Subgroups — C₂×#3494 #62797

Order 256.

4003 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3494	C₂	1	32	yes	maximal, direct product factor
2	C₂×#555	C₂	1	2	yes	maximal, complemented
3	C₂×#553	C₂	1	2	yes	maximal, complemented
4	C₂×#553	C₂	1	2	yes	maximal, complemented
5	C₂×#551	C₂	1	4	yes	maximal, complemented
6	C₂×#547	C₂	1	2	yes	maximal, complemented
7	C₂×#546	C₂	1	4	yes	maximal, complemented
8	C₂×#544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#542	C₂	1	2	yes	maximal, complemented
10	C₂×#540	C₂	1	2	yes	maximal, complemented
11	C₂×#535	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#532	C₂	1	2	yes	maximal, complemented
13	C₂×#529	C₂	1	2	yes	maximal, complemented
14	C₂×#525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#520	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#518	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#117	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41	C₂²	1	1	yes	characteristic
20	C₂²×#41	C₂²	1	4	yes	complemented
21	C₂³×D₄	C₂²	1	1	yes	characteristic
22	C₂³×D₄	C₂²	1	2	yes	—
23	C₂⁴×C₄	C₂²	1	1	yes	characteristic
24	#555	C₂²	1	32	yes	complemented
25	#553	C₂²	1	32	yes	complemented
26	#553	C₂²	1	32	yes	complemented
27	#551	C₂²	1	64	yes	complemented
28	#547	C₂²	1	32	yes	complemented
29	#546	C₂²	1	64	yes	complemented
30	#544	C₂²	1	16	yes	complemented
31	#542	C₂²	1	32	yes	complemented
32	#540	C₂²	1	32	yes	complemented
33	#535	C₂²	1	16	yes	complemented
34	#532	C₂²	1	32	yes	complemented
35	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
36	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×#127	C₂²	1	2	yes	complemented
38	#529	C₂²	1	32	yes	complemented
39	C₂×#126	C₂²	1	4	yes	complemented
40	C₂×#126	C₂²	1	4	yes	complemented
41	C₂×#125	C₂²	1	2	yes	complemented
42	C₂×#125	C₂²	1	2	yes	complemented
43	C₂×#124	C₂²	1	2	yes	complemented
44	C₂×#124	C₂²	1	4	yes	complemented
45	C₂×#124	C₂²	1	4	yes	complemented
46	#525	C₂²	1	16	yes	complemented
47	C₂×#123	C₂²	1	2	yes	—
48	C₂×#123	C₂²	1	4	yes	complemented
49	C₂×#123	C₂²	1	4	yes	complemented
50	C₂×#123	C₂²	1	4	yes	complemented
51	C₂×#123	C₂²	1	4	yes	complemented
52	C₂×C₂²⋊Q₈	C₂²	1	4	yes	—
53	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
56	C₂×#121	C₂²	1	2	yes	—
57	C₂×#121	C₂²	1	2	yes	—
58	C₂×#121	C₂²	1	2	yes	—
59	C₂×#121	C₂²	1	2	yes	—
60	C₂×#121	C₂²	1	16	yes	complemented
61	C₂×#121	C₂²	1	1	yes	characteristic, complemented
