Subgroups — C₆₇×#34988 #30714239

Order 17152.

4082 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#538×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2847	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2846	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2626	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2622	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2617	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2480	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2472	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2424	C₂	1	4	yes	maximal, complemented
12	C₆₇×#2418	C₂	1	4	yes	maximal, complemented
13	C₆₇×#2321	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2312	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#120×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₂⁶×C₆₇	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
19	#538×C₆₇	—	2	8	no	—
20	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
21	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
22	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
25	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
26	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
28	C₂×#120×C₆₇	C₂²	1	2	yes	—
29	C₂×#120×C₆₇	C₂²	1	2	yes	—
30	C₂×#120×C₆₇	C₂²	1	2	yes	—
31	C₂×#120×C₆₇	C₂²	1	4	yes	—
32	C₂×#120×C₆₇	C₂²	1	4	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
35	C₂²×C₂²⋊C₄×C₆₇	—	2	8	no	—
36	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
40	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
41	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
42	#399×C₆₇	C₂²	1	2	yes	complemented
43	#397×C₆₇	C₂²	1	2	yes	complemented
44	#397×C₆₇	C₂²	1	4	yes	complemented
45	#397×C₆₇	C₂²	1	4	yes	complemented
46	#396×C₆₇	C₂²	1	4	yes	complemented
47	#394×C₆₇	C₂²	1	4	yes	complemented
48	#394×C₆₇	C₂²	1	4	yes	complemented
49	#394×C₆₇	C₂²	1	4	yes	complemented
50	#393×C₆₇	C₂²	1	2	yes	complemented
51	#392×C₆₇	C₂²	1	2	yes	complemented
52	#390×C₆₇	C₂²	1	4	yes	complemented
53	#388×C₆₇	C₂²	1	4	yes	complemented
54	#388×C₆₇	C₂²	1	4	yes	complemented
55	#388×C₆₇	C₂²	1	4	yes	complemented
56	#388×C₆₇	C₂²	1	4	yes	complemented
57	#386×C₆₇	C₂²	1	4	yes	complemented
58	#386×C₆₇	C₂²	1	2	yes	complemented
59	#386×C₆₇	C₂²	1	4	yes	complemented
60	#386×C₆₇	C₂²	1	2	yes	complemented
61	#386×C₆₇	C₂²	1	4	yes	complemented
62	#385×C₆₇	C₂²	1	2	yes	complemented
63	#385×C₆₇	C₂²	1	4	yes	complemented
64	#385×C₆₇	C₂²	1	2	yes	complemented
65	#385×C₆₇	C₂²	1	4	yes	complemented
66	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#380×C₆₇	C₂²	1	2	yes	complemented
69	#380×C₆₇	C₂²	1	2	yes	complemented
70	#379×C₆₇	C₂²	1	2	yes	—
71	#379×C₆₇	C₂²	1	2	yes	—
72	#379×C₆₇	C₂²	1	2	yes	—
73	#379×C₆₇	C₂²	1	4	yes	—
74	#379×C₆₇	C₂²	1	4	yes	—
75	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
77	C₂⁵×C₆₇	—	2	4	no	—
78	C₂⁵×C₆₇	—	2	4	no	—
79	C₂⁵×C₆₇	—	2	4	no	—
80	C₂⁵×C₆₇	—	4	4	no	—
81	C₂⁵×C₆₇	—	4	4	no	—
82	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
83	C₂⁵×C₆₇	C₂³	1	4	yes	—
84	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
85	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
87	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
88	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
89	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
90	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
91	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
92	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
93	C₂³×C₄×C₆₇	—	2	4	no	—
94	C₂³×C₄×C₆₇	—	2	4	no	—
95	C₂³×C₄×C₆₇	—	4	4	no	—
96	C₂³×C₄×C₆₇	—	4	4	no	—
97	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
98	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
