Subgroups — C₂×H(5,𝔽₂)×#261 #16809635

Order 3328.

12378 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(5,𝔽₂)×#261	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719631	C₂	1	6	yes	maximal, complemented
3	C₂×#11719623	C₂	1	9	yes	maximal, complemented
4	C₂×#41×#261	C₂	1	6	yes	maximal, complemented
5	C₂²×D₄×#261	C₂	1	9	yes	maximal, complemented
6	C₂×D₁₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
7	C₂⁴×#261	C₂²	1	6	yes	complemented
8	C₂×C₁₃×H(5,𝔽₂)	C₄	1	1	yes	characteristic, complemented
9	D₁₃×H(5,𝔽₂)	C₄	1	16	yes	complemented
10	D₁₃×H(5,𝔽₂)	C₂²	1	16	yes	—
11	C₂×#88256	C₄	1	6	yes	complemented
12	C₂×#41×D₁₃	C₂²	1	6	yes	—
13	C₂×#88251	C₄	1	9	yes	complemented
14	C₂²×D₄×D₁₃	C₂²	1	9	yes	—
15	C₂²×C₂²⋊#261	C₂²	1	18	yes	complemented
16	#11719631	C₂²	1	96	yes	complemented
17	#41×#261	C₂²	1	96	yes	complemented
18	C₂×Q₈×#261	C₂²	1	2	yes	complemented
19	C₂×Q₈×#261	C₂²	1	6	yes	complemented
20	#11719623	C₂²	1	144	yes	complemented
21	C₂×D₄×#261	C₂²	1	18	yes	complemented
22	C₂×D₄×#261	C₂²	1	36	yes	complemented
23	C₂×D₄×#261	C₂²	1	18	yes	complemented
24	C₂×D₄×#261	C₂²	1	144	yes	complemented
25	C₂×#88237	C₂²	1	18	yes	complemented
26	C₂²×C₄⋊#261	C₂²	1	9	yes	complemented
27	C₂²×C₄×#261	C₂²	1	9	yes	complemented
28	C₂⁴×D₁₃	C₂³	1	6	yes	—
29	C₂³×#261	—	4	24	no	—
30	C₂³×#261	C₂³	1	9	yes	—
31	C₂³×#261	C₂³	1	9	yes	—
32	C₂³×#261	C₂³	1	18	yes	—
33	C₂³×#261	C₂³	1	48	yes	complemented
34	C₁₃×H(5,𝔽₂)	C₂×C₄	1	16	yes	complemented
35	C₂×C₁₃×#41	C₂×C₄	1	6	yes	complemented
36	C₂²×D₄×C₁₃	C₂×C₄	1	9	yes	complemented
37	C₂²×C₂²⋊D₁₃	C₂×C₄	1	18	yes	complemented
38	#88256	C₂×C₄	1	96	yes	complemented
39	#41×D₁₃	C₂×C₄	1	48	yes	complemented
40	#41×D₁₃	C₂³	1	48	yes	—
41	C₂×#6131	C₂×C₄	1	6	yes	complemented
42	C₂×Q₈×D₁₃	C₂³	1	2	yes	—
43	#88251	C₂×C₄	1	144	yes	complemented
44	C₂×#6129	C₂×C₄	1	18	yes	complemented
45	C₂×D₄×D₁₃	C₂×C₄	1	36	yes	complemented
46	C₂×D₄×D₁₃	C₂×C₄	1	72	yes	complemented
47	C₂×D₄×D₁₃	C₂³	1	18	yes	—
48	C₂×D₄×D₁₃	C₂³	1	72	yes	—
49	C₂×#6127	C₂×C₄	1	18	yes	complemented
50	C₂²×D₅₂	C₂×C₄	1	9	yes	complemented