62	C₂×#121	C₂²	1	1	yes	characteristic, complemented
63	C₂×#121	C₂²	1	4	yes	complemented
64	C₂×#121	C₂²	1	2	yes	complemented
65	C₂×#121	C₂²	1	2	yes	complemented
66	C₂×#121	C₂²	1	4	yes	complemented
67	C₂×#121	C₂²	1	4	yes	complemented
68	C₂×#120	C₂²	1	2	yes	—
69	C₂×#120	C₂²	1	4	yes	—
70	#520	C₂²	1	16	yes	complemented
71	#518	C₂²	1	16	yes	complemented
72	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
73	C₂×C₄×D₄	C₂²	1	4	yes	—
74	C₂×C₄×D₄	C₂²	1	2	yes	complemented
75	C₂×C₄×D₄	C₂²	1	2	yes	complemented
76	C₂×C₄×D₄	C₂²	1	2	yes	complemented
77	C₂×C₄×D₄	C₂²	1	2	yes	complemented
78	C₂×C₄×D₄	C₂²	1	2	yes	complemented
79	C₂×C₄×D₄	C₂²	1	2	yes	complemented
80	C₂×C₄×D₄	C₂²	1	2	yes	complemented
81	C₂×C₄×D₄	C₂²	1	4	yes	complemented
82	C₂×C₄×D₄	C₂²	1	4	yes	complemented
83	C₂×#117	C₂²	1	1	yes	characteristic
84	C₂×#117	C₂²	1	1	yes	characteristic
85	C₂×#117	C₂²	1	2	yes	—
86	C₂×#117	C₂²	1	1	yes	characteristic
87	C₂×#117	C₂²	1	2	yes	complemented
88	C₂×#117	C₂²	1	1	yes	characteristic, complemented
89	C₂×#117	C₂²	1	1	yes	characteristic, complemented
90	C₂×#117	C₂²	1	2	yes	complemented
91	C₂×#117	C₂²	1	4	yes	complemented
92	C₂×#117	C₂²	1	16	yes	complemented
93	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
96	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₂²×C₂²⋊C₄	C₂²	1	4	yes	—
99	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₂²×C₄²	C₂²	1	2	yes	complemented
101	C₂⁵	C₂³	1	1	yes	characteristic
102	C₂⁵	C₂³	1	2	yes	—
103	C₂×#41	—	2	8	no	—
104	C₂×#41	—	4	16	no	—
105	C₂×#41	C₂³	1	8	yes	—
106	C₂×#41	C₂³	1	32	yes	complemented
107	C₂²×Q₈	C₂³	1	1	yes	characteristic
108	C₂²×Q₈	C₂³	1	4	yes	—
109	C₂²×D₄	—	2	8	no	—
110	C₂²×D₄	—	4	8	no	—
111	C₂²×D₄	C₂³	1	2	yes	—
112	C₂²×D₄	C₂³	1	2	yes	—
113	C₂²×D₄	C₂³	1	2	yes	—
114	C₂²×D₄	C₂³	1	1	yes	characteristic
115	C₂²×D₄	C₂³	1	2	yes	—
116	C₂²×D₄	C₂³	1	4	yes	—
117	C₂²×D₄	C₂³	1	8	yes	—
118	C₂²×D₄	C₂³	1	2	yes	—
119	C₂²×D₄	C₂³	1	4	yes	—
120	C₂²×D₄	C₂³	1	4	yes	—
121	C₂²×D₄	C₂³	1	4	yes	—
122	C₂²×D₄	C₂³	1	16	yes	—
123	C₂³×C₄	—	2	8	no	—
124	C₂³×C₄	C₂³	1	1	yes	characteristic
125	C₂³×C₄	C₂³	1	2	yes	—
126	C₂³×C₄	C₂³	1	1	yes	characteristic
127	C₂³×C₄	C₂³	1	2	yes	—
128	C₂³×C₄	C₂³	1	1	yes	characteristic
129	C₂³×C₄	C₂³	1	1	yes	characteristic
130	C₂³×C₄	C₂³	1	8	yes	—
131	C₂³×C₄	C₂³	1	1	yes	characteristic
132	C₂³×C₄	C₂³	1	2	yes	—
133	C₂³×C₄	C₂³	1	2	yes	—
134	C₂³×C₄	C₂³	1	4	yes	—
135	C₂³×C₄	C₂³	1	4	yes	—
136	C₂³×C₄	C₂³	1	4	yes	—
