Subgroups — #61729

Order 256.

911 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3519	C₂	1	1	yes	maximal, characteristic
2	C₂×#552	C₂	1	1	yes	maximal, characteristic, complemented
3	#3351	C₂	1	2	yes	maximal, complemented
4	#3348	C₂	1	2	yes	maximal, complemented
5	#3344	C₂	1	2	yes	maximal, complemented
6	#3337	C₂	1	2	yes	maximal, complemented
7	#3323	C₂	1	2	yes	maximal, complemented
8	#3317	C₂	1	2	yes	maximal, complemented
9	#3310	C₂	1	2	yes	maximal, complemented
10	#3296	C₂	1	2	yes	maximal, complemented
11	#3234	C₂	1	1	yes	maximal, characteristic, complemented
12	#3232	C₂	1	1	yes	maximal, characteristic, complemented
13	#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	#3193	C₂	1	1	yes	maximal, characteristic, complemented
15	#3190	C₂	1	1	yes	maximal, characteristic, complemented
16	#3187	C₂	1	1	yes	maximal, characteristic, complemented
17	#3117	C₂	1	1	yes	maximal, characteristic, complemented
18	#3103	C₂	1	1	yes	maximal, characteristic, complemented
19	#3094	C₂	1	1	yes	maximal, characteristic, complemented
20	#3092	C₂	1	1	yes	maximal, characteristic, complemented
21	#3091	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#481	C₂	1	1	yes	maximal, characteristic, complemented
23	#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	#555	C₂²	1	1	yes	characteristic
25	#554	C₂²	1	1	yes	characteristic
26	#553	—	2	1	no	—
27	#553	C₂²	1	1	yes	characteristic
28	#553	C₂²	1	1	yes	characteristic
29	#552	—	2	1	no	—
30	#552	—	2	1	no	—
31	#552	—	2	1	no	—
32	#552	—	2	1	no	—
33	#552	C₂²	1	2	yes	—
34	#552	C₂²	1	2	yes	complemented
35	#552	C₂²	1	2	yes	complemented
36	#552	C₂²	1	2	yes	complemented
37	#550	C₂²	1	1	yes	characteristic
38	#546	—	2	1	no	—
39	#546	—	2	1	no	—
40	#546	C₂²	1	1	yes	characteristic
41	#546	C₂²	1	1	yes	characteristic
42	D₄²	—	2	1	no	—
43	D₄²	C₂²	1	1	yes	characteristic
44	#540	—	2	1	no	—
45	#538	—	2	1	no	—
46	#538	—	2	1	no	—
47	#532	C₂²	1	1	yes	characteristic
48	#529	C₂²	1	1	yes	characteristic
49	C₂×#126	—	2	1	no	—
50	C₂×#125	—	2	1	no	—
51	C₂×#125	C₂²	1	1	yes	characteristic, complemented
52	#525	C₂²	1	1	yes	characteristic
53	#525	C₂²	1	1	yes	characteristic
54	C₂×#123	—	2	1	no	—
55	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
57	C₂×#121	C₂²	1	1	yes	characteristic
58	C₂×#121	C₂²	1	1	yes	characteristic
59	#518	—	2	1	no	—
60	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
62	C₂×#117	—	2	1	no	—
63	C₂×#117	C₂²	1	1	yes	characteristic, complemented
64	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
65	#501	C₂²	1	2	yes	complemented
66	#499	C₂²	1	2	yes	complemented
67	#490	C₂²	1	2	yes	complemented
68	#488	C₂²	1	2	yes	complemented
