Subgroups — #61607

Order 256.

1056 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41	C₂	1	1	yes	maximal, characteristic
3	#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	#3331	C₂	1	1	yes	maximal, characteristic, complemented
5	#3316	C₂	1	2	yes	maximal, complemented
6	#3314	C₂	1	2	yes	maximal, complemented
7	#3299	C₂	1	1	yes	maximal, characteristic, complemented
8	#3295	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	#3276	C₂	1	1	yes	maximal, characteristic, complemented
13	#3270	C₂	1	2	yes	maximal, complemented
14	#3266	C₂	1	2	yes	maximal, complemented
15	#3216	C₂	1	1	yes	maximal, characteristic, complemented
16	#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	#3196	C₂	1	2	yes	maximal, complemented
18	#3190	C₂	1	2	yes	maximal, complemented
19	#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	#3007	C₂	1	2	yes	maximal, complemented
22	C₂×#452	C₂	1	2	yes	maximal, complemented
23	#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41	C₂²	1	2	yes	—
25	C₂×#137	C₂²	1	2	yes	complemented
26	C₂×#137	C₂²	1	2	yes	complemented
27	C₂²×Q₁₆	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆	C₂²	1	2	yes	complemented
29	#554	—	2	1	no	—
30	#554	—	2	2	no	—
31	#554	—	2	1	no	—
32	#554	C₂²	1	1	yes	characteristic
33	#554	C₂²	1	1	yes	characteristic, complemented
34	#554	C₂²	1	2	yes	complemented
35	#550	C₂²	1	1	yes	characteristic
36	D₄×Q₈	C₂²	1	1	yes	characteristic
37	D₄×Q₈	C₂²	1	1	yes	characteristic
38	D₄×Q₈	C₂²	1	2	yes	complemented
39	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	#548	C₂²	1	2	yes	—
41	#547	—	2	1	no	—
42	#547	C₂²	1	1	yes	characteristic
43	#546	—	2	2	no	—
44	#546	C₂²	1	2	yes	—
45	D₄²	—	2	1	no	—
46	D₄²	C₂²	1	1	yes	characteristic
47	#544	—	2	1	no	—
48	#543	—	2	2	no	—
49	#533	C₂²	1	1	yes	characteristic, complemented
50	#533	C₂²	1	1	yes	characteristic, complemented
51	#532	—	2	1	no	—
52	#532	C₂²	1	1	yes	characteristic
53	#525	—	2	2	no	—
54	#525	C₂²	1	2	yes	—
55	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
57	#518	—	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	#497	C₂²	1	2	yes	complemented
62	#494	C₂²	1	1	yes	characteristic, complemented
63	#492	C₂²	1	1	yes	characteristic, complemented
64	#489	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	1	yes	characteristic, complemented
69	#485	C₂²	1	2	yes	complemented
70	#484	C₂²	1	2	yes	complemented
71	#483	C₂²	1	2	yes	complemented
72	#481	C₂²	1	2	yes	complemented
73	#480	C₂²	1	2	yes	complemented
74	#477	C₂²	1	1	yes	characteristic, complemented
75	#476	C₂²	1	1	yes	characteristic, complemented
76	#475	C₂²	1	1	yes	characteristic, complemented
77	#474	C₂²	1	1	yes	characteristic, complemented
78	#470	C₂²	1	2	yes	complemented
79	#470	C₂²	1	2	yes	complemented
80	#468	C₂²	1	2	yes	complemented
81	#468	C₂²	1	2	yes	complemented
82	#467	C₂²	1	2	yes	complemented
83	#467	C₂²	1	2	yes	complemented
84	#465	C₂²	1	2	yes	complemented
