Subgroups — C₂×#72241315 #72341277

Order 2048.

Only the 2584 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 592 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#494596	C₂	1	4	yes	maximal, complemented
2	C₂×#147767	C₂	1	4	yes	maximal, complemented
3	C₂×#493430	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#146577	C₂	1	2	yes	maximal, complemented
5	C₂×#6385980	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#60388	C₂	1	1	yes	maximal, characteristic
7	#72241315	C₂	1	16	yes	maximal, direct product factor
8	C₂×#392135	C₂	1	2	yes	maximal, complemented
9	C₂²×H(7,𝔽₂)	C₂²	1	1	yes	characteristic
10	C₂²×#3498	C₂²	1	1	yes	characteristic
11	C₂×#60388	C₄	1	8	yes	complemented
12	C₂×#60388	C₂²	1	8	yes	—
13	C₂²×#3018	C₄	1	2	yes	complemented
14	C₂²×#3021	C₄	1	2	yes	complemented
15	C₂²×#3019	C₄	1	2	yes	complemented
16	C₂²×#3019	C₂²	1	2	yes	—
17	C₂³×#453	C₄	1	2	yes	complemented
18	C₂³×#453	C₂²	1	2	yes	—
19	C₂²×#2888	C₂²	1	1	yes	characteristic
20	C₂×#34364	C₂²	1	2	yes	complemented
21	C₂²×#2127	C₂²	1	2	yes	complemented
22	C₂³×#353	C₂²	1	2	yes	complemented
23	#6385980	C₂²	1	8	yes	complemented
24	C₂×#21750	C₂²	1	2	yes	complemented
25	C₂×#20609	C₂²	1	8	yes	complemented
26	C₂×#20585	C₂²	1	2	yes	—
27	C₂×#20585	C₂²	1	2	yes	—
28	#494596	C₂²	1	32	yes	complemented
29	#493430	C₂²	1	8	yes	complemented
30	C₂×#12574	C₂²	1	8	yes	complemented
31	#392135	C₂²	1	16	yes	complemented
32	#147767	C₂²	1	32	yes	complemented
33	#146577	C₂²	1	16	yes	complemented
34	C₂×H(7,𝔽₂)	C₂×C₄	1	4	yes	complemented
35	C₂×H(7,𝔽₂)	C₂³	1	4	yes	—
36	C₂²×#585	C₂×C₄	1	2	yes	complemented
37	C₂³×H(5,𝔽₂)	C₂×C₄	1	2	yes	complemented
38	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
39	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
40	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
41	C₂×#3498	C₂×C₄	1	4	yes	—
42	C₂×#3498	D₄	1	4	yes	—
43	C₂×#3498	D₄	1	4	yes	—
44	C₂×#3498	C₂³	1	4	yes	—
45	C₂²×#535	C₂×C₄	1	1	yes	characteristic
46	C₂²×#535	C₂×C₄	1	1	yes	characteristic
47	C₂²×#535	D₄	1	1	yes	characteristic
48	C₂²×#535	D₄	1	1	yes	characteristic
49	C₂²×#535	D₄	1	1	yes	characteristic
50	C₂²×#535	C₂³	1	1	yes	characteristic
51	C₂²×#532	C₂×C₄	1	1	yes	characteristic
52	C₂²×#532	D₄	1	1	yes	characteristic
53	C₂²×#532	D₄	1	1	yes	characteristic
54	C₂³×#127	C₂×C₄	1	1	yes	characteristic
55	C₂³×#127	D₄	1	1	yes	characteristic
56	C₂³×#127	C₂³	1	1	yes	characteristic
57	C₂²×C₄×#41	D₄	1	1	yes	characteristic
58	C₂×#3021	C₂×C₄	1	16	yes	complemented
59	C₂×#3019	C₂×C₄	1	8	yes	complemented
60	C₂×#3019	C₂×C₄	1	16	yes	complemented
61	C₂×#3019	C₂³	1	8	yes	—
62	C₂×#3018	C₂×C₄	1	16	yes	complemented
63	C₂²×#455	C₂×C₄	1	4	yes	complemented
64	C₂²×#453	C₂×C₄	1	4	yes	—
65	C₂²×#453	C₂×C₄	1	4	yes	—
66	C₂²×#453	C₂×C₄	1	8	yes	—
67	C₂²×#453	C₂×C₄	1	4	yes	complemented
68	C₂²×#453	C₂×C₄	1	16	yes	complemented
69	C₂²×#453	D₄	1	16	yes	—
70	C₂²×#453	D₄	1	16	yes	—
71	C₂²×#453	C₂³	1	8	yes	—
72	C₂×#2888	C₂×C₄	1	4	yes	complemented
73	C₂×#2888	C₂³	1	4	yes	—
74	C₂²×#413	C₂×C₄	1	2	yes	complemented
75	C₂³×#100	C₂×C₄	1	2	yes	complemented
76	C₂³×#100	C₂³	1	2	yes	—
77	C₂³×#99	D₄	1	4	yes	—
78	C₂³×#99	D₄	1	4	yes	—
79	C₂³×#99	C₂³	1	4	yes	—
80	#34364	C₂³	1	8	yes	complemented
81	C₂×#2308	C₂³	1	4	yes	—
