄	—	26	128	no	—
347	C₂×D₄	—	26	16	no	—
348	C₂×D₄	—	26	16	no	—
349	C₂×D₄	—	26	64	no	—
350	C₂×D₄	—	52	32	no	—
351	C₂²×C₄	—	4	8	no	—
352	C₂²×C₄	—	13	8	no	—
353	C₂²×C₄	—	13	16	no	—
354	C₂²×C₄	—	13	32	no	—
355	C₂²×C₄	—	13	32	no	—
356	C₂²×C₄	—	26	16	no	—
357	C₂²×C₄	—	26	32	no	—
358	C₂²×C₄	—	26	32	no	—
359	C₂²×C₄	—	26	128	no	—
360	C₂²×C₄	C₂×D₅₂	1	16	yes	—
361	C₂²×C₄	C₂×D₅₂	1	16	yes	—
362	C₂²×C₄	C₂×D₅₂	1	8	yes	—
363	C₂²×C₄	C₂×D₅₂	1	8	yes	—
364	C₂²×C₄	C₂×D₅₂	1	64	yes	complemented
365	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
366	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
367	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
369	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
370	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
371	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
372	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
373	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
374	C₄⋊C₄	—	13	64	no	—
375	C₄⋊C₄	C₂³×D₁₃	1	32	yes	—
376	C₂²⋊C₄	—	13	128	no	—
377	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
378	C₄²	C₂³×D₁₃	1	16	yes	—
379	C₄²	C₂³×D₁₃	1	16	yes	—
380	C₁₃	C₂×#3449	1	1	yes	characteristic, complemented, Sylow
381	C₂³	—	2	4	no	—
382	C₂³	—	2	8	no	—
383	C₂³	—	4	16	no	—
384	C₂³	—	4	8	no	—
385	C₂³	—	13	16	no	—
386	C₂³	—	26	32	no	—
387	C₂³	—	26	16	no	—
388	C₂³	—	26	32	no	—
389	C₂³	—	52	32	no	—
390	C₂³	—	52	64	no	—
391	C₂³	C₂²×D₅₂	1	8	yes	—
392	C₂³	C₂²×D₅₂	1	4	yes	—
393	C₂³	C₂²×D₅₂	1	16	yes	—
394	C₂³	C₂⁴×D₁₃	1	4	yes	—
395	C₂³	C₂⁴×D₁₃	1	2	yes	—
396	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
397	Q₈	—	26	32	no	—
398	Q₈	—	26	32	no	—
399	D₄	—	26	64	no	—
400	D₄	—	26	64	no	—
401	D₄	—	26	32	no	—
402	D₄	—	26	32	no	—
403	D₄	—	52	64	no	—
404	C₂×C₄	—	2	16	no	—
405	C₂×C₄	—	4	16	no	—
406	C₂×C₄	—	13	16	no	—
407	C₂×C₄	—	26	32	no	—
408	C₂×C₄	—	26	16	no	—
409	C₂×C₄	—	26	64	no	—
410	C₂×C₄	—	26	64	no	—
411	C₂×C₄	C₂²×D₅₂	1	4	yes	—
412	C₂×C₄	C₂²×D₅₂	1	8	yes	—
413	C₂×C₄	C₂²×D₅₂	1	32	yes	—
414	C₂×C₄	C₂²×D₅₂	1	4	yes	—
415	C₂×C₄	C₂²×D₅₂	1	32	yes	—
416	C₂×C₄	C₂²×D₅₂	1	16	yes	—
417	C₂×C₄	C₂²×D₅₂	1	16	yes	—
418	C₂×C₄	C₂⁴×D₁₃	1	16	yes	—
419	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
420	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
421	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	8	no	—
424	C₂²	—	2	16	no	—
425	C₂²	—	2	8	no	—
426	C₂²	—	4	16	no	—
427	C₂²	—	26	16	no	—
428	C₂²	—	26	32	no	—
429	C₂²	—	52	64	no	—
430	C₂²	—	52	32	no	—
431	C₂²	C₂³×D₅₂	1	8	yes	—
432	C₂²	C₂³×D₅₂	1	4	yes	—
433	C₂²	C₂³×D₅₂	1	2	yes	—
434	C₂²	#11719648	1	4	yes	—
435	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
436	C₄	—	2	16	no	—
437	C₄	—	26	16	no	—
438	C₄	C₂³×D₅₂	1	4	yes	—
439	C₄	C₂³×D₅₂	1	8	yes	—
440	C₄	C₂³×D₅₂	1	4	yes	—
441	C₂	—	2	8	no	—
442	C₂	—	2	4	no	—