69	#485	C₂²	1	2	yes	complemented
70	#485	C₂²	1	2	yes	complemented
71	#485	C₂²	1	2	yes	complemented
72	#484	C₂²	1	2	yes	complemented
73	#484	C₂²	1	1	yes	characteristic, complemented
74	#484	C₂²	1	1	yes	characteristic, complemented
75	#483	C₂²	1	2	yes	complemented
76	#483	C₂²	1	2	yes	complemented
77	#483	C₂²	1	1	yes	characteristic, complemented
78	#482	C₂²	1	2	yes	complemented
79	#482	C₂²	1	2	yes	complemented
80	#482	C₂²	1	2	yes	complemented
81	#481	C₂²	1	1	yes	characteristic
82	#481	C₂²	1	1	yes	characteristic
83	#481	C₂²	1	1	yes	characteristic, complemented
84	#481	C₂²	1	2	yes	complemented
85	#481	C₂²	1	2	yes	complemented
86	#481	C₂²	1	1	yes	characteristic, complemented
87	#481	C₂²	1	1	yes	characteristic, complemented
88	#481	C₂²	1	1	yes	characteristic, complemented
89	#480	C₂²	1	1	yes	characteristic
90	#480	C₂²	1	2	yes	complemented
91	#480	C₂²	1	1	yes	characteristic, complemented
92	#480	C₂²	1	1	yes	characteristic, complemented
93	#479	C₂²	1	2	yes	complemented
94	#479	C₂²	1	2	yes	complemented
95	#478	C₂²	1	2	yes	complemented
96	#478	C₂²	1	2	yes	complemented
97	#478	C₂²	1	2	yes	complemented
98	#475	C₂²	1	2	yes	complemented
99	#470	C₂²	1	2	yes	complemented
100	#468	C₂²	1	2	yes	complemented
101	#468	C₂²	1	2	yes	complemented
102	#468	C₂²	1	2	yes	complemented
103	#467	C₂²	1	2	yes	complemented
104	#465	C₂²	1	2	yes	complemented
105	#465	C₂²	1	2	yes	complemented
106	#465	C₂²	1	2	yes	complemented
107	#464	C₂²	1	2	yes	complemented
108	#460	C₂²	1	2	yes	complemented
109	#452	C₂²	1	2	yes	complemented
110	#452	C₂²	1	2	yes	complemented
111	#451	C₂²	1	1	yes	characteristic, complemented
112	#450	C₂²	1	2	yes	complemented
113	#450	C₂²	1	2	yes	complemented
114	#448	C₂²	1	1	yes	characteristic
115	#448	C₂²	1	1	yes	characteristic, complemented
116	#448	C₂²	1	1	yes	characteristic, complemented
117	#441	C₂²	1	2	yes	complemented
118	#440	C₂²	1	2	yes	complemented
119	C₄×SD₁₆	C₂²	1	2	yes	complemented
120	C₄×SD₁₆	C₂²	1	2	yes	complemented
121	#436	C₂²	1	2	yes	complemented
122	#435	C₂²	1	2	yes	—
123	#435	C₂²	1	2	yes	complemented
124	C₈×D₄	C₂²	1	2	yes	complemented
125	#432	C₂²	1	1	yes	characteristic, complemented
126	#431	C₂²	1	1	yes	characteristic, complemented
127	#428	C₂²	1	2	yes	complemented
128	#428	C₂²	1	2	yes	complemented
129	#427	C₂²	1	2	yes	complemented
130	C₂×#106	C₂²	1	2	yes	complemented
131	#418	C₂²	1	2	yes	complemented
132	#417	C₂²	1	2	yes	complemented
133	#416	C₂²	1	2	yes	complemented
134	C₂×#102	C₂²	1	2	yes	complemented
135	#407	C₂²	1	1	yes	characteristic, complemented
136	#407	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
138	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