137	C₂³×C₄	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈	C₂³	1	16	yes	complemented
139	C₄⋊Q₈	C₂³	1	16	yes	complemented
140	#127	C₂³	1	16	yes	complemented
141	#126	C₂³	1	32	yes	complemented
142	#126	C₂³	1	32	yes	complemented
143	#125	C₂³	1	16	yes	complemented
144	#125	C₂³	1	16	yes	complemented
145	#124	C₂³	1	16	yes	complemented
146	#124	C₂³	1	32	yes	complemented
147	#124	C₂³	1	32	yes	complemented
148	#123	C₂³	1	16	yes	—
149	#123	C₂³	1	32	yes	complemented
150	#123	C₂³	1	32	yes	complemented
151	#123	C₂³	1	32	yes	complemented
152	#123	C₂³	1	32	yes	complemented
153	C₂²⋊Q₈	C₂³	1	32	yes	—
154	C₂²⋊Q₈	C₂³	1	8	yes	complemented
155	C₂²⋊Q₈	C₂³	1	8	yes	complemented
156	C₂²⋊Q₈	C₂³	1	32	yes	complemented
157	#121	C₂³	1	16	yes	—
158	#121	C₂³	1	16	yes	—
159	#121	C₂³	1	16	yes	—
160	#121	C₂³	1	16	yes	—
161	#121	C₂³	1	8	yes	complemented
162	#121	C₂³	1	8	yes	complemented
163	#121	C₂³	1	32	yes	complemented
164	#121	C₂³	1	16	yes	complemented
165	#121	C₂³	1	16	yes	complemented
166	#121	C₂³	1	32	yes	complemented
167	#121	C₂³	1	32	yes	complemented
168	#120	C₂³	1	16	yes	—
169	#120	C₂³	1	32	yes	—
170	C₄×Q₈	C₂³	1	16	yes	complemented
171	C₄×D₄	C₂³	1	32	yes	—
172	C₄×D₄	C₂³	1	16	yes	complemented
173	C₄×D₄	C₂³	1	16	yes	complemented
174	C₄×D₄	C₂³	1	16	yes	complemented
175	C₄×D₄	C₂³	1	16	yes	complemented
176	C₄×D₄	C₂³	1	16	yes	complemented
177	C₄×D₄	C₂³	1	16	yes	complemented
178	C₄×D₄	C₂³	1	16	yes	complemented
179	C₄×D₄	C₂³	1	32	yes	complemented
180	C₄×D₄	C₂³	1	32	yes	complemented
181	#117	C₂³	1	8	yes	—
182	#117	C₂³	1	8	yes	—
183	#117	C₂³	1	16	yes	—
184	#117	C₂³	1	8	yes	—
185	#117	C₂³	1	16	yes	complemented
186	#117	C₂³	1	8	yes	complemented
187	#117	C₂³	1	8	yes	complemented
188	#117	C₂³	1	16	yes	complemented
189	#117	C₂³	1	32	yes	complemented
190	C₂×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄	C₂³	1	8	yes	—
193	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄	C₂³	1	4	yes	—
200	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄	C₂³	1	4	yes	—
204	C₂×C₄⋊C₄	C₂³	1	4	yes	—
205	C₂×C₄⋊C₄	C₂³	1	4	yes	—
206	C₂×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
208	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
209	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
210	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
216	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
217	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
