Subgroups — C₂×#66104 #10619086

Order 640.

1460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#4150	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#4149	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#4097	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#4095	C₂	1	1	yes	maximal, characteristic, complemented
6	#66104	C₂	1	16	yes	maximal, direct product factor
7	C₂×#4064	C₂	1	2	yes	maximal, complemented
8	C₂×#4062	C₂	1	2	yes	maximal, complemented
9	C₂×D₅×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₂×#4057	C₂	1	2	yes	maximal, complemented
11	C₂²×#677	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#4047	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₅×#41	C₂²	1	1	yes	characteristic, complemented
15	#4150	—	2	4	no	—
16	#4150	C₂²	1	8	yes	complemented
17	#4149	—	2	4	no	—
18	#4149	C₂²	1	8	yes	complemented
19	C₂×#713	C₂²	1	2	yes	—
20	C₂×Q₈×D₅	C₂²	1	2	yes	complemented
21	C₂×#711	—	2	2	no	—
22	C₂×#711	C₂²	1	2	yes	complemented
23	C₂×D₄×D₅	—	2	2	no	—
24	C₂×D₄×D₅	C₂²	1	2	yes	—
25	C₂×#709	—	2	1	no	—
26	C₂×#709	—	2	1	no	—
27	C₂×#709	C₂²	1	1	yes	characteristic
28	C₂²×D₂₀	—	2	1	no	—
29	C₂²×D₂₀	C₂²	1	1	yes	characteristic
30	C₂²×Dic₁₀	—	2	1	no	—
31	C₂²×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
32	C₅×#135	C₂²	1	8	yes	complemented
33	C₂×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
38	#4097	C₂²	1	8	yes	complemented
39	#4095	C₂²	1	8	yes	complemented
40	C₂×#689	C₂²	1	2	yes	complemented
41	C₂×#688	C₂²	1	2	yes	complemented
42	C₂×#687	C₂²	1	2	yes	complemented
43	C₂×#686	C₂²	1	2	yes	complemented
44	C₂×#681	C₂²	1	1	yes	characteristic, complemented
45	#4064	C₂²	1	16	yes	complemented
46	#4062	C₂²	1	16	yes	complemented
47	D₅×SD₁₆	C₂²	1	16	yes	complemented
48	#4057	C₂²	1	16	yes	complemented
49	C₂×#677	C₂²	1	2	yes	complemented
50	C₂×#677	C₂²	1	2	yes	complemented
51	C₂×#677	C₂²	1	8	yes	complemented
52	#4047	C₂²	1	8	yes	complemented
53	C₂×#676	C₂²	1	2	yes	complemented
54	C₂×C₈×D₅	C₂²	1	2	yes	complemented
55	C₂×#577	—	5	1	no	maximal, Sylow
56	C₂³×D₅	—	2	1	no	—
57	C₂³×D₅	—	2	2	no	—
58	C₅×#41	—	2	2	no	—
59	C₅×#41	—	2	2	no	—
60	C₅×#41	C₂³	1	4	yes	—
61	C₅×#41	C₂³	1	4	yes	complemented
62	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂×C₅×D₄	—	2	1	no	—
