Subgroups — C₂×#72313181 #72313190

Order 2048.

At least 9108 conjugacy classes of subgroups; only the 2544 normal subgroups are shown.

The subgroup lattice has 805 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#379775	C₂	1	2	yes	maximal, complemented
2	C₂×#553150	C₂	1	1	yes	maximal, characteristic, complemented
3	#72313181	C₂	1	16	yes	maximal, direct product factor
4	C₂×#187925	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#106331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#114839	C₂	1	2	yes	maximal, complemented
7	C₂×#185258	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#114579	C₂	1	2	yes	maximal, complemented
9	C₂×#10577301	C₂	1	1	yes	maximal, characteristic
10	C₂×#108224	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#198404	C₂	1	2	yes	maximal, complemented
12	C₂×#185643	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#62773	C₂²	1	1	yes	characteristic
14	C₂³×D₄²	C₂²	1	1	yes	characteristic
15	#10577301	C₄	1	8	yes	complemented
16	#10577301	C₂²	1	8	yes	—
17	C₂×#61571	C₄	1	4	yes	complemented
18	C₂×#61560	C₄	1	2	yes	complemented
19	C₂×#61559	C₄	1	2	yes	complemented
20	C₂×#60750	C₂²	1	2	yes	—
21	C₂²×#3003	C₂²	1	2	yes	—
22	C₂×#60230	C₂²	1	1	yes	characteristic
23	C₂²×D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₂²×#2309	C₂²	1	1	yes	characteristic, complemented
25	C₂×#21420	C₂²	1	2	yes	complemented
26	C₂×#20983	C₂²	1	2	yes	complemented
27	C₂×#20979	C₂²	1	2	yes	complemented
28	C₂×#20722	C₂²	1	1	yes	characteristic
29	C₂×#20598	C₂²	1	2	yes	complemented
30	C₂×#17592	C₂²	1	2	yes	complemented
31	C₂×#17577	C₂²	1	2	yes	complemented
32	C₂×#17362	C₂²	1	1	yes	characteristic
33	#553150	C₂²	1	8	yes	complemented
34	C₂×#14257	C₂²	1	1	yes	characteristic, complemented
35	C₂×#14136	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13871	C₂²	1	1	yes	characteristic
37	C₂×#13839	C₂²	1	1	yes	characteristic
38	#379775	C₂²	1	16	yes	complemented
39	C₂×#10738	C₂²	1	2	yes	complemented
40	C₂×#10716	C₂²	1	2	yes	complemented
41	#198404	C₂²	1	16	yes	complemented
42	#187925	C₂²	1	8	yes	complemented
43	#185643	C₂²	1	8	yes	complemented
44	#185258	C₂²	1	8	yes	complemented
45	C₂×#7983	C₂²	1	2	yes	complemented
46	C₂×#7929	C₂²	1	2	yes	complemented
47	#114839	C₂²	1	16	yes	complemented
48	#114579	C₂²	1	16	yes	complemented
49	#108224	C₂²	1	8	yes	complemented
50	#106331	C₂²	1	8	yes	complemented
51	C₂⁵×D₄	D₄	1	1	yes	characteristic
52	C₂⁵×D₄	C₂³	1	1	yes	characteristic
53	C₂³×AGL(1,ℤ/8)	D₄	1	4	yes	—
54	#62773	C₂×C₄	1	4	yes	complemented
55	#62773	C₂³	1	4	yes	—
56	C₂×#3505	C₂×C₄	1	2	yes	complemented
57	C₂×#3501	C₂×C₄	1	1	yes	characteristic, complemented
58	C₂×#3496	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂²×D₄²	C₂×C₄	1	2	yes	—
60	C₂²×D₄²	C₂×C₄	1	2	yes	—
61	C₂²×D₄²	C₂×C₄	1	4	yes	—
62	C₂²×D₄²	D₄	1	2	yes	—
63	C₂²×D₄²	D₄	1	2	yes	—
64	C₂²×D₄²	D₄	1	4	yes	—
65	C₂²×D₄²	D₄	1	4	yes	—
66	C₂²×D₄²	C₂³	1	4	yes	—
67	C₂³×#127	D₄	1	1	yes	characteristic
68	C₂²×#525	C₂³	1	2	yes	—
69	C₂³×#121	D₄	1	1	yes	characteristic
70	C₂³×#121	C₂³	1	1	yes	characteristic
71	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
72	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
73	C₂³×#117	C₂³	1	1	yes	characteristic
74	C₂³×#117	C₂³	1	1	yes	characteristic
75	#61571	C₂×C₄	1	32	yes	complemented
76	#61560	C₂×C₄	1	16	yes	complemented
77	#61559	C₂×C₄	1	16	yes	complemented
78	#60750	C₂×C₄	1	8	yes	complemented
79	#60750	C₂³	1	8	yes	—
80	C₂×#3187	C₂×C₄	1	4	yes	complemented
81	C₂×#3186	C₂×C₄	1	4	yes	complemented
82	C₂×#3003	C₂×C₄	1	8	yes	—
83	C₂×#3003	D₄	1	8	yes	—
84	C₂×#3003	D₄	1	8	yes	—
85	C₂×#3003	C₂³	1	8	yes	—
86	C₂²×#450	C₂×C₄	1	4	yes	—
87	C₂²×#450	D₄	1	4	yes	—
88	C₂²×#447	C₂×C₄	1	4	yes	—
89	C₂²×#447	D₄	1	4	yes	—
90	#60230	C₂×C₄	1	4	yes	complemented
91	#60230	C₂³	1	4	yes	—
92	C₂×#2973	C₂×C₄	1	2	yes	complemented
93	C₂×#2972	C₂×C₄	1	2	yes	complemented
94	C₂²×#418	D₄	1	4	yes	—
95	C₂²×#407	C₂³	1	2	yes	—
96	C₂²×#407	C₂³	1	2	yes	—
97	C₂×D₄×C₂²⋊C₄	C₂³	1	4	yes	complemented
98	C₂×#2309	C₂³	1	4	yes	complemented
99	C₂×#2280	C₂³	1	2	yes	—
100	C₂²×#380	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
102	#21420	C₂³	1	8	yes	complemented
103	#20983	C₂³	1	8	yes	complemented
104	#20979	C₂³	1	8	yes	complemented