85	#465	C₂²	1	2	yes	complemented
86	#464	C₂²	1	2	yes	complemented
87	#464	C₂²	1	2	yes	complemented
88	#462	C₂²	1	1	yes	characteristic, complemented
89	#462	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	#460	C₂²	1	1	yes	characteristic, complemented
96	#452	C₂²	1	1	yes	characteristic
97	#452	C₂²	1	1	yes	characteristic
98	#452	C₂²	1	2	yes	—
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	#452	C₂²	1	2	yes	complemented
107	#451	C₂²	1	2	yes	complemented
108	#451	C₂²	1	2	yes	complemented
109	#451	C₂²	1	2	yes	complemented
110	#451	C₂²	1	2	yes	complemented
111	#450	C₂²	1	2	yes	complemented
112	#450	C₂²	1	2	yes	complemented
113	#448	C₂²	1	2	yes	complemented
114	#448	C₂²	1	2	yes	complemented
115	#441	C₂²	1	2	yes	complemented
116	#440	C₂²	1	2	yes	complemented
117	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
121	#436	C₂²	1	1	yes	characteristic, complemented
122	#436	C₂²	1	1	yes	characteristic, complemented
123	#435	C₂²	1	2	yes	complemented
124	#435	C₂²	1	2	yes	complemented
125	C₈×D₄	C₂²	1	1	yes	characteristic
126	C₈×D₄	C₂²	1	1	yes	characteristic
127	#432	C₂²	1	1	yes	characteristic, complemented
128	#431	C₂²	1	1	yes	characteristic, complemented
129	#417	C₂²	1	2	yes	complemented
130	#417	C₂²	1	2	yes	complemented
131	C₂×#103	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	complemented
133	#407	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₂×#41	—	2	2	no	—
136	C₂×#41	—	2	2	no	—
137	C₂×#41	—	4	4	no	—
138	C₂×#41	—	4	4	no	—
139	C₂×#41	C₂³	1	1	yes	characteristic
140	C₂×#41	C₂³	1	2	yes	—
141	C₂×#41	C₂³	1	2	yes	—
142	C₂×#41	C₂³	1	2	yes	—
143	C₂²×Q₈	C₂³	1	2	yes	—
144	C₂²×Q₈	C₂³	1	2	yes	—
145	C₂²×Q₈	C₂³	1	2	yes	—
146	C₂²×D₄	—	2	2	no	—
147	C₂²×D₄	—	2	1	no	—
148	C₂²×D₄	D₄	1	1	yes	characteristic
149	C₂²×D₄	C₂³	1	2	yes	—
150	C₂³×C₄	—	2	2	no	—
151	C₂³×C₄	C₂³	1	2	yes	—
152	#137	—	4	4	no	—
153	#137	—	4	4	no	—
154	C₂×Q₁₆	—	4	4	no	—
155	C₂×Q₁₆	C₂³	1	1	yes	characteristic
156	C₂×Q₁₆	C₂³	1	2	yes	—
157	C₂×Q₁₆	C₂³	1	1	yes	characteristic
158	C₂×Q₁₆	C₂³	1	2	yes	—
159	C₂×Q₁₆	C₂³	1	2	yes	—
160	C₂×Q₁₆	C₂³	1	2	yes	—
161	C₂×Q₁₆	C₂³	1	2	yes	—
162	C₂×SD₁₆	—	4	4	no	—
163	C₂×SD₁₆	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆	C₂³	1	2	yes	—
165	C₂×SD₁₆	C₂³	1	1	yes	characteristic
166	C₂×SD₁₆	C₂³	1	2	yes	—
167	C₂×SD₁₆	C₂³	1	2	yes	—
168	C₂×SD₁₆	C₂³	1	2	yes	—
169	C₂×SD₁₆	C₂³	1	2	yes	—
170	C₂×M₁₆	C₂³	1	2	yes	—
171	C₂×M₁₆	C₂³	1	2	yes	—
172	C₂²×C₈	C₂³	1	2	yes	—
173	C₂²×C₈	C₂³	1	2	yes	—
174	C₄⋊Q₈	—	2	1	no	—
175	C₄⋊Q₈	—	2	1	no	—
176	C₄⋊Q₈	—	2	1	no	—
177	C₄⋊Q₈	—	2	2	no	—
178	C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₄⋊Q₈	C₂³	1	1	yes	characteristic
181	C₄⋊Q₈	C₂³	1	1	yes	characteristic
182	C₄⋊Q₈	C₂³	1	1	yes	characteristic
183	#127	—	2	1	no	—
184	#127	C₂³	1	1	yes	characteristic
185	#125	—	2	1	no	—
186	#125	—	2	1	no	—
187	#125	—	2	2	no	—
188	#125	—	2	1	no	—
189	#125	—	2	1	no	—
190	#124	—	2	2	no	—
191	#124	C₂³	1	2	yes	—
192	#123	—	2	2	no	—
