Subgroups — C₆₇×#59476 #30738727

Order 17152.

2642 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#551×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2696	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2685	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2598	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2542	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2496	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2491	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2472	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2471	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2463	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2445	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2445	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2433	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2422	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2418	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2366	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2354	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#127×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#126×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
25	#551×C₆₇	—	2	16	no	—
26	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#126×C₆₇	C₂²	1	2	yes	—
30	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#124×C₆₇	C₂²	1	2	yes	—
32	C₂×#123×C₆₇	C₂²	1	2	yes	—
33	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
34	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
38	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#120×C₆₇	C₂²	1	2	yes	—
40	C₂×#120×C₆₇	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
46	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
49	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
50	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
51	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
52	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
53	#400×C₆₇	C₂²	1	2	yes	complemented
54	#399×C₆₇	C₂²	1	2	yes	complemented
55	#399×C₆₇	C₂²	1	2	yes	complemented
56	#397×C₆₇	C₂²	1	2	yes	—
57	#397×C₆₇	C₂²	1	2	yes	complemented
58	#396×C₆₇	C₂²	1	2	yes	complemented
59	#394×C₆₇	C₂²	1	2	yes	—
60	#394×C₆₇	C₂²	1	2	yes	—
61	#394×C₆₇	C₂²	1	2	yes	complemented
62	#394×C₆₇	C₂²	1	2	yes	complemented
63	#394×C₆₇	C₂²	1	2	yes	complemented
64	#394×C₆₇	C₂²	1	2	yes	complemented
65	#393×C₆₇	C₂²	1	2	yes	complemented
66	#393×C₆₇	C₂²	1	2	yes	complemented
67	#392×C₆₇	C₂²	1	2	yes	—
68	#392×C₆₇	C₂²	1	2	yes	—
69	#390×C₆₇	C₂²	1	1	yes	characteristic
70	#390×C₆₇	C₂²	1	1	yes	characteristic
71	#390×C₆₇	C₂²	1	1	yes	characteristic
72	#390×C₆₇	C₂²	1	1	yes	characteristic
73	#390×C₆₇	C₂²	1	1	yes	characteristic
74	#390×C₆₇	C₂²	1	1	yes	characteristic
75	#390×C₆₇	C₂²	1	2	yes	complemented
76	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#390×C₆₇	C₂²	1	2	yes	complemented
78	#390×C₆₇	C₂²	1	2	yes	complemented
79	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#388×C₆₇	C₂²	1	1	yes	characteristic
85	#388×C₆₇	C₂²	1	1	yes	characteristic
86	#388×C₆₇	C₂²	1	1	yes	characteristic
87	#388×C₆₇	C₂²	1	2	yes	complemented
88	#388×C₆₇	C₂²	1	2	yes	complemented
89	#388×C₆₇	C₂²	1	2	yes	complemented