82	C₂×#2127	C₂³	1	8	yes	complemented
83	C₂²×#353	C₂³	1	8	yes	complemented
84	#21750	C₂³	1	8	yes	complemented
85	#20609	C₂³	1	32	yes	complemented
86	#20585	D₄	1	8	yes	—
87	#20585	C₂³	1	8	yes	—
88	#20585	C₂³	1	8	yes	—
89	#12574	C₂³	1	32	yes	complemented
90	C₂×#585	C₂²×C₄	1	8	yes	complemented
91	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	4	yes	complemented
92	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
93	C₂²×H(5,𝔽₂)	C₂²×C₄	1	4	yes	—
94	C₂²×H(5,𝔽₂)	C₂²×C₄	1	4	yes	—
95	C₂²×H(5,𝔽₂)	C₂²×C₄	1	8	yes	complemented
96	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
97	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
98	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
99	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
100	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
101	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
102	C₂²×H(5,𝔽₂)	#41	1	4	yes	—
103	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
104	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	—
105	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
106	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
107	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
108	C₂³×#41	C₂×D₄	1	1	yes	characteristic
109	C₂³×#41	C₂×D₄	1	1	yes	characteristic
110	C₂³×#41	C₂×D₄	1	1	yes	characteristic
111	C₂³×#41	C₂×D₄	1	1	yes	characteristic
112	C₂³×#41	#41	1	2	yes	—
113	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
114	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
115	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
116	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×D₄	C₂×D₄	1	2	yes	—
118	C₂⁴×D₄	C₂×D₄	1	2	yes	—
119	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
120	C₂⁴×D₄	#41	1	2	yes	—
121	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
122	C₂×#535	C₂²⋊C₄	1	4	yes	complemented
123	C₂×#535	C₂²⋊C₄	1	4	yes	complemented
124	C₂×#535	C₂²⋊C₄	1	4	yes	complemented
125	C₂×#535	C₂²⋊C₄	1	4	yes	complemented
126	C₂×#535	C₂²⋊C₄	1	4	yes	complemented
127	C₂×#535	C₂²×C₄	1	2	yes	—
128	C₂×#535	C₂²×C₄	1	4	yes	—
129	C₂×#535	C₂²×C₄	1	4	yes	—
130	C₂×#535	C₂×D₄	1	2	yes	—
131	C₂×#535	C₂×D₄	1	4	yes	—
132	C₂×#535	C₂×D₄	1	4	yes	—
133	C₂×#535	C₂×D₄	1	2	yes	—
134	C₂×#535	C₂×D₄	1	4	yes	—
135	C₂×#535	C₂⁴	1	2	yes	—
136	C₂×#532	C₂²⋊C₄	1	4	yes	complemented
137	C₂×#532	C₂²⋊C₄	1	4	yes	complemented
138	C₂×#532	C₂²⋊C₄	1	4	yes	complemented
139	C₂×#532	C₂²×C₄	1	4	yes	—
140	C₂×#532	C₂×D₄	1	4	yes	—
141	C₂×#532	C₂×D₄	1	4	yes	—
142	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic, complemented
143	C₂²×#127	C₂²⋊C₄	1	4	yes	complemented
144	C₂²×#127	C₂²⋊C₄	1	4	yes	complemented
145	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic, complemented
146	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic, complemented
147	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic, complemented
148	C₂²×#127	C₂²×C₄	1	2	yes	—
149	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
150	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
151	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
152	C₂²×#127	C₂²×C₄	1	4	yes	—
153	C₂²×#127	C₂×D₄	1	2	yes	—
154	C₂²×#127	C₂×D₄	1	8	yes	—
155	C₂²×#127	C₂×D₄	1	8	yes	—