51	C₂²×C₄×D₁₃	C₂³	1	9	yes	—
52	C₂×C₂²⋊#261	C₂³	1	36	yes	—
53	C₂×C₂²⋊#261	C₂³	1	144	yes	complemented
54	Q₈×#261	C₂³	1	16	yes	complemented
55	Q₈×#261	C₂³	1	48	yes	complemented
56	D₄×#261	C₂³	1	144	yes	complemented
57	D₄×#261	C₂³	1	288	yes	complemented
58	D₄×#261	C₂³	1	144	yes	complemented
59	#88237	C₂³	1	144	yes	complemented
60	C₂×C₄⋊#261	C₂³	1	18	yes	—
61	C₂×C₄⋊#261	C₂³	1	6	yes	—
62	C₂×C₄⋊#261	C₂³	1	72	yes	complemented
63	C₂×C₄×#261	C₂³	1	6	yes	—
64	C₂×C₄×#261	C₂³	1	18	yes	—
65	C₂×C₄×#261	C₂³	1	72	yes	complemented
66	C₂×C₄×H(5,𝔽₂)	—	13	1	no	maximal, Sylow
67	C₂⁴×C₁₃	C₂²×C₄	1	6	yes	complemented
68	C₂³×D₁₃	—	4	12	no	—
69	C₂³×D₁₃	—	4	12	no	—
70	C₂³×D₁₃	C₂²×C₄	1	24	yes	complemented
71	C₂³×D₁₃	C₂²×C₄	1	18	yes	complemented
72	C₂³×D₁₃	C₂⁴	1	9	yes	—
73	C₂³×D₁₃	C₂⁴	1	24	yes	—
74	C₂²×#261	—	2	36	no	—
75	C₂²×#261	—	4	96	no	—
76	C₂²×#261	—	4	36	no	—
77	C₂²×#261	—	4	18	no	—
78	C₂²×#261	C₂⁴	1	6	yes	—
79	C₂²×#261	C₂⁴	1	9	yes	—
80	C₂²×#261	C₂⁴	1	36	yes	—
81	C₂²×#261	C₂⁴	1	36	yes	—
82	C₂²×#261	C₂⁴	1	72	yes	—
83	C₂²×#261	C₂⁴	1	1	yes	characteristic
84	C₁₃×#41	C₂²×C₄	1	48	yes	complemented
85	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	complemented
86	C₂×D₄×C₁₃	C₂²×C₄	1	18	yes	complemented
87	C₂×D₄×C₁₃	C₂²×C₄	1	72	yes	complemented
88	C₂²×C₄×C₁₃	C₂²×C₄	1	9	yes	complemented
89	C₂×C₂²⋊D₁₃	C₂²×C₄	1	36	yes	complemented
90	C₂×C₂²⋊D₁₃	C₂²×C₄	1	144	yes	complemented
91	C₂²×Dic₁₃	C₂²×C₄	1	9	yes	complemented
92	#6131	C₂²×C₄	1	48	yes	complemented
93	Q₈×D₁₃	C₂²×C₄	1	8	yes	complemented
94	Q₈×D₁₃	C₂⁴	1	8	yes	—
95	#6129	C₂²×C₄	1	144	yes	complemented
96	D₄×D₁₃	C₂²×C₄	1	72	yes	complemented
97	D₄×D₁₃	C₂²×C₄	1	288	yes	complemented
98	D₄×D₁₃	C₂⁴	1	72	yes	—
99	#6127	C₂²×C₄	1	144	yes	complemented
100	C₂×D₅₂	C₂²×C₄	1	18	yes	complemented
101	C₂×D₅₂	C₂²×C₄	1	72	yes	complemented
102	C₂×C₄×D₁₃	C₂²×C₄	1	36	yes	complemented
103	C₂×C₄×D₁₃	C₂²×C₄	1	18	yes	complemented
104	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
105	C₂×C₄×D₁₃	C₂⁴	1	36	yes	—
106	C₂×Dic₂₆	C₂²×C₄	1	6	yes	complemented
107	C₂²⋊#261	C₂⁴	1	144	yes	—
