Subgroups — #60240

Order 256.

1068 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41	C₂	1	1	yes	maximal, characteristic
2	#2981	C₂	1	2	yes	maximal, complemented
3	#2980	C₂	1	2	yes	maximal, complemented
4	#2978	C₂	1	2	yes	maximal, complemented
5	#2977	C₂	1	2	yes	maximal, complemented
6	#2976	C₂	1	2	yes	maximal, complemented
7	#2976	C₂	1	2	yes	maximal, complemented
8	#2974	C₂	1	2	yes	maximal, complemented
9	#2973	C₂	1	2	yes	maximal, complemented
10	#2935	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#2933	C₂	1	1	yes	maximal, characteristic, complemented
13	#2933	C₂	1	1	yes	maximal, characteristic, complemented
14	#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	#2929	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#435	C₂	1	1	yes	maximal, characteristic, complemented
18	#2925	C₂	1	1	yes	maximal, characteristic, complemented
19	#2923	C₂	1	1	yes	maximal, characteristic, complemented
20	#2880	C₂	1	1	yes	maximal, characteristic, complemented
21	#2880	C₂	1	1	yes	maximal, characteristic, complemented
22	#2879	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#408	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41	C₂²	1	1	yes	characteristic
25	C₂²×#41	C₂²	1	1	yes	characteristic
26	C₂×#131	C₂²	1	1	yes	characteristic, complemented
27	C₂×#131	C₂²	1	1	yes	characteristic, complemented
28	C₂×#131	C₂²	1	1	yes	characteristic, complemented
29	C₂×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂²×M₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₂²×M₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₂²×M₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂³×C₈	C₂²	1	1	yes	characteristic, complemented
34	#550	C₄	1	1	yes	characteristic
35	D₄×Q₈	C₄	1	1	yes	characteristic
36	#548	C₄	1	1	yes	characteristic
37	#548	C₄	1	1	yes	characteristic
38	#547	C₄	1	2	yes	—
39	#547	C₄	1	1	yes	characteristic
40	#546	C₄	1	2	yes	—
41	#546	C₄	1	2	yes	—
42	#546	C₄	1	1	yes	characteristic
43	#546	C₄	1	1	yes	characteristic
44	D₄²	C₄	1	1	yes	characteristic
45	D₄²	C₄	1	2	yes	—
46	#532	C₂²	1	1	yes	characteristic
47	#532	C₂²	1	2	yes	—
48	#525	C₂²	1	1	yes	characteristic
49	#525	C₂²	1	1	yes	characteristic
50	#525	C₂²	1	2	yes	—
51	#525	C₂²	1	2	yes	—
52	C₄×#41	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄	C₂²	1	2	yes	—
55	#436	C₂²	1	2	yes	complemented
56	#436	C₂²	1	2	yes	complemented
57	#436	C₂²	1	2	yes	complemented
58	#436	C₂²	1	2	yes	complemented
59	#436	C₂²	1	2	yes	complemented
60	#436	C₂²	1	2	yes	complemented
61	#435	C₂²	1	1	yes	characteristic
62	#435	C₂²	1	1	yes	characteristic
63	#435	C₂²	1	2	yes	—
64	#435	C₂²	1	1	yes	characteristic, complemented
65	#435	C₂²	1	1	yes	characteristic, complemented
66	#435	C₂²	1	1	yes	characteristic, complemented
67	#435	C₂²	1	1	yes	characteristic, complemented
68	#435	C₂²	1	1	yes	characteristic, complemented
69	#435	C₂²	1	1	yes	characteristic, complemented
70	#435	C₂²	1	2	yes	complemented
71	#435	C₂²	1	2	yes	complemented
72	#435	C₂²	1	2	yes	complemented
73	#435	C₂²	1	2	yes	complemented
74	#435	C₂²	1	2	yes	complemented