65	C₂×C₅×D₄	—	2	1	no	—
66	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₅	—	2	1	no	—
69	C₂²×C₄×C₅	—	2	1	no	—
70	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊D₅	—	2	2	no	—
72	C₂×C₂²⋊D₅	—	2	2	no	—
73	C₂×C₂²⋊D₅	D₄	1	2	yes	—
74	C₂²×Dic₅	—	2	1	no	—
75	C₂²×Dic₅	—	2	2	no	—
76	#713	—	2	4	no	—
77	#713	C₂³	1	8	yes	—
78	Q₈×D₅	—	2	4	no	—
79	Q₈×D₅	C₂³	1	8	yes	complemented
80	#711	—	2	16	no	—
81	#711	—	2	4	no	—
82	#711	C₂³	1	8	yes	complemented
83	D₄×D₅	—	2	16	no	—
84	D₄×D₅	—	2	4	no	—
85	D₄×D₅	C₂³	1	8	yes	—
86	#709	—	2	8	no	—
87	#709	—	2	8	no	—
88	#709	D₄	1	4	yes	—
89	#709	C₂³	1	4	yes	—
90	C₂×D₂₀	—	2	2	no	—
91	C₂×D₂₀	—	2	1	no	—
92	C₂×D₂₀	—	2	2	no	—
93	C₂×D₂₀	—	2	8	no	—
94	C₂×D₂₀	D₄	1	1	yes	characteristic
95	C₂×D₂₀	C₂³	1	2	yes	—
96	C₂×D₂₀	C₂³	1	4	yes	—
97	C₂×C₄×D₅	—	2	2	no	—
98	C₂×C₄×D₅	—	2	2	no	—
99	C₂×C₄×D₅	C₂³	1	2	yes	—
100	C₂×Dic₁₀	—	2	1	no	—
101	C₂×Dic₁₀	—	2	2	no	—
102	C₂×Dic₁₀	—	2	2	no	—
103	C₂×Dic₁₀	—	2	8	no	—
104	C₂×Dic₁₀	D₄	1	1	yes	characteristic
105	C₂×Dic₁₀	C₂³	1	2	yes	—
106	C₂×Dic₁₀	C₂³	1	4	yes	complemented
107	C₅×Q₁₆	C₂³	1	4	yes	complemented
108	C₅×SD₁₆	C₂³	1	4	yes	complemented
109	C₅×SD₁₆	C₂³	1	4	yes	complemented
110	C₅×D₈	C₂³	1	4	yes	complemented
111	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
112	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
113	C₂×C₅×C₈	C₂³	1	4	yes	complemented
114	#689	C₂³	1	8	yes	complemented
115	#688	C₂³	1	8	yes	complemented
116	#687	C₂³	1	8	yes	complemented
117	#686	C₂³	1	8	yes	complemented
118	#681	C₂³	1	4	yes	complemented
119	C₂×#168	C₂³	1	2	yes	—
120	#677	C₂³	1	8	yes	complemented
121	#677	C₂³	1	8	yes	complemented
122	#676	C₂³	1	8	yes	complemented
123	C₈×D₅	C₂³	1	8	yes	complemented
124	C₂×2₋¹⁺⁴	—	5	1	no	—
125	C₂×H(5,𝔽₂)	—	5	1	no	—
126	#577	—	5	16	no	—
127	C₂×#137	—	5	1	no	—
128	C₂×#137	—	5	2	no	—
129	C₂×AGL(1,ℤ/8)	—	5	1	no	—
130	C₂×AGL(1,ℤ/8)	—	5	2	no	—
131	C₂×#135	—	5	2	no	—
132	C₂×#135	D₅	1	1	yes	characteristic, complemented
133	C₂²×SD₁₆	—	5	2	no	—
134	C₂²×SD₁₆	—	5	1	no	—
135	C₂×#131	—	5	1	no	—
136	C₂³×C₅	—	2	1	no	—
137	C₂³×C₅	—	2	1	no	—
138	C₂³×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×D₅	—	2	2	no	—
140	C₂²×D₅	—	2	4	no	—
141	C₂²×D₅	—	2	8	no	—
142	C₂²×D₅	—	8	4	no	—