108	C₄⋊#261	C₂⁴	1	72	yes	—
109	C₄⋊#261	C₂⁴	1	24	yes	—
110	C₄×#261	C₂⁴	1	24	yes	—
111	C₄×#261	C₂⁴	1	72	yes	—
112	C₂²×H(5,𝔽₂)	—	13	1	no	—
113	C₄×H(5,𝔽₂)	—	13	32	no	—
114	C₂×#520	—	13	6	no	—
115	C₂×#518	—	13	9	no	—
116	C₂×C₄×#41	—	13	6	no	—
117	C₂²×C₄×D₄	—	13	9	no	—
118	C₂³×C₁₃	—	4	12	no	—
119	C₂³×C₁₃	C₂³×C₄	1	9	yes	—
120	C₂³×C₁₃	C₂³×C₄	1	24	yes	complemented
121	C₂²×D₁₃	—	2	18	no	—
122	C₂²×D₁₃	—	2	18	no	—
123	C₂²×D₁₃	—	4	24	no	—
124	C₂²×D₁₃	—	4	48	no	—
125	C₂²×D₁₃	—	4	24	no	—
126	C₂²×D₁₃	—	4	36	no	—
127	C₂²×D₁₃	C₂³×C₄	1	9	yes	—
128	C₂²×D₁₃	C₂³×C₄	1	18	yes	—
129	C₂²×D₁₃	C₂³×C₄	1	72	yes	complemented
130	C₂²×D₁₃	C₂⁵	1	18	yes	—
131	C₂²×D₁₃	C₂⁵	1	1	yes	characteristic
132	C₂×#261	—	2	18	no	—
133	C₂×#261	—	2	12	no	—
134	C₂×#261	—	2	72	no	—
135	C₂×#261	—	4	72	no	—
136	C₂×#261	—	4	36	no	—
137	C₂×#261	H(5,𝔽₂)	1	4	yes	direct product factor
138	C₂×#261	C₂⁵	1	12	yes	—
139	C₂×#261	C₂⁵	1	18	yes	—
140	C₂×#261	C₂⁵	1	2	yes	—
141	Q₈×C₁₃	C₂³×C₄	1	8	yes	complemented
142	D₄×C₁₃	C₂³×C₄	1	72	yes	complemented
143	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
144	C₂×C₄×C₁₃	C₂³×C₄	1	36	yes	complemented
145	C₂²⋊D₁₃	C₂³×C₄	1	144	yes	complemented
146	C₂×Dic₁₃	C₂³×C₄	1	6	yes	—
147	C₂×Dic₁₃	C₂³×C₄	1	36	yes	complemented
148	D₅₂	C₂³×C₄	1	72	yes	complemented
149	C₄×D₁₃	C₂³×C₄	1	12	yes	—
150	C₄×D₁₃	C₂³×C₄	1	72	yes	complemented
151	C₄×D₁₃	C₂⁵	1	12	yes	—
152	Dic₂₆	C₂³×C₄	1	24	yes	complemented
153	C₂×H(5,𝔽₂)	—	13	16	no	—
154	C₂×H(5,𝔽₂)	—	13	16	no	—
155	C₂×H(5,𝔽₂)	—	13	6	no	—
156	C₂×H(5,𝔽₂)	—	13	9	no	—
157	C₂×H(5,𝔽₂)	#261	1	1	yes	characteristic, direct product factor
158	C₂²×#41	—	13	6	no	—
159	C₂³×D₄	—	13	9	no	—
160	C₂⁴×C₄	—	13	6	no	—
161	#520	—	13	96	no	—
162	#518	—	13	144	no	—
163	C₄×#41	—	13	96	no	—
164	C₂×C₄×Q₈	—	13	2	no	—
165	C₂×C₄×Q₈	—	13	6	no	—
166	C₂×C₄×D₄	—	13	18	no	—
167	C₂×C₄×D₄	—	13	36	no	—
168	C₂×C₄×D₄	—	13	144	no	—
169	C₂×C₄×D₄	—	13	18	no	—
170	C₂×#117	—	13	18	no	—
171	C₂²×C₄⋊C₄	—	13	9	no	—
172	C₂²×C₂²⋊C₄	—	13	18	no	—
173	C₂²×C₄²	—	13	9	no	—
174	C₂²×C₁₃	—	2	18	no	—
175	C₂²×C₁₃	—	4	24	no	—
176	C₂²×C₁₃	C₂⁴×C₄	1	18	yes	—