105	#20722	C₂³	1	4	yes	—
106	#20598	C₂³	1	8	yes	complemented
107	#17592	C₂³	1	8	yes	complemented
108	#17577	C₂³	1	8	yes	complemented
109	#17362	C₂³	1	4	yes	—
110	#14257	C₂³	1	4	yes	complemented
111	#14136	C₂³	1	4	yes	complemented
112	#13871	D₄	1	4	yes	—
113	#13871	C₂³	1	4	yes	—
114	#13839	D₄	1	4	yes	—
115	#13839	C₂³	1	4	yes	—
116	C₂×#1440	D₄	1	1	yes	characteristic
117	C₂×#1440	D₄	1	1	yes	characteristic
118	C₂×#1438	D₄	1	1	yes	characteristic
119	C₂×#1438	D₄	1	1	yes	characteristic
120	C₂×#1437	D₄	1	2	yes	—
121	C₂×#1436	D₄	1	2	yes	—
122	#10738	C₂³	1	8	yes	complemented
123	#10716	C₂³	1	8	yes	complemented
124	#7983	C₂³	1	8	yes	complemented
125	#7929	C₂³	1	8	yes	complemented
126	C₂³×#41	C₂×D₄	1	2	yes	—
127	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
128	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
129	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	—
130	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
131	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
132	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
133	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
134	C₂⁴×D₄	C₂×D₄	1	4	yes	—
135	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
136	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
137	C₂⁴×D₄	C₂×D₄	1	4	yes	—
138	C₂⁴×D₄	C₂×D₄	1	4	yes	—
139	C₂⁴×D₄	C₂×D₄	1	4	yes	—
140	C₂⁴×D₄	C₂×D₄	1	2	yes	—
141	C₂⁴×D₄	C₂×D₄	1	2	yes	—
142	C₂⁴×D₄	C₂×D₄	1	2	yes	—
143	C₂⁴×D₄	C₂×D₄	1	4	yes	—
144	C₂⁴×D₄	C₂⁴	1	2	yes	—
145	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
146	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
147	C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	1	16	yes	complemented
148	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	—
149	C₂³×SD₁₆	C₂²⋊C₄	1	8	yes	complemented
150	C₂³×D₈	C₂²⋊C₄	1	8	yes	complemented
151	C₂³×M₁₆	C₂×D₄	1	4	yes	—
152	#3505	C₂²×C₄	1	8	yes	complemented
153	#3501	C₂²×C₄	1	4	yes	complemented
154	#3496	C₂²×C₄	1	4	yes	complemented
155	C₂×D₄²	C₂²⋊C₄	1	8	yes	—
156	C₂×D₄²	C₂²⋊C₄	1	8	yes	—
157	C₂×D₄²	C₂²⋊C₄	1	8	yes	—
158	C₂×D₄²	C₂²⋊C₄	1	8	yes	—
159	C₂×D₄²	C₂²×C₄	1	8	yes	—
160	C₂×D₄²	C₂²×C₄	1	8	yes	—
161	C₂×D₄²	C₂×D₄	1	8	yes	—
162	C₂×D₄²	C₂×D₄	1	8	yes	—
163	C₂²×#127	C₂²⋊C₄	1	2	yes	—
164	C₂²×#127	C₂²⋊C₄	1	2	yes	—
165	C₂²×#127	C₂²⋊C₄	1	4	yes	—
166	C₂²×#127	C₂×D₄	1	4	yes	—
167	C₂×#525	C₂²×C₄	1	4	yes	—
168	C₂×#525	C₂×D₄	1	4	yes	—
169	C₂×#525	C₂×D₄	1	4	yes	—
170	C₂×#525	C₂⁴	1	4	yes	—
171	C₂²×C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
172	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
173	C₂²×#121	C₂²⋊C₄	1	2	yes	—
174	C₂²×#121	C₂²⋊C₄	1	2	yes	—
175	C₂²×#121	C₂²⋊C₄	1	4	yes	—
176	C₂²×#121	C₂²×C₄	1	2	yes	—
177	C₂²×#121	C₂²×C₄	1	2	yes	—
178	C₂²×#121	C₂²×C₄	1	2	yes	—
179	C₂²×#121	C₂×D₄	1	2	yes	—
180	C₂²×#121	C₂×D₄	1	2	yes	—
181	C₂²×#121	C₂×D₄	1	2	yes	—
182	C₂²×#121	C₂×D₄	1	2	yes	—
183	C₂²×#121	C₂×D₄	1	4	yes	—
184	C₂²×#121	C₂⁴	1	2	yes	—
185	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
186	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
187	C₂²×C₄×D₄	C₂²⋊C₄	1	4	yes	—
188	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
191	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
192	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
193	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
194	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
195	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
198	C₂²×C₄×D₄	#41	1	2	yes	—
199	C₂²×C₄×D₄	#41	1	1	yes	characteristic
200	C₂²×C₄×D₄	#41	1	1	yes	characteristic
201	C₂²×C₄×D₄	#41	1	2	yes	—
202	C₂²×C₄×D₄	#41	1	1	yes	characteristic
203	C₂²×C₄×D₄	#41	1	1	yes	characteristic
204	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
205	C₂²×#117	C₂×D₄	1	2	yes	—
206	C₂²×#117	C₂×D₄	1	2	yes	—
207	C₂²×#117	C₂×D₄	1	2	yes	—
208	C₂²×#117	C₂⁴	1	2	yes	—
209	C₂²×#117	C₂⁴	1	2	yes	—
210	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
211	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
212	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
213	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
214	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
215	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
