Subgroups — #72313535

Order 2048.

At least 8426 conjugacy classes of subgroups; only the 2584 normal subgroups are shown.

The subgroup lattice has 822 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72313519	C₂	1	4	yes	maximal, complemented
2	#72313511	C₂	1	2	yes	maximal, complemented
3	#72313506	C₂	1	2	yes	maximal, complemented
4	#72313493	C₂	1	4	yes	maximal, complemented
5	#72313483	C₂	1	2	yes	maximal, complemented
6	C₂×#185346	C₂	1	1	yes	maximal, characteristic, complemented
7	#72313473	C₂	1	1	yes	maximal, characteristic, complemented
8	#72313465	C₂	1	1	yes	maximal, characteristic, complemented
9	#72313456	C₂	1	1	yes	maximal, characteristic, complemented
10	#72313449	C₂	1	2	yes	maximal, complemented
11	#72313446	C₂	1	2	yes	maximal, complemented
12	#72313309	C₂	1	2	yes	maximal, complemented
13	#72305947	C₂	1	2	yes	maximal, complemented
14	#72264594	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×D₄×#410	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10580309	C₂	1	1	yes	maximal, characteristic
17	C₂×#198406	C₂	1	2	yes	maximal, complemented
18	C₂×#62781	C₂²	1	1	yes	characteristic
19	C₂²×D₄×#41	C₂²	1	1	yes	characteristic
20	#10580309	C₄	1	16	yes	complemented
21	C₂×#61706	C₂²	1	2	yes	—
22	C₂×#61695	C₂²	1	1	yes	characteristic
23	C₂×#61694	C₂²	1	1	yes	characteristic
24	C₂×#61571	C₂²	1	2	yes	—
25	C₂×#61560	C₂²	1	1	yes	characteristic
26	C₂×#61559	C₂²	1	1	yes	characteristic
27	C₂×#60958	C₂²	1	2	yes	—
28	C₂²×#3114	C₂²	1	2	yes	—
29	C₂×#60282	C₂²	1	1	yes	characteristic
30	C₂×D₄×#117	C₂²	1	2	yes	complemented
31	C₂×#22406	C₂²	1	2	yes	—
32	C₂×#22406	C₂²	1	2	yes	complemented
33	C₂×D₄×#99	C₂²	1	2	yes	—
34	C₂×D₄×#99	C₂²	1	2	yes	complemented
35	C₂×#21421	C₂²	1	2	yes	complemented
36	C₂×#21408	C₂²	1	1	yes	characteristic, complemented
37	C₂×#21406	C₂²	1	2	yes	complemented
38	C₂×#21395	C₂²	1	1	yes	characteristic, complemented
39	C₂×#21379	C₂²	1	1	yes	characteristic
40	C₂×#21212	C₂²	1	2	yes	complemented
41	C₂×#20739	C₂²	1	1	yes	characteristic, complemented
42	C₂×#20632	C₂²	1	1	yes	characteristic
43	C₂²×#1762	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×#410	C₂²	1	1	yes	characteristic
45	C₂×#17581	C₂²	1	2	yes	complemented
46	#514648	C₂²	1	2	yes	complemented
47	#514213	C₂²	1	1	yes	characteristic
48	#374178	C₂²	1	4	yes	complemented
49	#374176	C₂²	1	4	yes	complemented
50	#374077	C₂²	1	4	yes	complemented
51	#374075	C₂²	1	4	yes	—
52	#363929	C₂²	1	2	yes	—
53	#363929	C₂²	1	2	yes	complemented
54	#363228	C₂²	1	4	yes	complemented
55	#362740	C₂²	1	2	yes	complemented
56	#361643	C₂²	1	2	yes	complemented
57	#359621	C₂²	1	2	yes	—
58	#359621	C₂²	1	2	yes	complemented
59	#353811	C₂²	1	2	yes	complemented
60	#353771	C₂²	1	2	yes	complemented
61	C₂×#9260	C₂²	1	4	yes	complemented
62	C₂×#9259	C₂²	1	4	yes	—
63	C₂×#9256	C₂²	1	4	yes	complemented
64	C₂×#9255	C₂²	1	4	yes	complemented
65	C₂×#8352	C₂²	1	4	yes	complemented
66	C₂×#8351	C₂²	1	2	yes	complemented
67	C₂×#8350	C₂²	1	2	yes	complemented
68	C₂×#7984	C₂²	1	2	yes	complemented
69	C₂×#7930	C₂²	1	2	yes	complemented
70	#114965	C₂²	1	4	yes	complemented
71	#114965	C₂²	1	4	yes	complemented
72	#114963	C₂²	1	4	yes	complemented
73	#114963	C₂²	1	4	yes	complemented
74	#111488	C₂²	1	4	yes	complemented
75	#111488	C₂²	1	4	yes	complemented
76	#111487	C₂²	1	4	yes	complemented
77	#111487	C₂²	1	4	yes	complemented
78	#108187	C₂²	1	4	yes	complemented
79	#108186	C₂²	1	2	yes	complemented
80	#108186	C₂²	1	2	yes	complemented
81	#106323	C₂²	1	4	yes	complemented
82	#106322	C₂²	1	2	yes	complemented
83	#106322	C₂²	1	2	yes	complemented
84	#62781	C₂×C₄	1	8	yes	complemented
85	C₂×#3505	C₂³	1	2	yes	—
86	C₂×#3501	C₂³	1	1	yes	characteristic
87	C₂×#3496	C₂³	1	1	yes	characteristic
88	C₂×D₄×#41	C₂×C₄	1	8	yes	—
89	C₂×D₄×#41	D₄	1	8	yes	—
90	C₂²×#550	D₄	1	1	yes	characteristic
91	C₂²×#547	D₄	1	1	yes	characteristic
92	C₂²×#547	C₂³	1	1	yes	characteristic
93	C₂²×#547	C₂³	1	1	yes	characteristic
94	C₂²×D₄×Q₈	D₄	1	1	yes	characteristic
95	C₂²×D₄²	D₄	1	1	yes	characteristic
96	C₂²×D₄²	C₂³	1	1	yes	characteristic
97	C₂²×D₄²	C₂³	1	1	yes	characteristic
98	C₂²×#532	D₄	1	1	yes	characteristic
99	C₂²×#532	D₄	1	1	yes	characteristic