193	#123	—	2	2	no	—
194	#123	—	2	2	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	—	2	2	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	—	2	1	no	—
200	C₂²⋊Q₈	—	2	1	no	—
201	C₂²⋊Q₈	—	2	2	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	—	2	2	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	—	2	2	no	—
210	C₂²⋊Q₈	—	2	2	no	—
211	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₂²⋊Q₈	C₂³	1	2	yes	—
220	#121	—	2	2	no	—
221	#121	—	2	1	no	—
222	#121	—	2	1	no	—
223	#121	—	2	1	no	—
224	#121	—	2	1	no	—
225	#121	—	2	2	no	—
226	#121	—	2	2	no	—
227	#121	C₂³	1	2	yes	—
228	#121	C₂³	1	2	yes	—
229	#120	—	2	2	no	—
230	#120	—	2	2	no	—
231	#120	—	2	2	no	—
232	C₄×Q₈	—	2	1	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	C₂³	1	1	yes	characteristic
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	1	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	1	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	D₄	1	1	yes	characteristic
255	C₄×D₄	D₄	1	2	yes	—
256	C₄×D₄	D₄	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	1	no	—
264	#117	—	2	1	no	—
265	#117	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
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	1	yes	characteristic
280	#107	C₂³	1	2	yes	—
281	#106	C₂³	1	1	yes	characteristic
282	#106	C₂³	1	1	yes	characteristic
283	#106	C₂³	1	2	yes	—
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	1	yes	characteristic
297	#103	C₂³	1	1	yes	characteristic
298	#103	C₂³	1	1	yes	characteristic
299	#103	C₂³	1	2	yes	—
300	#103	C₂³	1	2	yes	—
301	#102	C₂³	1	1	yes	characteristic
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	1	yes	characteristic
306	#102	C₂³	1	2	yes	—
307	#102	C₂³	1	2	yes	—
308	C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂²⋊C₈	C₂³	1	1	yes	characteristic
313	C₂²⋊C₈	C₂³	1	2	yes	—
314	C₂²⋊C₈	C₂³	1	2	yes	—
315	#97	C₂³	1	2	yes	—
316	C₄×C₈	C₂³	1	1	yes	characteristic
317	C₄×C₈	C₂³	1	1	yes	characteristic
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	8	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	—	4	2	no	—
339	C₂×Q₈	—	4	2	no	—
340	C₂×Q₈	—	4	2	no	—
341	C₂×Q₈	C₂⁴	1	2	yes	—
342	C₂×Q₈	C₂⁴	1	1	yes	characteristic
343	C₂×Q₈	C₂⁴	1	2	yes	—
344	C₂×Q₈	C₂⁴	1	1	yes	characteristic
345	C₂×Q₈	C₂⁴	1	1	yes	characteristic
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	4	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	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	8	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	C₂×D₄	1	2	yes	—
361	C₂×D₄	C₂×D₄	1	1	yes	characteristic
362	C₂×D₄	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄	C₂⁴	1	2	yes	—
364	C₂×D₄	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	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	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	8	no	—
379	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄	1	2	yes	—
382	C₂²×C₄	C₂×D₄	1	2	yes	—
