Subgroups — C₂³×#3488 #72278218

Order 1024.

884421 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁵×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#3488	C₂	1	224	yes	maximal, direct product factor
4	C₂³×#550	C₂	1	2	yes	maximal, complemented
5	C₂³×#548	C₂	1	2	yes	maximal, complemented
6	C₂³×#546	C₂	1	6	yes	maximal, complemented
7	C₂³×D₄²	C₂	1	6	yes	maximal, complemented
8	C₂³×#537	C₂	1	3	yes	maximal, complemented
9	C₂³×#535	C₂	1	3	yes	maximal, complemented
10	C₂³×#525	C₂	1	3	yes	maximal, complemented
11	C₂⁴×#121	C₂	1	3	yes	maximal, complemented
12	C₂³×#520	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×H(5,𝔽₂)	—	2	64	no	—
14	C₂³×H(5,𝔽₂)	C₂²	1	112	yes	complemented
15	C₂⁴×#41	—	2	64	no	—
16	C₂⁴×#41	C₂²	1	1	yes	characteristic
17	C₂⁴×#41	C₂²	1	3	yes	complemented
18	C₂⁴×#41	C₂²	1	3	yes	complemented
19	C₂⁴×#41	C₂²	1	3	yes	complemented
20	C₂⁴×#41	C₂²	1	2	yes	complemented
21	C₂⁴×#41	C₂²	1	1	yes	characteristic, complemented
22	C₂⁴×#41	C₂²	1	112	yes	complemented
23	C₂⁵×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂⁵×D₄	C₂²	1	3	yes	complemented
25	C₂⁵×D₄	C₂²	1	3	yes	complemented
26	C₂⁵×D₄	C₂²	1	6	yes	complemented
27	C₂⁵×D₄	C₂²	1	6	yes	complemented
28	C₂⁶×C₄	C₂²	1	3	yes	complemented
29	C₂×#3488	C₂²	1	7168	yes	direct product factor
30	C₂²×#550	C₂²	1	224	yes	complemented
31	C₂²×#548	C₂²	1	224	yes	complemented
32	C₂²×#546	C₂²	1	672	yes	complemented
33	C₂²×D₄²	C₂²	1	672	yes	complemented
34	C₂²×#537	C₂²	1	336	yes	complemented
35	C₂²×#535	C₂²	1	336	yes	complemented
36	C₂³×#127	C₂²	1	6	yes	complemented
37	C₂³×#124	C₂²	1	6	yes	complemented
38	C₂²×#525	C₂²	1	336	yes	complemented
39	C₂³×#123	C₂²	1	6	yes	complemented
40	C₂³×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂³×C₂²⋊Q₈	C₂²	1	3	yes	complemented
42	C₂³×C₂²⋊Q₈	C₂²	1	6	yes	complemented
43	C₂³×#121	C₂²	1	3	yes	complemented
44	C₂³×#121	C₂²	1	6	yes	complemented
45	C₂³×#121	C₂²	1	6	yes	complemented
46	C₂³×#121	C₂²	1	6	yes	complemented
47	C₂³×#121	C₂²	1	3	yes	complemented
48	C₂³×#121	C₂²	1	12	yes	complemented
49	C₂³×#121	C₂²	1	6	yes	complemented
50	C₂³×#121	C₂²	1	336	yes	complemented
51	C₂³×#120	C₂²	1	6	yes	complemented
52	C₂³×#120	C₂²	1	12	yes	complemented
53	C₂²×#520	C₂²	1	112	yes	complemented
54	C₂³×C₄×Q₈	C₂²	1	2	yes	complemented
55	C₂³×C₄×D₄	C₂²	1	6	yes	complemented
56	C₂³×C₄×D₄	C₂²	1	6	yes	complemented
57	C₂³×C₄×D₄	C₂²	1	6	yes	complemented
58	C₂³×#117	C₂²	1	3	yes	complemented
59	C₂⁴×C₄⋊C₄	C₂²	1	3	yes	complemented
60	C₂⁴×C₂²⋊C₄	C₂²	1	6	yes	complemented
61	C₂⁷	C₂³	1	3	yes	—
62	C₂⁷	C₂³	1	6	yes	—
63	C₂²×H(5,𝔽₂)	—	2	3584	no	—
64	C₂²×H(5,𝔽₂)	C₂³	1	1792	yes	complemented
65	C₂³×#41	—	2	3584	no	—
66	C₂³×#41	—	2	32	no	—
67	C₂³×#41	—	2	64	no	—
68	C₂³×#41	—	2	96	no	—
69	C₂³×#41	—	2	96	no	—
70	C₂³×#41	—	2	96	no	—
71	C₂³×#41	D₄	1	64	yes	complemented
72	C₂³×#41	C₂³	1	56	yes	—
73	C₂³×#41	C₂³	1	168	yes	complemented
74	C₂³×#41	C₂³	1	168	yes	complemented
75	C₂³×#41	C₂³	1	56	yes	complemented
76	C₂³×#41	C₂³	1	168	yes	complemented
77	C₂³×#41	C₂³	1	112	yes	complemented
78	C₂³×#41	C₂³	1	1792	yes	complemented
79	C₂⁴×Q₈	—	2	32	no	—
80	C₂⁴×Q₈	C₂³	1	3	yes	—
81	C₂⁴×Q₈	C₂³	1	1	yes	characteristic
82	C₂⁴×Q₈	C₂³	1	1	yes	characteristic