100	C₂²×#532	C₂³	1	1	yes	characteristic
101	C₂²×#529	C₂³	1	2	yes	—
102	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
103	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
104	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
105	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
106	#61706	C₂×C₄	1	16	yes	complemented
107	#61695	C₂×C₄	1	8	yes	complemented
108	#61694	C₂×C₄	1	8	yes	complemented
109	#61571	C₂×C₄	1	16	yes	—
110	#61560	C₂×C₄	1	8	yes	—
111	#61559	C₂×C₄	1	8	yes	—
112	#60958	C₂×C₄	1	16	yes	complemented
113	C₂×#3187	C₂³	1	2	yes	—
114	C₂×#3187	C₂³	1	2	yes	—
115	C₂×#3186	C₂³	1	2	yes	—
116	C₂×#3186	C₂³	1	2	yes	—
117	C₂×#3114	C₂×C₄	1	16	yes	—
118	C₂×#3114	D₄	1	16	yes	—
119	C₂²×#483	C₂³	1	2	yes	—
120	C₂²×#480	C₂³	1	2	yes	—
121	C₂²×#478	D₄	1	2	yes	—
122	C₂²×#478	D₄	1	2	yes	—
123	C₂²×#463	D₄	1	2	yes	—
124	C₂²×#463	D₄	1	2	yes	—
125	C₂²×#450	C₂³	1	2	yes	—
126	C₂²×#447	C₂³	1	2	yes	—
127	#60282	C₂×C₄	1	8	yes	complemented
128	C₂×#2973	C₂³	1	2	yes	—
129	C₂×#2972	C₂³	1	1	yes	characteristic
130	C₂×#2972	C₂³	1	1	yes	characteristic
131	C₂²×#442	D₄	1	2	yes	—
132	C₂²×#442	D₄	1	2	yes	—
133	C₂²×#440	D₄	1	2	yes	—
134	C₂²×#440	D₄	1	2	yes	—
135	C₂²×#432	C₂³	1	1	yes	characteristic
136	C₂²×#432	C₂³	1	2	yes	—
137	C₂³×#102	C₂³	1	2	yes	—
138	C₂²×#410	D₄	1	1	yes	characteristic
139	C₂²×#410	D₄	1	1	yes	characteristic
140	C₂³×#97	C₂³	1	1	yes	characteristic
141	C₂×#2344	C₂³	1	4	yes	—
142	C₂×D₄×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×#2285	C₂³	1	2	yes	—
144	C₂×#2283	C₂³	1	1	yes	characteristic
145	C₂×C₄×#117	C₂³	1	2	yes	—
146	C₂²×C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×#1996	C₂³	1	4	yes	—
148	C₂×#1964	C₂³	1	4	yes	—
149	C₂×#1964	C₂³	1	4	yes	—
150	C₂×#1964	C₂³	1	4	yes	—
151	C₂×#1893	C₂³	1	4	yes	—
152	C₂×#1893	C₂³	1	2	yes	—
153	C₂×#1893	C₂³	1	2	yes	—
154	C₂×#1892	C₂³	1	4	yes	—
155	C₂×#1874	C₂³	1	2	yes	—
156	C₂×#1874	C₂³	1	2	yes	—
157	C₂×#1869	C₂³	1	2	yes	—
158	C₂×#1869	C₂³	1	2	yes	—
159	C₂×#1823	C₂³	1	2	yes	—
160	#20632	D₄	1	8	yes	—
161	C₂×#1799	C₂³	1	2	yes	—
162	C₂×#1799	C₂³	1	2	yes	—
163	C₂×#1786	C₂³	1	2	yes	—
164	C₂×C₄×#99	D₄	1	2	yes	—
165	C₂×C₄×#99	D₄	1	2	yes	—
166	C₂×C₄×#99	C₂³	1	2	yes	—
167	C₂×C₄×#99	C₂³	1	2	yes	—
168	C₂×#1740	D₄	1	2	yes	—
169	C₂²×#340	C₂³	1	2	yes	—
170	C₂×#1520	C₂³	1	4	yes	—
171	C₂×#1519	C₂³	1	4	yes	—
172	#14139	C₂³	1	4	yes	—
173	#14137	C₂³	1	4	yes	—
174	#13872	C₂³	1	2	yes	—
175	#13872	C₂³	1	2	yes	—
176	#10730	C₂³	1	4	yes	—
177	#10730	C₂³	1	4	yes	—
178	#10714	C₂³	1	4	yes	—
179	#10714	C₂³	1	4	yes	—
180	C₂×#1289	C₂³	1	4	yes	—
181	C₂×#1289	C₂³	1	4	yes	—
182	C₂×#1282	C₂³	1	4	yes	—
183	C₂×#1282	C₂³	1	4	yes	—
184	C₂³×#41	C₂×D₄	1	1	yes	characteristic
185	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
186	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
187	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
188	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
189	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
190	C₂³×D₈	C₂×D₄	1	2	yes	—
191	C₂³×D₈	C₂×D₄	1	2	yes	—
192	C₂⁴×C₈	C₂⁴	1	2	yes	—
193	#3505	C₂²×C₄	1	8	yes	—
194	#3501	C₂²×C₄	1	4	yes	—
195	#3496	C₂²×C₄	1	4	yes	—
196	C₂×#550	C₂²⋊C₄	1	8	yes	complemented
197	C₂×D₄×Q₈	C₂²⋊C₄	1	8	yes	complemented
198	C₂×#547	C₂²⋊C₄	1	8	yes	complemented
199	C₂×#547	C₂²×C₄	1	4	yes	—
200	C₂×#547	C₂²×C₄	1	4	yes	—
201	C₂×#547	C₂×D₄	1	4	yes	—
202	C₂×#547	C₂×D₄	1	4	yes	—
203	C₂×D₄²	C₂²⋊C₄	1	8	yes	complemented
204	C₂×D₄²	C₂²×C₄	1	4	yes	—
205	C₂×D₄²	C₂²×C₄	1	4	yes	—
206	C₂×D₄²	C₂×D₄	1	4	yes	—
207	C₂×D₄²	C₂×D₄	1	4	yes	—
208	C₂×#532	C₂²⋊C₄	1	8	yes	complemented
209	C₂×#532	C₂²⋊C₄	1	8	yes	complemented
210	C₂×#532	C₂²×C₄	1	4	yes	—
211	C₂×#532	C₂×D₄	1	4	yes	—
212	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
215	C₂²×#127	C₂×D₄	1	1	yes	characteristic
216	C₂²×#127	C₂×D₄	1	1	yes	characteristic
217	C₂²×#127	C₂×D₄	1	1	yes	characteristic
218	C₂×#529	C₂²×C₄	1	8	yes	—
219	C₂×#529	C₂×D₄	1	8	yes	—
220	C₂²×#125	C₂×D₄	1	2	yes	—
221	C₂²×#124	C₂×D₄	1	2	yes	—
222	C₂²×C₂²⋊Q₈	C₂⁴	1	2	yes	—
223	C₂²×#121	C₂×D₄	1	1	yes	characteristic
224	C₂²×#121	C₂×D₄	1	1	yes	characteristic
225	C₂²×#121	C₂×D₄	1	1	yes	characteristic
226	C₂²×#121	C₂×D₄	1	1	yes	characteristic