139	C₂×#41	—	2	1	no	—
140	C₂×#41	C₂³	1	1	yes	characteristic
141	C₂×#41	C₂³	1	1	yes	characteristic
142	C₂²×Q₈	C₂³	1	1	yes	characteristic
143	C₂²×D₄	—	2	1	no	—
144	C₂²×D₄	—	2	1	no	—
145	C₂²×D₄	—	2	1	no	—
146	C₂²×D₄	D₄	1	1	yes	characteristic
147	C₂²×D₄	C₂³	1	1	yes	characteristic
148	C₂²×D₄	C₂³	1	1	yes	characteristic
149	C₂³×C₄	—	2	1	no	—
150	C₂³×C₄	C₂³	1	1	yes	characteristic
151	C₂³×C₄	C₂³	1	1	yes	characteristic
152	C₂×Q₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	C₂×SD₁₆	C₂³	1	2	yes	—
156	C₂×M₁₆	C₂³	1	2	yes	—
157	C₂×M₁₆	C₂³	1	2	yes	—
158	C₂²×C₈	C₂³	1	2	yes	—
159	C₂²×C₈	C₂³	1	2	yes	—
160	C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	#127	—	2	1	no	—
162	#127	C₂³	1	1	yes	characteristic
163	#126	—	2	1	no	—
164	#126	—	2	1	no	—
165	#126	—	2	2	no	—
166	#126	—	2	2	no	—
167	#126	—	2	2	no	—
168	#126	—	2	2	no	—
169	#126	—	2	1	no	—
170	#125	—	2	2	no	—
171	#125	—	2	2	no	—
172	#125	—	2	2	no	—
173	#125	—	2	2	no	—
174	#125	—	2	1	no	—
175	#125	—	2	1	no	—
176	#125	—	2	1	no	—
177	#125	C₂³	1	2	yes	—
178	#125	C₂³	1	2	yes	—
179	#125	C₂³	1	1	yes	characteristic
180	#124	—	2	1	no	—
181	#124	—	2	1	no	—
182	#124	—	2	1	no	—
183	#124	C₂³	1	1	yes	characteristic
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	#123	—	2	1	no	—
189	#123	—	2	1	no	—
190	#123	—	2	1	no	—
191	#123	—	2	1	no	—
192	#123	—	2	1	no	—
193	#123	—	2	1	no	—
194	#123	—	2	1	no	—
195	C₂²⋊Q₈	—	2	1	no	—
196	C₂²⋊Q₈	—	2	1	no	—
197	C₂²⋊Q₈	—	2	1	no	—
198	C₂²⋊Q₈	—	2	1	no	—
199	C₂²⋊Q₈	—	2	1	no	—
200	C₂²⋊Q₈	—	2	1	no	—
201	C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
206	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
207	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
208	#121	—	2	1	no	—
209	#121	—	2	1	no	—
210	#121	—	2	1	no	—
211	#121	—	2	1	no	—
212	#121	—	2	1	no	—
213	#121	—	2	1	no	—
214	#121	—	2	1	no	—
215	#121	—	2	1	no	—
216	#121	—	2	1	no	—
217	#121	—	2	1	no	—
218	#121	—	2	1	no	—
219	#121	—	2	1	no	—
220	#121	—	2	1	no	—
221	#121	C₂³	1	1	yes	characteristic
222	#121	C₂³	1	1	yes	characteristic
223	#121	C₂³	1	1	yes	characteristic
224	#121	C₂³	1	1	yes	characteristic
225	#121	C₂³	1	1	yes	characteristic
226	#121	C₂³	1	1	yes	characteristic
227	#121	C₂³	1	1	yes	characteristic
228	#121	C₂³	1	1	yes	characteristic
229	#121	C₂³	1	1	yes	characteristic
230	#120	—	2	1	no	—
231	#120	—	2	1	no	—
232	#120	—	2	1	no	—
233	#120	—	2	1	no	—
234	#120	—	2	1	no	—
235	#120	—	2	1	no	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	C₂³	1	2	yes	—
239	C₄×Q₈	C₂³	1	2	yes	—
240	C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	D₄	1	1	yes	characteristic
252	C₄×D₄	D₄	1	1	yes	characteristic