216	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
217	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
218	C₂³×C₄²	C₂×D₄	1	2	yes	—
219	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
220	#3187	C₂²×C₄	1	16	yes	complemented
221	#3186	C₂²×C₄	1	16	yes	complemented
222	C₂×#450	C₂²⋊C₄	1	16	yes	complemented
223	C₂×#450	C₂²⋊C₄	1	16	yes	complemented
224	C₂×#450	C₂²×C₄	1	16	yes	—
225	C₂×#450	C₂×D₄	1	16	yes	—
226	C₂×#447	C₂²⋊C₄	1	16	yes	complemented
227	C₂×#447	C₂²⋊C₄	1	16	yes	complemented
228	C₂×#447	C₂²×C₄	1	16	yes	—
229	C₂×#447	C₂×D₄	1	16	yes	—
230	#2973	C₂²×C₄	1	8	yes	complemented
231	#2972	C₂²×C₄	1	8	yes	complemented
232	C₂×#418	C₂²⋊C₄	1	16	yes	complemented
233	C₂×#418	C₂×D₄	1	16	yes	—
234	C₂²×#102	C₂²⋊C₄	1	8	yes	complemented
235	C₂²×#102	C₂²⋊C₄	1	8	yes	complemented
236	C₂×#407	C₂²×C₄	1	4	yes	—
237	C₂×#407	C₂×D₄	1	4	yes	—
238	C₂×#407	C₂×D₄	1	4	yes	—
239	C₂×#407	C₂⁴	1	4	yes	—
240	C₂×#407	C₂⁴	1	4	yes	—
241	C₂²×C₂²⋊C₈	C₂²×C₄	1	4	yes	—
242	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	—
243	#2280	C₂⁴	1	4	yes	—
244	C₂×#380	C₂×D₄	1	2	yes	—
245	C₂×#380	C₂⁴	1	2	yes	—
246	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
247	C₂×C₄×C₂²⋊C₄	C₂⁴	1	2	yes	—
248	C₂²×#95	C₂×D₄	1	2	yes	—
249	#1440	C₂×D₄	1	4	yes	—
250	#1440	C₂×D₄	1	4	yes	—
251	#1438	C₂×D₄	1	4	yes	—
252	#1438	C₂×D₄	1	4	yes	—
253	#1437	C₂×D₄	1	8	yes	—
254	#1436	C₂×D₄	1	8	yes	—
255	C₂⁶	#120	1	1	yes	characteristic
256	C₂⁶	C₂²×D₄	1	1	yes	characteristic
257	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	—
258	C₂²×#41	C₂²×D₄	1	4	yes	—
259	C₂³×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
261	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
264	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
265	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
266	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
267	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
269	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
270	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
271	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
272	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
273	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
274	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
275	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
276	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
277	C₂³×D₄	C₄×D₄	1	2	yes	—
278	C₂³×D₄	#120	1	2	yes	—
279	C₂³×D₄	#120	1	2	yes	—
280	C₂³×D₄	#120	1	2	yes	—
281	C₂³×D₄	#120	1	2	yes	—
282	C₂³×D₄	#120	1	2	yes	—
283	C₂³×D₄	#120	1	2	yes	—
284	C₂³×D₄	#120	1	8	yes	—
285	C₂³×D₄	#120	1	8	yes	—
286	C₂³×D₄	#120	1	8	yes	—
287	C₂³×D₄	#120	1	2	yes	—
288	C₂³×D₄	#120	1	2	yes	—
289	C₂³×D₄	#120	1	2	yes	—
290	C₂³×D₄	#120	1	8	yes	—
291	C₂³×D₄	#120	1	8	yes	—
292	C₂³×D₄	#120	1	8	yes	—
293	C₂³×D₄	#121	1	1	yes	characteristic
294	C₂³×D₄	#121	1	1	yes	characteristic
295	C₂³×D₄	#121	1	2	yes	—
296	C₂³×D₄	C₂³×C₄	1	4	yes	—
297	C₂³×D₄	C₂²×D₄	1	2	yes	—
298	C₂³×D₄	C₂²×D₄	1	2	yes	—
299	C₂³×D₄	C₂²×D₄	1	2	yes	—
300	C₂³×D₄	C₂²×D₄	1	8	yes	—
301	C₂³×D₄	C₂²×D₄	1	2	yes	—
302	C₂³×D₄	C₂²×D₄	1	8	yes	—
303	C₂³×D₄	C₂²×D₄	1	4	yes	—
304	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
305	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
307	C₂⁴×C₄	#120	1	1	yes	characteristic
308	C₂⁴×C₄	#120	1	1	yes	characteristic
309	C₂⁴×C₄	#120	1	2	yes	—
310	C₂⁴×C₄	#120	1	1	yes	characteristic
311	C₂⁴×C₄	#123	1	1	yes	characteristic
312	C₂⁴×C₄	#123	1	1	yes	characteristic
313	C₂⁴×C₄	#123	1	2	yes	—
314	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
315	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
316	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
317	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
318	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
319	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
320	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
321	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
322	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
323	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
324	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
325	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