75	#435	C₂²	1	2	yes	complemented
76	#435	C₂²	1	2	yes	complemented
77	#435	C₂²	1	2	yes	complemented
78	#435	C₂²	1	2	yes	complemented
79	#435	C₂²	1	2	yes	complemented
80	#435	C₂²	1	2	yes	complemented
81	#435	C₂²	1	2	yes	complemented
82	#435	C₂²	1	2	yes	complemented
83	#435	C₂²	1	2	yes	complemented
84	#435	C₂²	1	2	yes	complemented
85	C₈×D₄	C₂²	1	2	yes	complemented
86	C₈×D₄	C₂²	1	2	yes	complemented
87	C₈×D₄	C₂²	1	2	yes	complemented
88	C₈×D₄	C₂²	1	2	yes	complemented
89	C₈×D₄	C₂²	1	2	yes	complemented
90	C₈×D₄	C₂²	1	2	yes	complemented
91	#433	C₂²	1	2	yes	complemented
92	#433	C₂²	1	2	yes	complemented
93	#433	C₂²	1	2	yes	complemented
94	#433	C₂²	1	2	yes	complemented
95	#432	C₂²	1	2	yes	complemented
96	#432	C₂²	1	2	yes	complemented
97	#432	C₂²	1	2	yes	complemented
98	#431	C₂²	1	2	yes	complemented
99	#424	C₂²	1	1	yes	characteristic, complemented
100	#424	C₂²	1	1	yes	characteristic, complemented
101	#423	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
103	#408	C₂²	1	1	yes	characteristic
104	#408	C₂²	1	1	yes	characteristic
105	#408	C₂²	1	1	yes	characteristic
106	#408	C₂²	1	1	yes	characteristic
107	#408	C₂²	1	1	yes	characteristic, complemented
108	#408	C₂²	1	1	yes	characteristic, complemented
109	#408	C₂²	1	2	yes	complemented
110	#408	C₂²	1	2	yes	complemented
111	#408	C₂²	1	1	yes	characteristic, complemented
112	#408	C₂²	1	1	yes	characteristic, complemented
113	#408	C₂²	1	2	yes	complemented
114	#408	C₂²	1	2	yes	complemented
115	#408	C₂²	1	2	yes	complemented
116	#408	C₂²	1	2	yes	complemented
117	#408	C₂²	1	2	yes	complemented
118	#408	C₂²	1	2	yes	complemented
119	#407	C₂²	1	2	yes	complemented
120	#407	C₂²	1	2	yes	complemented
121	#407	C₂²	1	1	yes	characteristic, complemented
122	#407	C₂²	1	1	yes	characteristic, complemented
123	#407	C₂²	1	2	yes	complemented
124	#407	C₂²	1	2	yes	complemented
125	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
126	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
127	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
130	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
131	#405	C₂²	1	1	yes	characteristic, complemented
132	#405	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
134	C₂×#97	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	4	2	no	—
136	C₂×#41	—	4	2	no	—
137	C₂×#41	—	4	2	no	—
138	C₂×#41	—	4	2	no	—
139	C₂×#41	C₂×C₄	1	2	yes	—
140	C₂×#41	C₂×C₄	1	2	yes	—
141	C₂×#41	C₂×C₄	1	1	yes	characteristic
142	C₂×#41	C₂×C₄	1	1	yes	characteristic
143	C₂×#41	C₂×C₄	1	1	yes	characteristic
144	C₂×#41	C₂×C₄	1	1	yes	characteristic
145	C₂×#41	C₂³	1	1	yes	characteristic
146	C₂×#41	C₂³	1	1	yes	characteristic
147	C₂×#41	C₂³	1	1	yes	characteristic
148	C₂×#41	C₂³	1	2	yes	—
149	C₂×#41	C₂³	1	2	yes	—
150	C₂²×Q₈	C₂×C₄	1	1	yes	characteristic
151	C₂²×Q₈	C₂×C₄	1	1	yes	characteristic
152	C₂²×D₄	C₂×C₄	1	1	yes	characteristic
153	C₂²×D₄	C₂×C₄	1	2	yes	—
154	C₂²×D₄	C₂×C₄	1	1	yes	characteristic
155	C₂²×D₄	C₂×C₄	1	1	yes	characteristic
156	C₂²×D₄	C₂×C₄	1	2	yes	—
157	C₂²×D₄	C₂×C₄	1	2	yes	—
158	C₂³×C₄	C₂³	1	1	yes	characteristic