218	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄	C₂³	1	32	yes	—
220	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
222	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
223	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
224	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
227	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₄²	C₂³	1	2	yes	—
230	C₂×C₄²	C₂³	1	2	yes	—
231	C₂×C₄²	C₂³	1	2	yes	—
232	C₂×C₄²	C₂³	1	2	yes	—
233	C₂×C₄²	C₂³	1	2	yes	—
234	C₂×C₄²	C₂³	1	4	yes	—
235	C₂×C₄²	C₂³	1	16	yes	complemented
236	C₂⁴	—	2	4	no	—
237	C₂⁴	—	2	4	no	—
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	4	2	no	—
240	C₂⁴	—	4	4	no	—
241	C₂⁴	—	4	4	no	—
242	C₂⁴	C₂⁴	1	1	yes	characteristic
243	C₂⁴	C₂⁴	1	4	yes	—
244	C₂⁴	C₂⁴	1	2	yes	—
245	C₂⁴	C₂⁴	1	4	yes	—
246	C₂⁴	C₂⁴	1	1	yes	characteristic
247	C₂⁴	C₂⁴	1	1	yes	characteristic
248	C₂⁴	C₂⁴	1	8	yes	—
249	#41	—	2	32	no	—
250	#41	—	4	64	no	—
251	C₂×Q₈	—	2	4	no	—
252	C₂×Q₈	—	4	8	no	—
253	C₂×Q₈	C₂⁴	1	4	yes	—
254	C₂×Q₈	C₂⁴	1	16	yes	—
255	C₂×D₄	—	2	8	no	—
256	C₂×D₄	—	2	16	no	—
257	C₂×D₄	—	2	8	no	—
258	C₂×D₄	—	2	8	no	—
259	C₂×D₄	—	2	8	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	32	no	—
262	C₂×D₄	—	4	8	no	—
263	C₂×D₄	—	4	4	no	—
264	C₂×D₄	—	4	8	no	—
265	C₂×D₄	—	4	8	no	—
266	C₂×D₄	—	4	32	no	—
267	C₂×D₄	C₂⁴	1	8	yes	—
268	C₂×D₄	C₂⁴	1	8	yes	—
269	C₂×D₄	C₂⁴	1	8	yes	—
270	C₂×D₄	C₂⁴	1	4	yes	—
271	C₂×D₄	C₂⁴	1	8	yes	—
272	C₂×D₄	C₂⁴	1	16	yes	—
273	C₂×D₄	C₂⁴	1	8	yes	—
274	C₂×D₄	C₂⁴	1	16	yes	—
275	C₂×D₄	C₂⁴	1	16	yes	—
276	C₂×D₄	C₂⁴	1	16	yes	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	8	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	2	32	no	—
285	C₂²×C₄	—	4	8	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	—	4	4	no	—
288	C₂²×C₄	—	4	8	no	—
289	C₂²×C₄	—	4	8	no	—
290	C₂²×C₄	#41	1	8	yes	complemented
291	C₂²×C₄	C₂⁴	1	4	yes	—
292	C₂²×C₄	C₂⁴	1	8	yes	—
293	C₂²×C₄	C₂⁴	1	4	yes	—
294	C₂²×C₄	C₂⁴	1	4	yes	—
295	C₂²×C₄	C₂⁴	1	8	yes	—
296	C₂²×C₄	C₂⁴	1	4	yes	—
297	C₂²×C₄	C₂⁴	1	4	yes	—
298	C₂²×C₄	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄	C₂⁴	1	2	yes	—
300	C₂²×C₄	C₂⁴	1	2	yes	—
301	C₂²×C₄	C₂⁴	1	2	yes	—
302	C₂²×C₄	C₂⁴	1	2	yes	—
303	C₂²×C₄	C₂⁴	1	2	yes	—
304	C₂²×C₄	C₂⁴	1	2	yes	—
305	C₂²×C₄	C₂⁴	1	2	yes	—
306	C₂²×C₄	C₂⁴	1	4	yes	—
307	C₂²×C₄	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄	C₂⁴	1	8	yes	—
309	C₂²×C₄	C₂⁴	1	8	yes	—
310	C₂²×C₄	C₂⁴	1	16	yes	—
311	C₂²×C₄	C₂⁴	1	16	yes	—