383	C₂²×C₄	C₂×D₄	1	2	yes	—
384	C₂²×C₄	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄	C₂⁴	1	2	yes	—
386	C₂²×C₄	C₂⁴	1	2	yes	—
387	Q₁₆	—	2	2	no	—
388	Q₁₆	—	2	4	no	—
389	Q₁₆	—	2	2	no	—
390	Q₁₆	—	4	2	no	—
391	Q₁₆	—	4	2	no	—
392	Q₁₆	—	4	2	no	—
393	Q₁₆	—	4	2	no	—
394	SD₁₆	—	2	2	no	—
395	SD₁₆	—	2	4	no	—
396	SD₁₆	—	2	2	no	—
397	SD₁₆	—	4	2	no	—
398	SD₁₆	—	4	2	no	—
399	SD₁₆	—	4	2	no	—
400	SD₁₆	—	4	2	no	—
401	M₁₆	—	4	2	no	—
402	M₁₆	—	4	2	no	—
403	C₂×C₈	—	4	2	no	—
404	C₂×C₈	—	4	2	no	—
405	C₂×C₈	C₂⁴	1	1	yes	characteristic
406	C₂×C₈	C₂⁴	1	1	yes	characteristic
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	2	yes	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	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	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄	C₂×D₄	1	2	yes	—
438	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄	C₂⁴	1	2	yes	—
440	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
442	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	2	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	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	C₂×D₄	1	1	yes	characteristic
470	C₄²	C₂×D₄	1	1	yes	characteristic
471	C₄²	C₂⁴	1	1	yes	characteristic
472	C₄²	C₂⁴	1	1	yes	characteristic
473	C₂³	—	2	1	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	4	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	8	2	no	—
481	C₂³	C₂²×D₄	1	1	yes	characteristic
482	C₂³	C₂²×D₄	1	2	yes	—
483	C₂³	C₂²×D₄	1	2	yes	—
484	Q₈	—	2	1	no	—
485	Q₈	—	2	1	no	—
486	Q₈	—	2	2	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	2	2	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	2	no	—
492	Q₈	—	2	2	no	—
493	Q₈	—	4	4	no	—
494	Q₈	—	8	1	no	—
495	Q₈	—	8	1	no	—
496	Q₈	—	8	2	no	—
497	Q₈	—	8	2	no	—
498	Q₈	H(5,𝔽₂)	1	2	yes	—
499	D₄	—	2	4	no	—
500	D₄	—	2	4	no	—
501	D₄	—	2	2	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	4	no	—
509	D₄	—	4	4	no	—
510	D₄	—	4	2	no	—
511	D₄	—	8	1	no	—
512	D₄	—	8	2	no	—
513	D₄	#137	1	4	yes	complemented
514	D₄	H(5,𝔽₂)	1	2	yes	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	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	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	8	1	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	—	8	2	no	—
547	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
553	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄	C₂⁵	1	1	yes	characteristic
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	2	2	no	—
558	C₈	—	2	2	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	8	4	no	—
576	C₂²	—	8	8	no	—
577	C₂²	C₂×#137	1	4	yes	—
578	C₂²	C₂³×D₄	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	C₂×#137	1	2	yes	—
596	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
597	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
598	C₂	—	2	4	no	—
599	C₂	—	4	2	no	—
600	C₂	—	4	1	no	—
601	C₂	—	4	2	no	—
602	C₂	—	8	2	no	—
603	C₂	#3484	1	1	yes	characteristic