159	C₂³×C₄	C₂³	1	1	yes	characteristic
160	C₂³×C₄	C₂³	1	2	yes	—
161	C₂³×C₄	C₂³	1	2	yes	—
162	#131	—	4	2	no	—
163	#131	—	4	2	no	—
164	#131	—	4	2	no	—
165	#131	—	4	2	no	—
166	C₂×M₁₆	—	4	2	no	—
167	C₂×M₁₆	—	4	2	no	—
168	C₂×M₁₆	—	4	2	no	—
169	C₂×M₁₆	C₂³	1	1	yes	characteristic
170	C₂×M₁₆	C₂³	1	1	yes	characteristic
171	C₂×M₁₆	C₂³	1	1	yes	characteristic
172	C₂×M₁₆	C₂³	1	1	yes	characteristic
173	C₂×M₁₆	C₂³	1	1	yes	characteristic
174	C₂×M₁₆	C₂³	1	1	yes	characteristic
175	C₂×M₁₆	C₂³	1	2	yes	—
176	C₂×M₁₆	C₂³	1	1	yes	characteristic
177	C₂×M₁₆	C₂³	1	1	yes	characteristic
178	C₂×M₁₆	C₂³	1	2	yes	—
179	C₂×M₁₆	C₂³	1	2	yes	—
180	C₂×M₁₆	C₂³	1	2	yes	—
181	C₂×M₁₆	C₂³	1	2	yes	—
182	C₂×M₁₆	C₂³	1	2	yes	—
183	C₂²×C₈	—	4	2	no	—
184	C₂²×C₈	C₂³	1	1	yes	characteristic
185	C₂²×C₈	C₂³	1	1	yes	characteristic
186	C₂²×C₈	C₂³	1	1	yes	characteristic
187	C₂²×C₈	C₂³	1	1	yes	characteristic
188	C₂²×C₈	C₂³	1	1	yes	characteristic
189	C₂²×C₈	C₂³	1	1	yes	characteristic
190	C₂²×C₈	C₂³	1	1	yes	characteristic
191	C₂²×C₈	C₂³	1	1	yes	characteristic
192	C₂²×C₈	C₂³	1	2	yes	—
193	C₂²×C₈	C₂³	1	2	yes	—
194	C₂²×C₈	C₂³	1	2	yes	—
195	C₂²×C₈	C₂³	1	2	yes	—
196	C₂²×C₈	C₂³	1	2	yes	—
197	C₂²×C₈	C₂³	1	2	yes	—
198	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
199	C₄⋊Q₈	C₂×C₄	1	2	yes	—
200	#127	C₂×C₄	1	1	yes	characteristic
201	#127	C₂×C₄	1	2	yes	—
202	#124	C₂×C₄	1	1	yes	characteristic
203	#124	C₂×C₄	1	1	yes	characteristic
204	#124	C₂×C₄	1	2	yes	—
205	#124	C₂×C₄	1	2	yes	—
206	#123	C₂×C₄	1	2	yes	—
207	#123	C₂×C₄	1	2	yes	—
208	#123	C₂×C₄	1	2	yes	—
209	#123	C₂×C₄	1	2	yes	—
210	#123	C₂×C₄	1	2	yes	—
211	#123	C₂×C₄	1	2	yes	—
212	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
213	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
214	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
215	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
216	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
217	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
218	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
219	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
220	#121	C₂×C₄	1	1	yes	characteristic
221	#121	C₂×C₄	1	1	yes	characteristic
222	#121	C₂×C₄	1	2	yes	—
223	#121	C₂×C₄	1	2	yes	—
224	#121	C₂×C₄	1	1	yes	characteristic
225	#121	C₂×C₄	1	1	yes	characteristic
226	#121	C₂×C₄	1	2	yes	—
227	#121	C₂×C₄	1	2	yes	—
228	#121	C₂×C₄	1	2	yes	—
229	#121	C₂×C₄	1	2	yes	—
230	#121	C₂×C₄	1	2	yes	—
231	#121	C₂×C₄	1	2	yes	—
232	#121	C₂×C₄	1	2	yes	—
233	#121	C₂×C₄	1	2	yes	—
234	#120	C₂×C₄	1	2	yes	—
235	#120	C₂×C₄	1	2	yes	—
236	#120	C₂×C₄	1	2	yes	—
237	#120	C₂×C₄	1	2	yes	—
238	#120	C₂×C₄	1	2	yes	—
239	#120	C₂×C₄	1	2	yes	—
240	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
241	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
242	C₄×D₄	C₂×C₄	1	1	yes	characteristic
243	C₄×D₄	C₂×C₄	1	2	yes	—
244	C₄×D₄	C₂×C₄	1	1	yes	characteristic
245	C₄×D₄	C₂×C₄	1	1	yes	characteristic
246	C₄×D₄	C₂×C₄	1	2	yes	—
247	C₄×D₄	C₂×C₄	1	2	yes	—
248	C₄×D₄	C₂×C₄	1	1	yes	characteristic
249	C₄×D₄	C₂×C₄	1	2	yes	—
250	C₄×D₄	C₂×C₄	1	2	yes	—