326	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
329	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
330	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
331	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
332	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
333	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
334	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
335	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
336	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
337	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	32	yes	complemented
338	C₂²×D₈	C₂×C₂²⋊C₄	1	32	yes	complemented
339	C₂²×M₁₆	C₂×C₂²⋊C₄	1	8	yes	—
340	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
341	C₂³×C₈	C₂×C₂²⋊C₄	1	8	yes	—
342	C₂×#127	C₂×C₂²⋊C₄	1	8	yes	—
343	C₂×#127	C₂×C₂²⋊C₄	1	8	yes	—
344	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	4	yes	—
345	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	4	yes	—
346	C₂×C₂²⋊Q₈	C₂³×C₄	1	4	yes	—
347	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
348	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
349	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
350	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
351	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
352	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	—
353	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	—
354	C₂×#121	C₂³×C₄	1	4	yes	—
355	C₂×#121	C₂³×C₄	1	4	yes	—
356	C₂×#121	C₂²×D₄	1	4	yes	—
357	C₂×#121	C₂²×D₄	1	4	yes	—
358	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
359	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
360	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
361	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
362	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
363	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
364	C₂×C₄×D₄	C₄×D₄	1	2	yes	—
365	C₂×C₄×D₄	C₄×D₄	1	2	yes	—
366	C₂×C₄×D₄	C₄×D₄	1	2	yes	—
367	C₂×C₄×D₄	C₄×D₄	1	2	yes	—
368	C₂×C₄×D₄	C₄×D₄	1	2	yes	—
369	C₂×C₄×D₄	C₄×D₄	1	2	yes	—
370	C₂×C₄×D₄	C₄×D₄	1	2	yes	—
371	C₂×C₄×D₄	C₄×D₄	1	2	yes	—
372	C₂×C₄×D₄	#121	1	2	yes	—
373	C₂×C₄×D₄	#121	1	2	yes	—
374	C₂×C₄×D₄	#121	1	2	yes	—
375	C₂×C₄×D₄	#121	1	2	yes	—
376	C₂×C₄×D₄	#121	1	2	yes	—
377	C₂×C₄×D₄	#121	1	2	yes	—
378	C₂×C₄×D₄	#121	1	2	yes	—
379	C₂×C₄×D₄	#121	1	2	yes	—
380	C₂×C₄×D₄	#123	1	2	yes	—
381	C₂×C₄×D₄	#123	1	2	yes	—
382	C₂×C₄×D₄	#123	1	2	yes	—
383	C₂×C₄×D₄	#123	1	2	yes	—
384	C₂×C₄×D₄	C₂³×C₄	1	2	yes	—
385	C₂×C₄×D₄	C₂³×C₄	1	2	yes	—
386	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
387	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
388	C₂×C₄×D₄	C₂×#41	1	2	yes	—
389	C₂×C₄×D₄	C₂×#41	1	2	yes	—
390	C₂×C₄×D₄	C₂×#41	1	2	yes	—
391	C₂×C₄×D₄	C₂×#41	1	2	yes	—
392	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	—
393	C₂×#117	C₂²×D₄	1	4	yes	—
394	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
395	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
396	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
397	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
398	C₂²×C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
399	C₂²×C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
400	C₂²×C₄⋊C₄	C₄×D₄	1	2	yes	—
401	C₂²×C₄⋊C₄	#120	1	2	yes	—
402	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
404	C₂²×C₄⋊C₄	#121	1	2	yes	—
405	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
406	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
407	C₂²×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₄×D₄	1	2	yes	—
410	C₂²×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
411	C₂²×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
412	C₂²×C₂²⋊C₄	C₄×D₄	1	2	yes	—
413	C₂²×C₂²⋊C₄	#120	1	2	yes	—
414	C₂²×C₂²⋊C₄	#120	1	2	yes	—
415	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
417	C₂²×C₂²⋊C₄	#121	1	2	yes	—
418	C₂²×C₂²⋊C₄	#121	1	2	yes	—
419	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
420	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
421	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
422	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
423	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
