Subgroups — #61568

Order 256.

1071 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	#3304	C₂	1	1	yes	maximal, characteristic, complemented
4	#3302	C₂	1	1	yes	maximal, characteristic, complemented
5	#3300	C₂	1	2	yes	maximal, complemented
6	#3298	C₂	1	1	yes	maximal, characteristic, complemented
7	#3296	C₂	1	2	yes	maximal, complemented
8	#3294	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#3285	C₂	1	2	yes	maximal, complemented
11	#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	#3283	C₂	1	1	yes	maximal, characteristic, complemented
13	#3282	C₂	1	2	yes	maximal, complemented
14	D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	#3191	C₂	1	2	yes	maximal, complemented
18	#3190	C₂	1	2	yes	maximal, complemented
19	#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	#3002	C₂	1	2	yes	maximal, complemented
22	C₂×#452	C₂	1	2	yes	maximal, complemented
23	#2972	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41	C₂²	1	2	yes	—
25	C₂×#135	C₂²	1	2	yes	complemented
26	C₂×#135	C₂²	1	2	yes	complemented
27	C₂²×Q₁₆	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆	C₂²	1	2	yes	complemented
29	#556	C₂²	1	1	yes	characteristic, complemented
30	#554	—	2	1	no	—
31	#552	C₂²	1	2	yes	complemented
32	#551	—	2	2	no	—
33	#550	C₂²	1	1	yes	characteristic
34	D₄×Q₈	C₂²	1	1	yes	characteristic
35	D₄×Q₈	C₂²	1	1	yes	characteristic
36	#548	C₂²	1	2	yes	—
37	#548	C₂²	1	2	yes	complemented
38	#547	—	2	1	no	—
39	#547	C₂²	1	1	yes	characteristic
40	#547	C₂²	1	1	yes	characteristic
41	#547	C₂²	1	1	yes	characteristic, complemented
42	#546	—	2	1	no	—
43	#546	—	2	2	no	—
44	#546	C₂²	1	2	yes	—
45	D₄²	—	2	1	no	—
46	D₄²	C₂²	1	1	yes	characteristic
47	#542	—	2	1	no	—
48	#539	—	2	2	no	—
49	#533	C₂²	1	1	yes	characteristic, complemented
50	#532	—	2	1	no	—
51	#532	C₂²	1	1	yes	characteristic
52	#529	C₂²	1	1	yes	characteristic, complemented
53	#525	—	2	2	no	—
54	#525	C₂²	1	2	yes	—
55	#525	C₂²	1	2	yes	complemented
56	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
57	#520	—	2	1	no	—
58	C₄×#41	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄	—	2	1	no	—
60	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
61	#495	C₂²	1	2	yes	complemented
62	#494	C₂²	1	1	yes	characteristic, complemented
63	#492	C₂²	1	1	yes	characteristic, complemented
64	#488	C₂²	1	2	yes	complemented
65	#487	C₂²	1	1	yes	characteristic, complemented
66	#486	C₂²	1	1	yes	characteristic, complemented
67	#485	C₂²	1	1	yes	characteristic, complemented
68	#485	C₂²	1	2	yes	complemented
69	#485	C₂²	1	2	yes	complemented
70	#483	C₂²	1	2	yes	complemented
71	#482	C₂²	1	1	yes	characteristic, complemented
72	#482	C₂²	1	2	yes	complemented
73	#480	C₂²	1	2	yes	complemented
74	#479	C₂²	1	1	yes	characteristic, complemented
75	#478	C₂²	1	1	yes	characteristic, complemented
76	#475	C₂²	1	1	yes	characteristic, complemented
77	#474	C₂²	1	1	yes	characteristic, complemented
78	#467	C₂²	1	2	yes	complemented
79	#467	C₂²	1	2	yes	complemented
80	#467	C₂²	1	2	yes	complemented
81	#466	C₂²	1	2	yes	complemented
82	#465	C₂²	1	2	yes	complemented
83	#465	C₂²	1	2	yes	complemented
84	#465	C₂²	1	2	yes	complemented
85	#465	C₂²	1	2	yes	complemented
86	#464	C₂²	1	1	yes	characteristic, complemented