253	C₄×D₄	D₄	1	1	yes	characteristic
254	C₄×D₄	D₄	1	1	yes	characteristic
255	C₄×D₄	C₂³	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	1	yes	characteristic
261	C₄×D₄	C₂³	1	1	yes	characteristic
262	#117	—	2	1	no	—
263	#117	—	2	1	no	—
264	#117	—	2	1	no	—
265	#117	—	2	2	no	—
266	#117	—	2	2	no	—
267	#117	—	2	2	no	—
268	#117	—	2	2	no	—
269	#117	—	2	1	no	—
270	#117	C₂³	1	2	yes	—
271	#117	C₂³	1	2	yes	—
272	#117	C₂³	1	1	yes	characteristic
273	#117	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³	1	1	yes	characteristic
302	#107	C₂³	1	2	yes	—
303	#107	C₂³	1	2	yes	—
304	#107	C₂³	1	2	yes	—
305	#107	C₂³	1	2	yes	—
306	#107	C₂³	1	2	yes	—
307	#106	C₂³	1	2	yes	—
308	#106	C₂³	1	2	yes	—
309	#106	C₂³	1	2	yes	—
310	#106	C₂³	1	2	yes	—
311	#106	C₂³	1	2	yes	—
312	#106	C₂³	1	2	yes	—
313	#106	C₂³	1	2	yes	—
314	C₄⋊C₈	C₂³	1	2	yes	—
315	C₄⋊C₈	C₂³	1	2	yes	—
316	#103	C₂³	1	2	yes	—
317	#103	C₂³	1	2	yes	—
318	#103	C₂³	1	2	yes	—
319	#103	C₂³	1	2	yes	—
320	#103	C₂³	1	2	yes	—
321	#103	C₂³	1	2	yes	—
322	#103	C₂³	1	2	yes	—
323	#102	C₂³	1	2	yes	—
324	#102	C₂³	1	2	yes	—
325	#102	C₂³	1	2	yes	—
326	#102	C₂³	1	2	yes	—
327	#102	C₂³	1	2	yes	—
328	#102	C₂³	1	2	yes	—
329	#102	C₂³	1	2	yes	—
330	#102	C₂³	1	2	yes	—
331	#102	C₂³	1	2	yes	—
332	C₂²⋊C₈	C₂³	1	1	yes	characteristic
333	C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₂²⋊C₈	C₂³	1	1	yes	characteristic
335	C₂²⋊C₈	C₂³	1	2	yes	—
336	C₂²⋊C₈	C₂³	1	2	yes	—
337	C₂²⋊C₈	C₂³	1	1	yes	characteristic
338	C₂²⋊C₈	C₂³	1	2	yes	—
339	C₂²⋊C₈	C₂³	1	2	yes	—
340	#97	C₂³	1	2	yes	—
341	C₄×C₈	C₂³	1	2	yes	—
342	C₂⁴	—	2	1	no	—
343	C₂⁴	—	2	1	no	—
344	C₂⁴	C₂×D₄	1	1	yes	characteristic
345	C₂⁴	C₂×D₄	1	1	yes	characteristic
346	#41	—	4	2	no	—
347	#41	—	4	2	no	—
348	#41	—	8	2	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	C₂⁴	1	1	yes	characteristic
353	C₂×Q₈	C₂⁴	1	2	yes	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	—	8	2	no	—
374	C₂×D₄	—	8	2	no	—
375	C₂×D₄	C₂×D₄	1	1	yes	characteristic
376	C₂×D₄	C₂×D₄	1	1	yes	characteristic
377	C₂×D₄	C₂×D₄	1	1	yes	characteristic
378	C₂×D₄	C₂×D₄	1	1	yes	characteristic
379	C₂×D₄	C₂⁴	1	1	yes	characteristic
380	C₂×D₄	C₂⁴	1	1	yes	characteristic
381	C₂×D₄	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄	C₂⁴	1	1	yes	characteristic
411	Q₁₆	—	4	2	no	—
412	SD₁₆	—	4	2	no	—
413	SD₁₆	—	4	2	no	—
414	SD₁₆	—	4	2	no	—
415	M₁₆	—	4	2	no	—
416	M₁₆	—	4	2	no	—
417	C₂×C₈	—	4	2	no	—
418	C₂×C₈	—	4	2	no	—
419	C₂×C₈	C₂⁴	1	2	yes	—
420	C₂×C₈	C₂⁴	1	2	yes	—
421	C₂×C₈	C₂⁴	1	2	yes	—
422	C₂×C₈	C₂⁴	1	2	yes	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄	C₂⁴	1	2	yes	—
452	C₄⋊C₄	C₂⁴	1	2	yes	—
453	C₄⋊C₄	C₂⁴	1	2	yes	—