83	C₂⁴×Q₈	C₂³	1	56	yes	complemented
84	C₂⁴×D₄	—	2	96	no	—
85	C₂⁴×D₄	—	2	192	no	—
86	C₂⁴×D₄	—	2	96	no	—
87	C₂⁴×D₄	—	4	96	no	—
88	C₂⁴×D₄	C₂³	1	6	yes	—
89	C₂⁴×D₄	C₂³	1	3	yes	—
90	C₂⁴×D₄	C₂³	1	6	yes	—
91	C₂⁴×D₄	C₂³	1	6	yes	—
92	C₂⁴×D₄	C₂³	1	6	yes	—
93	C₂⁴×D₄	C₂³	1	3	yes	—
94	C₂⁴×D₄	C₂³	1	12	yes	—
95	C₂⁴×D₄	C₂³	1	6	yes	—
96	C₂⁴×D₄	C₂³	1	3	yes	—
97	C₂⁴×D₄	C₂³	1	168	yes	complemented
98	C₂⁴×D₄	C₂³	1	168	yes	complemented
99	C₂⁴×D₄	C₂³	1	336	yes	complemented
100	C₂⁴×D₄	C₂³	1	336	yes	complemented
101	C₂⁵×C₄	—	2	96	no	—
102	C₂⁵×C₄	C₂³	1	1	yes	characteristic
103	C₂⁵×C₄	C₂³	1	3	yes	—
104	C₂⁵×C₄	C₂³	1	3	yes	—
105	C₂⁵×C₄	C₂³	1	3	yes	—
106	C₂⁵×C₄	C₂³	1	3	yes	—
107	C₂⁵×C₄	C₂³	1	6	yes	—
108	C₂⁵×C₄	C₂³	1	6	yes	—
109	C₂⁵×C₄	C₂³	1	3	yes	—
110	C₂⁵×C₄	C₂³	1	168	yes	complemented
111	#3488	C₂³	1	32768	yes	direct product factor
112	C₂×#550	C₂³	1	3584	yes	complemented
113	C₂×#548	C₂³	1	3584	yes	complemented
114	C₂×#546	C₂³	1	10752	yes	complemented
115	C₂×D₄²	C₂³	1	10752	yes	complemented
116	C₂×#537	C₂³	1	5376	yes	complemented
117	C₂×#535	C₂³	1	5376	yes	complemented
118	C₂²×#127	C₂³	1	336	yes	complemented
119	C₂²×#124	C₂³	1	336	yes	complemented
120	C₂×#525	C₂³	1	5376	yes	complemented
121	C₂²×#123	C₂³	1	336	yes	complemented
122	C₂²×C₂²⋊Q₈	C₂³	1	56	yes	complemented
123	C₂²×C₂²⋊Q₈	C₂³	1	168	yes	complemented
124	C₂²×C₂²⋊Q₈	C₂³	1	336	yes	complemented
125	C₂²×#121	C₂³	1	168	yes	complemented
126	C₂²×#121	C₂³	1	336	yes	complemented
127	C₂²×#121	C₂³	1	336	yes	complemented
128	C₂²×#121	C₂³	1	336	yes	complemented
129	C₂²×#121	C₂³	1	168	yes	complemented
130	C₂²×#121	C₂³	1	672	yes	complemented
131	C₂²×#121	C₂³	1	336	yes	complemented
132	C₂²×#121	C₂³	1	5376	yes	complemented
133	C₂²×#120	C₂³	1	336	yes	complemented
134	C₂²×#120	C₂³	1	672	yes	complemented
135	C₂×#520	C₂³	1	1792	yes	complemented
136	C₂²×C₄×Q₈	C₂³	1	112	yes	complemented
137	C₂²×C₄×D₄	C₂³	1	336	yes	complemented
138	C₂²×C₄×D₄	C₂³	1	336	yes	complemented
139	C₂²×C₄×D₄	C₂³	1	336	yes	complemented
140	C₂²×#117	C₂³	1	168	yes	complemented
141	C₂³×C₄⋊C₄	C₂³	1	3	yes	—
142	C₂³×C₄⋊C₄	C₂³	1	6	yes	—
143	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂³×C₄⋊C₄	C₂³	1	6	yes	—
146	C₂³×C₄⋊C₄	C₂³	1	168	yes	complemented
147	C₂³×C₂²⋊C₄	C₂³	1	6	yes	—
148	C₂³×C₂²⋊C₄	C₂³	1	12	yes	—
149	C₂³×C₂²⋊C₄	C₂³	1	6	yes	—
150	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂³×C₂²⋊C₄	C₂³	1	6	yes	—
152	C₂³×C₂²⋊C₄	C₂³	1	6	yes	—
153	C₂³×C₂²⋊C₄	C₂³	1	336	yes	complemented
154	C₂³×C₄²	C₂³	1	6	yes	—
155	C₂⁶	—	2	48	no	—
156	C₂⁶	—	2	48	no	—
157	C₂⁶	—	2	96	no	—
158	C₂⁶	—	4	24	no	—
159	C₂⁶	—	4	48	no	—
160	C₂⁶	—	4	48	no	—
161	C₂⁶	C₂⁴	1	3	yes	—
162	C₂⁶	C₂⁴	1	6	yes	—
163	C₂⁶	C₂⁴	1	84	yes	—
164	C₂⁶	C₂⁴	1	3	yes	—
165	C₂⁶	C₂⁴	1	1	yes	characteristic
166	C₂⁶	C₂⁴	1	168	yes	—
167	C₂×H(5,𝔽₂)	—	2	28672	no	—
168	C₂×H(5,𝔽₂)	C₂⁴	1	4096	yes	complemented
169	C₂²×#41	—	2	28672	no	—
170	C₂²×#41	—	2	896	no	—
171	C₂²×#41	—	2	1792	no	—
172	C₂²×#41	—	2	2688	no	—
173	C₂²×#41	—	2	2688	no	—
174	C₂²×#41	—	2	2688	no	—
175	C₂²×#41	C₂×D₄	1	1792	yes	complemented
176	C₂²×#41	C₂⁴	1	448	yes	—
177	C₂²×#41	C₂⁴	1	1344	yes	complemented
178	C₂²×#41	C₂⁴	1	1344	yes	complemented
179	C₂²×#41	C₂⁴	1	448	yes	complemented
180	C₂²×#41	C₂⁴	1	1344	yes	complemented