87	#464	C₂²	1	2	yes	complemented
88	#464	C₂²	1	2	yes	complemented
89	#463	C₂²	1	1	yes	characteristic, complemented
90	#462	C₂²	1	1	yes	characteristic, complemented
91	#462	C₂²	1	1	yes	characteristic, complemented
92	#461	C₂²	1	1	yes	characteristic, complemented
93	#461	C₂²	1	1	yes	characteristic, complemented
94	#460	C₂²	1	1	yes	characteristic, complemented
95	#459	C₂²	1	1	yes	characteristic, complemented
96	#452	C₂²	1	1	yes	characteristic
97	#452	C₂²	1	2	yes	—
98	#452	C₂²	1	2	yes	complemented
99	#452	C₂²	1	2	yes	complemented
100	#452	C₂²	1	2	yes	complemented
101	#452	C₂²	1	2	yes	complemented
102	#452	C₂²	1	2	yes	complemented
103	#452	C₂²	1	2	yes	complemented
104	#452	C₂²	1	2	yes	complemented
105	#452	C₂²	1	2	yes	complemented
106	#451	C₂²	1	2	yes	complemented
107	#451	C₂²	1	2	yes	complemented
108	#450	C₂²	1	2	yes	complemented
109	#449	C₂²	1	1	yes	characteristic
110	#449	C₂²	1	2	yes	complemented
111	#449	C₂²	1	2	yes	complemented
112	#448	C₂²	1	2	yes	complemented
113	#448	C₂²	1	2	yes	complemented
114	#447	C₂²	1	2	yes	complemented
115	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆	C₂²	1	2	yes	complemented
117	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆	C₂²	1	2	yes	complemented
120	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
121	C₈×D₄	C₂²	1	1	yes	characteristic
122	C₈×D₄	C₂²	1	1	yes	characteristic
123	C₈×D₄	C₂²	1	2	yes	complemented
124	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
125	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄	C₂²	1	2	yes	complemented
127	#431	C₂²	1	1	yes	characteristic, complemented
128	#431	C₂²	1	1	yes	characteristic, complemented
129	#416	C₂²	1	2	yes	complemented
130	#416	C₂²	1	2	yes	complemented
131	C₂×#103	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	2	no	—
137	C₂×#41	—	2	2	no	—
138	C₂×#41	—	4	4	no	—
139	C₂×#41	—	4	4	no	—
140	C₂×#41	C₂³	1	1	yes	characteristic
141	C₂×#41	C₂³	1	2	yes	—
142	C₂×#41	C₂³	1	2	yes	—
143	C₂×#41	C₂³	1	2	yes	—
144	C₂×#41	C₂³	1	2	yes	—
145	C₂²×Q₈	C₂³	1	2	yes	—
146	C₂²×Q₈	C₂³	1	2	yes	—
147	C₂²×D₄	—	2	2	no	—
148	C₂²×D₄	—	2	1	no	—
149	C₂²×D₄	D₄	1	1	yes	characteristic
150	C₂²×D₄	C₂³	1	2	yes	—
151	C₂³×C₄	—	2	2	no	—
152	C₂³×C₄	C₂³	1	2	yes	—
153	#135	—	4	4	no	—
154	#135	—	4	4	no	—
155	C₂×Q₁₆	—	4	4	no	—
156	C₂×Q₁₆	C₂³	1	1	yes	characteristic
157	C₂×Q₁₆	C₂³	1	2	yes	—
158	C₂×Q₁₆	C₂³	1	2	yes	—
159	C₂×Q₁₆	C₂³	1	2	yes	—
160	C₂×Q₁₆	C₂³	1	2	yes	—
161	C₂×SD₁₆	—	4	4	no	—
162	C₂×SD₁₆	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆	C₂³	1	2	yes	—
164	C₂×SD₁₆	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆	C₂³	1	2	yes	—
166	C₂×SD₁₆	C₂³	1	2	yes	—
167	C₂×SD₁₆	C₂³	1	2	yes	—
168	C₂×SD₁₆	C₂³	1	2	yes	—
169	C₂×D₈	C₂³	1	1	yes	characteristic
170	C₂×D₈	C₂³	1	2	yes	—
171	C₂²×C₈	C₂³	1	2	yes	—
172	C₂²×C₈	C₂³	1	2	yes	—
173	C₂²×C₈	C₂³	1	2	yes	—
174	C₂²×C₈	C₂³	1	2	yes	—
175	C₄⋊Q₈	—	2	1	no	—
176	C₄⋊Q₈	—	2	1	no	—
177	C₄⋊Q₈	C₂³	1	1	yes	characteristic
178	C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	#127	—	2	1	no	—
181	#127	C₂³	1	1	yes	characteristic
182	#126	—	2	2	no	—
183	#126	—	2	2	no	—
184	#126	—	2	1	no	—
185	#125	—	2	2	no	—
186	#125	—	2	1	no	—
187	#125	C₂³	1	1	yes	characteristic
188	#124	—	2	1	no	—
189	#124	—	2	2	no	—
190	#124	—	2	2	no	—