143	C₂²×D₅	—	8	2	no	—
144	C₂²×D₅	C₂×D₄	1	2	yes	—
145	C₅×Q₈	—	2	1	no	—
146	C₅×Q₈	—	2	1	no	—
147	C₅×Q₈	C₂⁴	1	2	yes	—
148	C₅×Q₈	C₂⁴	1	2	yes	—
149	C₅×D₄	—	2	4	no	—
150	C₅×D₄	—	2	4	no	—
151	C₅×D₄	—	2	1	no	—
152	C₅×D₄	—	2	1	no	—
153	C₅×D₄	C₂⁴	1	2	yes	—
154	C₅×D₄	C₂⁴	1	2	yes	—
155	C₂×C₄×C₅	—	2	1	no	—
156	C₂×C₄×C₅	—	2	1	no	—
157	C₂×C₄×C₅	—	2	4	no	—
158	C₂×C₄×C₅	—	2	4	no	—
159	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
161	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₅	C₂⁴	1	2	yes	—
163	C₂²⋊D₅	—	2	8	no	—
164	C₂²⋊D₅	—	2	8	no	—
165	C₂²⋊D₅	C₂×D₄	1	8	yes	—
166	C₂×Dic₅	—	2	2	no	—
167	C₂×Dic₅	—	2	4	no	—
168	C₂×Dic₅	—	2	8	no	—
169	C₂×Dic₅	C₂×D₄	1	2	yes	—
170	D₂₀	—	2	8	no	—
171	D₂₀	—	2	4	no	—
172	D₂₀	—	2	2	no	—
173	D₂₀	C₂×D₄	1	4	yes	—
174	D₂₀	C₂⁴	1	4	yes	—
175	C₄×D₅	—	2	8	no	—
176	C₄×D₅	—	2	8	no	—
177	C₄×D₅	C₂×D₄	1	4	yes	—
178	C₄×D₅	C₂⁴	1	4	yes	—
179	Dic₁₀	—	2	4	no	—
180	Dic₁₀	—	2	2	no	—
181	Dic₁₀	—	2	8	no	—
182	Dic₁₀	C₂×D₄	1	4	yes	—
183	Dic₁₀	C₂⁴	1	4	yes	—
184	C₅×C₈	C₂⁴	1	2	yes	—
185	C₅×C₈	C₂⁴	1	2	yes	—
186	#168	C₂⁴	1	4	yes	—
187	2₋¹⁺⁴	—	5	8	no	—
188	2₋¹⁺⁴	—	10	4	no	—
189	H(5,𝔽₂)	—	5	8	no	—
190	H(5,𝔽₂)	—	10	4	no	—
191	C₂×#41	—	5	1	no	—
192	C₂×#41	—	5	2	no	—
193	C₂×#41	—	5	2	no	—
194	C₂×#41	—	10	1	no	—
195	C₂×#41	—	10	1	no	—
196	C₂×#41	—	10	2	no	—
197	C₂×#41	C₂×D₅	1	1	yes	characteristic
198	C₂×#41	C₂×D₅	1	1	yes	characteristic, complemented
199	C₂²×Q₈	—	5	2	no	—
200	C₂²×Q₈	—	5	1	no	—
201	C₂²×Q₈	—	10	1	no	—
202	C₂²×D₄	—	5	2	no	—
203	C₂²×D₄	—	5	1	no	—
204	C₂²×D₄	—	10	1	no	—
205	C₂²×D₄	—	10	2	no	—
206	#137	—	5	8	no	—
207	#137	—	5	16	no	—
208	AGL(1,ℤ/8)	—	5	8	no	—
209	AGL(1,ℤ/8)	—	5	16	no	—
210	#135	—	5	16	no	—
211	#135	C₂×D₅	1	8	yes	complemented
212	C₂×Q₁₆	—	5	2	no	—
213	C₂×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
214	C₂×SD₁₆	—	5	2	no	—
215	C₂×SD₁₆	—	5	2	no	—
216	C₂×SD₁₆	—	5	16	no	—
217	C₂×SD₁₆	—	5	2	no	—
218	C₂×SD₁₆	—	5	2	no	—
219	C₂×SD₁₆	—	5	8	no	—
220	C₂×SD₁₆	C₂×D₅	1	1	yes	characteristic, complemented
221	C₂×SD₁₆	C₂×D₅	1	1	yes	characteristic, complemented
222	C₂×D₈	—	5	2	no	—
223	C₂×D₈	C₂×D₅	1	1	yes	characteristic, complemented
224	#131	—	5	8	no	—
225	C₂×M₁₆	—	5	1	no	—
226	C₂×M₁₆	—	5	2	no	—
227	C₂²×C₈	—	5	2	no	—
228	C₂²×C₈	C₂×D₅	1	1	yes	characteristic, complemented