99	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
100	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₆₇	C₂³	1	2	yes	complemented
105	#126×C₆₇	—	2	8	no	—
106	#124×C₆₇	—	2	8	no	—
107	#123×C₆₇	—	2	8	no	—
108	C₂²⋊Q₈×C₆₇	—	2	4	no	—
109	C₂²⋊Q₈×C₆₇	—	4	4	no	—
110	#121×C₆₇	—	2	4	no	—
111	#121×C₆₇	—	2	8	no	—
112	#121×C₆₇	—	4	4	no	—
113	#120×C₆₇	—	2	8	no	—
114	#120×C₆₇	—	2	8	no	—
115	#120×C₆₇	—	2	8	no	—
116	#120×C₆₇	—	4	8	no	—
117	#120×C₆₇	—	4	8	no	—
118	C₄×D₄×C₆₇	—	2	8	no	—
119	C₄×D₄×C₆₇	—	4	8	no	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	complemented
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	complemented
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	complemented
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	complemented
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
128	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
129	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
130	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
131	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
132	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
133	C₂×C₂²⋊C₄×C₆₇	D₄	1	8	yes	complemented
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	complemented
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	complemented
155	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	complemented
156	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	complemented
157	C₂×C₄²×C₆₇	C₂³	1	2	yes	complemented
158	C₂×C₄²×C₆₇	C₂³	1	4	yes	complemented
159	#95×C₆₇	C₂³	1	4	yes	complemented
160	#95×C₆₇	C₂³	1	4	yes	complemented
161	#95×C₆₇	C₂³	1	4	yes	complemented
162	#95×C₆₇	C₂³	1	4	yes	complemented
163	#95×C₆₇	C₂³	1	2	yes	complemented
164	#95×C₆₇	C₂³	1	2	yes	complemented
165	#95×C₆₇	C₂³	1	4	yes	complemented
166	C₂⁴×C₆₇	—	2	2	no	—
167	C₂⁴×C₆₇	—	2	2	no	—
168	C₂⁴×C₆₇	—	2	4	no	—
169	C₂⁴×C₆₇	—	2	4	no	—
170	C₂⁴×C₆₇	—	2	32	no	—
171	C₂⁴×C₆₇	—	2	8	no	—
172	C₂⁴×C₆₇	—	2	2	no	—
173	C₂⁴×C₆₇	—	2	8	no	—
174	C₂⁴×C₆₇	—	2	8	no	—
175	C₂⁴×C₆₇	—	2	2	no	—
176	C₂⁴×C₆₇	—	2	2	no	—
177	C₂⁴×C₆₇	—	2	2	no	—
178	C₂⁴×C₆₇	—	2	8	no	—
179	C₂⁴×C₆₇	—	2	8	no	—
180	C₂⁴×C₆₇	—	4	2	no	—
181	C₂⁴×C₆₇	—	4	2	no	—
182	C₂⁴×C₆₇	—	4	2	no	—
183	C₂⁴×C₆₇	—	4	2	no	—
184	C₂⁴×C₆₇	—	4	4	no	—
185	C₂⁴×C₆₇	—	4	4	no	—
186	C₂⁴×C₆₇	—	4	16	no	—
187	C₂⁴×C₆₇	—	4	16	no	—
188	C₂⁴×C₆₇	—	4	32	no	—
189	C₂⁴×C₆₇	—	4	32	no	—
190	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
191	C₂⁴×C₆₇	#41	1	4	yes	—
192	C₂⁴×C₆₇	#41	1	4	yes	—
193	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
194	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
195	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
196	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
197	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
198	C₂×Q₈×C₆₇	—	2	2	no	—
199	C₂×Q₈×C₆₇	—	4	2	no	—
200	C₂×D₄×C₆₇	—	2	4	no	—
201	C₂×D₄×C₆₇	—	2	4	no	—
202	C₂×D₄×C₆₇	—	2	4	no	—
203	C₂×D₄×C₆₇	—	2	8	no	—
204	C₂×D₄×C₆₇	—	2	8	no	—
205	C₂×D₄×C₆₇	—	2	8	no	—
206	C₂×D₄×C₆₇	—	2	4	no	—
207	C₂×D₄×C₆₇	—	2	4	no	—
208	C₂×D₄×C₆₇	—	2	8	no	—
209	C₂×D₄×C₆₇	—	2	2	no	—
210	C₂×D₄×C₆₇	—	4	4	no	—
211	C₂×D₄×C₆₇	—	4	4	no	—
212	C₂×D₄×C₆₇	—	4	4	no	—
213	C₂×D₄×C₆₇	—	4	4	no	—
214	C₂×D₄×C₆₇	—	4	2	no	—
215	C₂²×C₄×C₆₇	—	2	2	no	—
216	C₂²×C₄×C₆₇	—	2	2	no	—
217	C₂²×C₄×C₆₇	—	2	8	no	—
218	C₂²×C₄×C₆₇	—	2	4	no	—
219	C₂²×C₄×C₆₇	—	2	4	no	—
220	C₂²×C₄×C₆₇	—	2	8	no	—
221	C₂²×C₄×C₆₇	—	2	4	no	—
222	C₂²×C₄×C₆₇	—	2	4	no	—
223	C₂²×C₄×C₆₇	—	2	4	no	—
224	C₂²×C₄×C₆₇	—	4	2	no	—
225	C₂²×C₄×C₆₇	—	4	4	no	—
226	C₂²×C₄×C₆₇	—	4	2	no	—
227	C₂²×C₄×C₆₇	—	4	2	no	—
228	C₂²×C₄×C₆₇	—	4	2	no	—
229	C₂²×C₄×C₆₇	—	4	2	no	—
230	C₂²×C₄×C₆₇	—	4	2	no	—
231	C₂²×C₄×C₆₇	—	4	4	no	—
232	C₂²×C₄×C₆₇	—	4	16	no	—
233	C₂²×C₄×C₆₇	—	4	16	no	—