191	#124	C₂³	1	1	yes	characteristic
192	#124	C₂³	1	2	yes	—
193	#123	—	2	2	no	—
194	#123	—	2	2	no	—
195	#123	—	2	2	no	—
196	#123	—	2	1	no	—
197	#123	—	2	2	no	—
198	#123	—	2	2	no	—
199	#123	—	2	2	no	—
200	#123	—	2	2	no	—
201	C₂²⋊Q₈	—	2	2	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	—	2	1	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	1	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₂²⋊Q₈	C₂³	1	2	yes	—
216	#121	—	2	2	no	—
217	#121	—	2	1	no	—
218	#121	—	2	2	no	—
219	#121	—	2	1	no	—
220	#121	—	2	1	no	—
221	#121	—	2	1	no	—
222	#121	—	2	1	no	—
223	#121	—	2	2	no	—
224	#121	—	2	2	no	—
225	#121	C₂³	1	2	yes	—
226	#121	C₂³	1	2	yes	—
227	#121	C₂³	1	1	yes	characteristic
228	#121	C₂³	1	2	yes	—
229	#120	—	2	2	no	—
230	#120	—	2	2	no	—
231	#120	—	2	2	no	—
232	#120	—	2	2	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	C₂³	1	1	yes	characteristic
236	C₄×Q₈	C₂³	1	1	yes	characteristic
237	C₄×Q₈	C₂³	1	1	yes	characteristic
238	C₄×Q₈	C₂³	1	2	yes	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	2	no	—
246	C₄×D₄	—	2	2	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	D₄	1	1	yes	characteristic
254	C₄×D₄	D₄	1	2	yes	—
255	C₄×D₄	D₄	1	1	yes	characteristic
256	C₄×D₄	C₂³	1	1	yes	characteristic
257	C₄×D₄	C₂³	1	1	yes	characteristic
258	C₄×D₄	C₂³	1	1	yes	characteristic
259	C₄×D₄	C₂³	1	1	yes	characteristic
260	C₄×D₄	C₂³	1	2	yes	—
261	C₄×D₄	C₂³	1	1	yes	characteristic
262	#117	—	2	1	no	—
263	#117	—	2	2	no	—
264	#117	—	2	1	no	—
265	#117	—	2	1	no	—
266	#117	C₂³	1	1	yes	characteristic
267	#117	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³	1	2	yes	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	D₄	1	2	yes	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	C₂³	1	1	yes	characteristic
278	#107	C₂³	1	1	yes	characteristic
279	#107	C₂³	1	2	yes	—
280	#107	C₂³	1	1	yes	characteristic
281	#106	C₂³	1	2	yes	—
282	#106	C₂³	1	1	yes	characteristic
283	#106	C₂³	1	1	yes	characteristic
284	C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₄⋊C₈	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	1	yes	characteristic
296	#103	C₂³	1	2	yes	—
297	#103	C₂³	1	2	yes	—
298	#103	C₂³	1	1	yes	characteristic
299	#102	C₂³	1	1	yes	characteristic
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	1	yes	characteristic
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	2	yes	—
306	#102	C₂³	1	1	yes	characteristic
307	#102	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂²⋊C₈	C₂³	1	2	yes	—
313	C₂²⋊C₈	C₂³	1	2	yes	—
314	C₂²⋊C₈	C₂³	1	2	yes	—
315	C₄×C₈	C₂³	1	1	yes	characteristic
316	C₄×C₈	C₂³	1	1	yes	characteristic
317	C₄×C₈	C₂³	1	2	yes	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	C₂×D₄	1	2	yes	—
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	4	no	—
323	#41	—	2	4	no	—
324	#41	—	4	2	no	—
325	#41	—	4	2	no	—
326	#41	—	4	2	no	—
327	#41	—	4	2	no	—
328	#41	—	4	8	no	—
329	#41	—	4	2	no	—
330	#41	—	4	2	no	—
331	#41	—	4	8	no	—
332	#41	—	4	4	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	—	4	2	no	—
339	C₂×Q₈	—	4	2	no	—
340	C₂×Q₈	C₂⁴	1	2	yes	—
341	C₂×Q₈	C₂⁴	1	1	yes	characteristic
342	C₂×Q₈	C₂⁴	1	2	yes	—
343	C₂×Q₈	C₂⁴	1	1	yes	characteristic
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	8	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	C₂×D₄	1	2	yes	—
