Subgroups — #60319

Order 256.

924 conjugacy classes of subgroups.

The subgroup lattice has 585 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3460	C₂	1	1	yes	maximal, characteristic
2	#2995	C₂	1	2	yes	maximal, complemented
3	#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	#2991	C₂	1	1	yes	maximal, characteristic, complemented
6	#2989	C₂	1	1	yes	maximal, characteristic, complemented
7	#2981	C₂	1	1	yes	maximal, characteristic, complemented
8	#2981	C₂	1	2	yes	maximal, complemented
9	#2979	C₂	1	1	yes	maximal, characteristic, complemented
10	#2978	C₂	1	2	yes	maximal, complemented
11	#2976	C₂	1	2	yes	maximal, complemented
12	#2974	C₂	1	1	yes	maximal, characteristic, complemented
13	#2970	C₂	1	1	yes	maximal, characteristic, complemented
14	#2969	C₂	1	1	yes	maximal, characteristic, complemented
15	#2968	C₂	1	2	yes	maximal, complemented
16	#2966	C₂	1	1	yes	maximal, characteristic, complemented
17	#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	#2935	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
20	#2933	C₂	1	2	yes	maximal, complemented
21	#2932	C₂	1	2	yes	maximal, complemented
22	#2931	C₂	1	1	yes	maximal, characteristic, complemented
23	#2930	C₂	1	2	yes	maximal, complemented
24	C₂×#131	C₂²	1	2	yes	complemented
25	C₂×#131	C₂²	1	2	yes	complemented
26	C₂²×M₁₆	C₂²	1	2	yes	—
27	#544	C₄	1	1	yes	characteristic
28	#542	C₄	1	1	yes	characteristic
29	#542	C₄	1	1	yes	characteristic
30	#542	C₄	1	2	yes	—
31	#540	C₄	1	1	yes	characteristic
32	#540	C₄	1	1	yes	characteristic
33	#540	C₄	1	2	yes	—
34	#538	C₄	1	2	yes	—
35	#538	C₄	1	2	yes	—
36	#537	C₄	1	1	yes	characteristic
37	#535	C₄	1	1	yes	characteristic
38	#535	C₄	1	1	yes	characteristic
39	#532	C₂²	1	1	yes	characteristic
40	#532	C₂²	1	2	yes	—
41	#532	C₂²	1	1	yes	characteristic
42	#529	C₂²	1	1	yes	characteristic
43	#529	C₂²	1	2	yes	—
44	#529	C₂²	1	1	yes	characteristic
45	#525	C₂²	1	2	yes	—
46	#525	C₂²	1	2	yes	—
47	C₄×#41	C₂²	1	1	yes	characteristic
48	C₄×#41	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
50	#446	C₂²	1	1	yes	characteristic, complemented
51	#446	C₂²	1	1	yes	characteristic, complemented
52	#446	C₂²	1	1	yes	characteristic, complemented
53	#446	C₂²	1	2	yes	complemented
54	#446	C₂²	1	1	yes	characteristic, complemented
55	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
57	#436	C₂²	1	2	yes	—
58	#436	C₂²	1	2	yes	—
59	#436	C₂²	1	1	yes	characteristic
60	#436	C₂²	1	1	yes	characteristic
61	#436	C₂²	1	2	yes	—
62	#436	C₂²	1	1	yes	characteristic
63	#436	C₂²	1	1	yes	characteristic
64	#436	C₂²	1	1	yes	characteristic
65	#436	C₂²	1	1	yes	characteristic
66	#436	C₂²	1	2	yes	complemented
67	#436	C₂²	1	2	yes	complemented
68	#436	C₂²	1	2	yes	complemented
69	#436	C₂²	1	1	yes	characteristic, complemented
70	#436	C₂²	1	1	yes	characteristic, complemented
71	#436	C₂²	1	2	yes	complemented
72	#435	C₂²	1	1	yes	characteristic
73	#435	C₂²	1	2	yes	—
74	#435	C₂²	1	2	yes	—
75	#435	C₂²	1	2	yes	—
76	#435	C₂²	1	2	yes	—
77	#435	C₂²	1	2	yes	—
78	#435	C₂²	1	1	yes	characteristic
79	#435	C₂²	1	2	yes	—
80	#435	C₂²	1	2	yes	—
81	#435	C₂²	1	2	yes	complemented
82	#435	C₂²	1	2	yes	complemented
83	#435	C₂²	1	1	yes	characteristic, complemented
84	#435	C₂²	1	2	yes	complemented
85	#435	C₂²	1	2	yes	complemented