234	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
239	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₄⋊C₄×C₆₇	—	2	4	no	—
247	C₄⋊C₄×C₆₇	—	2	4	no	—
248	C₄⋊C₄×C₆₇	—	2	2	no	—
249	C₄⋊C₄×C₆₇	—	2	2	no	—
250	C₄⋊C₄×C₆₇	—	4	4	no	—
251	C₄⋊C₄×C₆₇	—	4	2	no	—
252	C₄⋊C₄×C₆₇	—	4	2	no	—
253	C₄⋊C₄×C₆₇	—	4	4	no	—
254	C₂²⋊C₄×C₆₇	—	2	8	no	—
255	C₂²⋊C₄×C₆₇	—	2	4	no	—
256	C₂²⋊C₄×C₆₇	—	2	4	no	—
257	C₂²⋊C₄×C₆₇	—	2	4	no	—
258	C₂²⋊C₄×C₆₇	—	2	8	no	—
259	C₂²⋊C₄×C₆₇	—	2	4	no	—
260	C₂²⋊C₄×C₆₇	—	2	4	no	—
261	C₂²⋊C₄×C₆₇	—	2	8	no	—
262	C₂²⋊C₄×C₆₇	—	2	8	no	—
263	C₂²⋊C₄×C₆₇	—	2	8	no	—
264	C₂²⋊C₄×C₆₇	—	2	8	no	—
265	C₂²⋊C₄×C₆₇	—	2	4	no	—
266	C₂²⋊C₄×C₆₇	—	2	4	no	—
267	C₂²⋊C₄×C₆₇	—	2	4	no	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	4	4	no	—
270	C₂²⋊C₄×C₆₇	—	4	4	no	—
271	C₂²⋊C₄×C₆₇	—	4	4	no	—
272	C₂²⋊C₄×C₆₇	—	4	4	no	—
273	C₂²⋊C₄×C₆₇	—	4	4	no	—
274	C₂²⋊C₄×C₆₇	—	4	4	no	—
275	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
276	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
277	C₄²×C₆₇	—	2	4	no	—
278	C₄²×C₆₇	—	4	4	no	—
279	C₂³×C₆₇	—	2	8	no	—
280	C₂³×C₆₇	—	2	8	no	—
281	C₂³×C₆₇	—	2	16	no	—
282	C₂³×C₆₇	—	2	8	no	—
283	C₂³×C₆₇	—	2	16	no	—
284	C₂³×C₆₇	—	2	2	no	—
285	C₂³×C₆₇	—	2	2	no	—
286	C₂³×C₆₇	—	2	2	no	—
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	—	2	2	no	—
290	C₂³×C₆₇	—	2	32	no	—
291	C₂³×C₆₇	—	2	8	no	—
292	C₂³×C₆₇	—	2	8	no	—
293	C₂³×C₆₇	—	2	2	no	—
294	C₂³×C₆₇	—	2	2	no	—
295	C₂³×C₆₇	—	2	2	no	—
296	C₂³×C₆₇	—	2	2	no	—
297	C₂³×C₆₇	—	2	4	no	—
298	C₂³×C₆₇	—	2	4	no	—
299	C₂³×C₆₇	—	2	4	no	—
300	C₂³×C₆₇	—	2	4	no	—
301	C₂³×C₆₇	—	2	2	no	—
302	C₂³×C₆₇	—	2	2	no	—
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	—	2	4	no	—
305	C₂³×C₆₇	—	2	4	no	—
306	C₂³×C₆₇	—	4	4	no	—
307	C₂³×C₆₇	—	4	4	no	—
308	C₂³×C₆₇	—	4	8	no	—
309	C₂³×C₆₇	—	4	16	no	—
310	C₂³×C₆₇	—	4	16	no	—
311	C₂³×C₆₇	—	4	16	no	—
312	C₂³×C₆₇	—	4	16	no	—
313	C₂³×C₆₇	—	4	128	no	—
314	C₂³×C₆₇	—	4	8	no	—
315	C₂³×C₆₇	—	4	8	no	—
316	C₂³×C₆₇	—	4	16	no	—
317	C₂³×C₆₇	—	4	4	no	—
318	C₂³×C₆₇	—	4	4	no	—
319	C₂³×C₆₇	—	4	8	no	—
320	C₂³×C₆₇	—	4	16	no	—
321	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
322	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
323	C₂³×C₆₇	C₂×#41	1	4	yes	—
324	C₂³×C₆₇	C₂×#41	1	2	yes	—
325	C₂³×C₆₇	C₂×#41	1	2	yes	—
326	C₂³×C₆₇	C₂×#41	1	4	yes	—
327	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
328	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
329	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
330	Q₈×C₆₇	—	8	2	no	—
331	D₄×C₆₇	—	4	8	no	—
332	D₄×C₆₇	—	4	16	no	—
333	D₄×C₆₇	—	8	2	no	—
334	D₄×C₆₇	—	8	4	no	—
335	D₄×C₆₇	—	8	4	no	—
336	D₄×C₆₇	—	8	8	no	—
337	C₂×C₄×C₆₇	—	2	4	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	4	no	—
348	C₂×C₄×C₆₇	—	2	4	no	—
349	C₂×C₄×C₆₇	—	2	4	no	—
350	C₂×C₄×C₆₇	—	2	4	no	—
351	C₂×C₄×C₆₇	—	2	4	no	—
352	C₂×C₄×C₆₇	—	2	4	no	—
353	C₂×C₄×C₆₇	—	2	4	no	—
354	C₂×C₄×C₆₇	—	2	4	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	4	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	4	4	no	—
359	C₂×C₄×C₆₇	—	4	4	no	—
360	C₂×C₄×C₆₇	—	4	16	no	—
361	C₂×C₄×C₆₇	—	4	8	no	—
362	C₂×C₄×C₆₇	—	4	8	no	—
363	C₂×C₄×C₆₇	—	4	4	no	—
364	C₂×C₄×C₆₇	—	4	4	no	—
365	C₂×C₄×C₆₇	—	8	4	no	—
366	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
367	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
368	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
369	C₂²×C₆₇	—	2	32	no	—
370	C₂²×C₆₇	—	2	4	no	—
371	C₂²×C₆₇	—	2	4	no	—
372	C₂²×C₆₇	—	2	4	no	—
373	C₂²×C₆₇	—	2	2	no	—
374	C₂²×C₆₇	—	2	2	no	—
375	C₂²×C₆₇	—	2	4	no	—
376	C₂²×C₆₇	—	2	4	no	—
377	C₂²×C₆₇	—	2	4	no	—
378	C₂²×C₆₇	—	2	4	no	—
379	C₂²×C₆₇	—	2	4	no	—
380	C₂²×C₆₇	—	2	4	no	—
381	C₂²×C₆₇	—	2	4	no	—
382	C₂²×C₆₇	—	2	4	no	—
383	C₂²×C₆₇	—	2	4	no	—
384	C₂²×C₆₇	—	2	8	no	—