156	C₂²×#127	C₂×D₄	1	2	yes	—
157	C₂²×#127	C₂×D₄	1	1	yes	characteristic
158	C₂²×#127	C₂×D₄	1	1	yes	characteristic
159	C₂²×#127	C₂×D₄	1	1	yes	characteristic
160	C₂²×#127	C₂×D₄	1	4	yes	—
161	C₂²×#127	C₂⁴	1	2	yes	—
162	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic, complemented
163	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic, complemented
164	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic, complemented
165	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic, complemented
166	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
167	C₂²×#124	C₂×D₄	1	1	yes	characteristic
168	C₂×C₄×#41	C₂²⋊C₄	1	4	yes	complemented
169	C₂×C₄×#41	C₂×D₄	1	4	yes	—
170	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic, complemented
171	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic, complemented
172	C₂²×#117	C₂×D₄	1	1	yes	characteristic
173	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
174	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic, complemented
175	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic, complemented
176	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
177	C₂×#455	C₂²×C₄	1	16	yes	complemented
178	C₂×#453	C₂²⋊C₄	1	16	yes	complemented
179	C₂×#453	C₂²⋊C₄	1	16	yes	complemented
180	C₂×#453	C₂²⋊C₄	1	16	yes	complemented
181	C₂×#453	C₂²⋊C₄	1	16	yes	complemented
182	C₂×#453	C₂²⋊C₄	1	64	yes	complemented
183	C₂×#453	C₂²×C₄	1	16	yes	—
184	C₂×#453	C₂²×C₄	1	16	yes	—
185	C₂×#453	C₂²×C₄	1	16	yes	complemented
186	C₂×#453	C₂×D₄	1	64	yes	—
187	C₂×#413	C₂²×C₄	1	8	yes	complemented
188	C₂²×#100	C₂²×C₄	1	4	yes	—
189	C₂²×#100	C₂²×C₄	1	4	yes	—
190	C₂²×#100	C₂²×C₄	1	8	yes	complemented
191	C₂²×#100	C₂×D₄	1	8	yes	—
192	C₂²×#100	C₂×D₄	1	8	yes	—
193	C₂²×#100	C₂⁴	1	4	yes	—
194	C₂²×#99	C₂×D₄	1	16	yes	—
195	C₂²×#99	C₂×D₄	1	16	yes	—
196	C₂²×#99	C₂⁴	1	8	yes	—
197	#2308	C₂×D₄	1	8	yes	—
198	#2308	C₂⁴	1	8	yes	—
199	C₂⁶	C₄×D₄	1	2	yes	—
200	C₂⁶	#121	1	2	yes	—
201	C₂⁶	C₂²×D₄	1	2	yes	—
202	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	8	yes	—
203	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	8	yes	—
204	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	16	yes	—
205	C₂×H(5,𝔽₂)	C₂³×C₄	1	8	yes	—
206	C₂×H(5,𝔽₂)	C₂²×D₄	1	16	yes	—
207	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
209	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
211	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	complemented
213	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	complemented
214	C₂²×#41	C₄×D₄	1	4	yes	—
215	C₂²×#41	C₄×D₄	1	4	yes	—
216	C₂²×#41	#120	1	2	yes	—
217	C₂²×#41	#120	1	2	yes	—
218	C₂²×#41	#121	1	4	yes	—
219	C₂²×#41	#121	1	4	yes	—
220	C₂²×#41	#123	1	2	yes	—
221	C₂²×#41	#123	1	2	yes	—
222	C₂²×#41	#123	1	4	yes	—
223	C₂²×#41	C₂³×C₄	1	2	yes	—
224	C₂²×#41	C₂²×D₄	1	2	yes	—
225	C₂²×#41	C₂²×D₄	1	2	yes	—
226	C₂²×#41	C₂²×D₄	1	2	yes	—
227	C₂²×#41	C₂²×D₄	1	2	yes	—
228	C₂²×#41	C₂×#41	1	4	yes	—
229	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂³×Q₈	#123	1	1	yes	characteristic
232	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
236	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
238	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