177	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
178	C₂×D₁₃	—	2	18	no	—
179	C₂×D₁₃	—	2	18	no	—
180	C₂×D₁₃	—	2	18	no	—
181	C₂×D₁₃	—	2	36	no	—
182	C₂×D₁₃	—	4	72	no	—
183	C₂×D₁₃	C₂⁴×C₄	1	18	yes	—
184	C₂×D₁₃	C₂⁴×C₄	1	1	yes	characteristic
185	C₂×D₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
186	C₂×D₁₃	#585	1	2	yes	—
187	C₂×D₁₃	C₂⁶	1	1	yes	characteristic
188	#261	—	2	18	no	—
189	#261	—	2	12	no	—
190	#261	C₂×H(5,𝔽₂)	1	4	yes	direct product factor
191	C₄×C₁₃	C₂⁴×C₄	1	12	yes	—
192	Dic₁₃	C₂⁴×C₄	1	12	yes	—
193	C₂⁵	—	13	6	no	—
194	H(5,𝔽₂)	—	13	96	no	—
195	H(5,𝔽₂)	—	13	144	no	—
196	H(5,𝔽₂)	C₂×#261	1	16	yes	direct product factor
197	C₂×#41	—	13	48	no	—
198	C₂×#41	—	13	48	no	—
199	C₂×#41	—	13	6	no	—
200	C₂×#41	—	13	18	no	—
201	C₂×#41	—	13	18	no	—
202	C₂×#41	C₂×#261	1	6	yes	complemented
203	C₂²×Q₈	—	13	2	no	—
204	C₂²×D₄	—	13	18	no	—
205	C₂²×D₄	—	13	18	no	—
206	C₂²×D₄	—	13	72	no	—
207	C₂²×D₄	—	13	36	no	—
208	C₂²×D₄	—	13	72	no	—
209	C₂²×D₄	—	13	9	no	—
210	C₂²×D₄	C₂×#261	1	9	yes	complemented
211	C₂³×C₄	—	13	9	no	—
212	C₂³×C₄	—	13	9	no	—
213	C₂³×C₄	—	13	9	no	—
214	C₂³×C₄	—	13	18	no	—
215	C₂³×C₄	—	13	48	no	—
216	C₂³×C₄	—	52	24	no	—
217	C₄×Q₈	—	13	16	no	—
218	C₄×Q₈	—	13	48	no	—
219	C₄×D₄	—	13	144	no	—
220	C₄×D₄	—	13	288	no	—
221	C₄×D₄	—	13	144	no	—
222	#117	—	13	144	no	—
223	C₂×C₄⋊C₄	—	13	18	no	—
224	C₂×C₄⋊C₄	—	13	72	no	—
225	C₂×C₄⋊C₄	—	13	6	no	—
226	C₂×C₂²⋊C₄	—	13	36	no	—
227	C₂×C₂²⋊C₄	—	13	144	no	—
228	C₂×C₄²	—	13	18	no	—
229	C₂×C₄²	—	13	6	no	—
230	C₂×C₄²	—	13	72	no	—
231	C₂×C₁₃	—	2	18	no	—
232	C₂×C₁₃	C₄×H(5,𝔽₂)	1	2	yes	complemented
233	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
234	D₁₃	—	2	18	no	—
235	D₁₃	C₄×H(5,𝔽₂)	1	2	yes	complemented
236	D₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
237	D₁₃	C₂×#585	1	1	yes	characteristic
238	C₂⁴	—	13	9	no	—
239	C₂⁴	—	13	18	no	—
240	C₂⁴	—	13	24	no	—
241	C₂⁴	—	13	24	no	—
242	C₂⁴	—	52	12	no	—
243	C₂⁴	—	52	12	no	—
244	C₂⁴	C₂²×#261	1	6	yes	complemented
245	#41	—	13	48	no	—
246	#41	—	13	144	no	—
247	#41	—	13	144	no	—