385	C₂²×C₆₇	—	4	16	no	—
386	C₂²×C₆₇	—	4	16	no	—
387	C₂²×C₆₇	—	4	64	no	—
388	C₂²×C₆₇	—	4	4	no	—
389	C₂²×C₆₇	—	4	4	no	—
390	C₂²×C₆₇	—	4	2	no	—
391	C₂²×C₆₇	—	4	2	no	—
392	C₂²×C₆₇	—	4	4	no	—
393	C₂²×C₆₇	—	4	2	no	—
394	C₂²×C₆₇	—	4	4	no	—
395	C₂²×C₆₇	—	4	2	no	—
396	C₂²×C₆₇	—	4	2	no	—
397	C₂²×C₆₇	—	4	4	no	—
398	C₂²×C₆₇	#525	1	4	yes	—
399	C₂²×C₆₇	#538	1	8	yes	complemented
400	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
401	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
402	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
403	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
404	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
405	C₄×C₆₇	—	2	4	no	—
406	C₄×C₆₇	—	2	2	no	—
407	C₄×C₆₇	—	2	2	no	—
408	C₄×C₆₇	—	4	2	no	—
409	C₄×C₆₇	—	4	4	no	—
410	C₄×C₆₇	—	4	2	no	—
411	C₄×C₆₇	—	4	2	no	—
412	C₄×C₆₇	—	4	2	no	—
413	C₄×C₆₇	—	4	2	no	—
414	C₄×C₆₇	—	4	4	no	—
415	#34988	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
416	C₂×C₆₇	—	2	4	no	—
417	C₂×C₆₇	—	2	8	no	—
418	C₂×C₆₇	—	4	4	no	—
419	C₂×C₆₇	—	4	4	no	—
420	C₂×C₆₇	—	8	2	no	—
421	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
422	C₂×C₆₇	C₂×#538	1	2	yes	—
423	C₂×C₆₇	#3484	1	1	yes	characteristic
424	C₂×C₆₇	#3484	1	1	yes	characteristic
425	C₂×C₆₇	#3490	1	2	yes	—
426	C₂×#538	C₂×C₆₇	1	1	yes	characteristic, complemented
427	C₂³×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
428	#2848	C₂×C₆₇	1	1	yes	characteristic, complemented
429	#2847	C₂×C₆₇	1	1	yes	characteristic, complemented
430	#2846	C₂×C₆₇	1	2	yes	complemented
431	#2626	C₂×C₆₇	1	1	yes	characteristic, complemented
432	#2622	C₂×C₆₇	1	2	yes	complemented
433	#2617	C₂×C₆₇	1	1	yes	characteristic, complemented
434	#2480	C₂×C₆₇	1	4	yes	complemented
435	#2472	C₂×C₆₇	1	4	yes	complemented
436	#2424	C₂×C₆₇	1	4	yes	complemented
437	#2418	C₂×C₆₇	1	4	yes	complemented
438	#2321	C₂×C₆₇	1	2	yes	complemented
439	#2312	C₂×C₆₇	1	1	yes	characteristic, complemented
440	C₄×#120	C₂×C₆₇	1	2	yes	complemented
441	C₆₇	#34988	1	1	yes	characteristic, direct product factor, Sylow
442	C₂⁶	C₂²×C₆₇	1	1	yes	characteristic
443	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
444	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
445	#538	—	2	8	no	—
446	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
447	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
448	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
449	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
450	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
451	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
452	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
453	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
454	C₂×#120	C₂²×C₆₇	1	2	yes	—
455	C₂×#120	C₂²×C₆₇	1	2	yes	—
456	C₂×#120	C₂²×C₆₇	1	2	yes	—
457	C₂×#120	C₂²×C₆₇	1	4	yes	—
458	C₂×#120	C₂²×C₆₇	1	4	yes	—
459	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
460	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
461	C₂²×C₂²⋊C₄	—	2	8	no	—
462	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
463	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
464	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
465	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
466	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
467	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
468	#399	C₂²×C₆₇	1	2	yes	complemented
469	#397	C₂²×C₆₇	1	2	yes	complemented
470	#397	C₂²×C₆₇	1	4	yes	complemented
471	#397	C₂²×C₆₇	1	4	yes	complemented
472	#396	C₂²×C₆₇	1	4	yes	complemented
473	#394	C₂²×C₆₇	1	4	yes	complemented
474	#394	C₂²×C₆₇	1	4	yes	complemented
475	#394	C₂²×C₆₇	1	4	yes	complemented
476	#393	C₂²×C₆₇	1	2	yes	complemented
477	#392	C₂²×C₆₇	1	2	yes	complemented