90	#388×C₆₇	C₂²	1	2	yes	complemented
91	#388×C₆₇	C₂²	1	2	yes	complemented
92	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#387×C₆₇	C₂²	1	2	yes	complemented
96	#386×C₆₇	C₂²	1	2	yes	—
97	#386×C₆₇	C₂²	1	2	yes	—
98	#386×C₆₇	C₂²	1	2	yes	—
99	#386×C₆₇	C₂²	1	2	yes	—
100	#386×C₆₇	C₂²	1	2	yes	complemented
101	#386×C₆₇	C₂²	1	2	yes	complemented
102	#386×C₆₇	C₂²	1	2	yes	complemented
103	#386×C₆₇	C₂²	1	2	yes	complemented
104	#385×C₆₇	C₂²	1	2	yes	complemented
105	#385×C₆₇	C₂²	1	2	yes	complemented
106	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#383×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	#380×C₆₇	C₂²	1	1	yes	characteristic
110	#380×C₆₇	C₂²	1	1	yes	characteristic
111	#380×C₆₇	C₂²	1	2	yes	complemented
112	#379×C₆₇	C₂²	1	2	yes	—
113	#379×C₆₇	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
123	C₄³×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₆₇	C₂³	1	2	yes	—
125	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₇	—	2	4	no	—
127	C₂²×D₄×C₆₇	—	2	4	no	—
128	C₂²×D₄×C₆₇	—	4	2	no	—
129	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
131	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
132	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
133	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
134	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
137	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
140	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
141	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
142	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
144	C₄⋊Q₈×C₆₇	—	4	2	no	—
145	#127×C₆₇	—	2	4	no	—
146	#127×C₆₇	—	2	4	no	—
147	#126×C₆₇	—	2	8	no	—
148	#126×C₆₇	D₄	1	8	yes	complemented
149	#124×C₆₇	—	2	8	no	—
150	#123×C₆₇	—	2	8	no	—
151	#123×C₆₇	—	2	8	no	—
152	#123×C₆₇	—	2	8	no	—
153	C₂²⋊Q₈×C₆₇	—	2	8	no	—
154	C₂²⋊Q₈×C₆₇	—	2	8	no	—
155	C₂²⋊Q₈×C₆₇	—	4	4	no	—
156	#121×C₆₇	—	4	2	no	—
157	#120×C₆₇	—	2	8	no	—
158	#120×C₆₇	—	4	4	no	—
159	C₄×D₄×C₆₇	—	2	4	no	—
160	C₄×D₄×C₆₇	—	2	4	no	—
161	C₄×D₄×C₆₇	—	2	8	no	—
162	C₄×D₄×C₆₇	—	2	8	no	—
163	C₄×D₄×C₆₇	—	4	2	no	—
164	C₄×D₄×C₆₇	—	4	2	no	—
165	C₄×D₄×C₆₇	—	4	2	no	—
166	C₄×D₄×C₆₇	—	4	4	no	—
167	#117×C₆₇	—	2	8	no	—
168	#117×C₆₇	—	2	8	no	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
189	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
223	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
224	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
234	#95×C₆₇	C₂³	1	1	yes	characteristic
235	#95×C₆₇	C₂³	1	1	yes	characteristic
236	#95×C₆₇	C₂³	1	1	yes	characteristic
237	#95×C₆₇	C₂³	1	1	yes	characteristic
238	#95×C₆₇	C₂³	1	1	yes	characteristic
239	#95×C₆₇	C₂³	1	1	yes	characteristic
240	#95×C₆₇	C₂³	1	2	yes	—
241	#95×C₆₇	C₂³	1	2	yes	—
242	#95×C₆₇	C₂³	1	2	yes	—
243	#95×C₆₇	C₂³	1	2	yes	—
244	#95×C₆₇	C₂³	1	1	yes	characteristic
245	#95×C₆₇	C₂³	1	1	yes	characteristic
246	#95×C₆₇	C₂³	1	1	yes	characteristic
247	#95×C₆₇	C₂³	1	1	yes	characteristic
248	#95×C₆₇	C₂³	1	1	yes	characteristic
249	#95×C₆₇	C₂³	1	1	yes	characteristic
250	#95×C₆₇	C₂³	1	2	yes	—
251	#95×C₆₇	C₂³	1	2	yes	—
252	#95×C₆₇	C₂³	1	2	yes	—
253	C₂⁴×C₆₇	—	2	4	no	—
254	C₂⁴×C₆₇	—	2	4	no	—
255	C₂⁴×C₆₇	—	2	4	no	—
256	C₂⁴×C₆₇	—	4	2	no	—
257	C₂⁴×C₆₇	—	4	2	no	—
258	C₂⁴×C₆₇	—	4	2	no	—
259	C₂⁴×C₆₇	—	4	2	no	—