181	C₂²×#41	C₂⁴	1	896	yes	complemented
182	C₂²×#41	C₂⁴	1	4096	yes	complemented
183	C₂³×Q₈	—	2	896	no	—
184	C₂³×Q₈	—	2	48	no	—
185	C₂³×Q₈	—	2	16	no	—
186	C₂³×Q₈	C₂×D₄	1	32	yes	complemented
187	C₂³×Q₈	C₂⁴	1	84	yes	—
188	C₂³×Q₈	C₂⁴	1	28	yes	—
189	C₂³×Q₈	C₂⁴	1	28	yes	—
190	C₂³×Q₈	C₂⁴	1	448	yes	complemented
191	C₂³×D₄	—	2	96	no	—
192	C₂³×D₄	—	2	96	no	—
193	C₂³×D₄	—	2	96	no	—
194	C₂³×D₄	—	2	2688	no	—
195	C₂³×D₄	—	2	5376	no	—
196	C₂³×D₄	—	2	48	no	—
197	C₂³×D₄	—	2	96	no	—
198	C₂³×D₄	—	2	48	no	—
199	C₂³×D₄	—	2	2688	no	—
200	C₂³×D₄	—	4	96	no	—
201	C₂³×D₄	—	4	48	no	—
202	C₂³×D₄	—	4	2688	no	—
203	C₂³×D₄	C₂×D₄	1	96	yes	complemented
204	C₂³×D₄	C₂⁴	1	168	yes	—
205	C₂³×D₄	C₂⁴	1	84	yes	—
206	C₂³×D₄	C₂⁴	1	168	yes	—
207	C₂³×D₄	C₂⁴	1	168	yes	—
208	C₂³×D₄	C₂⁴	1	168	yes	—
209	C₂³×D₄	C₂⁴	1	84	yes	—
210	C₂³×D₄	C₂⁴	1	336	yes	—
211	C₂³×D₄	C₂⁴	1	168	yes	—
212	C₂³×D₄	C₂⁴	1	84	yes	—
213	C₂³×D₄	C₂⁴	1	1344	yes	complemented
214	C₂³×D₄	C₂⁴	1	1344	yes	complemented
215	C₂³×D₄	C₂⁴	1	2688	yes	complemented
216	C₂³×D₄	C₂⁴	1	2688	yes	complemented
217	C₂⁴×C₄	—	2	48	no	—
218	C₂⁴×C₄	—	2	16	no	—
219	C₂⁴×C₄	—	2	48	no	—
220	C₂⁴×C₄	—	2	48	no	—
221	C₂⁴×C₄	—	2	48	no	—
222	C₂⁴×C₄	—	2	96	no	—
223	C₂⁴×C₄	—	2	2688	no	—
224	C₂⁴×C₄	—	4	48	no	—
225	C₂⁴×C₄	C₂×D₄	1	96	yes	complemented
226	C₂⁴×C₄	C₂⁴	1	28	yes	—
227	C₂⁴×C₄	C₂⁴	1	84	yes	—
228	C₂⁴×C₄	C₂⁴	1	84	yes	—
229	C₂⁴×C₄	C₂⁴	1	84	yes	—
230	C₂⁴×C₄	C₂⁴	1	84	yes	—
231	C₂⁴×C₄	C₂⁴	1	168	yes	—
232	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
233	C₂⁴×C₄	C₂⁴	1	2	yes	—
234	C₂⁴×C₄	C₂⁴	1	3	yes	—
235	C₂⁴×C₄	C₂⁴	1	6	yes	—
236	C₂⁴×C₄	C₂⁴	1	2	yes	—
237	C₂⁴×C₄	C₂⁴	1	168	yes	—
238	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
239	C₂⁴×C₄	C₂⁴	1	3	yes	—
240	C₂⁴×C₄	C₂⁴	1	84	yes	—
241	C₂⁴×C₄	C₂⁴	1	1344	yes	complemented
242	#550	C₂⁴	1	8192	yes	complemented
243	#548	C₂⁴	1	8192	yes	complemented
244	#546	C₂⁴	1	24576	yes	complemented
245	D₄²	C₂⁴	1	24576	yes	complemented
246	#537	C₂⁴	1	12288	yes	complemented
247	#535	C₂⁴	1	12288	yes	complemented
248	C₂×#127	C₂⁴	1	2688	yes	complemented
249	C₂×#124	C₂⁴	1	2688	yes	complemented
250	#525	C₂⁴	1	12288	yes	complemented
251	C₂×#123	C₂⁴	1	2688	yes	complemented
252	C₂×C₂²⋊Q₈	C₂⁴	1	448	yes	complemented
253	C₂×C₂²⋊Q₈	C₂⁴	1	1344	yes	complemented
254	C₂×C₂²⋊Q₈	C₂⁴	1	2688	yes	complemented
255	C₂×#121	C₂⁴	1	1344	yes	complemented
256	C₂×#121	C₂⁴	1	2688	yes	complemented
257	C₂×#121	C₂⁴	1	2688	yes	complemented
258	C₂×#121	C₂⁴	1	2688	yes	complemented
259	C₂×#121	C₂⁴	1	1344	yes	complemented
260	C₂×#121	C₂⁴	1	5376	yes	complemented
261	C₂×#121	C₂⁴	1	2688	yes	complemented
262	C₂×#121	C₂⁴	1	12288	yes	complemented
263	C₂×#120	C₂⁴	1	2688	yes	complemented
264	C₂×#120	C₂⁴	1	5376	yes	complemented
265	#520	C₂⁴	1	4096	yes	complemented
266	C₂×C₄×Q₈	C₂⁴	1	896	yes	complemented
267	C₂×C₄×D₄	C₂⁴	1	2688	yes	complemented
268	C₂×C₄×D₄	C₂⁴	1	2688	yes	complemented
269	C₂×C₄×D₄	C₂⁴	1	2688	yes	complemented
270	C₂×#117	C₂⁴	1	1344	yes	complemented
271	C₂²×C₄⋊C₄	C₂⁴	1	84	yes	—
272	C₂²×C₄⋊C₄	C₂⁴	1	168	yes	—
273	C₂²×C₄⋊C₄	C₂⁴	1	28	yes	—
274	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
275	C₂²×C₄⋊C₄	C₂⁴	1	168	yes	—
276	C₂²×C₄⋊C₄	C₂⁴	1	1344	yes	complemented
277	C₂²×C₂²⋊C₄	C₂⁴	1	168	yes	—
278	C₂²×C₂²⋊C₄	C₂⁴	1	336	yes	—