478	#390	C₂²×C₆₇	1	4	yes	complemented
479	#388	C₂²×C₆₇	1	4	yes	complemented
480	#388	C₂²×C₆₇	1	4	yes	complemented
481	#388	C₂²×C₆₇	1	4	yes	complemented
482	#388	C₂²×C₆₇	1	4	yes	complemented
483	#386	C₂²×C₆₇	1	4	yes	complemented
484	#386	C₂²×C₆₇	1	2	yes	complemented
485	#386	C₂²×C₆₇	1	4	yes	complemented
486	#386	C₂²×C₆₇	1	2	yes	complemented
487	#386	C₂²×C₆₇	1	4	yes	complemented
488	#385	C₂²×C₆₇	1	2	yes	complemented
489	#385	C₂²×C₆₇	1	4	yes	complemented
490	#385	C₂²×C₆₇	1	2	yes	complemented
491	#385	C₂²×C₆₇	1	4	yes	complemented
492	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
493	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
494	#380	C₂²×C₆₇	1	2	yes	complemented
495	#380	C₂²×C₆₇	1	2	yes	complemented
496	#379	C₂²×C₆₇	1	2	yes	—
497	#379	C₂²×C₆₇	1	2	yes	—
498	#379	C₂²×C₆₇	1	2	yes	—
499	#379	C₂²×C₆₇	1	4	yes	—
500	#379	C₂²×C₆₇	1	4	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
502	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
503	C₂⁵	—	2	4	no	—
504	C₂⁵	—	2	4	no	—
505	C₂⁵	—	2	4	no	—
506	C₂⁵	—	4	4	no	—
507	C₂⁵	—	4	4	no	—
508	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
509	C₂⁵	C₂³×C₆₇	1	4	yes	—
510	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
511	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
512	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
513	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
514	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
515	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
516	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
517	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
518	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
519	C₂³×C₄	—	2	4	no	—
520	C₂³×C₄	—	2	4	no	—
521	C₂³×C₄	—	4	4	no	—
522	C₂³×C₄	—	4	4	no	—
523	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
524	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
525	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
526	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
528	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₆₇	1	2	yes	complemented
531	#126	—	2	8	no	—
532	#124	—	2	8	no	—
533	#123	—	2	8	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	4	4	no	—
536	#121	—	2	4	no	—
537	#121	—	2	8	no	—
538	#121	—	4	4	no	—
539	#120	—	2	8	no	—
540	#120	—	2	8	no	—
541	#120	—	2	8	no	—
542	#120	—	4	8	no	—
543	#120	—	4	8	no	—
544	C₄×D₄	—	2	8	no	—
545	C₄×D₄	—	4	8	no	—
546	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	complemented
547	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	complemented
548	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
549	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
550	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	complemented
551	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	complemented
552	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	complemented
553	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	complemented
554	C₂×C₂²⋊C₄	—	2	4	no	—
555	C₂×C₂²⋊C₄	—	2	4	no	—
556	C₂×C₂²⋊C₄	—	2	4	no	—
557	C₂×C₂²⋊C₄	—	2	16	no	—
558	C₂×C₂²⋊C₄	—	2	16	no	—
559	C₂×C₂²⋊C₄	D₄×C₆₇	1	8	yes	complemented
560	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	complemented
580	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	complemented
581	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	complemented
582	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	complemented
583	C₂×C₄²	C₂³×C₆₇	1	2	yes	complemented
584	C₂×C₄²	C₂³×C₆₇	1	4	yes	complemented
585	#95	C₂³×C₆₇	1	4	yes	complemented
586	#95	C₂³×C₆₇	1	4	yes	complemented
587	#95	C₂³×C₆₇	1	4	yes	complemented
588	#95	C₂³×C₆₇	1	4	yes	complemented
589	#95	C₂³×C₆₇	1	2	yes	complemented