229	C₂²×C₅	—	2	2	no	—
230	C₂²×C₅	—	2	2	no	—
231	C₂²×C₅	—	2	2	no	—
232	C₂²×C₅	—	4	2	no	—
233	C₂²×C₅	—	4	2	no	—
234	C₂²×C₅	C₂²×D₄	1	2	yes	—
235	C₂²×C₅	C₂²×D₄	1	1	yes	characteristic
236	C₂×D₅	—	2	4	no	—
237	C₂×D₅	—	2	4	no	—
238	C₂×D₅	—	4	4	no	—
239	C₂×D₅	—	8	8	no	—
240	C₂×D₅	—	8	4	no	—
241	C₂×D₅	C₂²×D₄	1	4	yes	—
242	C₄×C₅	—	2	2	no	—
243	C₄×C₅	—	2	2	no	—
244	C₄×C₅	C₂²×D₄	1	2	yes	—
245	C₄×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₄×C₅	C₂⁵	1	1	yes	characteristic
247	Dic₅	—	2	4	no	—
248	Dic₅	C₂²×D₄	1	4	yes	—
249	C₂⁴	—	10	2	no	—
250	C₂⁴	—	10	1	no	—
251	#41	—	2	2	no	—
252	#41	—	2	2	no	—
253	#41	—	5	4	no	—
254	#41	—	5	4	no	—
255	#41	—	5	8	no	—
256	#41	—	5	8	no	—
257	#41	—	10	8	no	—
258	#41	—	10	8	no	—
259	#41	—	10	4	no	—
260	#41	—	10	4	no	—
261	#41	—	10	16	no	—
262	#41	C₂²×D₅	1	4	yes	—
263	#41	C₂²×D₅	1	4	yes	complemented
264	C₂×Q₈	—	5	1	no	—
265	C₂×Q₈	—	5	8	no	—
266	C₂×Q₈	—	5	2	no	—
267	C₂×Q₈	—	5	4	no	—
268	C₂×Q₈	—	10	2	no	—
269	C₂×Q₈	—	10	8	no	—
270	C₂×Q₈	—	10	4	no	—
271	C₂×Q₈	—	10	1	no	—
272	C₂×Q₈	—	10	2	no	—
273	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
274	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	5	2	no	—
278	C₂×D₄	—	5	8	no	—
279	C₂×D₄	—	5	1	no	—
280	C₂×D₄	—	5	2	no	—
281	C₂×D₄	—	5	4	no	—
282	C₂×D₄	—	10	8	no	—
283	C₂×D₄	—	10	2	no	—
284	C₂×D₄	—	10	4	no	—
285	C₂×D₄	—	10	2	no	—
286	C₂×D₄	—	10	16	no	—
287	C₂×D₄	—	10	2	no	—
288	C₂×D₄	—	10	1	no	—
289	C₂×D₄	—	10	2	no	—
290	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
291	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	5	2	no	—
295	C₂²×C₄	—	10	2	no	—
296	C₂²×C₄	—	10	2	no	—
297	C₂²×C₄	—	10	2	no	—
298	C₂²×C₄	—	10	1	no	—
299	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
300	Q₁₆	—	5	8	no	—
301	Q₁₆	C₂²×D₅	1	4	yes	complemented
302	SD₁₆	—	5	8	no	—
303	SD₁₆	—	5	8	no	—
304	SD₁₆	—	5	8	no	—
305	SD₁₆	—	5	8	no	—
306	SD₁₆	C₂²×D₅	1	4	yes	complemented
307	SD₁₆	C₂²×D₅	1	4	yes	complemented
308	D₈	—	5	8	no	—
309	D₈	C₂²×D₅	1	4	yes	complemented
310	M₁₆	—	5	4	no	—
311	M₁₆	—	5	8	no	—
312	C₂×C₈	—	5	2	no	—
313	C₂×C₈	—	5	8	no	—
314	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
315	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
316	C₂×C₈	C₂²×D₅	1	4	yes	complemented