248	#41	C₂²×#261	1	48	yes	complemented
249	C₂×Q₈	—	13	8	no	—
250	C₂×Q₈	—	13	8	no	—
251	C₂×Q₈	—	13	6	no	—
252	C₂×Q₈	C₂²×#261	1	2	yes	complemented
253	C₂×D₄	—	13	36	no	—
254	C₂×D₄	—	13	144	no	—
255	C₂×D₄	—	13	72	no	—
256	C₂×D₄	—	13	72	no	—
257	C₂×D₄	—	13	288	no	—
258	C₂×D₄	—	13	18	no	—
259	C₂×D₄	—	13	72	no	—
260	C₂×D₄	C₂²×#261	1	18	yes	complemented
261	C₂×D₄	C₂²×#261	1	72	yes	complemented
262	C₂²×C₄	—	13	1	no	—
263	C₂²×C₄	—	13	9	no	—
264	C₂²×C₄	—	13	6	no	—
265	C₂²×C₄	—	13	18	no	—
266	C₂²×C₄	—	13	36	no	—
267	C₂²×C₄	—	13	36	no	—
268	C₂²×C₄	—	13	6	no	—
269	C₂²×C₄	—	13	9	no	—
270	C₂²×C₄	—	13	36	no	—
271	C₂²×C₄	—	13	36	no	—
272	C₂²×C₄	—	13	72	no	—
273	C₂²×C₄	—	26	36	no	—
274	C₂²×C₄	—	52	96	no	—
275	C₂²×C₄	—	52	36	no	—
276	C₂²×C₄	—	52	18	no	—
277	C₂²×C₄	C₂²×#261	1	9	yes	complemented
278	C₄⋊C₄	—	13	72	no	—
279	C₄⋊C₄	—	13	24	no	—
280	C₂²⋊C₄	—	13	144	no	—
281	C₄²	—	13	24	no	—
282	C₄²	—	13	72	no	—
283	C₁₃	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
284	C₂³	—	4	12	no	—
285	C₂³	—	13	1	no	—
286	C₂³	—	13	18	no	—
287	C₂³	—	13	18	no	—
288	C₂³	—	13	9	no	—
289	C₂³	—	13	72	no	—
290	C₂³	—	26	18	no	—
291	C₂³	—	26	18	no	—
292	C₂³	—	52	36	no	—
293	C₂³	—	52	24	no	—
294	C₂³	—	52	24	no	—
295	C₂³	—	52	48	no	—
296	C₂³	C₂³×#261	1	9	yes	—
297	C₂³	C₂³×#261	1	24	yes	complemented
298	Q₈	—	13	24	no	—
299	Q₈	C₂³×#261	1	8	yes	complemented
300	D₄	—	13	144	no	—
301	D₄	—	13	72	no	—
302	D₄	C₂³×#261	1	72	yes	complemented
303	C₂×C₄	—	13	2	no	—
304	C₂×C₄	—	13	4	no	—
305	C₂×C₄	—	13	36	no	—
306	C₂×C₄	—	13	6	no	—
307	C₂×C₄	—	13	12	no	—
308	C₂×C₄	—	13	12	no	—
309	C₂×C₄	—	13	72	no	—
310	C₂×C₄	—	13	12	no	—
311	C₂×C₄	—	13	18	no	—
312	C₂×C₄	—	26	72	no	—
313	C₂×C₄	—	26	18	no	—
314	C₂×C₄	—	26	12	no	—
315	C₂×C₄	—	52	72	no	—
316	C₂×C₄	—	52	36	no	—
317	C₂×C₄	C₂³×#261	1	6	yes	—
318	C₂×C₄	C₂³×#261	1	36	yes	complemented
319	C₂²	—	2	18	no	—
320	C₂²	—	4	24	no	—
321	C₂²	—	13	2	no	—
322	C₂²	—	13	2	no	—
323	C₂²	—	13	1	no	—
324	C₂²	—	13	1	no	—
325	C₂²	—	13	18	no	—
326	C₂²	—	26	18	no	—
327	C₂²	—	26	18	no	—
328	C₂²	—	26	36	no	—
329	C₂²	—	26	18	no	—