443	C₂	—	52	16	no	—
444	C₂	#13128169	1	4	yes	direct product factor
445	C₂	C₂⁴×D₅₂	1	1	yes	characteristic
446	C₂	C₂×#11719648	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#117	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂²×#117	D₁₃
hypocenter	C₁₃	C₂×#3449
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. C₂³×#6127	C₂	semidirect
2. #13128169	C₂	direct (N × H)
3. C₂×#11719215	C₂	semidirect
4. C₂×#11719231	C₂	semidirect
5. C₂×#11719230	C₂	semidirect
6. C₂×#11719198	C₂	semidirect
7. C₂×#11719182	C₂	semidirect
8. C₂×#11719229	C₂	semidirect
9. C₂²×C₁₃×#117	C₂	semidirect
15. C₂²×#6127	C₂²	semidirect
16. C₂²×#6127	C₂²	semidirect
17. C₂²×#6127	C₂²	semidirect
18. C₂³×D₅₂	C₂²	semidirect
19. C₂³×C₄×D₁₃	C₂²	semidirect
20. C₂³×Dic₂₆	C₂²	semidirect
21. C₂×C₁₃×#117	C₂²	semidirect
22. C₂×C₁₃×#117	C₂²	semidirect
23. C₂×C₁₃×#117	C₂²	semidirect
24. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
26. C₂²×C₄²×C₁₃	C₂²	semidirect
27. C₂×#88184	C₂²	semidirect
28. #11719231	C₂²	semidirect
29. #11719230	C₂²	semidirect
30. #11719229	C₂²	semidirect
31. #11719215	C₂²	semidirect
32. C₂×#88151	C₂²	semidirect
33. C₂×#88149	C₂²	semidirect
34. #11719198	C₂²	semidirect
35. C₂×#88140	C₂²	semidirect
36. C₂×#88136	C₂²	semidirect
37. #11719182	C₂²	semidirect
38. C₂×#88129	C₂²	semidirect
39. C₂×#88128	C₂²	semidirect
40. C₂×C₄×D₅₂	C₂²	semidirect
41. C₂×#88123	C₂²	semidirect
44. C₂³×C₄×C₁₃	D₄	semidirect
63. C₂×#6127	C₂³	semidirect
64. C₂×#6127	C₂³	semidirect
69. C₂²×D₅₂	C₂³	semidirect
73. C₂²×C₄×D₁₃	C₂³	semidirect
77. C₂²×Dic₂₆	C₂³	semidirect
78. C₁₃×#117	C₂³	semidirect
79. C₁₃×#117	C₂³	semidirect
81. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
86. C₂×C₄²×C₁₃	C₂³	semidirect
87. #88184	C₂³	semidirect
90. #88151	C₂³	semidirect
91. #88149	C₂³	semidirect
92. #88140	C₂³	semidirect
93. #88136	C₂³	semidirect
94. #88129	C₂³	semidirect
95. #88128	C₂³	semidirect
96. C₄×D₅₂	C₂³	semidirect
97. #88123	C₂³	semidirect
113. C₂²×C₄×C₁₃	C₂×D₄	semidirect
166. C₂²×#117	D₁₃	semidirect
234. C₂×#117	C₂×D₁₃	semidirect
235. C₂×#117	C₂×D₁₃	semidirect
236. C₂×#117	C₂×D₁₃	semidirect
237. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
239. C₂²×C₄²	C₂×D₁₃	semidirect
288. C₂³×C₄	D₅₂	semidirect
304. #117	C₂²×D₁₃	semidirect
305. #117	C₂²×D₁₃	semidirect
308. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
314. C₂×C₄²	C₂²×D₁₃	semidirect
317. C₂×C₁₃	#3449	semidirect
364. C₂²×C₄	C₂×D₅₂	semidirect
380. C₁₃	C₂×#3449	semidirect
444. C₂	#13128169	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#6127	2
#13128169	2
C₂×#11719215	2
C₂×#11719231	2
C₂×#11719230	2
C₂×#11719198	2
C₂×#11719182	2
C₂×#11719229	2
C₂²×C₁₃×#117	2
C₂×#3449	13

Subgroups — C2×#13128169 #16769758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128169 #16769758