454	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
487	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
488	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
489	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
490	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
491	C₄²	—	2	2	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	C₂×D₄	1	1	yes	characteristic
499	C₄²	C₂×D₄	1	1	yes	characteristic
500	C₄²	C₂⁴	1	1	yes	characteristic
501	C₄²	C₂⁴	1	1	yes	characteristic
502	C₂³	—	2	2	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	4	1	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	8	1	no	—
514	C₂³	—	8	1	no	—
515	C₂³	—	8	1	no	—
516	C₂³	—	8	1	no	—
517	C₂³	C₂²×D₄	1	1	yes	characteristic
518	C₂³	C₂²×D₄	1	1	yes	characteristic
519	C₂³	C₂²×D₄	1	1	yes	characteristic
520	C₂³	C₂²×D₄	1	1	yes	characteristic
521	C₂³	C₂²×D₄	1	1	yes	characteristic
522	Q₈	—	2	2	no	—
523	Q₈	—	2	2	no	—
524	Q₈	—	2	2	no	—
525	Q₈	—	4	2	no	—
526	Q₈	—	8	1	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	2	2	no	—
530	D₄	—	2	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	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	D₄	—	8	1	no	—
541	D₄	—	8	1	no	—
542	D₄	—	8	1	no	—
543	D₄	—	8	1	no	—
544	D₄	—	8	1	no	—
545	D₄	—	8	1	no	—
546	D₄	—	8	1	no	—
547	D₄	—	8	1	no	—
548	D₄	—	8	1	no	—
549	C₂×C₄	—	2	2	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	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	8	1	no	—
579	C₂×C₄	—	8	1	no	—
580	C₂×C₄	—	8	1	no	—
581	C₂×C₄	—	8	1	no	—
582	C₂×C₄	—	8	1	no	—
583	C₂×C₄	—	8	1	no	—
584	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄	C₂⁵	1	1	yes	characteristic
594	C₈	—	2	2	no	—
595	C₈	—	2	2	no	—
596	C₈	—	2	2	no	—
597	C₈	—	2	2	no	—
598	C₂²	—	2	1	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	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	4	4	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	8	2	no	—
622	C₂²	—	16	2	no	—
623	C₂²	—	16	2	no	—
624	C₂²	#575	1	2	yes	—
625	C₂²	#577	1	2	yes	—
626	C₂²	C₂³×D₄	1	1	yes	characteristic
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	2	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	1	no	—
645	C₄	#585	1	2	yes	—
646	C₂	—	2	2	no	—
647	C₂	—	2	2	no	—
648	C₂	—	4	1	no	—
649	C₂	—	4	1	no	—
650	C₂	—	4	1	no	—
651	C₂	—	8	1	no	—
652	C₂	—	8	1	no	—
653	C₂	—	8	1	no	—
654	C₂	#3485	1	1	yes	characteristic
655	C₂	C₂×#575	1	1	yes	characteristic
656	C₂	C₂×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3519	C₂
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
2. C₂×#552	C₂	semidirect
3. #3351	C₂	semidirect
4. #3348	C₂	semidirect
5. #3344	C₂	semidirect
6. #3337	C₂	semidirect
7. #3323	C₂	semidirect