251	C₄×D₄	C₂×C₄	1	1	yes	characteristic
252	C₄×D₄	C₂×C₄	1	2	yes	—
253	C₄×D₄	C₂×C₄	1	1	yes	characteristic
254	C₄×D₄	C₂³	1	1	yes	characteristic
255	C₄×D₄	C₂³	1	1	yes	characteristic
256	C₄×D₄	C₂³	1	2	yes	—
257	C₄×D₄	C₂³	1	1	yes	characteristic
258	C₄×D₄	C₂³	1	2	yes	—
259	C₄×D₄	C₂³	1	1	yes	characteristic
260	C₄×D₄	C₂³	1	2	yes	—
261	C₄×D₄	C₂³	1	2	yes	—
262	C₄×D₄	C₂³	1	2	yes	—
263	C₄×D₄	C₂³	1	2	yes	—
264	#117	C₂³	1	1	yes	characteristic
265	#117	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂×C₄	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
271	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
272	C₂×C₄²	C₂³	1	1	yes	characteristic
273	C₂×C₄²	C₂³	1	2	yes	—
274	C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₄⋊C₈	C₂³	1	2	yes	—
279	C₄⋊C₈	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	2	yes	—
282	C₄⋊C₈	C₂³	1	2	yes	—
283	C₄⋊C₈	C₂³	1	2	yes	—
284	C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈	C₂³	1	2	yes	—
287	C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂²⋊C₈	C₂³	1	2	yes	—
289	C₂²⋊C₈	C₂³	1	1	yes	characteristic
290	C₂²⋊C₈	C₂³	1	2	yes	—
291	C₂²⋊C₈	C₂³	1	2	yes	—
292	C₂²⋊C₈	C₂³	1	2	yes	—
293	C₂²⋊C₈	C₂³	1	2	yes	—
294	C₂²⋊C₈	C₂³	1	2	yes	—
295	C₂²⋊C₈	C₂³	1	2	yes	—
296	C₂²⋊C₈	C₂³	1	2	yes	—
297	C₂²⋊C₈	C₂³	1	1	yes	characteristic
298	C₂²⋊C₈	C₂³	1	2	yes	—
299	C₂²⋊C₈	C₂³	1	1	yes	characteristic
300	C₂²⋊C₈	C₂³	1	1	yes	characteristic
301	C₂²⋊C₈	C₂³	1	2	yes	—
302	C₂²⋊C₈	C₂³	1	2	yes	—
303	C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂²⋊C₈	C₂³	1	2	yes	—
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂²⋊C₈	C₂³	1	2	yes	—
312	#97	C₂³	1	1	yes	characteristic
313	#97	C₂³	1	1	yes	characteristic
314	#97	C₂³	1	1	yes	characteristic
315	#97	C₂³	1	1	yes	characteristic
316	#97	C₂³	1	2	yes	—
317	#97	C₂³	1	2	yes	—
318	#97	C₂³	1	2	yes	—
319	C₄×C₈	C₂³	1	2	yes	—
320	C₄×C₈	C₂³	1	2	yes	—
321	C₄×C₈	C₂³	1	2	yes	—
322	C₂⁴	C₂²×C₄	1	1	yes	characteristic
323	C₂⁴	C₂²×C₄	1	1	yes	characteristic
324	C₂⁴	C₂²×C₄	1	2	yes	—
325	C₂⁴	C₂²×C₄	1	2	yes	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	—	4	2	no	—
333	#41	—	4	2	no	—
334	#41	—	4	2	no	—
335	#41	—	4	2	no	—
336	#41	—	4	4	no	—
337	#41	—	4	4	no	—
338	#41	—	4	2	no	—
339	#41	—	4	2	no	—
340	#41	—	4	2	no	—
341	#41	—	4	2	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
345	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
346	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
347	C₂×Q₈	C₂²×C₄	1	2	yes	—
348	C₂×Q₈	C₂²×C₄	1	2	yes	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
356	C₂×D₄	C₂²×C₄	1	2	yes	—
357	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
358	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
359	C₂×D₄	C₂²×C₄	1	2	yes	—
360	C₂×D₄	C₂²×C₄	1	2	yes	—
361	C₂×D₄	C₂²×C₄	1	2	yes	—
362	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
363	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
364	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
365	C₂×D₄	C₂²×C₄	1	2	yes	—
366	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
367	C₂×D₄	C₂²×C₄	1	2	yes	—