260	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
261	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
263	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
264	C₂×Q₈×C₆₇	—	2	4	no	—
265	C₂×Q₈×C₆₇	—	4	2	no	—
266	C₂×Q₈×C₆₇	—	4	2	no	—
267	C₂×D₄×C₆₇	—	2	4	no	—
268	C₂×D₄×C₆₇	—	2	4	no	—
269	C₂×D₄×C₆₇	—	2	4	no	—
270	C₂×D₄×C₆₇	—	2	4	no	—
271	C₂×D₄×C₆₇	—	2	4	no	—
272	C₂×D₄×C₆₇	—	2	4	no	—
273	C₂×D₄×C₆₇	—	2	4	no	—
274	C₂×D₄×C₆₇	—	2	4	no	—
275	C₂×D₄×C₆₇	—	2	4	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	2	no	—
278	C₂×D₄×C₆₇	—	2	2	no	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	—	2	2	no	—
281	C₂×D₄×C₆₇	—	2	2	no	—
282	C₂×D₄×C₆₇	—	2	4	no	—
283	C₂×D₄×C₆₇	—	2	2	no	—
284	C₂×D₄×C₆₇	—	4	2	no	—
285	C₂×D₄×C₆₇	—	4	2	no	—
286	C₂×D₄×C₆₇	—	4	2	no	—
287	C₂×D₄×C₆₇	—	4	2	no	—
288	C₂×D₄×C₆₇	—	4	2	no	—
289	C₂×D₄×C₆₇	—	4	2	no	—
290	C₂×D₄×C₆₇	—	4	2	no	—
291	C₂×D₄×C₆₇	—	4	2	no	—
292	C₂×D₄×C₆₇	—	4	16	no	—
293	C₂×D₄×C₆₇	#41	1	4	yes	—
294	C₂×D₄×C₆₇	#41	1	4	yes	—
295	C₂²×C₄×C₆₇	—	2	4	no	—
296	C₂²×C₄×C₆₇	—	2	4	no	—
297	C₂²×C₄×C₆₇	—	2	4	no	—
298	C₂²×C₄×C₆₇	—	2	4	no	—
299	C₂²×C₄×C₆₇	—	2	2	no	—
300	C₂²×C₄×C₆₇	—	2	2	no	—
301	C₂²×C₄×C₆₇	—	2	2	no	—
302	C₂²×C₄×C₆₇	—	2	4	no	—
303	C₂²×C₄×C₆₇	—	2	4	no	—
304	C₂²×C₄×C₆₇	—	2	4	no	—
305	C₂²×C₄×C₆₇	—	4	2	no	—
306	C₂²×C₄×C₆₇	—	4	2	no	—
307	C₂²×C₄×C₆₇	—	4	2	no	—
308	C₂²×C₄×C₆₇	—	4	2	no	—
309	C₂²×C₄×C₆₇	—	4	2	no	—
310	C₂²×C₄×C₆₇	—	4	2	no	—
311	C₂²×C₄×C₆₇	—	4	2	no	—
312	C₂²×C₄×C₆₇	—	4	2	no	—
313	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₄⋊C₄×C₆₇	—	2	4	no	—
333	C₄⋊C₄×C₆₇	—	2	4	no	—
334	C₄⋊C₄×C₆₇	—	2	4	no	—
335	C₄⋊C₄×C₆₇	—	2	4	no	—
336	C₄⋊C₄×C₆₇	—	2	4	no	—
337	C₄⋊C₄×C₆₇	—	2	2	no	—
338	C₄⋊C₄×C₆₇	—	2	2	no	—
339	C₄⋊C₄×C₆₇	—	2	2	no	—
340	C₄⋊C₄×C₆₇	—	2	4	no	—
341	C₄⋊C₄×C₆₇	—	2	2	no	—
342	C₄⋊C₄×C₆₇	—	2	2	no	—
343	C₄⋊C₄×C₆₇	—	2	2	no	—
344	C₄⋊C₄×C₆₇	—	4	1	no	—
345	C₄⋊C₄×C₆₇	—	4	1	no	—
346	C₄⋊C₄×C₆₇	—	4	2	no	—
347	C₄⋊C₄×C₆₇	—	4	2	no	—
348	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	complemented
349	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	complemented
350	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	complemented
351	C₂²⋊C₄×C₆₇	—	2	4	no	—
352	C₂²⋊C₄×C₆₇	—	2	4	no	—
353	C₂²⋊C₄×C₆₇	—	2	4	no	—
354	C₂²⋊C₄×C₆₇	—	2	4	no	—
355	C₂²⋊C₄×C₆₇	—	2	4	no	—
356	C₂²⋊C₄×C₆₇	—	2	4	no	—
357	C₂²⋊C₄×C₆₇	—	2	4	no	—
358	C₂²⋊C₄×C₆₇	—	2	4	no	—
359	C₂²⋊C₄×C₆₇	—	2	4	no	—
360	C₂²⋊C₄×C₆₇	—	2	4	no	—
361	C₂²⋊C₄×C₆₇	—	2	4	no	—
362	C₂²⋊C₄×C₆₇	—	2	4	no	—
363	C₂²⋊C₄×C₆₇	—	2	4	no	—
364	C₂²⋊C₄×C₆₇	—	2	2	no	—
365	C₂²⋊C₄×C₆₇	—	2	4	no	—
366	C₂²⋊C₄×C₆₇	—	4	2	no	—
367	C₂²⋊C₄×C₆₇	—	4	1	no	—
368	C₂²⋊C₄×C₆₇	—	4	1	no	—
369	C₂²⋊C₄×C₆₇	—	4	2	no	—
370	C₂²⋊C₄×C₆₇	—	4	2	no	—
371	C₂²⋊C₄×C₆₇	—	4	2	no	—
372	C₂²⋊C₄×C₆₇	—	4	2	no	—
373	C₂²⋊C₄×C₆₇	—	4	2	no	—
374	C₂²⋊C₄×C₆₇	—	4	2	no	—
375	C₂²⋊C₄×C₆₇	—	4	2	no	—
376	C₂²⋊C₄×C₆₇	—	4	2	no	—
377	C₂²⋊C₄×C₆₇	—	4	2	no	—
378	C₂²⋊C₄×C₆₇	—	4	2	no	—
379	C₂²⋊C₄×C₆₇	—	4	2	no	—
380	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
381	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
382	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
383	C₄²×C₆₇	—	2	4	no	—
384	C₄²×C₆₇	—	2	4	no	—
385	C₄²×C₆₇	—	2	2	no	—
386	C₄²×C₆₇	—	2	2	no	—
387	C₄²×C₆₇	—	2	2	no	—
388	C₄²×C₆₇	—	2	2	no	—
389	C₄²×C₆₇	—	2	2	no	—