424	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
425	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
426	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
427	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
428	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
429	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
430	C₂²×C₄²	#120	1	2	yes	—
431	C₂²×C₄²	#123	1	1	yes	characteristic
432	C₂²×C₄²	#123	1	1	yes	characteristic
433	C₂²×C₄²	#123	1	2	yes	—
434	C₂²×C₄²	C₂²×D₄	1	2	yes	—
435	C₂²×C₄²	C₂²×D₄	1	4	yes	—
436	C₂×#102	C₂×C₂²⋊C₄	1	32	yes	complemented
437	C₂×#102	C₂×C₂²⋊C₄	1	32	yes	complemented
438	C₂×C₂²⋊C₈	C₂×C₂²⋊C₄	1	8	yes	—
439	C₂×C₂²⋊C₈	C₂×C₂²⋊C₄	1	8	yes	—
440	C₂×C₂²⋊C₈	C₂³×C₄	1	8	yes	—
441	C₂×C₂²⋊C₈	C₂²×D₄	1	8	yes	—
442	C₂×#95	C₂²×D₄	1	4	yes	—
443	C₂⁵	#386	1	1	yes	characteristic
444	C₂⁵	#386	1	2	yes	—
445	C₂⁵	#386	1	1	yes	characteristic
446	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
447	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
448	C₂⁵	C₂×#120	1	1	yes	characteristic
449	C₂⁵	C₂×#120	1	2	yes	—
450	C₂⁵	C₂×#120	1	1	yes	characteristic
451	C₂⁵	C₂×#121	1	1	yes	characteristic
452	C₂⁵	C₂×#121	1	1	yes	characteristic
453	C₂⁵	D₄²	1	2	yes	—
454	C₂⁵	D₄²	1	2	yes	—
455	C₂⁵	D₄²	1	2	yes	—
456	C₂⁵	D₄²	1	2	yes	—
457	C₂⁵	C₂³×D₄	1	1	yes	characteristic
458	C₂²×Q₈	C₂²×C₂²⋊C₄	1	4	yes	—
459	C₂²×D₄	#379	1	4	yes	—
460	C₂²×D₄	#379	1	4	yes	—
461	C₂²×D₄	#379	1	4	yes	—
462	C₂²×D₄	#379	1	4	yes	—
463	C₂²×D₄	#379	1	4	yes	—
464	C₂²×D₄	#379	1	4	yes	—
465	C₂²×D₄	#379	1	4	yes	—
466	C₂²×D₄	#379	1	4	yes	—
467	C₂²×D₄	#379	1	16	yes	—
468	C₂²×D₄	#379	1	16	yes	—
469	C₂²×D₄	#386	1	2	yes	—
470	C₂²×D₄	#386	1	2	yes	—
471	C₂²×D₄	#386	1	2	yes	—
472	C₂²×D₄	#386	1	2	yes	—
473	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
474	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
475	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
476	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
477	C₂²×D₄	C₂²×C₂²⋊C₄	1	16	yes	—
478	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
479	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
480	C₂²×D₄	C₂×#120	1	4	yes	—
481	C₂²×D₄	C₂×#120	1	4	yes	—
482	C₂²×D₄	C₂×#120	1	4	yes	—
483	C₂²×D₄	C₂×#120	1	4	yes	—
484	C₂²×D₄	C₂×#120	1	16	yes	—
485	C₂²×D₄	C₂×#121	1	2	yes	—
486	C₂²×D₄	C₂×#121	1	2	yes	—
487	C₂³×C₄	#386	1	1	yes	characteristic
488	C₂³×C₄	#386	1	2	yes	—
489	C₂³×C₄	#386	1	1	yes	characteristic
490	C₂³×C₄	#386	1	1	yes	characteristic
491	C₂³×C₄	#386	1	1	yes	characteristic
492	C₂³×C₄	#386	1	2	yes	—
493	C₂³×C₄	#386	1	1	yes	characteristic
494	C₂³×C₄	#386	1	1	yes	characteristic
495	C₂³×C₄	#386	1	2	yes	—
496	C₂³×C₄	#386	1	2	yes	—
497	C₂³×C₄	#386	1	2	yes	—
498	C₂³×C₄	#386	1	2	yes	—
499	C₂³×C₄	#386	1	2	yes	—
500	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
501	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
502	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
503	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
504	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
505	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
506	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
507	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
508	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
509	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
510	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
511	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
512	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
513	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
514	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
515	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
516	C₂³×C₄	#518	1	2	yes	—
517	C₂³×C₄	#518	1	2	yes	—
518	C₂³×C₄	#518	1	2	yes	—
519	C₂³×C₄	#518	1	2	yes	—
520	C₂³×C₄	C₂×#120	1	2	yes	—
521	C₂³×C₄	C₂×#120	1	1	yes	characteristic
522	C₂³×C₄	C₂×#120	1	1	yes	characteristic
523	C₂³×C₄	C₂×#120	1	1	yes	characteristic
524	C₂³×C₄	C₂×#120	1	1	yes	characteristic
525	C₂³×C₄	C₂×#120	1	2	yes	—
526	C₂³×C₄	C₂×#120	1	2	yes	—
527	C₂³×C₄	C₂×#120	1	2	yes	—
528	C₂³×C₄	C₂×#120	1	2	yes	—
529	C₂³×C₄	C₂×#120	1	2	yes	—
530	C₂³×C₄	C₂×#120	1	1	yes	characteristic
531	C₂³×C₄	C₂×#120	1	2	yes	—