330	C₂²	—	52	72	no	—
331	C₂²	C₂⁴×#261	1	18	yes	—
332	C₂²	C₂⁴×#261	1	1	yes	characteristic
333	C₄	—	13	4	no	—
334	C₄	—	13	12	no	—
335	C₄	—	26	18	no	—
336	C₄	—	26	12	no	—
337	C₄	C₂⁴×#261	1	12	yes	—
338	C₂	—	2	18	no	—
339	C₂	—	13	1	no	—
340	C₂	—	13	1	no	—
341	C₂	—	13	2	no	—
342	C₂	—	26	18	no	—
343	C₂	H(5,𝔽₂)×#261	1	2	yes	direct product factor
344	C₂	C₂⁵×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂⁴×#261
commutator	C₂×C₁₃	C₂⁵×C₄
Frattini	C₂	C₂⁵×#261
Fitting	C₂×C₁₃×H(5,𝔽₂)	C₄
socle	C₂²×C₁₃	C₂⁴×C₄
prime radical	C₂×D₁₃×H(5,𝔽₂)	C₂
cosocle	C₂×D₁₃	C₂⁶
hypercenter	C₂×H(5,𝔽₂)	#261
hypocenter	C₁₃	C₂×C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. H(5,𝔽₂)×#261	C₂	direct (N × H)
2. C₂×#11719631	C₂	semidirect
3. C₂×#11719623	C₂	semidirect
4. C₂×#41×#261	C₂	semidirect
5. C₂²×D₄×#261	C₂	semidirect
7. C₂⁴×#261	C₂²	semidirect
8. C₂×C₁₃×H(5,𝔽₂)	C₄	semidirect
9. D₁₃×H(5,𝔽₂)	C₄	semidirect
11. C₂×#88256	C₄	semidirect
13. C₂×#88251	C₄	semidirect
15. C₂²×C₂²⋊#261	C₂²	semidirect
16. #11719631	C₂²	semidirect
17. #41×#261	C₂²	semidirect
18. C₂×Q₈×#261	C₂²	semidirect
19. C₂×Q₈×#261	C₂²	semidirect
20. #11719623	C₂²	semidirect
21. C₂×D₄×#261	C₂²	semidirect
22. C₂×D₄×#261	C₂²	semidirect
23. C₂×D₄×#261	C₂²	semidirect
24. C₂×D₄×#261	C₂²	semidirect
25. C₂×#88237	C₂²	semidirect
26. C₂²×C₄⋊#261	C₂²	semidirect
27. C₂²×C₄×#261	C₂²	semidirect
33. C₂³×#261	C₂³	semidirect
34. C₁₃×H(5,𝔽₂)	C₂×C₄	semidirect
35. C₂×C₁₃×#41	C₂×C₄	semidirect
36. C₂²×D₄×C₁₃	C₂×C₄	semidirect
37. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
38. #88256	C₂×C₄	semidirect
39. #41×D₁₃	C₂×C₄	semidirect
41. C₂×#6131	C₂×C₄	semidirect
43. #88251	C₂×C₄	semidirect
44. C₂×#6129	C₂×C₄	semidirect
45. C₂×D₄×D₁₃	C₂×C₄	semidirect
46. C₂×D₄×D₁₃	C₂×C₄	semidirect
49. C₂×#6127	C₂×C₄	semidirect
50. C₂²×D₅₂	C₂×C₄	semidirect
53. C₂×C₂²⋊#261	C₂³	semidirect
54. Q₈×#261	C₂³	semidirect
55. Q₈×#261	C₂³	semidirect
56. D₄×#261	C₂³	semidirect
57. D₄×#261	C₂³	semidirect
58. D₄×#261	C₂³	semidirect
59. #88237	C₂³	semidirect
62. C₂×C₄⋊#261	C₂³	semidirect