390	C₄²×C₆₇	—	2	2	no	—
391	C₄²×C₆₇	—	2	2	no	—
392	C₄²×C₆₇	—	4	1	no	—
393	C₄²×C₆₇	—	4	1	no	—
394	C₄²×C₆₇	C₂×D₄	1	4	yes	complemented
395	C₂³×C₆₇	—	2	2	no	—
396	C₂³×C₆₇	—	2	2	no	—
397	C₂³×C₆₇	—	2	1	no	—
398	C₂³×C₆₇	—	2	1	no	—
399	C₂³×C₆₇	—	2	2	no	—
400	C₂³×C₆₇	—	2	2	no	—
401	C₂³×C₆₇	—	2	2	no	—
402	C₂³×C₆₇	—	2	1	no	—
403	C₂³×C₆₇	—	2	2	no	—
404	C₂³×C₆₇	—	2	2	no	—
405	C₂³×C₆₇	—	2	2	no	—
406	C₂³×C₆₇	—	2	1	no	—
407	C₂³×C₆₇	—	2	2	no	—
408	C₂³×C₆₇	—	2	2	no	—
409	C₂³×C₆₇	—	2	1	no	—
410	C₂³×C₆₇	—	2	1	no	—
411	C₂³×C₆₇	—	2	2	no	—
412	C₂³×C₆₇	—	2	2	no	—
413	C₂³×C₆₇	—	2	2	no	—
414	C₂³×C₆₇	—	2	2	no	—
415	C₂³×C₆₇	—	2	2	no	—
416	C₂³×C₆₇	—	2	2	no	—
417	C₂³×C₆₇	—	2	2	no	—
418	C₂³×C₆₇	—	2	2	no	—
419	C₂³×C₆₇	—	2	2	no	—
420	C₂³×C₆₇	—	4	8	no	—
421	C₂³×C₆₇	—	4	8	no	—
422	C₂³×C₆₇	—	4	8	no	—
423	C₂³×C₆₇	—	8	4	no	—
424	C₂³×C₆₇	—	8	4	no	—
425	C₂³×C₆₇	—	8	4	no	—
426	C₂³×C₆₇	—	8	4	no	—
427	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
428	C₂³×C₆₇	C₂×#41	1	4	yes	—
429	C₂³×C₆₇	C₂×#41	1	4	yes	—
430	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
431	Q₈×C₆₇	—	8	4	no	—
432	D₄×C₆₇	—	2	8	no	—
433	D₄×C₆₇	—	2	8	no	—
434	D₄×C₆₇	—	4	8	no	—
435	D₄×C₆₇	—	4	8	no	—
436	D₄×C₆₇	—	4	8	no	—
437	D₄×C₆₇	—	4	8	no	—
438	D₄×C₆₇	—	4	4	no	—
439	D₄×C₆₇	—	8	4	no	—
440	D₄×C₆₇	—	8	4	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	1	no	—
444	C₂×C₄×C₆₇	—	2	1	no	—
445	C₂×C₄×C₆₇	—	2	1	no	—
446	C₂×C₄×C₆₇	—	2	1	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	1	no	—
453	C₂×C₄×C₆₇	—	2	1	no	—
454	C₂×C₄×C₆₇	—	2	1	no	—
455	C₂×C₄×C₆₇	—	2	2	no	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	2	2	no	—
458	C₂×C₄×C₆₇	—	2	2	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	1	no	—
461	C₂×C₄×C₆₇	—	2	1	no	—
462	C₂×C₄×C₆₇	—	2	1	no	—
463	C₂×C₄×C₆₇	—	2	2	no	—
464	C₂×C₄×C₆₇	—	2	2	no	—
465	C₂×C₄×C₆₇	—	2	1	no	—
466	C₂×C₄×C₆₇	—	2	1	no	—
467	C₂×C₄×C₆₇	—	2	1	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	2	no	—
472	C₂×C₄×C₆₇	—	2	1	no	—
473	C₂×C₄×C₆₇	—	2	2	no	—
474	C₂×C₄×C₆₇	—	2	2	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	2	no	—
477	C₂×C₄×C₆₇	—	2	2	no	—
478	C₂×C₄×C₆₇	—	2	2	no	—
479	C₂×C₄×C₆₇	—	2	1	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	1	no	—
484	C₂×C₄×C₆₇	—	2	1	no	—
485	C₂×C₄×C₆₇	—	2	2	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	1	no	—
488	C₂×C₄×C₆₇	—	4	8	no	—
489	C₂×C₄×C₆₇	—	4	8	no	—
490	C₂×C₄×C₆₇	—	4	4	no	—
491	C₂×C₄×C₆₇	—	8	4	no	—
492	C₂×C₄×C₆₇	—	8	4	no	—
493	C₂×C₄×C₆₇	—	8	4	no	—
494	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
501	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
502	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
503	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
504	C₂²×C₆₇	—	2	4	no	—
505	C₂²×C₆₇	—	2	4	no	—
506	C₂²×C₆₇	—	2	2	no	—
507	C₂²×C₆₇	—	2	2	no	—
508	C₂²×C₆₇	—	2	4	no	—
509	C₂²×C₆₇	—	2	4	no	—
510	C₂²×C₆₇	—	2	2	no	—
511	C₂²×C₆₇	—	2	4	no	—
512	C₂²×C₆₇	—	2	4	no	—
513	C₂²×C₆₇	—	4	2	no	—
514	C₂²×C₆₇	—	4	2	no	—
515	C₂²×C₆₇	—	4	1	no	—
516	C₂²×C₆₇	—	4	2	no	—
517	C₂²×C₆₇	—	4	2	no	—
518	C₂²×C₆₇	—	4	2	no	—
519	C₂²×C₆₇	—	4	1	no	—
520	C₂²×C₆₇	—	4	2	no	—
521	C₂²×C₆₇	—	4	1	no	—
522	C₂²×C₆₇	—	4	2	no	—
523	C₂²×C₆₇	—	4	2	no	—
524	C₂²×C₆₇	—	4	1	no	—
525	C₂²×C₆₇	—	4	2	no	—
526	C₂²×C₆₇	—	4	2	no	—
527	C₂²×C₆₇	—	4	2	no	—