227	C₂²×#121	C₂⁴	1	2	yes	—
228	C₂²×#121	C₂⁴	1	1	yes	characteristic
229	C₂²×#121	C₂⁴	1	1	yes	characteristic
230	C₂×C₄×#41	C₂²×C₄	1	4	yes	—
231	C₂×C₄×#41	C₂×D₄	1	4	yes	—
232	C₂×C₄×#41	C₂×D₄	1	4	yes	—
233	C₂×C₄×#41	#41	1	4	yes	—
234	C₂²×C₄×Q₈	C₂×D₄	1	2	yes	—
235	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×Q₈	#41	1	1	yes	characteristic
237	C₂²×C₄×D₄	C₂²⋊C₄	1	8	yes	complemented
238	C₂²×C₄×D₄	C₂²⋊C₄	1	8	yes	complemented
239	C₂²×C₄×D₄	C₂²×C₄	1	4	yes	—
240	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
243	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
248	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
249	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
250	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
251	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
256	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
257	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×D₄	#41	1	1	yes	characteristic
261	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
263	C₂²×#117	C₂×D₄	1	2	yes	—
264	C₂²×#117	C₂×D₄	1	2	yes	—
265	C₂²×#117	C₂×D₄	1	1	yes	characteristic
266	C₂²×#117	#41	1	1	yes	characteristic
267	C₂²×#117	#41	1	1	yes	characteristic
268	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
269	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
270	C₂³×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
271	C₂³×C₄⋊C₄	C₂⁴	1	2	yes	—
272	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
273	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
274	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
275	#3187	C₂²×C₄	1	8	yes	—
276	#3187	C₂²×C₄	1	8	yes	—
277	#3186	C₂²×C₄	1	8	yes	—
278	#3186	C₂²×C₄	1	8	yes	—
279	C₂×#483	C₂²×C₄	1	8	yes	—
280	C₂×#483	C₂×D₄	1	8	yes	—
281	C₂×#480	C₂²×C₄	1	8	yes	—
282	C₂×#480	C₂×D₄	1	8	yes	—
283	C₂×#478	C₂²⋊C₄	1	16	yes	complemented
284	C₂×#478	C₂²⋊C₄	1	16	yes	complemented
285	C₂×#463	C₂²⋊C₄	1	16	yes	complemented
286	C₂×#463	C₂²⋊C₄	1	16	yes	complemented
287	C₂×#450	C₂²×C₄	1	8	yes	—
288	C₂×#450	C₂×D₄	1	8	yes	—
289	C₂×#447	C₂²×C₄	1	8	yes	—
290	C₂×#447	C₂×D₄	1	8	yes	—
291	#2973	C₂²×C₄	1	8	yes	—
292	#2972	C₂²×C₄	1	4	yes	—
293	#2972	C₂²×C₄	1	4	yes	—
294	C₂×#442	C₂²⋊C₄	1	16	yes	complemented
295	C₂×#442	C₂²⋊C₄	1	16	yes	complemented
296	C₂×#440	C₂²⋊C₄	1	16	yes	complemented
297	C₂×#440	C₂²⋊C₄	1	16	yes	complemented
298	C₂×#432	C₂²×C₄	1	8	yes	—
299	C₂×#432	C₂×D₄	1	8	yes	—
300	C₂²×#107	C₂×D₄	1	2	yes	—
301	C₂²×#107	C₂×D₄	1	2	yes	—
302	C₂²×#106	C₂×D₄	1	2	yes	—
303	C₂²×#106	C₂×D₄	1	2	yes	—
304	C₂²×C₄⋊C₈	C₂×D₄	1	2	yes	—
305	C₂²×C₄⋊C₈	C₂×D₄	1	2	yes	—
306	C₂²×#103	C₂×D₄	1	2	yes	—
307	C₂²×#103	C₂×D₄	1	2	yes	—
308	C₂²×#102	C₂×D₄	1	2	yes	—
309	C₂²×#102	C₂×D₄	1	2	yes	—
310	C₂²×#102	C₂×D₄	1	2	yes	—
311	C₂²×#102	C₂×D₄	1	2	yes	—
312	C₂²×#102	C₂×D₄	1	2	yes	—
313	C₂²×#102	C₂×D₄	1	2	yes	—
314	C₂²×#99	C₂×D₄	1	2	yes	—
315	C₂²×#99	C₂×D₄	1	2	yes	—
316	C₂²×#99	C₂×D₄	1	2	yes	—
317	C₂²×#99	C₂×D₄	1	2	yes	—
318	C₂²×C₂²⋊C₈	C₂⁴	1	2	yes	—
319	C₂²×C₂²⋊C₈	C₂⁴	1	2	yes	—
320	C₂²×C₂²⋊C₈	C₂⁴	1	2	yes	—
321	C₂²×#97	C₂×D₄	1	2	yes	—
322	C₂²×#97	C₂×D₄	1	2	yes	—
323	#2285	C₂×D₄	1	8	yes	—
324	C₂×#380	C₂⁴	1	2	yes	—
325	C₂×#380	C₂⁴	1	4	yes	—
326	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
327	C₂×C₄×C₂²⋊C₄	C₂⁴	1	4	yes	—
328	#1799	C₂×D₄	1	8	yes	—
329	#1799	C₂×D₄	1	8	yes	—
330	C₂×#342	C₂×D₄	1	4	yes	—
331	C₂×#342	C₂×D₄	1	4	yes	—
332	C₂²×#41	C₄×D₄	1	4	yes	—
333	C₂²×#41	#120	1	4	yes	—
334	C₂³×Q₈	#121	1	1	yes	characteristic
335	C₂³×Q₈	C₂²×D₄	1	2	yes	—
336	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
337	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
338	C₂³×D₄	#121	1	1	yes	characteristic
339	C₂³×D₄	C₂³×C₄	1	2	yes	—
340	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
341	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
342	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
343	C₂³×D₄	C₂²×D₄	1	2	yes	—
344	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
345	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
346	C₂³×D₄	C₂²×D₄	1	2	yes	—
347	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
348	C₂³×D₄	C₂²×D₄	1	2	yes	—
349	C₂³×D₄	C₂²×D₄	1	2	yes	—