239	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	complemented
240	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	complemented
241	C₂³×D₄	C₄×D₄	1	4	yes	—
242	C₂³×D₄	C₄×D₄	1	2	yes	—
243	C₂³×D₄	C₄×D₄	1	4	yes	—
244	C₂³×D₄	C₄×D₄	1	2	yes	—
245	C₂³×D₄	C₄×D₄	1	4	yes	—
246	C₂³×D₄	C₄×D₄	1	4	yes	—
247	C₂³×D₄	#120	1	4	yes	—
248	C₂³×D₄	#120	1	4	yes	—
249	C₂³×D₄	#120	1	1	yes	characteristic
250	C₂³×D₄	#120	1	1	yes	characteristic
251	C₂³×D₄	#120	1	4	yes	—
252	C₂³×D₄	#120	1	4	yes	—
253	C₂³×D₄	#120	1	2	yes	—
254	C₂³×D₄	#121	1	4	yes	—
255	C₂³×D₄	#121	1	2	yes	—
256	C₂³×D₄	#121	1	2	yes	—
257	C₂³×D₄	#121	1	4	yes	—
258	C₂³×D₄	#121	1	4	yes	—
259	C₂³×D₄	#121	1	4	yes	—
260	C₂³×D₄	#123	1	1	yes	characteristic
261	C₂³×D₄	#123	1	4	yes	—
262	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
263	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
264	C₂³×D₄	C₂³×C₄	1	2	yes	—
265	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
266	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
267	C₂³×D₄	C₂²×D₄	1	2	yes	—
268	C₂³×D₄	C₂²×D₄	1	4	yes	—
269	C₂³×D₄	C₂²×D₄	1	4	yes	—
270	C₂³×D₄	C₂²×D₄	1	4	yes	—
271	C₂³×D₄	C₂²×D₄	1	2	yes	—
272	C₂³×D₄	C₂²×D₄	1	4	yes	—
273	C₂³×D₄	C₂²×D₄	1	2	yes	—
274	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
275	C₂³×D₄	C₂×#41	1	2	yes	—
276	C₂³×D₄	C₂×#41	1	2	yes	—
277	C₂³×D₄	C₂×#41	1	4	yes	—
278	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
279	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
280	C₂³×D₄	C₂⁵	1	1	yes	characteristic
281	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂⁴×C₄	C₄×D₄	1	2	yes	—
284	C₂⁴×C₄	#121	1	2	yes	—
285	C₂⁴×C₄	#123	1	2	yes	—
286	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	4	yes	complemented
288	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
293	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
294	C₂×#127	C₂×C₂²⋊C₄	1	16	yes	—
295	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
296	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
297	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
298	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
299	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	complemented
300	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	complemented
301	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	complemented
302	C₂×#127	#120	1	16	yes	—
303	C₂×#127	#120	1	16	yes	—
304	C₂×#127	#120	1	4	yes	—
305	C₂×#127	#120	1	4	yes	—
306	C₂×#127	#120	1	4	yes	—
307	C₂×#127	#120	1	4	yes	—
308	C₂×#127	C₂³×C₄	1	2	yes	—
309	C₂×#127	C₂³×C₄	1	2	yes	—
310	C₂×#127	C₂³×C₄	1	2	yes	—
311	C₂×#127	C₂²×D₄	1	2	yes	—
312	C₂×#127	C₂²×D₄	1	2	yes	—
313	C₂×#127	C₂²×D₄	1	2	yes	—
314	C₂×#127	C₂²×D₄	1	16	yes	—
315	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
316	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
317	C₂×#124	C₂×C₂²⋊C₄	1	4	yes	complemented
318	C₂×#124	C₂×C₂²⋊C₄	1	4	yes	complemented
319	C₂×#124	C₂×C₂²⋊C₄	1	4	yes	complemented
320	C₂×#124	C₂×C₂²⋊C₄	1	4	yes	complemented
321	C₂×#124	C₂³×C₄	1	2	yes	—
322	C₂×#124	C₂²×D₄	1	2	yes	—
323	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
324	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	complemented
325	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	complemented