86	#435	C₂²	1	2	yes	complemented
87	#435	C₂²	1	2	yes	complemented
88	#435	C₂²	1	2	yes	complemented
89	#435	C₂²	1	2	yes	complemented
90	#435	C₂²	1	1	yes	characteristic, complemented
91	#435	C₂²	1	2	yes	complemented
92	C₈×D₄	C₂²	1	1	yes	characteristic
93	C₈×D₄	C₂²	1	1	yes	characteristic
94	C₈×D₄	C₂²	1	1	yes	characteristic
95	C₈×D₄	C₂²	1	1	yes	characteristic
96	C₈×D₄	C₂²	1	2	yes	complemented
97	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
98	C₈×D₄	C₂²	1	2	yes	complemented
99	C₈×D₄	C₂²	1	2	yes	complemented
100	C₈×D₄	C₂²	1	2	yes	complemented
101	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
102	#433	C₂²	1	2	yes	complemented
103	#433	C₂²	1	2	yes	complemented
104	#433	C₂²	1	2	yes	complemented
105	#433	C₂²	1	2	yes	complemented
106	#432	C₂²	1	1	yes	characteristic
107	#432	C₂²	1	1	yes	characteristic, complemented
108	#432	C₂²	1	2	yes	complemented
109	#431	C₂²	1	1	yes	characteristic
110	#431	C₂²	1	1	yes	characteristic, complemented
111	#431	C₂²	1	1	yes	characteristic, complemented
112	#431	C₂²	1	2	yes	complemented
113	#431	C₂²	1	1	yes	characteristic, complemented
114	#424	C₂²	1	2	yes	complemented
115	#424	C₂²	1	2	yes	complemented
116	#423	C₂²	1	1	yes	characteristic
117	#423	C₂²	1	1	yes	characteristic, complemented
118	#423	C₂²	1	2	yes	complemented
119	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
120	#408	C₂²	1	2	yes	complemented
121	#408	C₂²	1	2	yes	complemented
122	#408	C₂²	1	2	yes	complemented
123	#408	C₂²	1	2	yes	complemented
124	#408	C₂²	1	2	yes	complemented
125	#408	C₂²	1	2	yes	complemented
126	#407	C₂²	1	2	yes	—
127	#407	C₂²	1	2	yes	—
128	C₂×C₂²⋊C₈	C₂²	1	2	yes	—
129	#405	C₂²	1	2	yes	complemented
130	#405	C₂²	1	2	yes	complemented
131	C₄×M₁₆	C₂²	1	1	yes	characteristic
132	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
133	C₂×#97	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	C₂×C₄	1	1	yes	characteristic
136	C₂×#41	C₂×C₄	1	1	yes	characteristic
137	C₂×#41	C₂³	1	2	yes	—
138	C₂×#41	C₂³	1	2	yes	—
139	C₂²×D₄	C₂×C₄	1	1	yes	characteristic
140	C₂³×C₄	C₂³	1	2	yes	—
141	#131	—	4	4	no	—
142	#131	—	4	4	no	—
143	C₂×M₁₆	—	4	4	no	—
144	C₂×M₁₆	C₂³	1	1	yes	characteristic
145	C₂×M₁₆	C₂³	1	2	yes	—
146	C₂×M₁₆	C₂³	1	1	yes	characteristic
147	C₂×M₁₆	C₂³	1	2	yes	—
148	C₂×M₁₆	C₂³	1	2	yes	—
149	C₂×M₁₆	C₂³	1	2	yes	—
150	C₂×M₁₆	C₂³	1	2	yes	—
151	C₂×M₁₆	C₂³	1	2	yes	—
152	C₂×M₁₆	C₂³	1	2	yes	—
153	C₂×M₁₆	C₂³	1	1	yes	characteristic
154	C₂×M₁₆	C₂³	1	1	yes	characteristic
155	C₂×M₁₆	C₂³	1	2	yes	—
156	C₂²×C₈	C₂³	1	2	yes	—
157	C₂²×C₈	C₂³	1	1	yes	characteristic
158	C₂²×C₈	C₂³	1	2	yes	—
159	C₂²×C₈	C₂³	1	2	yes	—
160	C₂²×C₈	C₂³	1	2	yes	—
161	C₂²×C₈	C₂³	1	2	yes	—
162	C₂²×C₈	C₂³	1	1	yes	characteristic
163	C₂²×C₈	C₂³	1	2	yes	—
164	C₂²×C₈	C₂³	1	2	yes	—
165	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
166	C₄⋊Q₈	C₂×C₄	1	2	yes	—
167	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
168	#127	C₂×C₄	1	1	yes	characteristic
169	#127	C₂×C₄	1	1	yes	characteristic
170	#127	C₂×C₄	1	2	yes	—
171	#126	C₂×C₄	1	2	yes	—
172	#126	C₂×C₄	1	2	yes	—
173	#126	C₂×C₄	1	2	yes	—
174	#126	C₂×C₄	1	2	yes	—
175	#125	C₂×C₄	1	1	yes	characteristic
176	#125	C₂×C₄	1	2	yes	—
177	#125	C₂×C₄	1	1	yes	characteristic
178	#124	C₂×C₄	1	1	yes	characteristic