279	C₂²×C₂²⋊C₄	C₂⁴	1	168	yes	—
280	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
281	C₂²×C₂²⋊C₄	C₂⁴	1	168	yes	—
282	C₂²×C₂²⋊C₄	C₂⁴	1	168	yes	—
283	C₂²×C₂²⋊C₄	C₂⁴	1	2688	yes	complemented
284	C₂²×C₄²	C₂⁴	1	168	yes	—
285	C₂⁵	—	2	8	no	—
286	C₂⁵	—	2	24	no	—
287	C₂⁵	—	2	8	no	—
288	C₂⁵	—	2	24	no	—
289	C₂⁵	—	2	672	no	—
290	C₂⁵	—	2	24	no	—
291	C₂⁵	—	2	48	no	—
292	C₂⁵	—	2	48	no	—
293	C₂⁵	—	2	24	no	—
294	C₂⁵	—	2	672	no	—
295	C₂⁵	—	2	24	no	—
296	C₂⁵	—	2	48	no	—
297	C₂⁵	—	2	1344	no	—
298	C₂⁵	—	4	336	no	—
299	C₂⁵	—	4	672	no	—
300	C₂⁵	—	4	672	no	—
301	C₂⁵	—	4	768	no	—
302	C₂⁵	—	8	768	no	—
303	C₂⁵	C₂²×D₄	1	48	yes	—
304	C₂⁵	H(5,𝔽₂)	1	16	yes	complemented
305	C₂⁵	C₂⁵	1	84	yes	—
306	C₂⁵	C₂⁵	1	42	yes	—
307	C₂⁵	C₂⁵	1	336	yes	—
308	C₂⁵	C₂⁵	1	42	yes	—
309	C₂⁵	C₂⁵	1	14	yes	—
310	C₂⁵	C₂⁵	1	672	yes	—
311	C₂⁵	C₂⁵	1	1	yes	characteristic
312	H(5,𝔽₂)	—	2	32768	no	—
313	C₂×#41	—	2	32768	no	—
314	C₂×#41	—	2	3584	no	—
315	C₂×#41	—	2	7168	no	—
316	C₂×#41	—	2	10752	no	—
317	C₂×#41	—	2	10752	no	—
318	C₂×#41	—	2	10752	no	—
319	C₂×#41	C₂²×D₄	1	7168	yes	complemented
320	C₂×#41	C₂⁵	1	512	yes	—
321	C₂×#41	C₂⁵	1	1536	yes	complemented
322	C₂×#41	C₂⁵	1	1536	yes	complemented
323	C₂×#41	C₂⁵	1	1536	yes	complemented
324	C₂×#41	C₂⁵	1	1024	yes	complemented
325	C₂×#41	C₂⁵	1	512	yes	complemented
326	C₂²×Q₈	—	2	3584	no	—
327	C₂²×Q₈	—	2	672	no	—
328	C₂²×Q₈	—	2	224	no	—
329	C₂²×Q₈	C₂²×D₄	1	448	yes	complemented
330	C₂²×Q₈	C₂⁵	1	112	yes	—
331	C₂²×Q₈	C₂⁵	1	336	yes	—
332	C₂²×Q₈	C₂⁵	1	112	yes	—
333	C₂²×Q₈	C₂⁵	1	512	yes	complemented
334	C₂²×D₄	—	2	1344	no	—
335	C₂²×D₄	—	2	1344	no	—
336	C₂²×D₄	—	2	1344	no	—
337	C₂²×D₄	—	2	10752	no	—
338	C₂²×D₄	—	2	21504	no	—
339	C₂²×D₄	—	2	672	no	—
340	C₂²×D₄	—	2	1344	no	—
341	C₂²×D₄	—	2	672	no	—
342	C₂²×D₄	—	2	10752	no	—
343	C₂²×D₄	—	4	1344	no	—
344	C₂²×D₄	—	4	672	no	—
345	C₂²×D₄	—	4	10752	no	—
346	C₂²×D₄	C₂²×D₄	1	1344	yes	complemented
347	C₂²×D₄	C₂⁵	1	672	yes	—
348	C₂²×D₄	C₂⁵	1	672	yes	—
349	C₂²×D₄	C₂⁵	1	672	yes	—
350	C₂²×D₄	C₂⁵	1	336	yes	—
351	C₂²×D₄	C₂⁵	1	672	yes	—
352	C₂²×D₄	C₂⁵	1	336	yes	—
353	C₂²×D₄	C₂⁵	1	672	yes	—
354	C₂²×D₄	C₂⁵	1	1344	yes	—
355	C₂²×D₄	C₂⁵	1	336	yes	—
356	C₂²×D₄	C₂⁵	1	1536	yes	complemented
357	C₂²×D₄	C₂⁵	1	1536	yes	complemented
358	C₂²×D₄	C₂⁵	1	3072	yes	complemented
359	C₂²×D₄	C₂⁵	1	3072	yes	complemented
360	C₂³×C₄	—	2	8	no	—
361	C₂³×C₄	—	2	16	no	—
362	C₂³×C₄	—	2	24	no	—
363	C₂³×C₄	—	2	672	no	—
364	C₂³×C₄	—	2	48	no	—
365	C₂³×C₄	—	2	16	no	—
366	C₂³×C₄	—	2	224	no	—
367	C₂³×C₄	—	2	672	no	—
368	C₂³×C₄	—	2	672	no	—
369	C₂³×C₄	—	2	672	no	—
370	C₂³×C₄	—	2	1344	no	—
371	C₂³×C₄	—	2	10752	no	—
372	C₂³×C₄	—	4	672	no	—
373	C₂³×C₄	C₂²×D₄	1	16	yes	—
374	C₂³×C₄	C₂²×D₄	1	48	yes	—
375	C₂³×C₄	C₂²×D₄	1	1344	yes	complemented
376	C₂³×C₄	C₂⁵	1	28	yes	—
377	C₂³×C₄	C₂⁵	1	14	yes	—
378	C₂³×C₄	C₂⁵	1	42	yes	—
379	C₂³×C₄	C₂⁵	1	84	yes	—
380	C₂³×C₄	C₂⁵	1	28	yes	—
381	C₂³×C₄	C₂⁵	1	336	yes	—
382	C₂³×C₄	C₂⁵	1	336	yes	—
383	C₂³×C₄	C₂⁵	1	336	yes	—
384	C₂³×C₄	C₂⁵	1	672	yes	—
385	C₂³×C₄	C₂⁵	1	112	yes	—
386	C₂³×C₄	C₂⁵	1	336	yes	—
387	C₂³×C₄	C₂⁵	1	672	yes	—
388	C₂³×C₄	C₂⁵	1	14	yes	—
389	C₂³×C₄	C₂⁵	1	42	yes	—
390	C₂³×C₄	C₂⁵	1	336	yes	—
391	C₂³×C₄	C₂⁵	1	1536	yes	complemented
392	#127	C₂⁵	1	3072	yes	complemented