312	C₂²×C₄	C₂⁴	1	16	yes	—
313	C₂²×C₄	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴	1	4	yes	—
316	C₄⋊C₄	C₂⁴	1	8	yes	—
317	C₄⋊C₄	C₂⁴	1	8	yes	—
318	C₄⋊C₄	C₂⁴	1	4	yes	—
319	C₄⋊C₄	C₂⁴	1	4	yes	—
320	C₄⋊C₄	C₂⁴	1	4	yes	—
321	C₄⋊C₄	C₂⁴	1	4	yes	—
322	C₄⋊C₄	C₂⁴	1	8	yes	—
323	C₄⋊C₄	C₂⁴	1	8	yes	—
324	C₄⋊C₄	C₂⁴	1	16	yes	—
325	C₄⋊C₄	C₂⁴	1	4	yes	—
326	C₄⋊C₄	C₂⁴	1	4	yes	—
327	C₄⋊C₄	C₂⁴	1	8	yes	—
328	C₄⋊C₄	C₂⁴	1	16	yes	—
329	C₄⋊C₄	C₂⁴	1	16	yes	—
330	C₄⋊C₄	C₂⁴	1	16	yes	—
331	C₄⋊C₄	C₂⁴	1	8	yes	—
332	C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₂²⋊C₄	C₂⁴	1	8	yes	—
334	C₂²⋊C₄	C₂⁴	1	8	yes	—
335	C₂²⋊C₄	C₂⁴	1	8	yes	—
336	C₂²⋊C₄	C₂⁴	1	8	yes	—
337	C₂²⋊C₄	C₂⁴	1	16	yes	—
338	C₂²⋊C₄	C₂⁴	1	16	yes	—
339	C₂²⋊C₄	C₂⁴	1	16	yes	—
340	C₂²⋊C₄	C₂⁴	1	16	yes	—
341	C₂²⋊C₄	C₂⁴	1	16	yes	—
342	C₂²⋊C₄	C₂⁴	1	16	yes	—
343	C₂²⋊C₄	C₂⁴	1	8	yes	—
344	C₂²⋊C₄	C₂⁴	1	8	yes	—
345	C₂²⋊C₄	C₂⁴	1	16	yes	—
346	C₂²⋊C₄	C₂⁴	1	8	yes	—
347	C₂²⋊C₄	C₂⁴	1	8	yes	—
348	C₄²	C₂⁴	1	8	yes	—
349	C₄²	C₂⁴	1	8	yes	—
350	C₄²	C₂⁴	1	8	yes	—
351	C₄²	C₂⁴	1	8	yes	—
352	C₄²	C₂⁴	1	8	yes	—
353	C₄²	C₂⁴	1	16	yes	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	8	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	16	no	—
370	C₂³	—	4	4	no	—
371	C₂³	—	4	8	no	—
372	C₂³	—	4	8	no	—
373	C₂³	—	4	16	no	—
374	C₂³	—	8	16	no	—
375	C₂³	C₂×#41	1	4	yes	—
376	C₂³	H(5,𝔽₂)	1	4	yes	—
377	C₂³	C₂⁵	1	2	yes	—
378	C₂³	C₂⁵	1	8	yes	—
379	C₂³	C₂⁵	1	4	yes	—
380	C₂³	C₂⁵	1	2	yes	—
381	C₂³	C₂⁵	1	2	yes	—
382	C₂³	C₂⁵	1	1	yes	characteristic
383	Q₈	—	2	8	no	—
384	Q₈	—	4	16	no	—
385	D₄	—	2	16	no	—
386	D₄	—	2	32	no	—
387	D₄	—	2	16	no	—
388	D₄	—	2	16	no	—
389	D₄	—	2	16	no	—
390	D₄	—	2	8	no	—
391	D₄	—	4	16	no	—
392	D₄	—	4	8	no	—
393	D₄	—	4	16	no	—
394	D₄	—	4	16	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	16	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	16	no	—
412	C₂×C₄	—	4	16	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	4	8	no	—
415	C₂×C₄	—	4	16	no	—
416	C₂×C₄	—	4	16	no	—
417	C₂×C₄	C₂×#41	1	4	yes	—
418	C₂×C₄	C₂×#41	1	4	yes	—
419	C₂×C₄	C₂×#41	1	16	yes	complemented
420	C₂×C₄	C₂⁵	1	2	yes	—
421	C₂×C₄	C₂⁵	1	4	yes	—
422	C₂×C₄	C₂⁵	1	4	yes	—
423	C₂×C₄	C₂⁵	1	4	yes	—
424	C₂×C₄	C₂⁵	1	4	yes	—
425	C₂×C₄	C₂⁵	1	4	yes	—
426	C₂×C₄	C₂⁵	1	4	yes	—
427	C₂×C₄	C₂⁵	1	4	yes	—
428	C₂×C₄	C₂⁵	1	8	yes	—
429	C₂×C₄	C₂⁵	1	2	yes	—
430	C₂×C₄	C₂⁵	1	2	yes	—