179	#124	C₂×C₄	1	1	yes	characteristic
180	#124	C₂×C₄	1	2	yes	—
181	#124	C₂×C₄	1	2	yes	—
182	#124	C₂×C₄	1	2	yes	—
183	#124	C₂×C₄	1	2	yes	—
184	#124	C₂×C₄	1	2	yes	—
185	#123	C₂×C₄	1	2	yes	—
186	#123	C₂×C₄	1	2	yes	—
187	#123	C₂×C₄	1	2	yes	—
188	#123	C₂×C₄	1	2	yes	—
189	#123	C₂×C₄	1	2	yes	—
190	#123	C₂×C₄	1	2	yes	—
191	#123	C₂×C₄	1	2	yes	—
192	#123	C₂×C₄	1	2	yes	—
193	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
194	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
195	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
196	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
197	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
198	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
199	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
200	#121	C₂×C₄	1	2	yes	—
201	#121	C₂×C₄	1	2	yes	—
202	#121	C₂×C₄	1	2	yes	—
203	#121	C₂×C₄	1	2	yes	—
204	#121	C₂×C₄	1	1	yes	characteristic
205	#121	C₂×C₄	1	1	yes	characteristic
206	#121	C₂×C₄	1	2	yes	—
207	#121	C₂×C₄	1	1	yes	characteristic
208	#121	C₂×C₄	1	1	yes	characteristic
209	#121	C₂×C₄	1	2	yes	—
210	#121	C₂×C₄	1	1	yes	characteristic
211	#121	C₂×C₄	1	1	yes	characteristic
212	#121	C₂×C₄	1	2	yes	—
213	#121	C₂×C₄	1	2	yes	—
214	#121	C₂×C₄	1	2	yes	—
215	#121	C₂×C₄	1	2	yes	—
216	#121	C₂×C₄	1	2	yes	—
217	#120	C₂×C₄	1	2	yes	—
218	#120	C₂×C₄	1	2	yes	—
219	#120	C₂×C₄	1	2	yes	—
220	#120	C₂×C₄	1	2	yes	—
221	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
222	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
223	C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₄×D₄	C₂×C₄	1	1	yes	characteristic
226	C₄×D₄	C₂×C₄	1	1	yes	characteristic
227	C₄×D₄	C₂×C₄	1	2	yes	—
228	C₄×D₄	C₂×C₄	1	1	yes	characteristic
229	C₄×D₄	C₂×C₄	1	1	yes	characteristic
230	C₄×D₄	C₂×C₄	1	2	yes	—
231	C₄×D₄	C₂×C₄	1	1	yes	characteristic
232	C₄×D₄	C₂×C₄	1	1	yes	characteristic
233	C₄×D₄	C₂³	1	1	yes	characteristic
234	C₄×D₄	C₂³	1	1	yes	characteristic
235	C₄×D₄	C₂³	1	2	yes	—
236	C₄×D₄	C₂³	1	1	yes	characteristic
237	C₄×D₄	C₂³	1	1	yes	characteristic
238	C₄×D₄	C₂³	1	2	yes	—
239	C₄×D₄	C₂³	1	1	yes	characteristic
240	C₄×D₄	C₂³	1	1	yes	characteristic
241	C₄×D₄	C₂³	1	2	yes	—
242	C₄×D₄	C₂³	1	2	yes	—
243	C₄×D₄	C₂³	1	2	yes	—
244	C₄×D₄	C₂³	1	2	yes	—
245	#117	C₂×C₄	1	1	yes	characteristic
246	#117	C₂×C₄	1	1	yes	characteristic
247	#117	C₂×C₄	1	1	yes	characteristic
248	#117	C₂×C₄	1	1	yes	characteristic
249	#117	C₂×C₄	1	2	yes	—
250	#117	C₂³	1	2	yes	—
251	#117	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
254	C₂×C₄²	C₂³	1	1	yes	characteristic
255	C₂×C₄²	C₂³	1	1	yes	characteristic
256	C₂×C₄²	C₂³	1	2	yes	—
257	C₂×C₄²	C₂³	1	1	yes	characteristic
258	C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₄⋊C₈	C₂³	1	2	yes	—
261	C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₄⋊C₈	C₂³	1	2	yes	—
263	C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₄⋊C₈	C₂³	1	2	yes	—
265	C₄⋊C₈	C₂³	1	2	yes	—
266	C₄⋊C₈	C₂³	1	2	yes	—
267	C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₄⋊C₈	C₂³	1	2	yes	—
270	C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₄⋊C₈	C₂³	1	2	yes	—
275	C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₂²⋊C₈	C₂³	1	2	yes	—
277	C₂²⋊C₈	C₂³	1	2	yes	—
278	C₂²⋊C₈	C₂³	1	2	yes	—