528	C₂²×C₆₇	—	4	2	no	—
529	C₂²×C₆₇	—	4	2	no	—
530	C₂²×C₆₇	—	4	2	no	—
531	C₂²×C₆₇	—	4	2	no	—
532	C₂²×C₆₇	—	8	16	no	—
533	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
534	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
535	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
536	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
537	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂²×C₆₇	#585	1	1	yes	characteristic
539	C₂²×C₆₇	#585	1	1	yes	characteristic
540	C₄×C₆₇	—	2	2	no	—
541	C₄×C₆₇	—	2	2	no	—
542	C₄×C₆₇	—	2	2	no	—
543	C₄×C₆₇	—	2	2	no	—
544	C₄×C₆₇	—	2	2	no	—
545	C₄×C₆₇	—	2	2	no	—
546	C₄×C₆₇	—	2	2	no	—
547	C₄×C₆₇	—	4	2	no	—
548	C₄×C₆₇	—	4	2	no	—
549	C₄×C₆₇	—	4	1	no	—
550	C₄×C₆₇	—	4	2	no	—
551	C₄×C₆₇	—	4	2	no	—
552	C₄×C₆₇	—	4	2	no	—
553	C₄×C₆₇	—	4	1	no	—
554	C₄×C₆₇	—	4	1	no	—
555	C₄×C₆₇	—	4	1	no	—
556	C₄×C₆₇	—	4	1	no	—
557	C₄×C₆₇	—	4	1	no	—
558	C₄×C₆₇	#551	1	4	yes	complemented
559	#59476	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
560	C₂×C₆₇	—	4	4	no	—
561	C₂×C₆₇	—	4	4	no	—
562	C₂×C₆₇	—	4	2	no	—
563	C₂×C₆₇	—	8	2	no	—
564	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
565	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
566	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
567	C₂×C₆₇	#3498	1	1	yes	characteristic
568	C₂×C₆₇	#3513	1	1	yes	characteristic
569	C₂×C₆₇	#3514	1	1	yes	characteristic
570	C₂×C₆₇	#3562	1	1	yes	characteristic
571	C₂×#551	C₂×C₆₇	1	2	yes	complemented
572	#2696	C₂×C₆₇	1	2	yes	complemented
573	#2685	C₂×C₆₇	1	2	yes	complemented
574	#2598	C₂×C₆₇	1	2	yes	complemented
575	#2542	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#2496	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#2491	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#2472	C₂×C₆₇	1	2	yes	complemented
579	#2471	C₂×C₆₇	1	2	yes	complemented
580	#2463	C₂×C₆₇	1	2	yes	complemented
581	#2452	C₂×C₆₇	1	1	yes	characteristic, complemented
582	#2445	C₂×C₆₇	1	1	yes	characteristic, complemented
583	#2445	C₂×C₆₇	1	1	yes	characteristic, complemented
584	#2433	C₂×C₆₇	1	1	yes	characteristic
585	#2422	C₂×C₆₇	1	1	yes	characteristic, complemented
586	#2418	C₂×C₆₇	1	2	yes	complemented
587	#2366	C₂×C₆₇	1	1	yes	characteristic, complemented
588	#2354	C₂×C₆₇	1	1	yes	characteristic, complemented
589	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
590	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
591	C₄×#127	C₂×C₆₇	1	1	yes	characteristic, complemented
592	C₄×#126	C₂×C₆₇	1	1	yes	characteristic, complemented
593	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
594	C₆₇	#59476	1	1	yes	characteristic, direct product factor, Sylow
595	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
596	#551	—	2	16	no	—
597	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
598	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
599	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
600	C₂×#126	C₂²×C₆₇	1	2	yes	—
601	C₂×#126	C₂²×C₆₇	1	1	yes	characteristic
602	C₂×#124	C₂²×C₆₇	1	2	yes	—
603	C₂×#123	C₂²×C₆₇	1	2	yes	—
604	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
605	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
606	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
607	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