326	C₂×#117	C₂²×D₄	1	2	yes	—
327	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
328	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
329	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
330	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
331	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
332	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
333	C₂²×C₄²	C₂×C₂²⋊C₄	1	4	yes	complemented
334	C₂²×C₄²	C₂×C₂²⋊C₄	1	4	yes	complemented
335	C₂²×C₄²	#120	1	4	yes	—
336	C₂²×C₄²	#120	1	4	yes	—
337	C₂²×C₄²	C₂²×D₄	1	2	yes	—
338	#453	C₂×C₂²⋊C₄	1	64	yes	complemented
339	#453	C₂×C₂²⋊C₄	1	64	yes	complemented
340	C₂×#100	C₂×C₂²⋊C₄	1	8	yes	—
341	C₂×#100	C₂×C₂²⋊C₄	1	8	yes	—
342	C₂×#100	C₂×C₂²⋊C₄	1	16	yes	—
343	C₂×#100	C₂³×C₄	1	8	yes	—
344	C₂×#100	C₂²×D₄	1	16	yes	—
345	C₂⁵	#386	1	1	yes	characteristic
346	C₂⁵	#386	1	1	yes	characteristic
347	C₂⁵	#386	1	2	yes	—
348	C₂⁵	#386	1	4	yes	—
349	C₂⁵	#386	1	4	yes	—
350	C₂⁵	C₂×C₄×D₄	1	2	yes	—
351	C₂⁵	C₂×C₄×D₄	1	2	yes	—
352	C₂⁵	C₂×C₄×D₄	1	4	yes	—
353	C₂⁵	C₂×#120	1	2	yes	—
354	C₂⁵	C₂×#120	1	1	yes	characteristic
355	C₂⁵	C₂×#121	1	2	yes	—
356	C₂⁵	C₂×#121	1	2	yes	—
357	C₂⁵	C₂×#121	1	4	yes	—
358	C₂⁵	D₄²	1	8	yes	—
359	C₂⁵	D₄²	1	8	yes	—
360	C₂⁵	C₂³×D₄	1	2	yes	—
361	H(5,𝔽₂)	C₂²×C₂²⋊C₄	1	16	yes	—
362	C₂²×Q₈	#386	1	2	yes	—
363	C₂²×Q₈	#386	1	2	yes	—
364	C₂²×Q₈	C₂²×C₂²⋊C₄	1	2	yes	—
365	C₂²×Q₈	C₂²×C₂²⋊C₄	1	2	yes	—
366	C₂²×Q₈	C₂×#123	1	2	yes	—
367	C₂²×D₄	#379	1	2	yes	—
368	C₂²×D₄	#379	1	2	yes	—
369	C₂²×D₄	#379	1	2	yes	—
370	C₂²×D₄	#379	1	2	yes	—
371	C₂²×D₄	#379	1	8	yes	—
372	C₂²×D₄	#386	1	2	yes	—
373	C₂²×D₄	#386	1	2	yes	—
374	C₂²×D₄	#386	1	4	yes	—
375	C₂²×D₄	#386	1	2	yes	—
376	C₂²×D₄	#386	1	4	yes	—
377	C₂²×D₄	#386	1	4	yes	—
378	C₂²×D₄	#386	1	4	yes	—
379	C₂²×D₄	#386	1	2	yes	—
380	C₂²×D₄	#386	1	4	yes	—
381	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
382	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
383	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
384	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
385	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
386	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
387	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
388	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
389	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
390	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
391	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
392	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
393	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
394	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
395	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
396	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
397	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
398	C₂²×D₄	#518	1	2	yes	—
399	C₂²×D₄	#518	1	2	yes	—
400	C₂²×D₄	#518	1	4	yes	—
401	C₂²×D₄	C₂×#120	1	4	yes	—
402	C₂²×D₄	C₂×#120	1	8	yes	—
403	C₂²×D₄	C₂×#120	1	2	yes	—
404	C₂²×D₄	C₂×#120	1	2	yes	—
405	C₂²×D₄	C₂×#120	1	4	yes	—
406	C₂²×D₄	C₂×#120	1	2	yes	—
407	C₂²×D₄	C₂×#120	1	2	yes	—
408	C₂²×D₄	C₂×#120	1	4	yes	—
409	C₂²×D₄	C₂×#121	1	2	yes	—
410	C₂²×D₄	C₂×#121	1	2	yes	—
411	C₂²×D₄	C₂×#121	1	4	yes	—