368	C₂×D₄	C₂²×C₄	1	2	yes	—
369	C₂×D₄	C₂²×C₄	1	2	yes	—
370	C₂×D₄	C₂²×C₄	1	2	yes	—
371	C₂×D₄	C₂²×C₄	1	2	yes	—
372	C₂×D₄	C₂²×C₄	1	2	yes	—
373	C₂×D₄	C₂²×C₄	1	2	yes	—
374	C₂×D₄	C₂²×C₄	1	2	yes	—
375	C₂×D₄	C₂²×C₄	1	2	yes	—
376	C₂×D₄	C₂²×C₄	1	2	yes	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
390	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄	1	2	yes	—
392	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₄	1	2	yes	—
394	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄	1	2	yes	—
396	C₂²×C₄	C₂²×C₄	1	2	yes	—
397	C₂²×C₄	C₂²×C₄	1	2	yes	—
398	C₂²×C₄	C₂²×C₄	1	2	yes	—
399	C₂²×C₄	C₂²×C₄	1	2	yes	—
400	C₂²×C₄	C₂²×C₄	1	2	yes	—
401	C₂²×C₄	C₂⁴	1	2	yes	—
402	C₂²×C₄	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴	1	2	yes	—
406	C₂²×C₄	C₂⁴	1	2	yes	—
407	C₂²×C₄	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴	1	1	yes	characteristic
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	2	2	no	—
413	M₁₆	—	4	1	no	—
414	M₁₆	—	4	1	no	—
415	M₁₆	—	4	1	no	—
416	M₁₆	—	4	1	no	—
417	M₁₆	—	4	2	no	—
418	M₁₆	—	4	2	no	—
419	M₁₆	—	4	2	no	—
420	M₁₆	—	4	2	no	—
421	M₁₆	—	4	2	no	—
422	M₁₆	—	4	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	4	1	no	—
428	C₂×C₈	—	4	1	no	—
429	C₂×C₈	—	4	1	no	—
430	C₂×C₈	—	4	1	no	—
431	C₂×C₈	—	4	2	no	—
432	C₂×C₈	—	4	2	no	—
433	C₂×C₈	—	4	2	no	—
434	C₂×C₈	—	4	2	no	—
435	C₂×C₈	—	4	2	no	—
436	C₂×C₈	—	4	2	no	—
437	C₂×C₈	C₂⁴	1	1	yes	characteristic
438	C₂×C₈	C₂⁴	1	1	yes	characteristic
439	C₂×C₈	C₂⁴	1	2	yes	—
440	C₂×C₈	C₂⁴	1	2	yes	—
441	C₂×C₈	C₂⁴	1	2	yes	—
442	C₂×C₈	C₂⁴	1	2	yes	—
443	C₂×C₈	C₂⁴	1	1	yes	characteristic
444	C₂×C₈	C₂⁴	1	1	yes	characteristic
445	C₂×C₈	C₂⁴	1	1	yes	characteristic
446	C₂×C₈	C₂⁴	1	1	yes	characteristic
447	C₂×C₈	C₂⁴	1	1	yes	characteristic
448	C₂×C₈	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
450	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
451	C₄⋊C₄	C₂²×C₄	1	2	yes	—
452	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
453	C₄⋊C₄	C₂²×C₄	1	2	yes	—
454	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
455	C₄⋊C₄	C₂²×C₄	1	2	yes	—
456	C₄⋊C₄	C₂²×C₄	1	2	yes	—
457	C₄⋊C₄	C₂²×C₄	1	2	yes	—
458	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
459	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
460	C₄⋊C₄	C₂²×C₄	1	2	yes	—
461	C₄⋊C₄	C₂²×C₄	1	2	yes	—
462	C₄⋊C₄	C₂²×C₄	1	2	yes	—
463	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
464	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
465	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
466	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
467	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
468	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
469	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
470	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
471	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
472	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
473	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
474	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
475	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