350	C₂³×D₄	C₂²×D₄	1	4	yes	—
351	C₂⁴×C₄	#121	1	1	yes	characteristic
352	C₂⁴×C₄	#121	1	1	yes	characteristic
353	C₂⁴×C₄	#121	1	1	yes	characteristic
354	C₂⁴×C₄	#121	1	1	yes	characteristic
355	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
356	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
357	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
358	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
359	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
360	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	8	yes	—
361	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	8	yes	—
362	C₂²×D₈	C₂×C₂²⋊C₄	1	8	yes	—
363	C₂²×D₈	C₂×C₂²⋊C₄	1	8	yes	—
364	C₂³×C₈	C₂²×D₄	1	2	yes	—
365	C₂³×C₈	C₂²×D₄	1	2	yes	—
366	C₂³×C₈	C₂²×D₄	1	2	yes	—
367	C₂³×C₈	C₂²×D₄	1	2	yes	—
368	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	4	yes	—
369	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	4	yes	—
370	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	4	yes	—
371	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
372	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
373	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
374	C₂×#125	C₂×C₂²⋊C₄	1	8	yes	—
375	C₂×#124	C₂×C₂²⋊C₄	1	8	yes	—
376	C₂×C₂²⋊Q₈	C₂³×C₄	1	4	yes	—
377	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
378	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
379	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
380	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
381	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
382	C₂×#121	C₂³×C₄	1	4	yes	—
383	C₂×#121	C₂³×C₄	1	2	yes	—
384	C₂×#121	C₂³×C₄	1	2	yes	—
385	C₂×#121	C₂²×D₄	1	4	yes	—
386	C₂×#121	C₂²×D₄	1	2	yes	—
387	C₂×#121	C₂²×D₄	1	2	yes	—
388	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	8	yes	—
389	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	4	yes	—
390	C₂×C₄×Q₈	C₄×D₄	1	4	yes	—
391	C₂×C₄×Q₈	#121	1	4	yes	—
392	C₂×C₄×Q₈	#123	1	4	yes	—
393	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
394	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
395	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
396	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
397	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
398	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
399	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
400	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
401	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
402	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
403	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
404	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
405	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
406	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
407	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
408	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
409	C₂×C₄×D₄	C₄×D₄	1	4	yes	—
410	C₂×C₄×D₄	C₄×D₄	1	4	yes	—
411	C₂×C₄×D₄	C₄×D₄	1	4	yes	—
412	C₂×C₄×D₄	#120	1	1	yes	characteristic
413	C₂×C₄×D₄	#120	1	1	yes	characteristic
414	C₂×C₄×D₄	#120	1	2	yes	—
415	C₂×C₄×D₄	#120	1	8	yes	—
416	C₂×C₄×D₄	#120	1	8	yes	—
417	C₂×C₄×D₄	#120	1	2	yes	—
418	C₂×C₄×D₄	#120	1	2	yes	—
419	C₂×C₄×D₄	#120	1	2	yes	—
420	C₂×C₄×D₄	#120	1	2	yes	—
421	C₂×C₄×D₄	#120	1	4	yes	—
422	C₂×C₄×D₄	#120	1	4	yes	—
423	C₂×C₄×D₄	#120	1	4	yes	—
424	C₂×C₄×D₄	#120	1	4	yes	—
425	C₂×C₄×D₄	#120	1	8	yes	—
426	C₂×C₄×D₄	#120	1	8	yes	—
427	C₂×C₄×D₄	#120	1	1	yes	characteristic
428	C₂×C₄×D₄	#120	1	1	yes	characteristic
429	C₂×C₄×D₄	#120	1	2	yes	—
430	C₂×C₄×D₄	#120	1	4	yes	—
431	C₂×C₄×D₄	#120	1	4	yes	—
432	C₂×C₄×D₄	#121	1	4	yes	—
433	C₂×C₄×D₄	#123	1	4	yes	—
434	C₂×C₄×D₄	C₂³×C₄	1	2	yes	—
435	C₂×C₄×D₄	C₂³×C₄	1	2	yes	—
436	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
437	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
438	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
439	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
440	C₂×C₄×D₄	C₂×#41	1	2	yes	—
441	C₂×C₄×D₄	C₂×#41	1	2	yes	—
442	C₂×#117	C₄×D₄	1	4	yes	—
443	C₂×#117	C₄×D₄	1	4	yes	—
444	C₂×#117	C₄×D₄	1	4	yes	—
445	C₂×#117	#120	1	4	yes	—