590	#95	C₂³×C₆₇	1	2	yes	complemented
591	#95	C₂³×C₆₇	1	4	yes	complemented
592	C₂⁴	—	2	2	no	—
593	C₂⁴	—	2	2	no	—
594	C₂⁴	—	2	4	no	—
595	C₂⁴	—	2	4	no	—
596	C₂⁴	—	2	32	no	—
597	C₂⁴	—	2	8	no	—
598	C₂⁴	—	2	2	no	—
599	C₂⁴	—	2	8	no	—
600	C₂⁴	—	2	8	no	—
601	C₂⁴	—	2	2	no	—
602	C₂⁴	—	2	2	no	—
603	C₂⁴	—	2	2	no	—
604	C₂⁴	—	2	8	no	—
605	C₂⁴	—	2	8	no	—
606	C₂⁴	—	4	2	no	—
607	C₂⁴	—	4	2	no	—
608	C₂⁴	—	4	2	no	—
609	C₂⁴	—	4	2	no	—
610	C₂⁴	—	4	4	no	—
611	C₂⁴	—	4	4	no	—
612	C₂⁴	—	4	16	no	—
613	C₂⁴	—	4	16	no	—
614	C₂⁴	—	4	32	no	—
615	C₂⁴	—	4	32	no	—
616	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
617	C₂⁴	#41×C₆₇	1	4	yes	—
618	C₂⁴	#41×C₆₇	1	4	yes	—
619	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
620	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
621	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
622	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
623	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	4	2	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	8	no	—
630	C₂×D₄	—	2	8	no	—
631	C₂×D₄	—	2	8	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	8	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	4	4	no	—
637	C₂×D₄	—	4	4	no	—
638	C₂×D₄	—	4	4	no	—
639	C₂×D₄	—	4	4	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	8	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	8	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	—	4	4	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	4	no	—
658	C₂²×C₄	—	4	16	no	—
659	C₂²×C₄	—	4	16	no	—
660	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
661	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
664	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	4	4	no	—
677	C₄⋊C₄	—	4	2	no	—
678	C₄⋊C₄	—	4	2	no	—
679	C₄⋊C₄	—	4	4	no	—
680	C₂²⋊C₄	—	2	8	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	8	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	8	no	—
688	C₂²⋊C₄	—	2	8	no	—
689	C₂²⋊C₄	—	2	8	no	—
690	C₂²⋊C₄	—	2	8	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	4	4	no	—
696	C₂²⋊C₄	—	4	4	no	—
697	C₂²⋊C₄	—	4	4	no	—
698	C₂²⋊C₄	—	4	4	no	—
699	C₂²⋊C₄	—	4	4	no	—
700	C₂²⋊C₄	—	4	4	no	—
701	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
702	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
703	C₄²	—	2	4	no	—
704	C₄²	—	4	4	no	—
705	C₂³	—	2	8	no	—
706	C₂³	—	2	8	no	—
707	C₂³	—	2	16	no	—
708	C₂³	—	2	8	no	—
709	C₂³	—	2	16	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	32	no	—
717	C₂³	—	2	8	no	—
718	C₂³	—	2	8	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	4	no	—
725	C₂³	—	2	4	no	—
726	C₂³	—	2	4	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	2	4	no	—
732	C₂³	—	4	4	no	—
733	C₂³	—	4	4	no	—
734	C₂³	—	4	8	no	—
735	C₂³	—	4	16	no	—
736	C₂³	—	4	16	no	—
737	C₂³	—	4	16	no	—
738	C₂³	—	4	16	no	—
739	C₂³	—	4	128	no	—
740	C₂³	—	4	8	no	—
741	C₂³	—	4	8	no	—
742	C₂³	—	4	16	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	4	no	—
745	C₂³	—	4	8	no	—
746	C₂³	—	4	16	no	—
747	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
748	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
749	C₂³	C₂×#41×C₆₇	1	4	yes	—
750	C₂³	C₂×#41×C₆₇	1	2	yes	—
751	C₂³	C₂×#41×C₆₇	1	2	yes	—
752	C₂³	C₂×#41×C₆₇	1	4	yes	—
753	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
754	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
755	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
756	Q₈	—	8	2	no	—
757	D₄	—	4	8	no	—
758	D₄	—	4	16	no	—
759	D₄	—	8	2	no	—
760	D₄	—	8	4	no	—
761	D₄	—	8	4	no	—
762	D₄	—	8	8	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	16	no	—
787	C₂×C₄	—	4	8	no	—
788	C₂×C₄	—	4	8	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	8	4	no	—
792	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