476	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
477	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
478	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
479	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
480	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
481	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
482	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
483	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
484	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
485	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
486	C₄²	C₂²×C₄	1	2	yes	—
487	C₄²	C₂²×C₄	1	1	yes	characteristic
488	C₄²	C₂²×C₄	1	2	yes	—
489	C₄²	C₂²×C₄	1	1	yes	characteristic
490	C₄²	C₂⁴	1	1	yes	characteristic
491	C₄²	C₂⁴	1	2	yes	—
492	C₄²	C₂⁴	1	1	yes	characteristic
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	C₂³×C₄	1	1	yes	characteristic
506	C₂³	C₂³×C₄	1	1	yes	characteristic
507	C₂³	C₂³×C₄	1	1	yes	characteristic
508	C₂³	C₂³×C₄	1	2	yes	—
509	C₂³	C₂³×C₄	1	2	yes	—
510	C₂³	C₂³×C₄	1	2	yes	—
511	C₂³	C₂³×C₄	1	1	yes	characteristic
512	C₂³	C₂³×C₄	1	1	yes	characteristic
513	Q₈	—	2	2	no	—
514	Q₈	—	2	2	no	—
515	Q₈	—	2	2	no	—
516	Q₈	—	4	2	no	—
517	Q₈	—	4	2	no	—
518	D₄	—	2	4	no	—
519	D₄	—	2	4	no	—
520	D₄	—	2	4	no	—
521	D₄	—	2	2	no	—
522	D₄	—	2	2	no	—
523	D₄	—	2	4	no	—
524	D₄	—	2	2	no	—
525	D₄	—	2	2	no	—
526	D₄	—	2	2	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
571	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
572	C₂×C₄	C₂³×C₄	1	2	yes	—
573	C₂×C₄	C₂³×C₄	1	2	yes	—
574	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
575	C₂×C₄	C₂³×C₄	1	2	yes	—
576	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
577	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
578	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
579	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
580	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
581	C₂×C₄	C₂³×C₄	1	2	yes	—
582	C₂×C₄	C₂³×C₄	1	2	yes	—
583	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
584	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
585	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
586	C₂×C₄	C₂⁵	1	1	yes	characteristic
587	C₈	—	2	1	no	—
588	C₈	—	2	1	no	—
589	C₈	—	2	1	no	—
590	C₈	—	2	1	no	—
591	C₈	—	2	1	no	—
592	C₈	—	2	1	no	—
593	C₈	—	2	1	no	—
594	C₈	—	2	1	no	—
595	C₈	—	2	2	no	—
596	C₈	—	2	2	no	—
597	C₈	—	2	2	no	—
598	C₈	—	2	2	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	8	4	no	—
623	C₂²	—	8	2	no	—
624	C₂²	—	8	4	no	—
625	C₂²	#518	1	2	yes	—
626	C₂²	#568	1	2	yes	—
627	C₂²	C₂⁴×C₄	1	1	yes	characteristic
628	C₄	—	2	1	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	2	no	—
641	C₄	#518	1	2	yes	—
642	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
643	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
644	C₂	—	2	2	no	—
645	C₂	—	2	2	no	—
646	C₂	—	4	1	no	—
647	C₂	—	4	1	no	—
648	C₂	—	4	2	no	—
649	C₂	—	4	2	no	—
650	C₂	—	4	2	no	—
651	C₂	—	4	1	no	—
652	C₂	C₂×#518	1	1	yes	characteristic
653	C₂	C₂×#568	1	1	yes	characteristic