446	C₂×#117	#123	1	4	yes	—
447	C₂×#117	#123	1	4	yes	—
448	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
449	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
450	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
451	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
452	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
453	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
454	C₂²×C₄⋊C₄	C₂³×C₄	1	2	yes	—
455	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
456	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
457	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
458	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
459	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
460	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
461	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
462	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
463	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
464	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
465	C₂²×C₄⋊C₄	C₂×#41	1	1	yes	characteristic
466	C₂²×C₄⋊C₄	C₂×#41	1	1	yes	characteristic
467	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
468	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
469	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
470	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
471	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
472	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
473	C₂²×C₂²⋊C₄	C₂×#41	1	1	yes	characteristic
474	C₂²×C₂²⋊C₄	C₂×#41	1	1	yes	characteristic
475	C₂²×C₄²	C₂×C₂²⋊C₄	1	4	yes	—
476	C₂²×C₄²	C₂×C₂²⋊C₄	1	4	yes	—
477	C₂²×C₄²	#121	1	4	yes	—
478	C₂²×C₄²	#121	1	4	yes	—
479	C₂²×C₄²	#121	1	1	yes	characteristic
480	C₂²×C₄²	#121	1	1	yes	characteristic
481	C₂²×C₄²	#121	1	1	yes	characteristic
482	C₂²×C₄²	#121	1	1	yes	characteristic
483	C₂²×C₄²	C₂³×C₄	1	2	yes	—
484	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
485	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
486	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
487	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
488	C₂²×C₄²	C₂²×D₄	1	2	yes	—
489	C₂²×C₄²	C₂²×D₄	1	2	yes	—
490	C₂²×C₄²	C₂²×D₄	1	2	yes	—
491	C₂²×C₄²	C₂²×D₄	1	4	yes	—
492	C₂²×C₄²	C₂²×D₄	1	2	yes	—
493	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
494	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
495	C₂²×C₄²	C₂×#41	1	2	yes	—
496	C₂²×C₄²	H(5,𝔽₂)	1	4	yes	—
497	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
498	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
499	C₂×#107	C₂×C₂²⋊C₄	1	8	yes	—
500	C₂×#107	C₂×C₂²⋊C₄	1	8	yes	—
501	C₂×#106	C₂×C₂²⋊C₄	1	8	yes	—
502	C₂×#106	C₂×C₂²⋊C₄	1	8	yes	—
503	C₂×C₄⋊C₈	C₂×C₂²⋊C₄	1	8	yes	—
504	C₂×C₄⋊C₈	C₂×C₂²⋊C₄	1	8	yes	—
505	C₂×#103	C₂×C₂²⋊C₄	1	8	yes	—
506	C₂×#103	C₂×C₂²⋊C₄	1	8	yes	—
507	C₂×#102	C₂×C₂²⋊C₄	1	8	yes	—
508	C₂×#102	C₂×C₂²⋊C₄	1	8	yes	—
509	C₂×#102	C₂×C₂²⋊C₄	1	8	yes	—
510	C₂×#102	C₂×C₂²⋊C₄	1	8	yes	—
511	C₂×#102	C₂×C₂²⋊C₄	1	8	yes	—
512	C₂×#102	C₂×C₂²⋊C₄	1	8	yes	—
513	C₂×#99	AGL(1,ℤ/8)	1	8	yes	complemented
514	C₂×C₂²⋊C₈	C₂³×C₄	1	4	yes	—
515	C₂×C₂²⋊C₈	C₂³×C₄	1	4	yes	—
516	C₂×C₂²⋊C₈	C₂²×D₄	1	4	yes	—
517	C₂×C₂²⋊C₈	C₂²×D₄	1	4	yes	—
518	C₂×#97	C₂×C₂²⋊C₄	1	8	yes	—
519	C₂×#97	C₂×C₂²⋊C₄	1	8	yes	—
520	#380	C₂²×D₄	1	8	yes	—
521	C₂⁵	C₂×#121	1	1	yes	characteristic
522	C₂⁵	C₂×#121	1	1	yes	characteristic
523	C₂⁵	C₂³×D₄	1	1	yes	characteristic
524	C₂²×Q₈	#386	1	4	yes	—
525	C₂²×Q₈	C₂²×C₂²⋊C₄	1	4	yes	—
526	C₂²×D₄	#386	1	4	yes	—
527	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
528	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
529	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
530	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
531	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
532	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
533	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
534	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
535	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
536	C₂²×D₄	C₂×#120	1	1	yes	characteristic
537	C₂²×D₄	C₂×#120	1	2	yes	—
538	C₂²×D₄	C₂×#120	1	2	yes	—
539	C₂²×D₄	C₂×#120	1	4	yes	—