393	#124	C₂⁵	1	3072	yes	complemented
394	#123	C₂⁵	1	3072	yes	complemented
395	C₂²⋊Q₈	C₂⁵	1	512	yes	complemented
396	C₂²⋊Q₈	C₂⁵	1	1536	yes	complemented
397	C₂²⋊Q₈	C₂⁵	1	3072	yes	complemented
398	#121	C₂⁵	1	1536	yes	complemented
399	#121	C₂⁵	1	3072	yes	complemented
400	#121	C₂⁵	1	3072	yes	complemented
401	#121	C₂⁵	1	3072	yes	complemented
402	#121	C₂⁵	1	1536	yes	complemented
403	#121	C₂⁵	1	6144	yes	complemented
404	#121	C₂⁵	1	3072	yes	complemented
405	#120	C₂⁵	1	3072	yes	complemented
406	#120	C₂⁵	1	6144	yes	complemented
407	C₄×Q₈	C₂⁵	1	1024	yes	complemented
408	C₄×D₄	C₂⁵	1	3072	yes	complemented
409	C₄×D₄	C₂⁵	1	3072	yes	complemented
410	C₄×D₄	C₂⁵	1	3072	yes	complemented
411	#117	C₂⁵	1	1536	yes	complemented
412	C₂×C₄⋊C₄	C₂⁵	1	336	yes	—
413	C₂×C₄⋊C₄	C₂⁵	1	672	yes	—
414	C₂×C₄⋊C₄	C₂⁵	1	112	yes	—
415	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
416	C₂×C₄⋊C₄	C₂⁵	1	672	yes	—
417	C₂×C₄⋊C₄	C₂⁵	1	1536	yes	complemented
418	C₂×C₂²⋊C₄	C₂⁵	1	672	yes	—
419	C₂×C₂²⋊C₄	C₂⁵	1	1344	yes	—
420	C₂×C₂²⋊C₄	C₂⁵	1	672	yes	—
421	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
422	C₂×C₂²⋊C₄	C₂⁵	1	672	yes	—
423	C₂×C₂²⋊C₄	C₂⁵	1	672	yes	—
424	C₂×C₂²⋊C₄	C₂⁵	1	3072	yes	complemented
425	C₂×C₄²	C₂⁵	1	672	yes	—
426	C₂⁴	—	2	56	no	—
427	C₂⁴	—	2	168	no	—
428	C₂⁴	—	2	56	no	—
429	C₂⁴	—	2	168	no	—
430	C₂⁴	—	2	128	no	—
431	C₂⁴	—	2	384	no	—
432	C₂⁴	—	2	1344	no	—
433	C₂⁴	—	2	168	no	—
434	C₂⁴	—	2	336	no	—
435	C₂⁴	—	2	336	no	—
436	C₂⁴	—	2	168	no	—
437	C₂⁴	—	2	1344	no	—
438	C₂⁴	—	2	168	no	—
439	C₂⁴	—	2	336	no	—
440	C₂⁴	—	2	2688	no	—
441	C₂⁴	—	4	672	no	—
442	C₂⁴	—	4	1344	no	—
443	C₂⁴	—	4	1344	no	—
444	C₂⁴	—	4	5376	no	—
445	C₂⁴	—	4	192	no	—
446	C₂⁴	—	4	384	no	—
447	C₂⁴	—	8	5376	no	—
448	C₂⁴	C₂³×D₄	1	336	yes	—
449	C₂⁴	C₂³×D₄	1	8	yes	—
450	C₂⁴	C₂×H(5,𝔽₂)	1	8	yes	—
451	C₂⁴	C₂×H(5,𝔽₂)	1	112	yes	complemented
452	C₂⁴	#585	1	8	yes	—
453	C₂⁴	C₂⁶	1	168	yes	—
454	C₂⁴	C₂⁶	1	84	yes	—
455	C₂⁴	C₂⁶	1	192	yes	—
456	C₂⁴	C₂⁶	1	84	yes	—
457	C₂⁴	C₂⁶	1	28	yes	—
458	C₂⁴	C₂⁶	1	384	yes	—
459	C₂⁴	C₂⁶	1	7	yes	—
460	#41	—	2	2048	no	—
461	#41	—	2	4096	no	—
462	#41	—	2	6144	no	—
463	#41	—	2	6144	no	—
464	#41	—	2	6144	no	—
465	#41	C₂³×D₄	1	4096	yes	complemented
466	C₂×Q₈	—	2	2048	no	—
467	C₂×Q₈	—	2	1344	no	—
468	C₂×Q₈	—	2	448	no	—
469	C₂×Q₈	C₂³×D₄	1	896	yes	complemented
470	C₂×Q₈	C₂⁶	1	64	yes	—
471	C₂×Q₈	C₂⁶	1	192	yes	—
472	C₂×Q₈	C₂⁶	1	64	yes	—
473	C₂×D₄	—	2	2688	no	—
474	C₂×D₄	—	2	2688	no	—
475	C₂×D₄	—	2	2688	no	—
476	C₂×D₄	—	2	6144	no	—
477	C₂×D₄	—	2	12288	no	—
478	C₂×D₄	—	2	1344	no	—
479	C₂×D₄	—	2	2688	no	—
480	C₂×D₄	—	2	1344	no	—
481	C₂×D₄	—	2	6144	no	—
482	C₂×D₄	—	4	2688	no	—
483	C₂×D₄	—	4	1344	no	—
484	C₂×D₄	—	4	6144	no	—
485	C₂×D₄	C₂³×D₄	1	2688	yes	complemented
486	C₂×D₄	C₂⁶	1	384	yes	—
487	C₂×D₄	C₂⁶	1	384	yes	—
488	C₂×D₄	C₂⁶	1	384	yes	—
489	C₂×D₄	C₂⁶	1	192	yes	—
490	C₂×D₄	C₂⁶	1	384	yes	—
491	C₂×D₄	C₂⁶	1	192	yes	—
492	C₂×D₄	C₂⁶	1	384	yes	—
493	C₂×D₄	C₂⁶	1	768	yes	—
494	C₂×D₄	C₂⁶	1	192	yes	—
495	C₂²×C₄	—	2	56	no	—
496	C₂²×C₄	—	2	112	no	—
497	C₂²×C₄	—	2	168	no	—
498	C₂²×C₄	—	2	1344	no	—
499	C₂²×C₄	—	2	336	no	—
500	C₂²×C₄	—	2	112	no	—
501	C₂²×C₄	—	2	448	no	—
502	C₂²×C₄	—	2	1344	no	—
503	C₂²×C₄	—	2	1344	no	—
504	C₂²×C₄	—	2	1344	no	—
505	C₂²×C₄	—	2	2688	no	—