608	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
609	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
610	C₂×#120	C₂²×C₆₇	1	2	yes	—
611	C₂×#120	C₂²×C₆₇	1	2	yes	—
612	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
613	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
614	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
615	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
616	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
617	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
618	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
619	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
620	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
621	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
622	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
623	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
624	#400	C₂²×C₆₇	1	2	yes	complemented
625	#399	C₂²×C₆₇	1	2	yes	complemented
626	#399	C₂²×C₆₇	1	2	yes	complemented
627	#397	C₂²×C₆₇	1	2	yes	—
628	#397	C₂²×C₆₇	1	2	yes	complemented
629	#396	C₂²×C₆₇	1	2	yes	complemented
630	#394	C₂²×C₆₇	1	2	yes	—
631	#394	C₂²×C₆₇	1	2	yes	—
632	#394	C₂²×C₆₇	1	2	yes	complemented
633	#394	C₂²×C₆₇	1	2	yes	complemented
634	#394	C₂²×C₆₇	1	2	yes	complemented
635	#394	C₂²×C₆₇	1	2	yes	complemented
636	#393	C₂²×C₆₇	1	2	yes	complemented
637	#393	C₂²×C₆₇	1	2	yes	complemented
638	#392	C₂²×C₆₇	1	2	yes	—
639	#392	C₂²×C₆₇	1	2	yes	—
640	#390	C₂²×C₆₇	1	1	yes	characteristic
641	#390	C₂²×C₆₇	1	1	yes	characteristic
642	#390	C₂²×C₆₇	1	1	yes	characteristic
643	#390	C₂²×C₆₇	1	1	yes	characteristic
644	#390	C₂²×C₆₇	1	1	yes	characteristic
645	#390	C₂²×C₆₇	1	1	yes	characteristic
646	#390	C₂²×C₆₇	1	2	yes	complemented
647	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
648	#390	C₂²×C₆₇	1	2	yes	complemented
649	#390	C₂²×C₆₇	1	2	yes	complemented
650	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
651	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
652	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
653	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
655	#388	C₂²×C₆₇	1	1	yes	characteristic
656	#388	C₂²×C₆₇	1	1	yes	characteristic
657	#388	C₂²×C₆₇	1	1	yes	characteristic
658	#388	C₂²×C₆₇	1	2	yes	complemented
659	#388	C₂²×C₆₇	1	2	yes	complemented
660	#388	C₂²×C₆₇	1	2	yes	complemented
661	#388	C₂²×C₆₇	1	2	yes	complemented
662	#388	C₂²×C₆₇	1	2	yes	complemented
663	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
665	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
666	#387	C₂²×C₆₇	1	2	yes	complemented
667	#386	C₂²×C₆₇	1	2	yes	—
668	#386	C₂²×C₆₇	1	2	yes	—
669	#386	C₂²×C₆₇	1	2	yes	—
670	#386	C₂²×C₆₇	1	2	yes	—
671	#386	C₂²×C₆₇	1	2	yes	complemented
672	#386	C₂²×C₆₇	1	2	yes	complemented
673	#386	C₂²×C₆₇	1	2	yes	complemented
674	#386	C₂²×C₆₇	1	2	yes	complemented
675	#385	C₂²×C₆₇	1	2	yes	complemented
676	#385	C₂²×C₆₇	1	2	yes	complemented
677	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
679	#383	C₂²×C₆₇	1	1	yes	characteristic, complemented
680	#380	C₂²×C₆₇	1	1	yes	characteristic
681	#380	C₂²×C₆₇	1	1	yes	characteristic
682	#380	C₂²×C₆₇	1	2	yes	complemented
683	#379	C₂²×C₆₇	1	2	yes	—
684	#379	C₂²×C₆₇	1	2	yes	—