65. C₂×C₄×#261	C₂³	semidirect
67. C₂⁴×C₁₃	C₂²×C₄	semidirect
70. C₂³×D₁₃	C₂²×C₄	semidirect
71. C₂³×D₁₃	C₂²×C₄	semidirect
84. C₁₃×#41	C₂²×C₄	semidirect
85. C₂×Q₈×C₁₃	C₂²×C₄	semidirect
86. C₂×D₄×C₁₃	C₂²×C₄	semidirect
87. C₂×D₄×C₁₃	C₂²×C₄	semidirect
88. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
89. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
90. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
91. C₂²×Dic₁₃	C₂²×C₄	semidirect
92. #6131	C₂²×C₄	semidirect
93. Q₈×D₁₃	C₂²×C₄	semidirect
95. #6129	C₂²×C₄	semidirect
96. D₄×D₁₃	C₂²×C₄	semidirect
97. D₄×D₁₃	C₂²×C₄	semidirect
99. #6127	C₂²×C₄	semidirect
100. C₂×D₅₂	C₂²×C₄	semidirect
101. C₂×D₅₂	C₂²×C₄	semidirect
102. C₂×C₄×D₁₃	C₂²×C₄	semidirect
103. C₂×C₄×D₁₃	C₂²×C₄	semidirect
106. C₂×Dic₂₆	C₂²×C₄	semidirect
120. C₂³×C₁₃	C₂³×C₄	semidirect
129. C₂²×D₁₃	C₂³×C₄	semidirect
137. C₂×#261	H(5,𝔽₂)	direct (N × H)
141. Q₈×C₁₃	C₂³×C₄	semidirect
142. D₄×C₁₃	C₂³×C₄	semidirect
144. C₂×C₄×C₁₃	C₂³×C₄	semidirect
145. C₂²⋊D₁₃	C₂³×C₄	semidirect
147. C₂×Dic₁₃	C₂³×C₄	semidirect
148. D₅₂	C₂³×C₄	semidirect
150. C₄×D₁₃	C₂³×C₄	semidirect
152. Dic₂₆	C₂³×C₄	semidirect
157. C₂×H(5,𝔽₂)	#261	direct (N × H)
190. #261	C₂×H(5,𝔽₂)	direct (N × H)
196. H(5,𝔽₂)	C₂×#261	direct (N × H)
202. C₂×#41	C₂×#261	semidirect
210. C₂²×D₄	C₂×#261	semidirect
232. C₂×C₁₃	C₄×H(5,𝔽₂)	semidirect
235. D₁₃	C₄×H(5,𝔽₂)	semidirect
244. C₂⁴	C₂²×#261	semidirect
248. #41	C₂²×#261	semidirect
252. C₂×Q₈	C₂²×#261	semidirect
260. C₂×D₄	C₂²×#261	semidirect
261. C₂×D₄	C₂²×#261	semidirect
277. C₂²×C₄	C₂²×#261	semidirect
283. C₁₃	C₂×C₄×H(5,𝔽₂)	semidirect
297. C₂³	C₂³×#261	semidirect
299. Q₈	C₂³×#261	semidirect
302. D₄	C₂³×#261	semidirect
318. C₂×C₄	C₂³×#261	semidirect
343. C₂	H(5,𝔽₂)×#261	direct (N × H)

Maximal subgroups

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

subgroup	index
H(5,𝔽₂)×#261	2
C₂×#11719631	2
C₂×#11719623	2
C₂×#41×#261	2
C₂²×D₄×#261	2
C₂×D₁₃×H(5,𝔽₂)	2
C₂×C₄×H(5,𝔽₂)	13

Subgroups — C2×H(5,𝔽2)×#261 #16809635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×H(5,𝔽₂)×#261 #16809635