317	C₂×C₅	—	2	2	no	—
318	C₂×C₅	—	4	2	no	—
319	C₂×C₅	—	4	2	no	—
320	C₂×C₅	#577	1	2	yes	complemented
321	C₂×C₅	C₂³×D₄	1	1	yes	characteristic
322	D₅	—	2	4	no	—
323	D₅	—	4	4	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	5	2	no	—
327	C₂³	—	10	8	no	—
328	C₂³	—	10	2	no	—
329	C₂³	—	10	4	no	—
330	C₂³	—	40	2	no	—
331	C₂³	—	40	4	no	—
332	C₂³	D₄×D₅	1	1	yes	characteristic
333	Q₈	—	2	1	no	—
334	Q₈	—	2	1	no	—
335	Q₈	—	5	4	no	—
336	Q₈	—	5	4	no	—
337	Q₈	—	10	8	no	—
338	Q₈	—	10	4	no	—
339	Q₈	—	10	2	no	—
340	Q₈	C₂³×D₅	1	2	yes	—
341	Q₈	C₂³×D₅	1	2	yes	—
342	D₄	—	2	4	no	—
343	D₄	—	2	4	no	—
344	D₄	—	2	1	no	—
345	D₄	—	2	1	no	—
346	D₄	—	5	8	no	—
347	D₄	—	5	4	no	—
348	D₄	—	5	4	no	—
349	D₄	—	10	8	no	—
350	D₄	—	10	8	no	—
351	D₄	—	10	8	no	—
352	D₄	—	10	4	no	—
353	D₄	—	10	2	no	—
354	D₄	C₂³×D₅	1	2	yes	—
355	D₄	C₂³×D₅	1	2	yes	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	5	2	no	—
361	C₂×C₄	—	5	4	no	—
362	C₂×C₄	—	5	4	no	—
363	C₂×C₄	—	10	8	no	—
364	C₂×C₄	—	10	8	no	—
365	C₂×C₄	—	10	8	no	—
366	C₂×C₄	—	10	4	no	—
367	C₂×C₄	—	10	2	no	—
368	C₂×C₄	D₄×D₅	1	2	yes	—
369	C₂×C₄	D₄×D₅	1	1	yes	characteristic
370	C₂×C₄	C₂³×D₅	1	2	yes	—
371	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
372	C₈	—	5	4	no	—
373	C₈	C₂³×D₅	1	2	yes	—
374	C₈	C₂³×D₅	1	2	yes	—
375	C₅	C₂×#577	1	1	yes	characteristic, complemented, Sylow
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	5	4	no	—
382	C₂²	—	10	4	no	—
383	C₂²	—	10	4	no	—
384	C₂²	—	20	4	no	—
385	C₂²	—	40	4	no	—
386	C₂²	—	40	8	no	—
387	C₂²	C₂×D₄×D₅	1	2	yes	—
388	C₂²	C₂×D₄×D₅	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	5	4	no	—
392	C₄	—	10	4	no	—
393	C₄	C₂×D₄×D₅	1	2	yes	—
394	C₄	C₂×D₄×D₅	1	1	yes	characteristic
395	C₄	C₂⁴×D₅	1	1	yes	characteristic
396	C₂	—	2	2	no	—
397	C₂	—	4	2	no	—
398	C₂	—	4	2	no	—
399	C₂	—	10	4	no	—
400	C₂	—	20	4	no	—
401	C₂	#66104	1	2	yes	direct product factor
402	C₂	C₂²×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁵
Frattini	C₄	C₂⁴×D₅
Fitting	C₂×C₅×#135	C₂
socle	C₂²×C₅	C₂²×D₄
hypercenter	C₂×#135	D₅
hypocenter	C₅	C₂×#577
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#4150	C₂	semidirect
2. C₂×#4149	C₂	semidirect
3. C₂×C₅×#135	C₂	semidirect
4. C₂×#4097	C₂	semidirect
5. C₂×#4095	C₂	semidirect