362	C₂×D₄	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄	C₂×D₄	1	1	yes	characteristic
364	C₂×D₄	C₂⁴	1	2	yes	—
365	C₂×D₄	C₂⁴	1	1	yes	characteristic
366	C₂×D₄	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	8	no	—
381	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄	1	2	yes	—
384	C₂²×C₄	C₂×D₄	1	2	yes	—
385	C₂²×C₄	C₂×D₄	1	2	yes	—
386	C₂²×C₄	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴	1	2	yes	—
388	C₂²×C₄	C₂⁴	1	2	yes	—
389	Q₁₆	—	2	2	no	—
390	Q₁₆	—	2	4	no	—
391	Q₁₆	—	4	2	no	—
392	Q₁₆	—	4	2	no	—
393	Q₁₆	—	4	2	no	—
394	SD₁₆	—	2	2	no	—
395	SD₁₆	—	2	2	no	—
396	SD₁₆	—	2	4	no	—
397	SD₁₆	—	4	2	no	—
398	SD₁₆	—	4	2	no	—
399	SD₁₆	—	4	2	no	—
400	SD₁₆	—	4	2	no	—
401	D₈	—	2	2	no	—
402	D₈	—	4	2	no	—
403	C₂×C₈	—	4	2	no	—
404	C₂×C₈	—	4	2	no	—
405	C₂×C₈	—	4	2	no	—
406	C₂×C₈	—	4	2	no	—
407	C₂×C₈	C₂⁴	1	1	yes	characteristic
408	C₂×C₈	C₂⁴	1	1	yes	characteristic
409	C₂×C₈	C₂⁴	1	2	yes	—
410	C₂×C₈	C₂⁴	1	1	yes	characteristic
411	C₂×C₈	C₂⁴	1	1	yes	characteristic
412	C₂×C₈	C₂⁴	1	2	yes	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
433	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄	C₂×D₄	1	2	yes	—
435	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄	C₂⁴	1	2	yes	—
437	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	1	no	—
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄	C₂×D₄	1	2	yes	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	1	no	—
470	C₄²	C₂×D₄	1	1	yes	characteristic
471	C₄²	C₂×D₄	1	1	yes	characteristic
472	C₄²	C₂⁴	1	1	yes	characteristic
473	C₄²	C₂⁴	1	1	yes	characteristic
474	C₂³	—	2	1	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	4	no	—
481	C₂³	—	4	4	no	—
482	C₂³	—	8	2	no	—
483	C₂³	C₂²×D₄	1	2	yes	—
484	C₂³	C₂²×D₄	1	1	yes	characteristic
485	C₂³	C₂²×D₄	1	2	yes	—
486	Q₈	—	2	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	2	2	no	—
489	Q₈	—	2	2	no	—
490	Q₈	—	2	2	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	2	no	—
493	Q₈	—	4	4	no	—
494	Q₈	—	4	2	no	—
495	Q₈	—	8	2	no	—
496	Q₈	H(5,𝔽₂)	1	2	yes	—
497	D₄	—	2	4	no	—
498	D₄	—	2	4	no	—
499	D₄	—	2	2	no	—
500	D₄	—	2	1	no	—
501	D₄	—	2	1	no	—
502	D₄	—	2	1	no	—
503	D₄	—	2	2	no	—
504	D₄	—	2	2	no	—
505	D₄	—	4	4	no	—
506	D₄	—	4	4	no	—
507	D₄	—	4	4	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	4	no	—
510	D₄	—	4	4	no	—
511	D₄	—	4	4	no	—
512	D₄	—	4	2	no	—
513	D₄	—	8	1	no	—
514	D₄	—	8	2	no	—
515	D₄	—	8	2	no	—
516	D₄	#135	1	4	yes	complemented
517	D₄	H(5,𝔽₂)	1	2	yes	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	8	1	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄	1	2	yes	—
552	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄	1	2	yes	—
555	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄	C₂⁵	1	1	yes	characteristic
557	C₈	—	2	1	no	—
558	C₈	—	2	2	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	2	no	—
562	C₈	—	2	1	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	8	4	no	—
581	C₂²	—	8	8	no	—
582	C₂²	C₂×#135	1	4	yes	—
583	C₂²	C₂³×D₄	1	1	yes	characteristic
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	2	no	—
599	C₄	C₂×#135	1	2	yes	—
600	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