412	C₂²×D₄	C₂×#121	1	4	yes	—
413	C₂²×D₄	C₂×#123	1	2	yes	—
414	C₂²×D₄	C₂×#123	1	2	yes	—
415	C₂²×D₄	#534	1	2	yes	—
416	C₂²×D₄	#534	1	2	yes	—
417	C₂²×D₄	#534	1	4	yes	—
418	C₂²×D₄	#534	1	4	yes	—
419	C₂²×D₄	D₄²	1	8	yes	—
420	C₂²×D₄	D₄²	1	8	yes	—
421	C₂²×D₄	#546	1	8	yes	—
422	C₂²×D₄	#546	1	8	yes	—
423	C₂²×D₄	#546	1	8	yes	—
424	C₂²×D₄	#546	1	8	yes	—
425	C₂²×D₄	C₂⁴×C₄	1	1	yes	characteristic
426	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
427	C₂²×D₄	C₂³×D₄	1	4	yes	—
428	C₂²×D₄	C₂²×#41	1	2	yes	—
429	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
430	C₂³×C₄	#386	1	1	yes	characteristic
431	C₂³×C₄	#386	1	1	yes	characteristic
432	C₂³×C₄	#386	1	2	yes	—
433	C₂³×C₄	#386	1	2	yes	—
434	C₂³×C₄	#386	1	2	yes	—
435	C₂³×C₄	#386	1	4	yes	—
436	C₂³×C₄	#386	1	4	yes	—
437	C₂³×C₄	#386	1	4	yes	—
438	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
439	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
440	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
441	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
442	C₂³×C₄	C₂×C₄×D₄	1	4	yes	—
443	C₂³×C₄	C₂×#120	1	1	yes	characteristic
444	C₂³×C₄	C₂×#120	1	2	yes	—
445	C₂³×C₄	C₂×#120	1	2	yes	—
446	C₂³×C₄	C₂×#121	1	4	yes	—
447	C₂³×C₄	C₂×#123	1	1	yes	characteristic
448	C₂³×C₄	C₂×#123	1	1	yes	characteristic
449	C₂³×C₄	C₂×#123	1	4	yes	—
450	C₂³×C₄	#534	1	2	yes	—
451	C₂³×C₄	#534	1	2	yes	—
452	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
453	#127	#379	1	8	yes	—
454	#127	#379	1	8	yes	—
455	#127	#379	1	8	yes	—
456	#127	#379	1	8	yes	—
457	#127	C₂²×C₂²⋊C₄	1	8	yes	—
458	#127	C₂²×C₂²⋊C₄	1	8	yes	—
459	#127	C₂×#120	1	8	yes	—
460	#127	C₂×#120	1	8	yes	—
461	C₂×C₄²	#379	1	2	yes	—
462	C₂×C₄²	#379	1	2	yes	—
463	C₂×C₄²	#379	1	2	yes	—
464	C₂×C₄²	#379	1	2	yes	—
465	C₂×C₄²	#379	1	8	yes	—
466	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
467	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
468	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
469	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
470	C₂×C₄²	C₂×#120	1	8	yes	—
471	#100	C₂²×C₂²⋊C₄	1	16	yes	—
472	C₂⁴	#1889	1	2	yes	—
473	C₂⁴	#1889	1	2	yes	—
474	C₂⁴	#1889	1	2	yes	—
475	C₂⁴	#1889	1	2	yes	—
476	C₂⁴	C₂×#386	1	1	yes	characteristic
477	C₂⁴	C₂×#386	1	1	yes	characteristic
478	C₂⁴	C₂×#386	1	2	yes	—
479	C₂⁴	C₂×#386	1	2	yes	—
480	C₂⁴	C₂×#386	1	2	yes	—
481	C₂⁴	C₂×#386	1	2	yes	—
482	C₂⁴	C₂×#386	1	4	yes	—
483	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
484	C₂⁴	D₄×C₂²⋊C₄	1	8	yes	—
485	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
486	C₂⁴	#2403	1	8	yes	—
487	C₂⁴	#2403	1	2	yes	—
488	C₂⁴	#2403	1	2	yes	—
489	C₂⁴	#2410	1	4	yes	—
490	C₂⁴	#2410	1	8	yes	—
491	C₂⁴	#2410	1	4	yes	—
492	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
493	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
494	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
495	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
496	C₂⁴	C₂²×C₄×D₄	1	2	yes	—
497	C₂⁴	C₂²×#120	1	1	yes	characteristic
498	C₂⁴	C₂²×#121	1	2	yes	—
499	C₂⁴	C₂×D₄²	1	8	yes	—
500	C₂×D₄	#1889	1	8	yes	—
501	C₂×D₄	#1889	1	8	yes	—
502	C₂×D₄	C₂×#379	1	4	yes	—
503	C₂×D₄	C₂×#379	1	4	yes	—
504	C₂×D₄	C₂×#379	1	2	yes	—
505	C₂×D₄	C₂×#379	1	2	yes	—
506	C₂×D₄	#2308	1	2	yes	—