540	C₂²×D₄	C₂×#120	1	1	yes	characteristic
541	C₂²×D₄	C₂×#120	1	2	yes	—
542	C₂²×D₄	C₂×#120	1	4	yes	—
543	C₂²×D₄	C₂×#120	1	2	yes	—
544	C₂²×D₄	C₂×#120	1	2	yes	—
545	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
546	C₂²×D₄	#575	1	4	yes	—
547	C₂³×C₄	#386	1	4	yes	—
548	C₂³×C₄	#386	1	4	yes	—
549	C₂³×C₄	#386	1	4	yes	—
550	C₂³×C₄	#386	1	4	yes	—
551	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
552	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
553	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
554	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
555	C₂³×C₄	C₂×#120	1	2	yes	—
556	C₂³×C₄	C₂×#120	1	2	yes	—
557	C₂³×C₄	C₂×#121	1	1	yes	characteristic
558	C₂³×C₄	C₂×#121	1	1	yes	characteristic
559	C₂³×C₄	C₂×#121	1	1	yes	characteristic
560	C₂³×C₄	C₂×#121	1	1	yes	characteristic
561	C₂³×C₄	C₂×#121	1	2	yes	—
562	C₂³×C₄	C₂×#121	1	2	yes	—
563	C₂³×C₄	C₂×#121	1	1	yes	characteristic
564	C₂³×C₄	C₂×#121	1	1	yes	characteristic
565	C₂³×C₄	C₂×#121	1	1	yes	characteristic
566	C₂³×C₄	C₂×#121	1	1	yes	characteristic
567	C₂³×C₄	C₂×#121	1	1	yes	characteristic
568	C₂³×C₄	C₂×#121	1	1	yes	characteristic
569	C₂³×C₄	D₄²	1	2	yes	—
570	C₂³×C₄	D₄²	1	2	yes	—
571	C₂³×C₄	D₄²	1	4	yes	—
572	C₂³×C₄	D₄²	1	2	yes	—
573	C₂³×C₄	D₄²	1	2	yes	—
574	C₂³×C₄	D₄²	1	4	yes	—
575	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
576	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
577	C₂³×C₄	C₂³×D₄	1	2	yes	—
578	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
579	C₂³×C₄	C₂³×D₄	1	2	yes	—
580	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
581	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
582	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
583	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
584	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
585	C₂²×C₈	C₂²×C₂²⋊C₄	1	4	yes	—
586	C₂²×C₈	C₂²×C₂²⋊C₄	1	4	yes	—
587	C₂²×C₈	C₂²×C₂²⋊C₄	1	4	yes	—
588	C₂²×C₈	C₂²×C₂²⋊C₄	1	4	yes	—
589	C₄×D₄	#379	1	4	yes	—
590	C₄×D₄	#379	1	4	yes	—
591	C₄×D₄	#379	1	4	yes	—
592	C₄×D₄	#379	1	4	yes	—
593	C₄×D₄	#379	1	8	yes	—
594	C₄×D₄	#379	1	8	yes	—
595	C₄×D₄	#379	1	8	yes	—
596	C₄×D₄	#379	1	8	yes	—
597	C₄×D₄	#379	1	8	yes	—
598	C₄×D₄	#379	1	8	yes	—
599	C₂×C₄⋊C₄	#386	1	4	yes	—
600	C₂×C₄⋊C₄	#386	1	4	yes	—
601	C₂×C₄⋊C₄	#386	1	4	yes	—
602	C₂×C₄⋊C₄	#386	1	4	yes	—
603	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
604	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
605	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
606	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
607	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
608	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
609	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
610	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
611	C₂×C₄⋊C₄	C₂×C₄×D₄	1	2	yes	—
612	C₂×C₄⋊C₄	C₂×C₄×D₄	1	2	yes	—
613	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
616	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
617	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
618	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
619	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
620	C₂×C₄⋊C₄	C₂×#123	1	2	yes	—
621	C₂×C₄⋊C₄	C₂×#123	1	2	yes	—
622	C₂×C₂²⋊C₄	#386	1	4	yes	—
623	C₂×C₂²⋊C₄	#386	1	4	yes	—
624	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂×#123	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂×#123	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	1	8	yes	—
633	C₂×C₄²	#386	1	4	yes	—
634	C₂×C₄²	#386	1	4	yes	—
635	C₂×C₄²	#386	1	4	yes	—
636	C₂×C₄²	#386	1	4	yes	—
637	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
638	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
639	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
640	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
641	C₂×C₄²	C₂²×C₂²⋊C₄	1	4	yes	—
642	C₂×C₄²	C₂²×C₂²⋊C₄	1	4	yes	—
643	C₂×C₄²	C₂×C₄×D₄	1	2	yes	—
644	C₂×C₄²	C₂×C₄×D₄	1	2	yes	—
645	C₂×C₄²	#518	1	4	yes	—
646	C₂×C₄²	#518	1	4	yes	—
647	C₂×C₄²	C₂×#120	1	4	yes	—
648	C₂×C₄²	C₂×#120	1	4	yes	—
649	C₂×C₄²	C₂×#120	1	1	yes	characteristic
650	C₂×C₄²	C₂×#120	1	2	yes	—
651	C₂×C₄²	C₂×#120	1	1	yes	characteristic