532	C₂³×C₄	C₂×#120	1	2	yes	—
533	C₂³×C₄	C₂×#120	1	2	yes	—
534	C₂³×C₄	C₂×#120	1	1	yes	characteristic
535	C₂³×C₄	C₂×#121	1	1	yes	characteristic
536	C₂³×C₄	C₂×#121	1	1	yes	characteristic
537	C₂³×C₄	C₂×#121	1	1	yes	characteristic
538	C₂³×C₄	C₂×#121	1	1	yes	characteristic
539	C₂³×C₄	C₂×#121	1	1	yes	characteristic
540	C₂³×C₄	C₂×#121	1	1	yes	characteristic
541	C₂³×C₄	C₂×#123	1	1	yes	characteristic
542	C₂³×C₄	C₂×#123	1	1	yes	characteristic
543	C₂³×C₄	C₂×#123	1	2	yes	—
544	C₂³×C₄	C₂×#123	1	2	yes	—
545	C₂³×C₄	C₂×#123	1	1	yes	characteristic
546	C₂³×C₄	C₂×#123	1	1	yes	characteristic
547	C₂³×C₄	#534	1	1	yes	characteristic
548	C₂³×C₄	#534	1	1	yes	characteristic
549	C₂³×C₄	#534	1	1	yes	characteristic
550	C₂³×C₄	#534	1	1	yes	characteristic
551	C₂³×C₄	#534	1	2	yes	—
552	C₂³×C₄	#534	1	2	yes	—
553	C₂³×C₄	#534	1	2	yes	—
554	C₂³×C₄	#534	1	2	yes	—
555	C₂³×C₄	#534	1	2	yes	—
556	C₂³×C₄	#534	1	2	yes	—
557	C₂³×C₄	D₄²	1	2	yes	—
558	C₂³×C₄	D₄²	1	2	yes	—
559	C₂³×C₄	D₄²	1	2	yes	—
560	C₂³×C₄	D₄²	1	2	yes	—
561	C₂³×C₄	D₄²	1	2	yes	—
562	C₂³×C₄	D₄²	1	2	yes	—
563	C₂³×C₄	D₄²	1	2	yes	—
564	C₂³×C₄	D₄²	1	2	yes	—
565	C₂³×C₄	D₄²	1	2	yes	—
566	C₂³×C₄	D₄²	1	2	yes	—
567	C₂³×C₄	D₄²	1	2	yes	—
568	C₂³×C₄	D₄²	1	2	yes	—
569	C₂³×C₄	#546	1	2	yes	—
570	C₂³×C₄	#546	1	2	yes	—
571	C₂³×C₄	#546	1	2	yes	—
572	C₂³×C₄	#546	1	2	yes	—
573	C₂³×C₄	#546	1	2	yes	—
574	C₂³×C₄	#546	1	2	yes	—
575	C₂³×C₄	#546	1	2	yes	—
576	C₂³×C₄	#546	1	2	yes	—
577	C₂³×C₄	#546	1	2	yes	—
578	C₂³×C₄	#546	1	2	yes	—
579	C₂³×C₄	#546	1	2	yes	—
580	C₂³×C₄	#546	1	2	yes	—
581	C₂³×C₄	#546	1	2	yes	—
582	C₂³×C₄	#546	1	2	yes	—
583	C₂³×C₄	#546	1	2	yes	—
584	C₂³×C₄	#546	1	2	yes	—
585	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
586	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
587	C₂³×C₄	C₂³×D₄	1	2	yes	—
588	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
589	C₂³×C₄	C₂³×D₄	1	2	yes	—
590	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
591	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
592	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
593	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
594	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
595	C₂²×C₈	C₂²×C₂²⋊C₄	1	16	yes	—
596	C₂×C₄⋊C₄	#386	1	2	yes	—
597	C₂×C₄⋊C₄	#386	1	2	yes	—
598	C₂×C₄⋊C₄	#386	1	2	yes	—
599	C₂×C₄⋊C₄	#386	1	2	yes	—
600	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
601	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
602	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
603	C₂×C₄⋊C₄	C₂×C₄×D₄	1	2	yes	—
604	C₂×C₄⋊C₄	C₂×C₄×D₄	1	2	yes	—
605	C₂×C₄⋊C₄	C₂×#121	1	2	yes	—
606	C₂×C₄⋊C₄	C₂×#121	1	2	yes	—
607	C₂×C₂²⋊C₄	#386	1	2	yes	—
608	C₂×C₂²⋊C₄	#386	1	2	yes	—
609	C₂×C₂²⋊C₄	#386	1	2	yes	—
610	C₂×C₂²⋊C₄	#386	1	2	yes	—
611	C₂×C₂²⋊C₄	#386	1	2	yes	—
612	C₂×C₂²⋊C₄	#386	1	2	yes	—
613	C₂×C₂²⋊C₄	#386	1	2	yes	—
614	C₂×C₂²⋊C₄	#386	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
623	C₂×C₄²	#386	1	2	yes	—
624	C₂×C₄²	#386	1	2	yes	—
625	C₂×C₄²	#386	1	2	yes	—
626	C₂×C₄²	#386	1	2	yes	—
627	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
628	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
629	C₂×C₄²	C₂×#123	1	2	yes	—
630	C₂×C₄²	C₂×#123	1	2	yes	—
631	C₂⁴	#1904	1	4	yes	—
632	C₂⁴	C₂×#386	1	1	yes	characteristic
633	C₂⁴	C₂×#386	1	1	yes	characteristic
634	C₂⁴	C₂×#386	1	2	yes	—
635	C₂⁴	C₂×#386	1	2	yes	—
636	C₂⁴	C₂×#386	1	1	yes	characteristic
637	C₂⁴	C₂×#386	1	1	yes	characteristic
638	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
639	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
640	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
641	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
642	C₂⁴	#2403	1	1	yes	characteristic
643	C₂⁴	#2403	1	1	yes	characteristic
644	C₂⁴	#2403	1	1	yes	characteristic
645	C₂⁴	#2403	1	1	yes	characteristic
646	C₂⁴	#2403	1	2	yes	—
647	C₂⁴	#2403	1	2	yes	—
648	C₂⁴	#2410	1	2	yes	—
649	C₂⁴	#2410	1	2	yes	—
650	C₂⁴	#2410	1	2	yes	—
651	C₂⁴	#2410	1	2	yes	—
652	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
653	C₂⁴	C₂²×#120	1	1	yes	characteristic
654	C₂⁴	C₂²×#121	1	1	yes	characteristic
655	C₂⁴	C₂×D₄²	1	2	yes	—
656	C₂⁴	C₂×D₄²	1	2	yes	—
657	C₂×D₄	C₂×#379	1	8	yes	—
658	C₂×D₄	C₂×#379	1	8	yes	—
659	C₂²×C₄	#1904	1	4	yes	—