604	C₂	C₂²×#137	1	1	yes	characteristic
605	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	D₄×#41	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
1. #3501	C₂	semidirect
3. #3333	C₂	semidirect
4. #3331	C₂	semidirect
5. #3316	C₂	semidirect
6. #3314	C₂	semidirect
7. #3299	C₂	semidirect
8. #3295	C₂	semidirect
9. D₄×Q₁₆	C₂	semidirect
10. D₄×SD₁₆	C₂	semidirect
11. #3278	C₂	semidirect
12. #3276	C₂	semidirect
13. #3270	C₂	semidirect
14. #3266	C₂	semidirect
15. #3216	C₂	semidirect
16. #3210	C₂	semidirect
17. #3196	C₂	semidirect
18. #3190	C₂	semidirect
19. #3116	C₂	semidirect
20. #3107	C₂	semidirect
21. #3007	C₂	semidirect
22. C₂×#452	C₂	semidirect
23. #2974	C₂	semidirect
25. C₂×#137	C₂²	semidirect
26. C₂×#137	C₂²	semidirect
27. C₂²×Q₁₆	C₂²	semidirect
28. C₂²×SD₁₆	C₂²	semidirect
33. #554	C₂²	semidirect
34. #554	C₂²	semidirect
38. D₄×Q₈	C₂²	semidirect
39. D₄×Q₈	C₂²	semidirect
49. #533	C₂²	semidirect
50. #533	C₂²	semidirect
55. C₂×C₂²⋊Q₈	C₂²	semidirect
56. C₂×C₂²⋊Q₈	C₂²	semidirect
61. #497	C₂²	semidirect
62. #494	C₂²	semidirect
63. #492	C₂²	semidirect
64. #489	C₂²	semidirect
65. #487	C₂²	semidirect
66. #486	C₂²	semidirect
67. #485	C₂²	semidirect
68. #485	C₂²	semidirect
69. #485	C₂²	semidirect
70. #484	C₂²	semidirect
71. #483	C₂²	semidirect
72. #481	C₂²	semidirect
73. #480	C₂²	semidirect
74. #477	C₂²	semidirect
75. #476	C₂²	semidirect
76. #475	C₂²	semidirect
77. #474	C₂²	semidirect
78. #470	C₂²	semidirect
79. #470	C₂²	semidirect
80. #468	C₂²	semidirect
81. #468	C₂²	semidirect
82. #467	C₂²	semidirect
83. #467	C₂²	semidirect
84. #465	C₂²	semidirect
85. #465	C₂²	semidirect
86. #464	C₂²	semidirect
87. #464	C₂²	semidirect
88. #462	C₂²	semidirect
89. #462	C₂²	semidirect
90. #462	C₂²	semidirect
91. #462	C₂²	semidirect
92. #461	C₂²	semidirect
93. #461	C₂²	semidirect
94. #460	C₂²	semidirect
95. #460	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. #452	C₂²	semidirect
107. #451	C₂²	semidirect
108. #451	C₂²	semidirect
109. #451	C₂²	semidirect
110. #451	C₂²	semidirect
111. #450	C₂²	semidirect
112. #450	C₂²	semidirect
113. #448	C₂²	semidirect
114. #448	C₂²	semidirect
115. #441	C₂²	semidirect
116. #440	C₂²	semidirect
117. C₄×Q₁₆	C₂²	semidirect
118. C₄×Q₁₆	C₂²	semidirect
119. C₄×SD₁₆	C₂²	semidirect
120. C₄×SD₁₆	C₂²	semidirect
121. #436	C₂²	semidirect
122. #436	C₂²	semidirect
123. #435	C₂²	semidirect
124. #435	C₂²	semidirect
127. #432	C₂²	semidirect
128. #431	C₂²	semidirect
129. #417	C₂²	semidirect
130. #417	C₂²	semidirect
131. C₂×#103	C₂²	semidirect
132. C₂×#102	C₂²	semidirect
133. #407	C₂²	semidirect
134. C₂×C₂²⋊C₈	C₂²	semidirect
513. D₄	#137	semidirect

Maximal subgroups

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

subgroup	index
#3501	2
D₄×#41	2
#3333	2
#3331	2
#3316	2
#3314	2
#3299	2
#3295	2
D₄×Q₁₆	2
D₄×SD₁₆	2
#3278	2
#3276	2
#3270	2
#3266	2
#3216	2
#3210	2
#3196	2
#3190	2
#3116	2
#3107	2
#3007	2
C₂×#452	2
#2974	2