279	C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₂²⋊C₈	C₂³	1	2	yes	—
281	C₂²⋊C₈	C₂³	1	2	yes	—
282	C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂²⋊C₈	C₂³	1	2	yes	—
285	C₂²⋊C₈	C₂³	1	2	yes	—
286	C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂²⋊C₈	C₂³	1	2	yes	—
288	C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₂²⋊C₈	C₂³	1	2	yes	—
290	C₂²⋊C₈	C₂³	1	1	yes	characteristic
291	C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	#97	C₂³	1	1	yes	characteristic
297	#97	C₂³	1	2	yes	—
298	#97	C₂³	1	2	yes	—
299	#97	C₂³	1	2	yes	—
300	#97	C₂³	1	1	yes	characteristic
301	#97	C₂³	1	1	yes	characteristic
302	#97	C₂³	1	1	yes	characteristic
303	#97	C₂³	1	2	yes	—
304	C₄×C₈	C₂³	1	1	yes	characteristic
305	C₄×C₈	C₂³	1	1	yes	characteristic
306	C₄×C₈	C₂³	1	1	yes	characteristic
307	C₄×C₈	C₂³	1	1	yes	characteristic
308	C₄×C₈	C₂³	1	1	yes	characteristic
309	C₄×C₈	C₂³	1	1	yes	characteristic
310	C₄×C₈	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	2	yes	—
312	C₄×C₈	C₂³	1	2	yes	—
313	C₂⁴	C₂²×C₄	1	2	yes	—
314	#41	—	4	2	no	—
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
321	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
322	C₂×Q₈	C₂²×C₄	1	2	yes	—
323	C₂×Q₈	C₂²×C₄	1	2	yes	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
327	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
328	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
329	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
330	C₂×D₄	C₂²×C₄	1	2	yes	—
331	C₂×D₄	C₂²×C₄	1	2	yes	—
332	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
333	C₂×D₄	C₂²×C₄	1	2	yes	—
334	C₂×D₄	C₂²×C₄	1	2	yes	—
335	C₂×D₄	C₂²×C₄	1	2	yes	—
336	C₂×D₄	C₂²×C₄	1	2	yes	—
337	C₂×D₄	C₂²×C₄	1	2	yes	—
338	C₂×D₄	C₂²×C₄	1	2	yes	—
339	C₂×D₄	C₂²×C₄	1	2	yes	—
340	C₂×D₄	C₂²×C₄	1	2	yes	—
341	C₂×D₄	C₂²×C₄	1	2	yes	—
342	C₂×D₄	C₂²×C₄	1	2	yes	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
348	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄	1	2	yes	—
350	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄	1	2	yes	—
352	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₄	1	2	yes	—
354	C₂²×C₄	C₂²×C₄	1	2	yes	—
355	C₂²×C₄	C₂²×C₄	1	2	yes	—
356	C₂²×C₄	C₂⁴	1	2	yes	—
357	C₂²×C₄	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄	C₂⁴	1	2	yes	—
361	C₂²×C₄	C₂⁴	1	2	yes	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	4	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	4	2	no	—
366	M₁₆	—	4	2	no	—
367	M₁₆	—	4	1	no	—
368	M₁₆	—	4	2	no	—
369	M₁₆	—	4	1	no	—
370	M₁₆	—	4	2	no	—
371	M₁₆	—	4	2	no	—
372	M₁₆	—	4	2	no	—
373	M₁₆	—	4	2	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	4	2	no	—
378	C₂×C₈	—	4	1	no	—
379	C₂×C₈	—	4	2	no	—
380	C₂×C₈	—	4	2	no	—
381	C₂×C₈	—	4	2	no	—
382	C₂×C₈	—	4	2	no	—
383	C₂×C₈	C₂⁴	1	1	yes	characteristic
384	C₂×C₈	C₂⁴	1	1	yes	characteristic
385	C₂×C₈	C₂⁴	1	1	yes	characteristic
386	C₂×C₈	C₂⁴	1	1	yes	characteristic
387	C₂×C₈	C₂⁴	1	2	yes	—
388	C₂×C₈	C₂⁴	1	1	yes	characteristic
389	C₂×C₈	C₂⁴	1	2	yes	—
390	C₂×C₈	C₂⁴	1	1	yes	characteristic
391	C₂×C₈	C₂⁴	1	1	yes	characteristic
392	C₂×C₈	C₂⁴	1	2	yes	—
393	C₂×C₈	C₂⁴	1	2	yes	—
394	C₂×C₈	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄	C₂²×C₄	1	2	yes	—
396	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
400	C₄⋊C₄	C₂²×C₄	1	2	yes	—