660	C₂²×C₄	C₂×#379	1	1	yes	characteristic
661	C₂²×C₄	C₂×#379	1	1	yes	characteristic
662	C₂²×C₄	C₂×#379	1	2	yes	—
663	C₂²×C₄	C₂×#379	1	2	yes	—
664	C₂²×C₄	C₂×#379	1	1	yes	characteristic
665	C₂²×C₄	C₂×#379	1	1	yes	characteristic
666	C₂²×C₄	C₂×#386	1	2	yes	—
667	C₂²×C₄	C₂×#386	1	2	yes	—
668	C₂²×C₄	C₂×#386	1	1	yes	characteristic
669	C₂²×C₄	C₂×#386	1	1	yes	characteristic
670	C₂²×C₄	C₂×#386	1	2	yes	—
671	C₂²×C₄	C₂×#386	1	2	yes	—
672	C₂²×C₄	C₂×#386	1	2	yes	—
673	C₂²×C₄	C₂×#386	1	2	yes	—
674	C₂²×C₄	C₂×#386	1	1	yes	characteristic
675	C₂²×C₄	C₂×#386	1	1	yes	characteristic
676	C₂²×C₄	#2308	1	1	yes	characteristic
677	C₂²×C₄	#2308	1	1	yes	characteristic
678	C₂²×C₄	#2308	1	1	yes	characteristic
679	C₂²×C₄	#2308	1	1	yes	characteristic
680	C₂²×C₄	#2308	1	2	yes	—
681	C₂²×C₄	#2308	1	2	yes	—
682	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
683	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
684	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
685	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
686	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
687	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
688	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
689	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
690	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
691	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
692	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
693	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
694	C₂²×C₄	#2403	1	1	yes	characteristic
695	C₂²×C₄	#2403	1	1	yes	characteristic
696	C₂²×C₄	#2403	1	1	yes	characteristic
697	C₂²×C₄	#2403	1	2	yes	—
698	C₂²×C₄	#2403	1	2	yes	—
699	C₂²×C₄	#2403	1	1	yes	characteristic
700	C₂²×C₄	#2405	1	1	yes	characteristic
701	C₂²×C₄	#2405	1	1	yes	characteristic
702	C₂²×C₄	#2405	1	1	yes	characteristic
703	C₂²×C₄	#2405	1	1	yes	characteristic
704	C₂²×C₄	#2405	1	1	yes	characteristic
705	C₂²×C₄	#2405	1	2	yes	—
706	C₂²×C₄	#2405	1	2	yes	—
707	C₂²×C₄	#2405	1	1	yes	characteristic
708	C₂²×C₄	#2405	1	2	yes	—
709	C₂²×C₄	#2405	1	2	yes	—
710	C₂²×C₄	#2405	1	1	yes	characteristic
711	C₂²×C₄	#2405	1	1	yes	characteristic
712	C₂²×C₄	#2410	1	2	yes	—
713	C₂²×C₄	#2410	1	2	yes	—
714	C₂²×C₄	#2410	1	2	yes	—
715	C₂²×C₄	#2410	1	2	yes	—
716	C₂²×C₄	#2410	1	2	yes	—
717	C₂²×C₄	#2410	1	2	yes	—
718	C₂²×C₄	#2410	1	2	yes	—
719	C₂²×C₄	#2410	1	2	yes	—
720	C₂²×C₄	#2410	1	2	yes	—
721	C₂²×C₄	#2410	1	2	yes	—
722	C₂²×C₄	#2410	1	2	yes	—
723	C₂²×C₄	#2410	1	2	yes	—
724	C₂²×C₄	#3026	1	4	yes	—
725	C₂²×C₄	#3026	1	4	yes	—
726	C₂²×C₄	C₂³×C₂²⋊C₄	1	2	yes	—
727	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
728	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
729	C₂²×C₄	C₂×#518	1	2	yes	—
730	C₂²×C₄	C₂²×#120	1	2	yes	—
731	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
732	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
733	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
734	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
735	C₂²×C₄	C₂×#534	1	1	yes	characteristic
736	C₂²×C₄	C₂×#534	1	1	yes	characteristic
737	C₂²×C₄	C₂×#534	1	2	yes	—
738	C₂²×C₄	C₂×D₄²	1	2	yes	—
739	C₂²×C₄	C₂×D₄²	1	2	yes	—
740	C₂²×C₄	C₂×#546	1	2	yes	—
741	C₂²×C₄	C₂×#546	1	2	yes	—
742	C₂²×C₄	C₂×#546	1	2	yes	—
743	C₂²×C₄	C₂×#546	1	2	yes	—
744	C₂³	#13867	1	2	yes	—
745	C₂³	#13867	1	2	yes	—
746	C₂³	#13867	1	1	yes	characteristic
747	C₂³	#13867	1	1	yes	characteristic
748	C₂³	#13867	1	1	yes	characteristic
749	C₂³	#13867	1	1	yes	characteristic
750	C₂³	C₂×#1904	1	2	yes	—
751	C₂³	C₂×#1904	1	2	yes	—
752	C₂³	C₂×#1904	1	4	yes	—
753	C₂³	#23882	1	2	yes	—
754	C₂³	#23883	1	2	yes	—
755	C₂³	#23903	1	2	yes	—
756	C₂³	#23903	1	2	yes	—
757	C₂³	C₂²×#386	1	1	yes	characteristic
758	C₂³	C₂×D₄×C₂²⋊C₄	1	2	yes	—
759	C₂³	C₂×#2403	1	1	yes	characteristic
760	C₂³	C₂×#2403	1	1	yes	characteristic
761	C₂³	C₂×#2410	1	2	yes	—
762	C₂×C₄	#13867	1	1	yes	characteristic
763	C₂×C₄	#13867	1	1	yes	characteristic
764	C₂×C₄	#13867	1	2	yes	—
765	C₂×C₄	#13867	1	2	yes	—
766	C₂×C₄	#13867	1	1	yes	characteristic
767	C₂×C₄	#13867	1	1	yes	characteristic
768	C₂×C₄	#20609	1	4	yes	—
769	C₂×C₄	#20609	1	4	yes	—
770	C₂×C₄	C₂×#1904	1	4	yes	—
771	C₂×C₄	#23903	1	2	yes	—
772	C₂×C₄	#23903	1	2	yes	—