793	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
795	C₂²	—	2	32	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	2	4	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	4	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	2	4	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	8	no	—
811	C₂²	—	4	16	no	—
812	C₂²	—	4	16	no	—
813	C₂²	—	4	64	no	—
814	C₂²	—	4	4	no	—
815	C₂²	—	4	4	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	4	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	4	no	—
824	C₂²	#525×C₆₇	1	4	yes	—
825	C₂²	#538×C₆₇	1	8	yes	complemented
826	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
827	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
828	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
829	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
830	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
831	C₄	—	2	4	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	4	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	4	no	—
841	C₂	—	2	4	no	—
842	C₂	—	2	8	no	—
843	C₂	—	4	4	no	—
844	C₂	—	4	4	no	—
845	C₂	—	8	2	no	—
846	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
847	C₂	C₂×#538×C₆₇	1	2	yes	—
848	C₂	C₆₇×#3484	1	1	yes	characteristic
849	C₂	C₆₇×#3484	1	1	yes	characteristic
850	C₂	C₆₇×#3490	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#538×C₆₇	C₂	semidirect
2. C₂³×C₂²⋊C₄×C₆₇	C₂	semidirect
3. C₆₇×#2848	C₂	semidirect
4. C₆₇×#2847	C₂	semidirect
5. C₆₇×#2846	C₂	semidirect
6. C₆₇×#2626	C₂	semidirect
7. C₆₇×#2622	C₂	semidirect
8. C₆₇×#2617	C₂	semidirect
9. C₆₇×#2480	C₂	semidirect
10. C₆₇×#2472	C₂	semidirect
11. C₆₇×#2424	C₂	semidirect
12. C₆₇×#2418	C₂	semidirect
13. C₆₇×#2321	C₂	semidirect
14. C₆₇×#2312	C₂	semidirect
15. C₄×#120×C₆₇	C₂	semidirect
20. C₂×#126×C₆₇	C₂²	semidirect
21. C₂×#124×C₆₇	C₂²	semidirect
22. C₂×#123×C₆₇	C₂²	semidirect
23. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
24. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
25. C₂×#121×C₆₇	C₂²	semidirect
26. C₂×#121×C₆₇	C₂²	semidirect
27. C₂×#121×C₆₇	C₂²	semidirect
33. C₂×C₄×D₄×C₆₇	C₂²	semidirect
34. C₂×C₄×D₄×C₆₇	C₂²	semidirect
42. #399×C₆₇	C₂²	semidirect
43. #397×C₆₇	C₂²	semidirect
44. #397×C₆₇	C₂²	semidirect
45. #397×C₆₇	C₂²	semidirect
46. #396×C₆₇	C₂²	semidirect
47. #394×C₆₇	C₂²	semidirect
48. #394×C₆₇	C₂²	semidirect
49. #394×C₆₇	C₂²	semidirect
50. #393×C₆₇	C₂²	semidirect
51. #392×C₆₇	C₂²	semidirect
52. #390×C₆₇	C₂²	semidirect
53. #388×C₆₇	C₂²	semidirect
54. #388×C₆₇	C₂²	semidirect
55. #388×C₆₇	C₂²	semidirect
56. #388×C₆₇	C₂²	semidirect
57. #386×C₆₇	C₂²	semidirect
58. #386×C₆₇	C₂²	semidirect
59. #386×C₆₇	C₂²	semidirect
60. #386×C₆₇	C₂²	semidirect
61. #386×C₆₇	C₂²	semidirect
62. #385×C₆₇	C₂²	semidirect
63. #385×C₆₇	C₂²	semidirect
64. #385×C₆₇	C₂²	semidirect
65. #385×C₆₇	C₂²	semidirect
66. #380×C₆₇	C₂²	semidirect
67. #380×C₆₇	C₂²	semidirect
68. #380×C₆₇	C₂²	semidirect
69. #380×C₆₇	C₂²	semidirect
75. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
86. C₂²×Q₈×C₆₇	C₂³	semidirect
92. C₂²×D₄×C₆₇	C₂³	semidirect
104. C₂³×C₄×C₆₇	C₂³	semidirect
120. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
121. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
122. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
123. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
124. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
125. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
126. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
127. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
133. C₂×C₂²⋊C₄×C₆₇	D₄	semidirect
153. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
154. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
155. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
156. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
157. C₂×C₄²×C₆₇	C₂³	semidirect
158. C₂×C₄²×C₆₇	C₂³	semidirect
159. #95×C₆₇	C₂³	semidirect
160. #95×C₆₇	C₂³	semidirect
161. #95×C₆₇	C₂³	semidirect
162. #95×C₆₇	C₂³	semidirect
163. #95×C₆₇	C₂³	semidirect
164. #95×C₆₇	C₂³	semidirect
165. #95×C₆₇	C₂³	semidirect
399. C₂²×C₆₇	#538	semidirect
415. #34988	C₆₇	direct (N × H)
426. C₂×#538	C₂×C₆₇	semidirect
427. C₂³×C₂²⋊C₄	C₂×C₆₇	semidirect
428. #2848	C₂×C₆₇	semidirect
429. #2847	C₂×C₆₇	semidirect
430. #2846	C₂×C₆₇	semidirect
431. #2626	C₂×C₆₇	semidirect
432. #2622	C₂×C₆₇	semidirect
433. #2617	C₂×C₆₇	semidirect
434. #2480	C₂×C₆₇	semidirect
435. #2472	C₂×C₆₇	semidirect
436. #2424	C₂×C₆₇	semidirect
437. #2418	C₂×C₆₇	semidirect
438. #2321	C₂×C₆₇	semidirect
439. #2312	C₂×C₆₇	semidirect
440. C₄×#120	C₂×C₆₇	semidirect
441. C₆₇	#34988	direct (N × H)
446. C₂×#126	C₂²×C₆₇	semidirect
447. C₂×#124	C₂²×C₆₇	semidirect
448. C₂×#123	C₂²×C₆₇	semidirect
449. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
450. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
451. C₂×#121	C₂²×C₆₇	semidirect
452. C₂×#121	C₂²×C₆₇	semidirect
453. C₂×#121	C₂²×C₆₇	semidirect
459. C₂×C₄×D₄	C₂²×C₆₇	semidirect
460. C₂×C₄×D₄	C₂²×C₆₇	semidirect
468. #399	C₂²×C₆₇	semidirect
469. #397	C₂²×C₆₇	semidirect
470. #397	C₂²×C₆₇	semidirect
471. #397	C₂²×C₆₇	semidirect
472. #396	C₂²×C₆₇	semidirect
473. #394	C₂²×C₆₇	semidirect
474. #394	C₂²×C₆₇	semidirect
475. #394	C₂²×C₆₇	semidirect
476. #393	C₂²×C₆₇	semidirect
477. #392	C₂²×C₆₇	semidirect
478. #390	C₂²×C₆₇	semidirect
479. #388	C₂²×C₆₇	semidirect
480. #388	C₂²×C₆₇	semidirect
481. #388	C₂²×C₆₇	semidirect
482. #388	C₂²×C₆₇	semidirect
483. #386	C₂²×C₆₇	semidirect
484. #386	C₂²×C₆₇	semidirect
485. #386	C₂²×C₆₇	semidirect
486. #386	C₂²×C₆₇	semidirect
487. #386	C₂²×C₆₇	semidirect
488. #385	C₂²×C₆₇	semidirect
489. #385	C₂²×C₆₇	semidirect
490. #385	C₂²×C₆₇	semidirect
491. #385	C₂²×C₆₇	semidirect
492. #380	C₂²×C₆₇	semidirect
493. #380	C₂²×C₆₇	semidirect
494. #380	C₂²×C₆₇	semidirect
495. #380	C₂²×C₆₇	semidirect
501. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
502. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
512. C₂²×Q₈	C₂³×C₆₇	semidirect
518. C₂²×D₄	C₂³×C₆₇	semidirect
530. C₂³×C₄	C₂³×C₆₇	semidirect
546. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
547. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
548. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
549. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
550. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
551. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
552. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
553. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
559. C₂×C₂²⋊C₄	D₄×C₆₇	semidirect
579. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
580. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
581. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
582. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
583. C₂×C₄²	C₂³×C₆₇	semidirect
584. C₂×C₄²	C₂³×C₆₇	semidirect
585. #95	C₂³×C₆₇	semidirect
586. #95	C₂³×C₆₇	semidirect
587. #95	C₂³×C₆₇	semidirect
588. #95	C₂³×C₆₇	semidirect
589. #95	C₂³×C₆₇	semidirect
590. #95	C₂³×C₆₇	semidirect
591. #95	C₂³×C₆₇	semidirect
825. C₂²	#538×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#538×C₆₇	2
C₂³×C₂²⋊C₄×C₆₇	2
C₆₇×#2848	2
C₆₇×#2847	2
C₆₇×#2846	2
C₆₇×#2626	2
C₆₇×#2622	2
C₆₇×#2617	2
C₆₇×#2480	2
C₆₇×#2472	2
C₆₇×#2424	2
C₆₇×#2418	2
C₆₇×#2321	2
C₆₇×#2312	2
C₄×#120×C₆₇	2
#34988	67

Subgroups — C67×#34988 #30714239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34988 #30714239