601	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂	—	2	4	no	—
603	C₂	—	4	2	no	—
604	C₂	—	4	1	no	—
605	C₂	—	4	2	no	—
606	C₂	—	8	1	no	—
607	C₂	—	8	2	no	—
608	C₂	#3484	1	1	yes	characteristic
609	C₂	C₂²×#135	1	1	yes	characteristic
610	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3520	C₂	semidirect
2. D₄×#41	C₂	semidirect
3. #3304	C₂	semidirect
4. #3302	C₂	semidirect
5. #3300	C₂	semidirect
6. #3298	C₂	semidirect
7. #3296	C₂	semidirect
8. #3294	C₂	semidirect
9. D₄×Q₁₆	C₂	semidirect
10. #3285	C₂	semidirect
11. #3284	C₂	semidirect
12. #3283	C₂	semidirect
13. #3282	C₂	semidirect
14. D₄×SD₁₆	C₂	semidirect
15. #3212	C₂	semidirect
16. #3210	C₂	semidirect
17. #3191	C₂	semidirect
18. #3190	C₂	semidirect
19. #3107	C₂	semidirect
20. #3102	C₂	semidirect
21. #3002	C₂	semidirect
22. C₂×#452	C₂	semidirect
23. #2972	C₂	semidirect
25. C₂×#135	C₂²	semidirect
26. C₂×#135	C₂²	semidirect
27. C₂²×Q₁₆	C₂²	semidirect
28. C₂²×SD₁₆	C₂²	semidirect
29. #556	C₂²	semidirect
31. #552	C₂²	semidirect
37. #548	C₂²	semidirect
41. #547	C₂²	semidirect
49. #533	C₂²	semidirect
52. #529	C₂²	semidirect
55. #525	C₂²	semidirect
56. C₂×C₂²⋊Q₈	C₂²	semidirect
61. #495	C₂²	semidirect
62. #494	C₂²	semidirect
63. #492	C₂²	semidirect
64. #488	C₂²	semidirect
65. #487	C₂²	semidirect
66. #486	C₂²	semidirect
67. #485	C₂²	semidirect
68. #485	C₂²	semidirect
69. #485	C₂²	semidirect
70. #483	C₂²	semidirect
71. #482	C₂²	semidirect
72. #482	C₂²	semidirect
73. #480	C₂²	semidirect
74. #479	C₂²	semidirect
75. #478	C₂²	semidirect
76. #475	C₂²	semidirect
77. #474	C₂²	semidirect
78. #467	C₂²	semidirect
79. #467	C₂²	semidirect
80. #467	C₂²	semidirect
81. #466	C₂²	semidirect
82. #465	C₂²	semidirect
83. #465	C₂²	semidirect
84. #465	C₂²	semidirect
85. #465	C₂²	semidirect
86. #464	C₂²	semidirect
87. #464	C₂²	semidirect
88. #464	C₂²	semidirect
89. #463	C₂²	semidirect
90. #462	C₂²	semidirect
91. #462	C₂²	semidirect
92. #461	C₂²	semidirect
93. #461	C₂²	semidirect
94. #460	C₂²	semidirect
95. #459	C₂²	semidirect
98. #452	C₂²	semidirect
99. #452	C₂²	semidirect
100. #452	C₂²	semidirect
101. #452	C₂²	semidirect
102. #452	C₂²	semidirect
103. #452	C₂²	semidirect
104. #452	C₂²	semidirect
105. #452	C₂²	semidirect
106. #451	C₂²	semidirect
107. #451	C₂²	semidirect
108. #450	C₂²	semidirect
110. #449	C₂²	semidirect
111. #449	C₂²	semidirect
112. #448	C₂²	semidirect
113. #448	C₂²	semidirect
114. #447	C₂²	semidirect
115. C₄×Q₁₆	C₂²	semidirect
116. C₄×Q₁₆	C₂²	semidirect
117. C₄×SD₁₆	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
119. C₄×SD₁₆	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
123. C₈×D₄	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. C₈×D₄	C₂²	semidirect
126. C₈×D₄	C₂²	semidirect
127. #431	C₂²	semidirect
128. #431	C₂²	semidirect
129. #416	C₂²	semidirect
130. #416	C₂²	semidirect
131. C₂×#103	C₂²	semidirect
132. C₂×#102	C₂²	semidirect
133. C₂×C₂²⋊C₈	C₂²	semidirect
134. C₂×C₂²⋊C₈	C₂²	semidirect
516. D₄	#135	semidirect

Maximal subgroups

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

subgroup	index
#3520	2
D₄×#41	2
#3304	2
#3302	2
#3300	2
#3298	2
#3296	2
#3294	2
D₄×Q₁₆	2
#3285	2
#3284	2
#3283	2
#3282	2
D₄×SD₁₆	2
#3212	2
#3210	2
#3191	2
#3190	2
#3107	2
#3102	2
#3002	2
C₂×#452	2
#2972	2