507	C₂×D₄	#2308	1	2	yes	—
508	C₂×D₄	D₄×C₂²⋊C₄	1	4	yes	—
509	C₂×D₄	D₄×C₂²⋊C₄	1	4	yes	—
510	C₂×D₄	D₄×C₂²⋊C₄	1	8	yes	—
511	C₂×D₄	#2405	1	8	yes	—
512	C₂×D₄	#2410	1	4	yes	—
513	C₂×D₄	#2410	1	4	yes	—
514	C₂×D₄	#2410	1	8	yes	—
515	C₂×D₄	C₂×B(4,𝔽₂)	1	8	yes	—
516	C₂×D₄	C₂×B(4,𝔽₂)	1	8	yes	—
517	C₂×D₄	C₂³×C₂²⋊C₄	1	2	yes	—
518	C₂×D₄	C₂×#518	1	2	yes	—
519	C₂×D₄	C₂²×#120	1	2	yes	—
520	C₂×D₄	C₂×#534	1	2	yes	—
521	C₂×D₄	C₂×#546	1	8	yes	—
522	C₂²×C₄	#1889	1	2	yes	—
523	C₂²×C₄	#1889	1	2	yes	—
524	C₂²×C₄	#1889	1	2	yes	—
525	C₂²×C₄	#1889	1	2	yes	—
526	C₂²×C₄	C₂×#379	1	2	yes	—
527	C₂²×C₄	C₂×#379	1	1	yes	characteristic
528	C₂²×C₄	C₂×#379	1	1	yes	characteristic
529	C₂²×C₄	C₂×#386	1	1	yes	characteristic
530	C₂²×C₄	C₂×#386	1	1	yes	characteristic
531	C₂²×C₄	C₂×#386	1	2	yes	—
532	C₂²×C₄	C₂×#386	1	2	yes	—
533	C₂²×C₄	C₂×#386	1	4	yes	—
534	C₂²×C₄	#2308	1	2	yes	—
535	C₂²×C₄	#2308	1	1	yes	characteristic
536	C₂²×C₄	#2308	1	1	yes	characteristic
537	C₂²×C₄	#2403	1	2	yes	—
538	C₂²×C₄	#2403	1	2	yes	—
539	C₂²×C₄	#2405	1	2	yes	—
540	C₂²×C₄	#2405	1	2	yes	—
541	C₂²×C₄	#2405	1	2	yes	—
542	C₂²×C₄	#2405	1	2	yes	—
543	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
544	C₂²×C₄	C₂²×#120	1	2	yes	—
545	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
546	C₂²×C₄	C₂×#534	1	2	yes	—
547	C₄²	C₂×#379	1	4	yes	—
548	C₄²	C₂×#379	1	4	yes	—
549	C₂³	#13867	1	1	yes	characteristic
550	C₂³	#13867	1	2	yes	—
551	C₂³	#13867	1	1	yes	characteristic
552	C₂³	#13867	1	4	yes	—
553	C₂³	#13867	1	4	yes	—
554	C₂³	C₂×#1889	1	1	yes	characteristic
555	C₂³	C₂×#1889	1	1	yes	characteristic
556	C₂³	C₂×#1889	1	2	yes	—
557	C₂³	C₂×#1889	1	2	yes	—
558	C₂³	C₂×#1889	1	1	yes	characteristic
559	C₂³	C₂×#1889	1	1	yes	characteristic
560	C₂³	C₂×#1889	1	4	yes	—
561	C₂³	C₂×#1889	1	4	yes	—
562	C₂³	#23900	1	4	yes	—
563	C₂³	#23900	1	4	yes	—
564	C₂³	#23900	1	4	yes	—
565	C₂³	#23900	1	4	yes	—
566	C₂³	C₂²×#386	1	1	yes	characteristic
567	C₂³	C₂×D₄×C₂²⋊C₄	1	4	yes	—
568	C₂³	C₂×#2403	1	2	yes	—
569	C₂³	C₂×#2410	1	4	yes	—
570	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
571	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
572	C₂×C₄	#13867	1	2	yes	—
573	C₂×C₄	#13867	1	1	yes	characteristic
574	C₂×C₄	#13867	1	1	yes	characteristic
575	C₂×C₄	C₂×#1889	1	4	yes	—
576	C₂×C₄	C₂×#1889	1	4	yes	—
577	C₂×C₄	C₂²×#379	1	1	yes	characteristic
578	C₂×C₄	C₂×#2308	1	1	yes	characteristic
579	C₂×C₄	C₂×#2405	1	2	yes	—
580	C₂²	#359501	1	1	yes	characteristic
581	C₂²	#359501	1	1	yes	characteristic
582	C₂²	#359501	1	4	yes	—
583	C₂²	#359501	1	1	yes	characteristic
584	C₂²	#359501	1	1	yes	characteristic
585	C₂²	C₂×#13867	1	1	yes	characteristic
586	C₂²	C₂²×#1889	1	1	yes	characteristic
587	C₂²	C₂²×#1889	1	1	yes	characteristic
588	C₂²	C₂×#23900	1	4	yes	—
589	C₂	#72241315	1	2	yes	direct product factor
590	C₂	C₂×#359501	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#359501
commutator	C₂²×D₄	C₂⁴×C₄
Frattini, cosocle	C₂³×D₄	C₂⁵
prime radical	C₂²×#60388	C₂
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#494596	C₂	semidirect
2. C₂×#147767	C₂	semidirect
3. C₂×#493430	C₂	semidirect
4. C₂×#146577	C₂	semidirect
5. C₂×#6385980	C₂	semidirect
7. #72241315	C₂	direct (N × H)
8. C₂×#392135	C₂	semidirect