6. #66104	C₂	direct (N × H)
7. C₂×#4064	C₂	semidirect
8. C₂×#4062	C₂	semidirect
9. C₂×D₅×SD₁₆	C₂	semidirect
10. C₂×#4057	C₂	semidirect
11. C₂²×#677	C₂	semidirect
12. C₂×#4047	C₂	semidirect
14. C₂×C₅×#41	C₂²	semidirect
16. #4150	C₂²	semidirect
18. #4149	C₂²	semidirect
20. C₂×Q₈×D₅	C₂²	semidirect
22. C₂×#711	C₂²	semidirect
31. C₂²×Dic₁₀	C₂²	semidirect
32. C₅×#135	C₂²	semidirect
33. C₂×C₅×Q₁₆	C₂²	semidirect
34. C₂×C₅×SD₁₆	C₂²	semidirect
35. C₂×C₅×SD₁₆	C₂²	semidirect
36. C₂×C₅×D₈	C₂²	semidirect
37. C₂²×C₅×C₈	C₂²	semidirect
38. #4097	C₂²	semidirect
39. #4095	C₂²	semidirect
40. C₂×#689	C₂²	semidirect
41. C₂×#688	C₂²	semidirect
42. C₂×#687	C₂²	semidirect
43. C₂×#686	C₂²	semidirect
44. C₂×#681	C₂²	semidirect
45. #4064	C₂²	semidirect
46. #4062	C₂²	semidirect
47. D₅×SD₁₆	C₂²	semidirect
48. #4057	C₂²	semidirect
49. C₂×#677	C₂²	semidirect
50. C₂×#677	C₂²	semidirect
51. C₂×#677	C₂²	semidirect
52. #4047	C₂²	semidirect
53. C₂×#676	C₂²	semidirect
54. C₂×C₈×D₅	C₂²	semidirect
61. C₅×#41	C₂³	semidirect
79. Q₈×D₅	C₂³	semidirect
82. #711	C₂³	semidirect
106. C₂×Dic₁₀	C₂³	semidirect
107. C₅×Q₁₆	C₂³	semidirect
108. C₅×SD₁₆	C₂³	semidirect
109. C₅×SD₁₆	C₂³	semidirect
110. C₅×D₈	C₂³	semidirect
113. C₂×C₅×C₈	C₂³	semidirect
114. #689	C₂³	semidirect
115. #688	C₂³	semidirect
116. #687	C₂³	semidirect
117. #686	C₂³	semidirect
118. #681	C₂³	semidirect
120. #677	C₂³	semidirect
121. #677	C₂³	semidirect
122. #676	C₂³	semidirect
123. C₈×D₅	C₂³	semidirect
132. C₂×#135	D₅	semidirect
198. C₂×#41	C₂×D₅	semidirect
211. #135	C₂×D₅	semidirect
213. C₂×Q₁₆	C₂×D₅	semidirect
220. C₂×SD₁₆	C₂×D₅	semidirect
221. C₂×SD₁₆	C₂×D₅	semidirect
223. C₂×D₈	C₂×D₅	semidirect
228. C₂²×C₈	C₂×D₅	semidirect
263. #41	C₂²×D₅	semidirect
301. Q₁₆	C₂²×D₅	semidirect
306. SD₁₆	C₂²×D₅	semidirect
307. SD₁₆	C₂²×D₅	semidirect
309. D₈	C₂²×D₅	semidirect
316. C₂×C₈	C₂²×D₅	semidirect
320. C₂×C₅	#577	semidirect
375. C₅	C₂×#577	semidirect
401. C₂	#66104	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×#4150	2
C₂×#4149	2
C₂×C₅×#135	2
C₂×#4097	2
C₂×#4095	2
#66104	2
C₂×#4064	2
C₂×#4062	2
C₂×D₅×SD₁₆	2
C₂×#4057	2
C₂²×#677	2
C₂×#4047	2
C₂×#577	5

Subgroups — C2×#66104 #10619086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#66104 #10619086