506	C₂²×C₄	—	2	6144	no	—
507	C₂²×C₄	—	4	1344	no	—
508	C₂²×C₄	C₂³×D₄	1	112	yes	—
509	C₂²×C₄	C₂³×D₄	1	336	yes	—
510	C₂²×C₄	C₂³×D₄	1	2688	yes	complemented
511	C₂²×C₄	C₂⁶	1	56	yes	—
512	C₂²×C₄	C₂⁶	1	168	yes	—
513	C₂²×C₄	C₂⁶	1	28	yes	—
514	C₂²×C₄	C₂⁶	1	84	yes	—
515	C₂²×C₄	C₂⁶	1	56	yes	—
516	C₂²×C₄	C₂⁶	1	192	yes	—
517	C₂²×C₄	C₂⁶	1	192	yes	—
518	C₂²×C₄	C₂⁶	1	192	yes	—
519	C₂²×C₄	C₂⁶	1	384	yes	—
520	C₂²×C₄	C₂⁶	1	64	yes	—
521	C₂²×C₄	C₂⁶	1	192	yes	—
522	C₂²×C₄	C₂⁶	1	384	yes	—
523	C₂²×C₄	C₂⁶	1	84	yes	—
524	C₂²×C₄	C₂⁶	1	28	yes	—
525	C₂²×C₄	C₂⁶	1	192	yes	—
526	C₄⋊C₄	C₂⁶	1	192	yes	—
527	C₄⋊C₄	C₂⁶	1	384	yes	—
528	C₄⋊C₄	C₂⁶	1	64	yes	—
529	C₄⋊C₄	C₂⁶	1	128	yes	—
530	C₄⋊C₄	C₂⁶	1	384	yes	—
531	C₂²⋊C₄	C₂⁶	1	384	yes	—
532	C₂²⋊C₄	C₂⁶	1	768	yes	—
533	C₂²⋊C₄	C₂⁶	1	384	yes	—
534	C₂²⋊C₄	C₂⁶	1	128	yes	—
535	C₂²⋊C₄	C₂⁶	1	384	yes	—
536	C₂²⋊C₄	C₂⁶	1	384	yes	—
537	C₄²	C₂⁶	1	384	yes	—
538	C₂³	—	2	448	no	—
539	C₂³	—	2	1344	no	—
540	C₂³	—	2	56	no	—
541	C₂³	—	2	168	no	—
542	C₂³	—	2	56	no	—
543	C₂³	—	2	168	no	—
544	C₂³	—	2	384	no	—
545	C₂³	—	2	168	no	—
546	C₂³	—	2	336	no	—
547	C₂³	—	2	336	no	—
548	C₂³	—	2	168	no	—
549	C₂³	—	2	384	no	—
550	C₂³	—	2	168	no	—
551	C₂³	—	2	336	no	—
552	C₂³	—	2	768	no	—
553	C₂³	—	4	192	no	—
554	C₂³	—	4	384	no	—
555	C₂³	—	4	384	no	—
556	C₂³	—	4	5376	no	—
557	C₂³	—	4	672	no	—
558	C₂³	—	4	1344	no	—
559	C₂³	—	8	5376	no	—
560	C₂³	#3488	1	64	yes	direct product factor
561	C₂³	C₂⁴×D₄	1	336	yes	—
562	C₂³	C₂⁴×D₄	1	28	yes	—
563	C₂³	C₂²×H(5,𝔽₂)	1	28	yes	—
564	C₂³	C₂²×H(5,𝔽₂)	1	112	yes	complemented
565	C₂³	C₂×#585	1	28	yes	—
566	C₂³	C₂⁷	1	48	yes	—
567	C₂³	C₂⁷	1	24	yes	—
568	C₂³	C₂⁷	1	24	yes	—
569	C₂³	C₂⁷	1	8	yes	—
570	C₂³	C₂⁷	1	7	yes	—
571	Q₈	—	2	384	no	—
572	Q₈	—	2	128	no	—
573	Q₈	C₂⁴×D₄	1	256	yes	complemented
574	D₄	—	2	768	no	—
575	D₄	—	2	768	no	—
576	D₄	—	2	768	no	—
577	D₄	—	2	384	no	—
578	D₄	—	2	768	no	—
579	D₄	—	2	384	no	—
580	D₄	—	4	768	no	—
581	D₄	—	4	384	no	—
582	D₄	C₂⁴×D₄	1	768	yes	complemented
583	C₂×C₄	—	2	56	no	—
584	C₂×C₄	—	2	112	no	—
585	C₂×C₄	—	2	168	no	—
586	C₂×C₄	—	2	384	no	—
587	C₂×C₄	—	2	336	no	—
588	C₂×C₄	—	2	112	no	—
589	C₂×C₄	—	2	128	no	—
590	C₂×C₄	—	2	384	no	—
591	C₂×C₄	—	2	384	no	—
592	C₂×C₄	—	2	384	no	—
593	C₂×C₄	—	2	768	no	—
594	C₂×C₄	—	4	384	no	—
595	C₂×C₄	C₂⁴×D₄	1	112	yes	—
596	C₂×C₄	C₂⁴×D₄	1	336	yes	—
597	C₂×C₄	C₂⁴×D₄	1	768	yes	complemented
598	C₂×C₄	C₂⁷	1	16	yes	—
599	C₂×C₄	C₂⁷	1	48	yes	—
600	C₂×C₄	C₂⁷	1	8	yes	—
601	C₂×C₄	C₂⁷	1	24	yes	—
602	C₂×C₄	C₂⁷	1	16	yes	—
603	C₂×C₄	C₂⁷	1	24	yes	—
604	C₂×C₄	C₂⁷	1	8	yes	—
605	C₂²	—	2	224	no	—
606	C₂²	—	2	672	no	—
607	C₂²	—	2	8	no	—
608	C₂²	—	2	24	no	—
609	C₂²	—	2	8	no	—
610	C₂²	—	2	24	no	—
611	C₂²	—	2	24	no	—
612	C₂²	—	2	48	no	—
613	C₂²	—	2	48	no	—
614	C₂²	—	2	24	no	—
615	C₂²	—	2	24	no	—
616	C₂²	—	2	48	no	—
617	C₂²	—	4	768	no	—
618	C₂²	—	4	336	no	—
619	C₂²	—	4	672	no	—
620	C₂²	—	8	768	no	—
621	C₂²	C₂×#3488	1	112	yes	direct product factor
622	C₂²	C₂⁵×D₄	1	48	yes	—
623	C₂²	C₂⁵×D₄	1	14	yes	—
624	C₂²	C₂³×H(5,𝔽₂)	1	14	yes	—
625	C₂²	C₂³×H(5,𝔽₂)	1	16	yes	complemented
626	C₂²	C₂²×#585	1	14	yes	—
627	C₂²	C₂⁸	1	1	yes	characteristic
628	C₄	—	2	8	no	—
629	C₄	—	2	16	no	—
630	C₄	—	2	24	no	—
631	C₄	—	2	48	no	—
632	C₄	—	2	16	no	—
633	C₄	C₂⁵×D₄	1	16	yes	—