11. C₂×#60388	C₄	semidirect
13. C₂²×#3018	C₄	semidirect
14. C₂²×#3021	C₄	semidirect
15. C₂²×#3019	C₄	semidirect
17. C₂³×#453	C₄	semidirect
20. C₂×#34364	C₂²	semidirect
21. C₂²×#2127	C₂²	semidirect
22. C₂³×#353	C₂²	semidirect
23. #6385980	C₂²	semidirect
24. C₂×#21750	C₂²	semidirect
25. C₂×#20609	C₂²	semidirect
28. #494596	C₂²	semidirect
29. #493430	C₂²	semidirect
30. C₂×#12574	C₂²	semidirect
31. #392135	C₂²	semidirect
32. #147767	C₂²	semidirect
33. #146577	C₂²	semidirect
34. C₂×H(7,𝔽₂)	C₂×C₄	semidirect
36. C₂²×#585	C₂×C₄	semidirect
37. C₂³×H(5,𝔽₂)	C₂×C₄	semidirect
58. C₂×#3021	C₂×C₄	semidirect
59. C₂×#3019	C₂×C₄	semidirect
60. C₂×#3019	C₂×C₄	semidirect
62. C₂×#3018	C₂×C₄	semidirect
63. C₂²×#455	C₂×C₄	semidirect
67. C₂²×#453	C₂×C₄	semidirect
68. C₂²×#453	C₂×C₄	semidirect
72. C₂×#2888	C₂×C₄	semidirect
74. C₂²×#413	C₂×C₄	semidirect
75. C₂³×#100	C₂×C₄	semidirect
80. #34364	C₂³	semidirect
82. C₂×#2127	C₂³	semidirect
83. C₂²×#353	C₂³	semidirect
84. #21750	C₂³	semidirect
85. #20609	C₂³	semidirect
89. #12574	C₂³	semidirect
90. C₂×#585	C₂²×C₄	semidirect
91. C₂²×H(5,𝔽₂)	C₂²⋊C₄	semidirect
95. C₂²×H(5,𝔽₂)	C₂²×C₄	semidirect
105. C₂³×#41	C₂²⋊C₄	semidirect
106. C₂³×#41	C₂²⋊C₄	semidirect
113. C₂⁴×D₄	C₂²⋊C₄	semidirect
114. C₂⁴×D₄	C₂²⋊C₄	semidirect
122. C₂×#535	C₂²⋊C₄	semidirect
123. C₂×#535	C₂²⋊C₄	semidirect
124. C₂×#535	C₂²⋊C₄	semidirect
125. C₂×#535	C₂²⋊C₄	semidirect
126. C₂×#535	C₂²⋊C₄	semidirect
136. C₂×#532	C₂²⋊C₄	semidirect
137. C₂×#532	C₂²⋊C₄	semidirect
138. C₂×#532	C₂²⋊C₄	semidirect
142. C₂²×C₄⋊Q₈	C₂²⋊C₄	semidirect
143. C₂²×#127	C₂²⋊C₄	semidirect
144. C₂²×#127	C₂²⋊C₄	semidirect
145. C₂²×#127	C₂²⋊C₄	semidirect
146. C₂²×#127	C₂²⋊C₄	semidirect
147. C₂²×#127	C₂²⋊C₄	semidirect
162. C₂²×#124	C₂²⋊C₄	semidirect
163. C₂²×#124	C₂²⋊C₄	semidirect
164. C₂²×#124	C₂²⋊C₄	semidirect
165. C₂²×#124	C₂²⋊C₄	semidirect
168. C₂×C₄×#41	C₂²⋊C₄	semidirect
170. C₂²×#117	C₂²⋊C₄	semidirect
171. C₂²×#117	C₂²⋊C₄	semidirect
174. C₂³×C₄²	C₂²⋊C₄	semidirect
175. C₂³×C₄²	C₂²⋊C₄	semidirect
177. C₂×#455	C₂²×C₄	semidirect
178. C₂×#453	C₂²⋊C₄	semidirect
179. C₂×#453	C₂²⋊C₄	semidirect
180. C₂×#453	C₂²⋊C₄	semidirect
181. C₂×#453	C₂²⋊C₄	semidirect
182. C₂×#453	C₂²⋊C₄	semidirect
185. C₂×#453	C₂²×C₄	semidirect
187. C₂×#413	C₂²×C₄	semidirect
190. C₂²×#100	C₂²×C₄	semidirect
212. C₂²×#41	C₂×C₂²⋊C₄	semidirect
213. C₂²×#41	C₂×C₂²⋊C₄	semidirect
239. C₂³×D₄	C₂×C₂²⋊C₄	semidirect
240. C₂³×D₄	C₂×C₂²⋊C₄	semidirect
287. C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	semidirect
299. C₂×#127	C₂×C₂²⋊C₄	semidirect
300. C₂×#127	C₂×C₂²⋊C₄	semidirect
301. C₂×#127	C₂×C₂²⋊C₄	semidirect
317. C₂×#124	C₂×C₂²⋊C₄	semidirect
318. C₂×#124	C₂×C₂²⋊C₄	semidirect
319. C₂×#124	C₂×C₂²⋊C₄	semidirect
320. C₂×#124	C₂×C₂²⋊C₄	semidirect
324. C₂×#117	C₂×C₂²⋊C₄	semidirect
325. C₂×#117	C₂×C₂²⋊C₄	semidirect
333. C₂²×C₄²	C₂×C₂²⋊C₄	semidirect
334. C₂²×C₄²	C₂×C₂²⋊C₄	semidirect
338. #453	C₂×C₂²⋊C₄	semidirect
339. #453	C₂×C₂²⋊C₄	semidirect
589. C₂	#72241315	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×#494596	2
C₂×#147767	2
C₂×#493430	2
C₂×#146577	2
C₂×#6385980	2
C₂²×#60388	2
#72241315	2
C₂×#392135	2

Subgroups — C2×#72241315 #72341277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72241315 #72341277