652	C₂×C₄²	C₂×#120	1	2	yes	—
653	C₂×C₄²	C₂×#120	1	2	yes	—
654	C₂×C₄²	C₂×#121	1	2	yes	—
655	C₂×C₄²	C₂×#121	1	2	yes	—
656	C₂×C₄²	C₂×#121	1	2	yes	—
657	C₂×C₄²	C₂×#121	1	2	yes	—
658	C₂×C₄²	C₂×#123	1	2	yes	—
659	C₂×C₄²	C₂×#123	1	2	yes	—
660	C₂×C₄²	#534	1	4	yes	—
661	C₂×C₄²	#534	1	4	yes	—
662	C₂×C₄²	#534	1	1	yes	characteristic
663	C₂×C₄²	#534	1	2	yes	—
664	C₂×C₄²	#534	1	1	yes	characteristic
665	C₂×C₄²	#534	1	2	yes	—
666	C₂×C₄²	#534	1	2	yes	—
667	C₂×C₄²	D₄²	1	4	yes	—
668	C₂×C₄²	D₄²	1	4	yes	—
669	C₂×C₄²	D₄²	1	4	yes	—
670	C₂×C₄²	D₄²	1	4	yes	—
671	C₂×C₄²	#546	1	2	yes	—
672	C₂×C₄²	#546	1	2	yes	—
673	C₂×C₄²	#546	1	4	yes	—
674	C₂×C₄²	#546	1	2	yes	—
675	C₂×C₄²	#546	1	2	yes	—
676	C₂×C₄²	#546	1	4	yes	—
677	C₂×C₄²	#546	1	4	yes	—
678	C₂×C₄²	#546	1	4	yes	—
679	C₂×C₄²	#546	1	4	yes	—
680	C₂×C₄²	#546	1	4	yes	—
681	C₂⁴	C₂×#386	1	2	yes	—
682	C₂⁴	C₂×#386	1	2	yes	—
683	C₂⁴	#3036	1	4	yes	—
684	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
685	C₂⁴	C₂²×#120	1	1	yes	characteristic
686	C₂⁴	C₂²×#121	1	1	yes	characteristic
687	C₂⁴	C₂×D₄²	1	2	yes	—
688	C₂⁴	C₂×D₄²	1	2	yes	—
689	C₂⁴	C₂²×AGL(1,ℤ/8)	1	2	yes	—
690	C₂⁴	C₂×#575	1	2	yes	—
691	C₂⁴	#3585	1	4	yes	—
692	C₂×D₄	C₂×#379	1	2	yes	—
693	C₂×D₄	C₂×#379	1	4	yes	—
694	C₂×D₄	C₂×#379	1	2	yes	—
695	C₂×D₄	C₄×AGL(1,ℤ/8)	1	8	yes	—
696	C₂×D₄	#3003	1	4	yes	—
697	C₂×D₄	#3005	1	4	yes	—
698	C₂×D₄	#3025	1	4	yes	—
699	C₂²×C₄	C₂×#386	1	2	yes	—
700	C₂²×C₄	C₂×#386	1	2	yes	—
701	C₂²×C₄	C₂×#386	1	2	yes	—
702	C₂²×C₄	C₂×#386	1	2	yes	—
703	C₂²×C₄	C₂×#386	1	2	yes	—
704	C₂²×C₄	C₂×#386	1	2	yes	—
705	C₂²×C₄	C₂×#386	1	2	yes	—
706	C₂²×C₄	C₂×#386	1	2	yes	—
707	C₂²×C₄	C₂×#386	1	2	yes	—
708	C₂²×C₄	C₂×#386	1	2	yes	—
709	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
710	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
711	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
712	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
713	C₂²×C₄	#2403	1	4	yes	—
714	C₂²×C₄	#2403	1	4	yes	—
715	C₂²×C₄	#2403	1	4	yes	—
716	C₂²×C₄	#2403	1	4	yes	—
717	C₂²×C₄	#2410	1	2	yes	—
718	C₂²×C₄	#2410	1	2	yes	—
719	C₂²×C₄	#2410	1	1	yes	characteristic
720	C₂²×C₄	#2410	1	1	yes	characteristic
721	C₂²×C₄	#2410	1	2	yes	—
722	C₂²×C₄	#2410	1	1	yes	characteristic
723	C₂²×C₄	#2410	1	1	yes	characteristic
724	C₂²×C₄	#2410	1	2	yes	—
725	C₂²×C₄	#2410	1	2	yes	—
726	C₂²×C₄	#2410	1	2	yes	—
727	C₂²×C₄	#3036	1	4	yes	—
728	C₂²×C₄	C₂³×C₂²⋊C₄	1	2	yes	—
729	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
730	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
731	C₂²×C₄	C₂×#518	1	2	yes	—
732	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
733	C₂²×C₄	C₂²×#120	1	2	yes	—
734	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
735	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
736	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
737	C₂²×C₄	C₂×#534	1	1	yes	characteristic
738	C₂²×C₄	C₂×#534	1	1	yes	characteristic
739	C₂²×C₄	C₂×#534	1	2	yes	—
740	C₂²×C₄	C₂×D₄²	1	2	yes	—
741	C₂²×C₄	C₂×D₄²	1	2	yes	—
742	C₂²×C₄	C₂×#546	1	2	yes	—
743	C₂²×C₄	C₂×#546	1	2	yes	—
744	C₂²×C₄	C₂×#546	1	2	yes	—
745	C₂²×C₄	C₂×#546	1	2	yes	—
746	C₄⋊C₄	C₂×#379	1	2	yes	—
747	C₄⋊C₄	C₂×#379	1	2	yes	—
748	C₄⋊C₄	C₂×#379	1	4	yes	—
749	C₄²	C₂×#379	1	2	yes	—
750	C₄²	C₂×#379	1	4	yes	—
751	C₄²	C₂×#379	1	2	yes	—
752	C₄²	#2308	1	2	yes	—
753	C₄²	#2308	1	2	yes	—
754	C₄²	#2308	1	4	yes	—
755	C₄²	D₄×C₂²⋊C₄	1	4	yes	—
756	C₄²	D₄×C₂²⋊C₄	1	4	yes	—
757	C₄²	D₄×C₂²⋊C₄	1	4	yes	—
758	C₄²	D₄×C₂²⋊C₄	1	4	yes	—
759	C₄²	#2405	1	4	yes	—
760	C₄²	#2405	1	4	yes	—
761	C₄²	#2405	1	4	yes	—
762	C₄²	#2405	1	4	yes	—
763	C₄²	#2410	1	2	yes	—
764	C₄²	#2410	1	2	yes	—
765	C₄²	#2410	1	2	yes	—
766	C₄²	#2410	1	2	yes	—
767	C₄²	#2410	1	4	yes	—
768	C₄²	#2410	1	4	yes	—
769	C₂³	#20925	1	4	yes	—
770	C₂³	C₂²×#386	1	1	yes	characteristic
771	C₂³	C₂×D₄×C₂²⋊C₄	1	2	yes	—
772	C₂³	C₂×#2403	1	2	yes	—
773	C₂³	C₂×#2410	1	1	yes	characteristic
774	C₂³	C₂×#2410	1	1	yes	characteristic
775	C₂³	C₂×C₄×AGL(1,ℤ/8)	1	2	yes	—
776	C₂³	#60168	1	2	yes	—
777	C₂³	C₂×#3003	1	1	yes	characteristic
778	C₂³	C₂×#3005	1	1	yes	characteristic
779	C₂³	#60367	1	2	yes	—
780	C₂³	C₂×#3036	1	2	yes	—
781	C₂³	#60423	1	2	yes	—
782	C₂³	D₄×AGL(1,ℤ/8)	1	4	yes	—