8. #3317	C₂	semidirect
9. #3310	C₂	semidirect
10. #3296	C₂	semidirect
11. #3234	C₂	semidirect
12. #3232	C₂	semidirect
13. #3196	C₂	semidirect
14. #3193	C₂	semidirect
15. #3190	C₂	semidirect
16. #3187	C₂	semidirect
17. #3117	C₂	semidirect
18. #3103	C₂	semidirect
19. #3094	C₂	semidirect
20. #3092	C₂	semidirect
21. #3091	C₂	semidirect
22. C₂×#481	C₂	semidirect
23. #2974	C₂	semidirect
34. #552	C₂²	semidirect
35. #552	C₂²	semidirect
36. #552	C₂²	semidirect
51. C₂×#125	C₂²	semidirect
55. C₂×C₂²⋊Q₈	C₂²	semidirect
56. C₂×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₄×Q₈	C₂²	semidirect
63. C₂×#117	C₂²	semidirect
64. C₂²×C₄⋊C₄	C₂²	semidirect
65. #501	C₂²	semidirect
66. #499	C₂²	semidirect
67. #490	C₂²	semidirect
68. #488	C₂²	semidirect
69. #485	C₂²	semidirect
70. #485	C₂²	semidirect
71. #485	C₂²	semidirect
72. #484	C₂²	semidirect
73. #484	C₂²	semidirect
74. #484	C₂²	semidirect
75. #483	C₂²	semidirect
76. #483	C₂²	semidirect
77. #483	C₂²	semidirect
78. #482	C₂²	semidirect
79. #482	C₂²	semidirect
80. #482	C₂²	semidirect
83. #481	C₂²	semidirect
84. #481	C₂²	semidirect
85. #481	C₂²	semidirect
86. #481	C₂²	semidirect
87. #481	C₂²	semidirect
88. #481	C₂²	semidirect
90. #480	C₂²	semidirect
91. #480	C₂²	semidirect
92. #480	C₂²	semidirect
93. #479	C₂²	semidirect
94. #479	C₂²	semidirect
95. #478	C₂²	semidirect
96. #478	C₂²	semidirect
97. #478	C₂²	semidirect
98. #475	C₂²	semidirect
99. #470	C₂²	semidirect
100. #468	C₂²	semidirect
101. #468	C₂²	semidirect
102. #468	C₂²	semidirect
103. #467	C₂²	semidirect
104. #465	C₂²	semidirect
105. #465	C₂²	semidirect
106. #465	C₂²	semidirect
107. #464	C₂²	semidirect
108. #460	C₂²	semidirect
109. #452	C₂²	semidirect
110. #452	C₂²	semidirect
111. #451	C₂²	semidirect
112. #450	C₂²	semidirect
113. #450	C₂²	semidirect
115. #448	C₂²	semidirect
116. #448	C₂²	semidirect
117. #441	C₂²	semidirect
118. #440	C₂²	semidirect
119. C₄×SD₁₆	C₂²	semidirect
120. C₄×SD₁₆	C₂²	semidirect
121. #436	C₂²	semidirect
123. #435	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #432	C₂²	semidirect
126. #431	C₂²	semidirect
127. #428	C₂²	semidirect
128. #428	C₂²	semidirect
129. #427	C₂²	semidirect
130. C₂×#106	C₂²	semidirect
131. #418	C₂²	semidirect
132. #417	C₂²	semidirect
133. #416	C₂²	semidirect
134. C₂×#102	C₂²	semidirect
135. #407	C₂²	semidirect
136. #407	C₂²	semidirect
137. C₂×C₂²⋊C₈	C₂²	semidirect
138. C₂×C₂²⋊C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3519	2
C₂×#552	2
#3351	2
#3348	2
#3344	2
#3337	2
#3323	2
#3317	2
#3310	2
#3296	2
#3234	2
#3232	2
#3196	2
#3193	2
#3190	2
#3187	2
#3117	2
#3103	2
#3094	2
#3092	2
#3091	2
C₂×#481	2
#2974	2