401	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
403	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
404	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
405	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
406	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊C₄	C₂²×C₄	1	2	yes	—
408	C₄⋊C₄	C₂²×C₄	1	2	yes	—
409	C₄⋊C₄	C₂²×C₄	1	2	yes	—
410	C₄⋊C₄	C₂²×C₄	1	2	yes	—
411	C₄⋊C₄	C₂²×C₄	1	2	yes	—
412	C₄⋊C₄	C₂²×C₄	1	2	yes	—
413	C₄⋊C₄	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄	C₂²×C₄	1	2	yes	—
415	C₄⋊C₄	C₂²×C₄	1	2	yes	—
416	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
417	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
419	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
420	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
421	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
422	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
424	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
425	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
426	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
428	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
429	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
430	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
431	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
432	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
433	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
434	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
435	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
436	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
437	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
438	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
441	C₄²	C₂²×C₄	1	1	yes	characteristic
442	C₄²	C₂²×C₄	1	1	yes	characteristic
443	C₄²	C₂²×C₄	1	2	yes	—
444	C₄²	C₂²×C₄	1	1	yes	characteristic
445	C₄²	C₂²×C₄	1	1	yes	characteristic
446	C₄²	C₂²×C₄	1	1	yes	characteristic
447	C₄²	C₂²×C₄	1	2	yes	—
448	C₄²	C₂²×C₄	1	1	yes	characteristic
449	C₄²	C₂⁴	1	1	yes	characteristic
450	C₄²	C₂⁴	1	1	yes	characteristic
451	C₄²	C₂⁴	1	2	yes	—
452	C₄²	C₂⁴	1	1	yes	characteristic
453	C₄²	C₂⁴	1	1	yes	characteristic
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	C₂³×C₄	1	2	yes	—
458	C₂³	C₂³×C₄	1	2	yes	—
459	C₂³	C₂³×C₄	1	1	yes	characteristic
460	C₂³	C₂³×C₄	1	1	yes	characteristic
461	C₂³	C₂³×C₄	1	1	yes	characteristic
462	C₂³	C₂³×C₄	1	2	yes	—
463	Q₈	—	2	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	1	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	1	no	—
483	D₄	—	4	1	no	—
484	D₄	—	4	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
509	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
510	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
511	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
512	C₂×C₄	C₂³×C₄	1	2	yes	—
513	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
514	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
515	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
516	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
517	C₂×C₄	C₂³×C₄	1	2	yes	—
518	C₂×C₄	C₂³×C₄	1	2	yes	—
519	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
520	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