634	C₄	C₂⁵×D₄	1	48	yes	—
635	C₂	—	2	16	no	—
636	C₂	—	2	48	no	—
637	C₂	—	4	24	no	—
638	C₂	—	4	48	no	—
639	C₂	C₂²×#3488	1	28	yes	direct product factor
640	C₂	C₂⁶×D₄	1	1	yes	characteristic
641	C₂	C₂⁴×H(5,𝔽₂)	1	1	yes	characteristic
642	C₂	C₂³×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁵	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁸
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂⁴×H(5,𝔽₂)	C₂	semidirect
2. C₂⁵×#41	C₂	semidirect
3. C₂²×#3488	C₂	direct (N × H)
4. C₂³×#550	C₂	semidirect
5. C₂³×#548	C₂	semidirect
6. C₂³×#546	C₂	semidirect
7. C₂³×D₄²	C₂	semidirect
8. C₂³×#537	C₂	semidirect
9. C₂³×#535	C₂	semidirect
10. C₂³×#525	C₂	semidirect
11. C₂⁴×#121	C₂	semidirect
12. C₂³×#520	C₂	semidirect
14. C₂³×H(5,𝔽₂)	C₂²	semidirect
17. C₂⁴×#41	C₂²	semidirect
18. C₂⁴×#41	C₂²	semidirect
19. C₂⁴×#41	C₂²	semidirect
20. C₂⁴×#41	C₂²	semidirect
21. C₂⁴×#41	C₂²	semidirect
22. C₂⁴×#41	C₂²	semidirect
23. C₂⁵×Q₈	C₂²	semidirect
24. C₂⁵×D₄	C₂²	semidirect
25. C₂⁵×D₄	C₂²	semidirect
26. C₂⁵×D₄	C₂²	semidirect
27. C₂⁵×D₄	C₂²	semidirect
28. C₂⁶×C₄	C₂²	semidirect
29. C₂×#3488	C₂²	direct (N × H)
30. C₂²×#550	C₂²	semidirect
31. C₂²×#548	C₂²	semidirect
32. C₂²×#546	C₂²	semidirect
33. C₂²×D₄²	C₂²	semidirect
34. C₂²×#537	C₂²	semidirect
35. C₂²×#535	C₂²	semidirect
36. C₂³×#127	C₂²	semidirect
37. C₂³×#124	C₂²	semidirect
38. C₂²×#525	C₂²	semidirect
39. C₂³×#123	C₂²	semidirect
40. C₂³×C₂²⋊Q₈	C₂²	semidirect
41. C₂³×C₂²⋊Q₈	C₂²	semidirect
42. C₂³×C₂²⋊Q₈	C₂²	semidirect
43. C₂³×#121	C₂²	semidirect
44. C₂³×#121	C₂²	semidirect
45. C₂³×#121	C₂²	semidirect
46. C₂³×#121	C₂²	semidirect
47. C₂³×#121	C₂²	semidirect
48. C₂³×#121	C₂²	semidirect
49. C₂³×#121	C₂²	semidirect
50. C₂³×#121	C₂²	semidirect
51. C₂³×#120	C₂²	semidirect
52. C₂³×#120	C₂²	semidirect
53. C₂²×#520	C₂²	semidirect
54. C₂³×C₄×Q₈	C₂²	semidirect
55. C₂³×C₄×D₄	C₂²	semidirect
56. C₂³×C₄×D₄	C₂²	semidirect
57. C₂³×C₄×D₄	C₂²	semidirect
58. C₂³×#117	C₂²	semidirect
59. C₂⁴×C₄⋊C₄	C₂²	semidirect
60. C₂⁴×C₂²⋊C₄	C₂²	semidirect
64. C₂²×H(5,𝔽₂)	C₂³	semidirect
71. C₂³×#41	D₄	semidirect
73. C₂³×#41	C₂³	semidirect
74. C₂³×#41	C₂³	semidirect
75. C₂³×#41	C₂³	semidirect
76. C₂³×#41	C₂³	semidirect
77. C₂³×#41	C₂³	semidirect
78. C₂³×#41	C₂³	semidirect
83. C₂⁴×Q₈	C₂³	semidirect
97. C₂⁴×D₄	C₂³	semidirect
98. C₂⁴×D₄	C₂³	semidirect
99. C₂⁴×D₄	C₂³	semidirect
100. C₂⁴×D₄	C₂³	semidirect
110. C₂⁵×C₄	C₂³	semidirect
111. #3488	C₂³	direct (N × H)
112. C₂×#550	C₂³	semidirect
113. C₂×#548	C₂³	semidirect
114. C₂×#546	C₂³	semidirect
115. C₂×D₄²	C₂³	semidirect
116. C₂×#537	C₂³	semidirect
117. C₂×#535	C₂³	semidirect
118. C₂²×#127	C₂³	semidirect
119. C₂²×#124	C₂³	semidirect
120. C₂×#525	C₂³	semidirect
121. C₂²×#123	C₂³	semidirect
122. C₂²×C₂²⋊Q₈	C₂³	semidirect
123. C₂²×C₂²⋊Q₈	C₂³	semidirect
124. C₂²×C₂²⋊Q₈	C₂³	semidirect
125. C₂²×#121	C₂³	semidirect
126. C₂²×#121	C₂³	semidirect
127. C₂²×#121	C₂³	semidirect
128. C₂²×#121	C₂³	semidirect
129. C₂²×#121	C₂³	semidirect
130. C₂²×#121	C₂³	semidirect
131. C₂²×#121	C₂³	semidirect
132. C₂²×#121	C₂³	semidirect
133. C₂²×#120	C₂³	semidirect
134. C₂²×#120	C₂³	semidirect
135. C₂×#520	C₂³	semidirect
136. C₂²×C₄×Q₈	C₂³	semidirect
137. C₂²×C₄×D₄	C₂³	semidirect