783	C₂³	D₄×AGL(1,ℤ/8)	1	4	yes	—
784	C₂³	#61066	1	4	yes	—
785	C₂³	#61066	1	4	yes	—
786	D₄	#20608	1	4	yes	—
787	C₂×C₄	#13867	1	2	yes	—
788	C₂×C₄	#13867	1	2	yes	—
789	C₂×C₄	#13867	1	2	yes	—
790	C₂×C₄	#13867	1	2	yes	—
791	C₂×C₄	#13867	1	4	yes	—
792	C₂×C₄	#13867	1	4	yes	—
793	C₂×C₄	#20925	1	4	yes	—
794	C₂×C₄	C₂²×#379	1	1	yes	characteristic
795	C₂×C₄	C₂×#2308	1	1	yes	characteristic
796	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	2	yes	—
797	C₂×C₄	C₂×#2410	1	1	yes	characteristic
798	C₂×C₄	C₂×#2410	1	1	yes	characteristic
799	C₂×C₄	C₂×#2405	1	2	yes	—
800	C₂×C₄	C₂×#3025	1	2	yes	—
801	C₂×C₄	#60398	1	2	yes	—
802	C₂²	C₂×#13867	1	1	yes	characteristic
803	C₂²	C₂×#20925	1	1	yes	characteristic
804	C₂²	#6371420	1	1	yes	characteristic
805	C₂²	C₂²⋊C₄×AGL(1,ℤ/8)	1	4	yes	—
806	C₂²	#6437510	1	2	yes	—
807	C₂²	#6437511	1	2	yes	—
808	C₂²	#6437680	1	2	yes	—
809	C₂²	#6437680	1	2	yes	—
810	C₂²	#6437994	1	2	yes	—
811	C₂²	#6438015	1	1	yes	characteristic
812	C₂²	#6438016	1	1	yes	characteristic
813	C₄	C₂×#20608	1	1	yes	characteristic
814	C₄	#6370734	1	1	yes	characteristic
815	C₄	#6437994	1	2	yes	—
816	C₂	#72268297	1	2	yes	—
817	C₂	#72310926	1	2	yes	—
818	C₂	#72310936	1	1	yes	characteristic
819	C₂	#72313408	1	1	yes	characteristic
820	C₂	#72313435	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2410
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂⁴×C₄	C₂⁵
prime radical	C₂×#10580309	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72313519	C₂	semidirect
2. #72313511	C₂	semidirect
3. #72313506	C₂	semidirect
4. #72313493	C₂	semidirect
5. #72313483	C₂	semidirect
6. C₂×#185346	C₂	semidirect
7. #72313473	C₂	semidirect
8. #72313465	C₂	semidirect
9. #72313456	C₂	semidirect
10. #72313449	C₂	semidirect
11. #72313446	C₂	semidirect
12. #72313309	C₂	semidirect
13. #72305947	C₂	semidirect
14. #72264594	C₂	semidirect
15. C₂×D₄×#410	C₂	semidirect
17. C₂×#198406	C₂	semidirect
20. #10580309	C₄	semidirect
30. C₂×D₄×#117	C₂²	semidirect
32. C₂×#22406	C₂²	semidirect
34. C₂×D₄×#99	C₂²	semidirect
35. C₂×#21421	C₂²	semidirect
36. C₂×#21408	C₂²	semidirect
37. C₂×#21406	C₂²	semidirect
38. C₂×#21395	C₂²	semidirect
40. C₂×#21212	C₂²	semidirect
41. C₂×#20739	C₂²	semidirect
43. C₂²×#1762	C₂²	semidirect
45. C₂×#17581	C₂²	semidirect
46. #514648	C₂²	semidirect
48. #374178	C₂²	semidirect
49. #374176	C₂²	semidirect
50. #374077	C₂²	semidirect
53. #363929	C₂²	semidirect
54. #363228	C₂²	semidirect
55. #362740	C₂²	semidirect
56. #361643	C₂²	semidirect
58. #359621	C₂²	semidirect
59. #353811	C₂²	semidirect
60. #353771	C₂²	semidirect
61. C₂×#9260	C₂²	semidirect
63. C₂×#9256	C₂²	semidirect
64. C₂×#9255	C₂²	semidirect
65. C₂×#8352	C₂²	semidirect
66. C₂×#8351	C₂²	semidirect
67. C₂×#8350	C₂²	semidirect
68. C₂×#7984	C₂²	semidirect
69. C₂×#7930	C₂²	semidirect
70. #114965	C₂²	semidirect
71. #114965	C₂²	semidirect
72. #114963	C₂²	semidirect
73. #114963	C₂²	semidirect
74. #111488	C₂²	semidirect
75. #111488	C₂²	semidirect
76. #111487	C₂²	semidirect
77. #111487	C₂²	semidirect
78. #108187	C₂²	semidirect
79. #108186	C₂²	semidirect
80. #108186	C₂²	semidirect
81. #106323	C₂²	semidirect
82. #106322	C₂²	semidirect
83. #106322	C₂²	semidirect
84. #62781	C₂×C₄	semidirect
106. #61706	C₂×C₄	semidirect
107. #61695	C₂×C₄	semidirect
108. #61694	C₂×C₄	semidirect
112. #60958	C₂×C₄	semidirect
127. #60282	C₂×C₄	semidirect
196. C₂×#550	C₂²⋊C₄	semidirect
197. C₂×D₄×Q₈	C₂²⋊C₄	semidirect
198. C₂×#547	C₂²⋊C₄	semidirect
203. C₂×D₄²	C₂²⋊C₄	semidirect
208. C₂×#532	C₂²⋊C₄	semidirect
209. C₂×#532	C₂²⋊C₄	semidirect
237. C₂²×C₄×D₄	C₂²⋊C₄	semidirect
238. C₂²×C₄×D₄	C₂²⋊C₄	semidirect
283. C₂×#478	C₂²⋊C₄	semidirect
284. C₂×#478	C₂²⋊C₄	semidirect
285. C₂×#463	C₂²⋊C₄	semidirect
286. C₂×#463	C₂²⋊C₄	semidirect
294. C₂×#442	C₂²⋊C₄	semidirect
295. C₂×#442	C₂²⋊C₄	semidirect
296. C₂×#440	C₂²⋊C₄	semidirect
297. C₂×#440	C₂²⋊C₄	semidirect
513. C₂×#99	AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
#72313519	2
#72313511	2
#72313506	2
#72313493	2
#72313483	2
C₂×#185346	2
#72313473	2
#72313465	2
#72313456	2
#72313449	2
#72313446	2
#72313309	2
#72305947	2
#72264594	2
C₂×D₄×#410	2
C₂×#10580309	2
C₂×#198406	2