431	C₂×C₄	C₂⁵	1	2	yes	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	8	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	8	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	8	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	8	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	16	no	—
448	C₂²	—	4	8	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	16	no	—
451	C₂²	—	8	16	no	—
452	C₂²	C₂²×#41	1	4	yes	—
453	C₂²	C₂²×#41	1	2	yes	—
454	C₂²	C₂×H(5,𝔽₂)	1	4	yes	—
455	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
456	C₂²	#585	1	2	yes	—
457	C₂²	C₂⁶	1	1	yes	characteristic
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	4	no	—
461	C₄	—	2	4	no	—
462	C₄	—	2	4	no	—
463	C₄	—	2	8	no	—
464	C₄	—	2	4	no	—
465	C₄	—	2	4	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	4	no	—
468	C₄	C₂²×#41	1	4	yes	—
469	C₄	C₂²×#41	1	4	yes	—
470	C₂	—	2	4	no	—
471	C₂	—	2	4	no	—
472	C₂	—	4	4	no	—
473	C₂	—	4	2	no	—
474	C₂	—	4	8	no	—
475	C₂	#3494	1	4	yes	direct product factor
476	C₂	C₂³×#41	1	1	yes	characteristic
477	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂	C₂×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3494	C₂	direct (N × H)
2. C₂×#555	C₂	semidirect
3. C₂×#553	C₂	semidirect
4. C₂×#553	C₂	semidirect
5. C₂×#551	C₂	semidirect
6. C₂×#547	C₂	semidirect
7. C₂×#546	C₂	semidirect
8. C₂×#544	C₂	semidirect
9. C₂×#542	C₂	semidirect
10. C₂×#540	C₂	semidirect
11. C₂×#535	C₂	semidirect
12. C₂×#532	C₂	semidirect
13. C₂×#529	C₂	semidirect
14. C₂×#525	C₂	semidirect
15. C₂²×#121	C₂	semidirect
16. C₂×#520	C₂	semidirect
17. C₂×#518	C₂	semidirect
18. C₂²×#117	C₂	semidirect
20. C₂²×#41	C₂²	semidirect
24. #555	C₂²	semidirect
25. #553	C₂²	semidirect
26. #553	C₂²	semidirect
27. #551	C₂²	semidirect
28. #547	C₂²	semidirect
29. #546	C₂²	semidirect
30. #544	C₂²	semidirect
31. #542	C₂²	semidirect
32. #540	C₂²	semidirect
33. #535	C₂²	semidirect
34. #532	C₂²	semidirect
35. C₂×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₄⋊Q₈	C₂²	semidirect
37. C₂×#127	C₂²	semidirect
38. #529	C₂²	semidirect
39. C₂×#126	C₂²	semidirect
40. C₂×#126	C₂²	semidirect
41. C₂×#125	C₂²	semidirect
42. C₂×#125	C₂²	semidirect
43. C₂×#124	C₂²	semidirect
44. C₂×#124	C₂²	semidirect
45. C₂×#124	C₂²	semidirect
46. #525	C₂²	semidirect
48. C₂×#123	C₂²	semidirect
49. C₂×#123	C₂²	semidirect
50. C₂×#123	C₂²	semidirect
51. C₂×#123	C₂²	semidirect
53. C₂×C₂²⋊Q₈	C₂²	semidirect
54. C₂×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₂²⋊Q₈	C₂²	semidirect
60. C₂×#121	C₂²	semidirect