654	C₂	#3573	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄	C₂⁵
commutator, socle	C₂²	C₂⁴×C₄
prime radical	D₄×#41	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #2981	C₂	semidirect
3. #2980	C₂	semidirect
4. #2978	C₂	semidirect
5. #2977	C₂	semidirect
6. #2976	C₂	semidirect
7. #2976	C₂	semidirect
8. #2974	C₂	semidirect
9. #2973	C₂	semidirect
10. #2935	C₂	semidirect
11. D₄×M₁₆	C₂	semidirect
12. #2933	C₂	semidirect
13. #2933	C₂	semidirect
14. #2932	C₂	semidirect
15. #2930	C₂	semidirect
16. #2929	C₂	semidirect
17. C₂×#435	C₂	semidirect
18. #2925	C₂	semidirect
19. #2923	C₂	semidirect
20. #2880	C₂	semidirect
21. #2880	C₂	semidirect
22. #2879	C₂	semidirect
23. C₂×#408	C₂	semidirect
26. C₂×#131	C₂²	semidirect
27. C₂×#131	C₂²	semidirect
28. C₂×#131	C₂²	semidirect
29. C₂×#131	C₂²	semidirect
30. C₂²×M₁₆	C₂²	semidirect
31. C₂²×M₁₆	C₂²	semidirect
32. C₂²×M₁₆	C₂²	semidirect
33. C₂³×C₈	C₂²	semidirect
55. #436	C₂²	semidirect
56. #436	C₂²	semidirect
57. #436	C₂²	semidirect
58. #436	C₂²	semidirect
59. #436	C₂²	semidirect
60. #436	C₂²	semidirect
64. #435	C₂²	semidirect
65. #435	C₂²	semidirect
66. #435	C₂²	semidirect
67. #435	C₂²	semidirect
68. #435	C₂²	semidirect
69. #435	C₂²	semidirect
70. #435	C₂²	semidirect
71. #435	C₂²	semidirect
72. #435	C₂²	semidirect
73. #435	C₂²	semidirect
74. #435	C₂²	semidirect
75. #435	C₂²	semidirect
76. #435	C₂²	semidirect
77. #435	C₂²	semidirect
78. #435	C₂²	semidirect
79. #435	C₂²	semidirect
80. #435	C₂²	semidirect
81. #435	C₂²	semidirect
82. #435	C₂²	semidirect
83. #435	C₂²	semidirect
84. #435	C₂²	semidirect
85. C₈×D₄	C₂²	semidirect
86. C₈×D₄	C₂²	semidirect
87. C₈×D₄	C₂²	semidirect
88. C₈×D₄	C₂²	semidirect
89. C₈×D₄	C₂²	semidirect
90. C₈×D₄	C₂²	semidirect
91. #433	C₂²	semidirect
92. #433	C₂²	semidirect
93. #433	C₂²	semidirect
94. #433	C₂²	semidirect
95. #432	C₂²	semidirect
96. #432	C₂²	semidirect
97. #432	C₂²	semidirect
98. #431	C₂²	semidirect
99. #424	C₂²	semidirect
100. #424	C₂²	semidirect
101. #423	C₂²	semidirect
102. C₂×C₄⋊C₈	C₂²	semidirect
107. #408	C₂²	semidirect
108. #408	C₂²	semidirect
109. #408	C₂²	semidirect
110. #408	C₂²	semidirect
111. #408	C₂²	semidirect
112. #408	C₂²	semidirect
113. #408	C₂²	semidirect
114. #408	C₂²	semidirect
115. #408	C₂²	semidirect
116. #408	C₂²	semidirect
117. #408	C₂²	semidirect
118. #408	C₂²	semidirect
119. #407	C₂²	semidirect
120. #407	C₂²	semidirect
121. #407	C₂²	semidirect
122. #407	C₂²	semidirect
123. #407	C₂²	semidirect
124. #407	C₂²	semidirect
125. C₂×C₂²⋊C₈	C₂²	semidirect
126. C₂×C₂²⋊C₈	C₂²	semidirect
127. C₂×C₂²⋊C₈	C₂²	semidirect
128. C₂×C₂²⋊C₈	C₂²	semidirect
129. C₂×C₂²⋊C₈	C₂²	semidirect
130. C₂×C₂²⋊C₈	C₂²	semidirect
131. #405	C₂²	semidirect
132. #405	C₂²	semidirect
133. C₄×M₁₆	C₂²	semidirect
134. C₂×#97	C₂²	semidirect

Maximal subgroups

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

subgroup	index
D₄×#41	2
#2981	2
#2980	2
#2978	2
#2977	2
#2976	2
#2974	2
#2973	2
#2935	2
D₄×M₁₆	2
#2933	2
#2932	2
#2930	2
#2929	2
C₂×#435	2
#2925	2
#2923	2
#2880	2
#2879	2
C₂×#408	2