521	C₂×C₄	C₂³×C₄	1	2	yes	—
522	C₂×C₄	C₂³×C₄	1	2	yes	—
523	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
524	C₂×C₄	C₂⁵	1	1	yes	characteristic
525	C₈	—	2	2	no	—
526	C₈	—	2	2	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	2	2	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	2	no	—
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	H(5,𝔽₂)	1	2	yes	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	8	4	no	—
556	C₂²	C₂⁴×C₄	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	1	no	—
572	C₄	#568	1	2	yes	—
573	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
574	C₄	#585	1	1	yes	characteristic
575	C₂	—	4	1	no	—
576	C₂	—	4	1	no	—
577	C₂	—	4	2	no	—
578	C₂	—	4	2	no	—
579	C₂	—	4	2	no	—
580	C₂	—	4	1	no	—
581	C₂	C₄×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂	C₂×#568	1	1	yes	characteristic
583	C₂	#3573	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄	C₂⁵
commutator, socle	C₂²	C₂⁴×C₄
prime radical	#3460	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. #2995	C₂	semidirect
3. #2994	C₂	semidirect
4. #2993	C₂	semidirect
5. #2991	C₂	semidirect
6. #2989	C₂	semidirect
7. #2981	C₂	semidirect
8. #2981	C₂	semidirect
9. #2979	C₂	semidirect
10. #2978	C₂	semidirect
11. #2976	C₂	semidirect
12. #2974	C₂	semidirect
13. #2970	C₂	semidirect
14. #2969	C₂	semidirect
15. #2968	C₂	semidirect
16. #2966	C₂	semidirect
17. #2965	C₂	semidirect
18. #2935	C₂	semidirect
19. D₄×M₁₆	C₂	semidirect
20. #2933	C₂	semidirect
21. #2932	C₂	semidirect
22. #2931	C₂	semidirect
23. #2930	C₂	semidirect
24. C₂×#131	C₂²	semidirect
25. C₂×#131	C₂²	semidirect
50. #446	C₂²	semidirect
51. #446	C₂²	semidirect
52. #446	C₂²	semidirect
53. #446	C₂²	semidirect
54. #446	C₂²	semidirect
55. C₈×Q₈	C₂²	semidirect
56. C₈×Q₈	C₂²	semidirect
66. #436	C₂²	semidirect
67. #436	C₂²	semidirect
68. #436	C₂²	semidirect
69. #436	C₂²	semidirect
70. #436	C₂²	semidirect
71. #436	C₂²	semidirect
81. #435	C₂²	semidirect
82. #435	C₂²	semidirect
83. #435	C₂²	semidirect
84. #435	C₂²	semidirect
85. #435	C₂²	semidirect
86. #435	C₂²	semidirect
87. #435	C₂²	semidirect
88. #435	C₂²	semidirect
89. #435	C₂²	semidirect
90. #435	C₂²	semidirect
91. #435	C₂²	semidirect
96. C₈×D₄	C₂²	semidirect
97. C₈×D₄	C₂²	semidirect
98. C₈×D₄	C₂²	semidirect
99. C₈×D₄	C₂²	semidirect
100. C₈×D₄	C₂²	semidirect
101. C₈×D₄	C₂²	semidirect
102. #433	C₂²	semidirect
103. #433	C₂²	semidirect
104. #433	C₂²	semidirect
105. #433	C₂²	semidirect
107. #432	C₂²	semidirect
108. #432	C₂²	semidirect
110. #431	C₂²	semidirect
111. #431	C₂²	semidirect
112. #431	C₂²	semidirect
113. #431	C₂²	semidirect
114. #424	C₂²	semidirect
115. #424	C₂²	semidirect
117. #423	C₂²	semidirect
118. #423	C₂²	semidirect
119. C₂×C₄⋊C₈	C₂²	semidirect
120. #408	C₂²	semidirect
121. #408	C₂²	semidirect
122. #408	C₂²	semidirect
123. #408	C₂²	semidirect
124. #408	C₂²	semidirect
125. #408	C₂²	semidirect
129. #405	C₂²	semidirect
130. #405	C₂²	semidirect
132. C₄×M₁₆	C₂²	semidirect
133. C₂×#97	C₂²	semidirect
134. C₂×C₄×C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3460	2
#2995	2
#2994	2
#2993	2
#2991	2
#2989	2
#2981	2
#2979	2
#2978	2
#2976	2
#2974	2
#2970	2
#2969	2
#2968	2
#2966	2
#2965	2
#2935	2
D₄×M₁₆	2
#2933	2
#2932	2
#2931	2
#2930	2