61. C₂×#121	C₂²	semidirect
62. C₂×#121	C₂²	semidirect
63. C₂×#121	C₂²	semidirect
64. C₂×#121	C₂²	semidirect
65. C₂×#121	C₂²	semidirect
66. C₂×#121	C₂²	semidirect
67. C₂×#121	C₂²	semidirect
70. #520	C₂²	semidirect
71. #518	C₂²	semidirect
72. C₂×C₄×Q₈	C₂²	semidirect
74. C₂×C₄×D₄	C₂²	semidirect
75. C₂×C₄×D₄	C₂²	semidirect
76. C₂×C₄×D₄	C₂²	semidirect
77. C₂×C₄×D₄	C₂²	semidirect
78. C₂×C₄×D₄	C₂²	semidirect
79. C₂×C₄×D₄	C₂²	semidirect
80. C₂×C₄×D₄	C₂²	semidirect
81. C₂×C₄×D₄	C₂²	semidirect
82. C₂×C₄×D₄	C₂²	semidirect
87. C₂×#117	C₂²	semidirect
88. C₂×#117	C₂²	semidirect
89. C₂×#117	C₂²	semidirect
90. C₂×#117	C₂²	semidirect
91. C₂×#117	C₂²	semidirect
92. C₂×#117	C₂²	semidirect
94. C₂²×C₄⋊C₄	C₂²	semidirect
95. C₂²×C₄⋊C₄	C₂²	semidirect
96. C₂²×C₄⋊C₄	C₂²	semidirect
100. C₂²×C₄²	C₂²	semidirect
106. C₂×#41	C₂³	semidirect
138. C₄⋊Q₈	C₂³	semidirect
139. C₄⋊Q₈	C₂³	semidirect
140. #127	C₂³	semidirect
141. #126	C₂³	semidirect
142. #126	C₂³	semidirect
143. #125	C₂³	semidirect
144. #125	C₂³	semidirect
145. #124	C₂³	semidirect
146. #124	C₂³	semidirect
147. #124	C₂³	semidirect
149. #123	C₂³	semidirect
150. #123	C₂³	semidirect
151. #123	C₂³	semidirect
152. #123	C₂³	semidirect
154. C₂²⋊Q₈	C₂³	semidirect
155. C₂²⋊Q₈	C₂³	semidirect
156. C₂²⋊Q₈	C₂³	semidirect
161. #121	C₂³	semidirect
162. #121	C₂³	semidirect
163. #121	C₂³	semidirect
164. #121	C₂³	semidirect
165. #121	C₂³	semidirect
166. #121	C₂³	semidirect
167. #121	C₂³	semidirect
170. C₄×Q₈	C₂³	semidirect
172. C₄×D₄	C₂³	semidirect
173. C₄×D₄	C₂³	semidirect
174. C₄×D₄	C₂³	semidirect
175. C₄×D₄	C₂³	semidirect
176. C₄×D₄	C₂³	semidirect
177. C₄×D₄	C₂³	semidirect
178. C₄×D₄	C₂³	semidirect
179. C₄×D₄	C₂³	semidirect
180. C₄×D₄	C₂³	semidirect
185. #117	C₂³	semidirect
186. #117	C₂³	semidirect
187. #117	C₂³	semidirect
188. #117	C₂³	semidirect
189. #117	C₂³	semidirect
207. C₂×C₄⋊C₄	C₂³	semidirect
208. C₂×C₄⋊C₄	C₂³	semidirect
209. C₂×C₄⋊C₄	C₂³	semidirect
235. C₂×C₄²	C₂³	semidirect
290. C₂²×C₄	#41	semidirect
419. C₂×C₄	C₂×#41	semidirect
475. C₂	#3494	direct (N × H)

Maximal subgroups

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

subgroup	index
#3494	2
C₂×#555	2
C₂×#553	2
C₂×#551	2
C₂×#547	2
C₂×#546	2
C₂×#544	2
C₂×#542	2
C₂×#540	2
C₂×#535	2
C₂×#532	2
C₂×#529	2
C₂×#525	2
C₂²×#121	2
C₂×#520	2
C₂×#518	2
C₂²×#117	2

Subgroups — C2×#3494 #62797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3494 #62797