138. C₂²×C₄×D₄	C₂³	semidirect
139. C₂²×C₄×D₄	C₂³	semidirect
140. C₂²×#117	C₂³	semidirect
146. C₂³×C₄⋊C₄	C₂³	semidirect
153. C₂³×C₂²⋊C₄	C₂³	semidirect
168. C₂×H(5,𝔽₂)	C₂⁴	semidirect
175. C₂²×#41	C₂×D₄	semidirect
177. C₂²×#41	C₂⁴	semidirect
178. C₂²×#41	C₂⁴	semidirect
179. C₂²×#41	C₂⁴	semidirect
180. C₂²×#41	C₂⁴	semidirect
181. C₂²×#41	C₂⁴	semidirect
182. C₂²×#41	C₂⁴	semidirect
186. C₂³×Q₈	C₂×D₄	semidirect
190. C₂³×Q₈	C₂⁴	semidirect
203. C₂³×D₄	C₂×D₄	semidirect
213. C₂³×D₄	C₂⁴	semidirect
214. C₂³×D₄	C₂⁴	semidirect
215. C₂³×D₄	C₂⁴	semidirect
216. C₂³×D₄	C₂⁴	semidirect
225. C₂⁴×C₄	C₂×D₄	semidirect
241. C₂⁴×C₄	C₂⁴	semidirect
242. #550	C₂⁴	semidirect
243. #548	C₂⁴	semidirect
244. #546	C₂⁴	semidirect
245. D₄²	C₂⁴	semidirect
246. #537	C₂⁴	semidirect
247. #535	C₂⁴	semidirect
248. C₂×#127	C₂⁴	semidirect
249. C₂×#124	C₂⁴	semidirect
250. #525	C₂⁴	semidirect
251. C₂×#123	C₂⁴	semidirect
252. C₂×C₂²⋊Q₈	C₂⁴	semidirect
253. C₂×C₂²⋊Q₈	C₂⁴	semidirect
254. C₂×C₂²⋊Q₈	C₂⁴	semidirect
255. C₂×#121	C₂⁴	semidirect
256. C₂×#121	C₂⁴	semidirect
257. C₂×#121	C₂⁴	semidirect
258. C₂×#121	C₂⁴	semidirect
259. C₂×#121	C₂⁴	semidirect
260. C₂×#121	C₂⁴	semidirect
261. C₂×#121	C₂⁴	semidirect
262. C₂×#121	C₂⁴	semidirect
263. C₂×#120	C₂⁴	semidirect
264. C₂×#120	C₂⁴	semidirect
265. #520	C₂⁴	semidirect
266. C₂×C₄×Q₈	C₂⁴	semidirect
267. C₂×C₄×D₄	C₂⁴	semidirect
268. C₂×C₄×D₄	C₂⁴	semidirect
269. C₂×C₄×D₄	C₂⁴	semidirect
270. C₂×#117	C₂⁴	semidirect
276. C₂²×C₄⋊C₄	C₂⁴	semidirect
283. C₂²×C₂²⋊C₄	C₂⁴	semidirect
304. C₂⁵	H(5,𝔽₂)	semidirect
319. C₂×#41	C₂²×D₄	semidirect
321. C₂×#41	C₂⁵	semidirect
322. C₂×#41	C₂⁵	semidirect
323. C₂×#41	C₂⁵	semidirect
324. C₂×#41	C₂⁵	semidirect
325. C₂×#41	C₂⁵	semidirect
329. C₂²×Q₈	C₂²×D₄	semidirect
333. C₂²×Q₈	C₂⁵	semidirect
346. C₂²×D₄	C₂²×D₄	semidirect
356. C₂²×D₄	C₂⁵	semidirect
357. C₂²×D₄	C₂⁵	semidirect
358. C₂²×D₄	C₂⁵	semidirect
359. C₂²×D₄	C₂⁵	semidirect
375. C₂³×C₄	C₂²×D₄	semidirect
391. C₂³×C₄	C₂⁵	semidirect
392. #127	C₂⁵	semidirect
393. #124	C₂⁵	semidirect
394. #123	C₂⁵	semidirect
395. C₂²⋊Q₈	C₂⁵	semidirect
396. C₂²⋊Q₈	C₂⁵	semidirect
397. C₂²⋊Q₈	C₂⁵	semidirect
398. #121	C₂⁵	semidirect
399. #121	C₂⁵	semidirect
400. #121	C₂⁵	semidirect
401. #121	C₂⁵	semidirect
402. #121	C₂⁵	semidirect
403. #121	C₂⁵	semidirect
404. #121	C₂⁵	semidirect
405. #120	C₂⁵	semidirect
406. #120	C₂⁵	semidirect
407. C₄×Q₈	C₂⁵	semidirect
408. C₄×D₄	C₂⁵	semidirect
409. C₄×D₄	C₂⁵	semidirect
410. C₄×D₄	C₂⁵	semidirect
411. #117	C₂⁵	semidirect
417. C₂×C₄⋊C₄	C₂⁵	semidirect
424. C₂×C₂²⋊C₄	C₂⁵	semidirect
451. C₂⁴	C₂×H(5,𝔽₂)	semidirect
465. #41	C₂³×D₄	semidirect
469. C₂×Q₈	C₂³×D₄	semidirect
485. C₂×D₄	C₂³×D₄	semidirect
510. C₂²×C₄	C₂³×D₄	semidirect
560. C₂³	#3488	direct (N × H)
564. C₂³	C₂²×H(5,𝔽₂)	semidirect
573. Q₈	C₂⁴×D₄	semidirect
582. D₄	C₂⁴×D₄	semidirect
597. C₂×C₄	C₂⁴×D₄	semidirect
621. C₂²	C₂×#3488	direct (N × H)
625. C₂²	C₂³×H(5,𝔽₂)	semidirect
639. C₂	C₂²×#3488	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×H(5,𝔽₂)	2
C₂⁵×#41	2
C₂²×#3488	2
C₂³×#550	2
C₂³×#548	2
C₂³×#546	2
C₂³×D₄²	2
C₂³×#537	2
C₂³×#535	2
C₂³×#525	2
C₂⁴×#121	2
C₂³×#520	2

Subgroups — C23×#3488 #72278218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#3488 #72278218