773	C₂×C₄	#24058	1	4	yes	—
774	C₂×C₄	#24058	1	4	yes	—
775	C₂×C₄	C₂²×#379	1	1	yes	characteristic
776	C₂×C₄	C₂×#2308	1	1	yes	characteristic
777	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	2	yes	—
778	C₂×C₄	C₂×#2410	1	2	yes	—
779	C₂×C₄	C₂×#2405	1	1	yes	characteristic
780	C₂×C₄	C₂×#2405	1	1	yes	characteristic
781	C₂×C₄	C₂×#3026	1	2	yes	—
782	C₂×C₄	C₂×#3026	1	2	yes	—
783	C₂²	#359472	1	2	yes	—
784	C₂²	#359472	1	2	yes	—
785	C₂²	#359554	1	2	yes	—
786	C₂²	#359554	1	2	yes	—
787	C₂²	#359576	1	2	yes	—
788	C₂²	#359576	1	2	yes	—
789	C₂²	C₂×#13867	1	1	yes	characteristic
790	C₂²	C₂²×#1904	1	1	yes	characteristic
791	C₂²	C₂²×#1904	1	1	yes	characteristic
792	C₂²	C₂×#23882	1	1	yes	characteristic
793	C₂²	C₂×#23883	1	1	yes	characteristic
794	C₂²	C₂×#23903	1	1	yes	characteristic
795	C₂²	C₂×#23903	1	1	yes	characteristic
796	C₄	#359554	1	2	yes	—
797	C₄	#359554	1	2	yes	—
798	C₄	C₂×#20609	1	2	yes	—
799	C₄	C₂×#24058	1	2	yes	—
800	C₂	C₂×#359576	1	1	yes	characteristic
801	C₂	C₂×#359472	1	1	yes	characteristic
802	C₂	C₂×#359554	1	1	yes	characteristic
803	C₂	#72313181	1	4	yes	direct product factor

	subgroup	G/H
center, socle	C₂³	#13867
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂⁴×C₄	C₂⁵
prime radical	C₂×#10577301	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#379775	C₂	semidirect
2. C₂×#553150	C₂	semidirect
3. #72313181	C₂	direct (N × H)
4. C₂×#187925	C₂	semidirect
5. C₂×#106331	C₂	semidirect
6. C₂×#114839	C₂	semidirect
7. C₂×#185258	C₂	semidirect
8. C₂×#114579	C₂	semidirect
10. C₂×#108224	C₂	semidirect
11. C₂×#198404	C₂	semidirect
12. C₂×#185643	C₂	semidirect
15. #10577301	C₄	semidirect
17. C₂×#61571	C₄	semidirect
18. C₂×#61560	C₄	semidirect
19. C₂×#61559	C₄	semidirect
23. C₂²×D₄×C₂²⋊C₄	C₂²	semidirect
24. C₂²×#2309	C₂²	semidirect
25. C₂×#21420	C₂²	semidirect
26. C₂×#20983	C₂²	semidirect
27. C₂×#20979	C₂²	semidirect
29. C₂×#20598	C₂²	semidirect
30. C₂×#17592	C₂²	semidirect
31. C₂×#17577	C₂²	semidirect
33. #553150	C₂²	semidirect
34. C₂×#14257	C₂²	semidirect
35. C₂×#14136	C₂²	semidirect
38. #379775	C₂²	semidirect
39. C₂×#10738	C₂²	semidirect
40. C₂×#10716	C₂²	semidirect
41. #198404	C₂²	semidirect
42. #187925	C₂²	semidirect
43. #185643	C₂²	semidirect
44. #185258	C₂²	semidirect
45. C₂×#7983	C₂²	semidirect
46. C₂×#7929	C₂²	semidirect
47. #114839	C₂²	semidirect
48. #114579	C₂²	semidirect
49. #108224	C₂²	semidirect
50. #106331	C₂²	semidirect
54. #62773	C₂×C₄	semidirect
56. C₂×#3505	C₂×C₄	semidirect
57. C₂×#3501	C₂×C₄	semidirect
58. C₂×#3496	C₂×C₄	semidirect
75. #61571	C₂×C₄	semidirect
76. #61560	C₂×C₄	semidirect
77. #61559	C₂×C₄	semidirect
78. #60750	C₂×C₄	semidirect
80. C₂×#3187	C₂×C₄	semidirect
81. C₂×#3186	C₂×C₄	semidirect
90. #60230	C₂×C₄	semidirect
92. C₂×#2973	C₂×C₄	semidirect
93. C₂×#2972	C₂×C₄	semidirect
97. C₂×D₄×C₂²⋊C₄	C₂³	semidirect
98. C₂×#2309	C₂³	semidirect
102. #21420	C₂³	semidirect
103. #20983	C₂³	semidirect
104. #20979	C₂³	semidirect
106. #20598	C₂³	semidirect
107. #17592	C₂³	semidirect
108. #17577	C₂³	semidirect
110. #14257	C₂³	semidirect
111. #14136	C₂³	semidirect
122. #10738	C₂³	semidirect
123. #10716	C₂³	semidirect
124. #7983	C₂³	semidirect
125. #7929	C₂³	semidirect
147. C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	semidirect
149. C₂³×SD₁₆	C₂²⋊C₄	semidirect
150. C₂³×D₈	C₂²⋊C₄	semidirect
152. #3505	C₂²×C₄	semidirect
153. #3501	C₂²×C₄	semidirect
154. #3496	C₂²×C₄	semidirect
220. #3187	C₂²×C₄	semidirect
221. #3186	C₂²×C₄	semidirect
222. C₂×#450	C₂²⋊C₄	semidirect
223. C₂×#450	C₂²⋊C₄	semidirect
226. C₂×#447	C₂²⋊C₄	semidirect
227. C₂×#447	C₂²⋊C₄	semidirect
230. #2973	C₂²×C₄	semidirect
231. #2972	C₂²×C₄	semidirect
232. C₂×#418	C₂²⋊C₄	semidirect
234. C₂²×#102	C₂²⋊C₄	semidirect
235. C₂²×#102	C₂²⋊C₄	semidirect
337. C₂²×SD₁₆	C₂×C₂²⋊C₄	semidirect
338. C₂²×D₈	C₂×C₂²⋊C₄	semidirect
436. C₂×#102	C₂×C₂²⋊C₄	semidirect
437. C₂×#102	C₂×C₂²⋊C₄	semidirect
803. C₂	#72313181	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#379775	2
C₂×#553150	2
#72313181	2
C₂×#187925	2
C₂×#106331	2
C₂×#114839	2
C₂×#185258	2
C₂×#114579	2
C₂×#10577301	2
C₂×#108224	2
C₂×#198404	2
C₂×#185643	2

Subgroups — C2×#72313181 #72313190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72313181 #72313190