685	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
686	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
689	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
691	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
692	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
693	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
694	C₄³	C₂²×C₆₇	1	1	yes	characteristic, complemented
695	C₂⁵	C₂³×C₆₇	1	2	yes	—
696	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
697	C₂²×D₄	—	2	4	no	—
698	C₂²×D₄	—	2	4	no	—
699	C₂²×D₄	—	4	2	no	—
700	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
701	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
702	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
703	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
704	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
705	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
706	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
707	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
708	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
709	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
710	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
711	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
712	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
713	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
714	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
715	C₄⋊Q₈	—	4	2	no	—
716	#127	—	2	4	no	—
717	#127	—	2	4	no	—
718	#126	—	2	8	no	—
719	#126	D₄×C₆₇	1	8	yes	complemented
720	#124	—	2	8	no	—
721	#123	—	2	8	no	—
722	#123	—	2	8	no	—
723	#123	—	2	8	no	—
724	C₂²⋊Q₈	—	2	8	no	—
725	C₂²⋊Q₈	—	2	8	no	—
726	C₂²⋊Q₈	—	4	4	no	—
727	#121	—	4	2	no	—
728	#120	—	2	8	no	—
729	#120	—	4	4	no	—
730	C₄×D₄	—	2	4	no	—
731	C₄×D₄	—	2	4	no	—
732	C₄×D₄	—	2	8	no	—
733	C₄×D₄	—	2	8	no	—
734	C₄×D₄	—	4	2	no	—
735	C₄×D₄	—	4	2	no	—
736	C₄×D₄	—	4	2	no	—
737	C₄×D₄	—	4	4	no	—
738	#117	—	2	8	no	—
739	#117	—	2	8	no	—
740	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	—	2	8	no	—
760	C₂×C₂²⋊C₄	—	2	8	no	—
761	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
774	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
785	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
786	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
791	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
792	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
794	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
795	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
796	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
797	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
798	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
799	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
800	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
801	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
802	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
803	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
804	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
805	#95	C₂³×C₆₇	1	1	yes	characteristic
806	#95	C₂³×C₆₇	1	1	yes	characteristic
807	#95	C₂³×C₆₇	1	1	yes	characteristic
808	#95	C₂³×C₆₇	1	1	yes	characteristic
809	#95	C₂³×C₆₇	1	1	yes	characteristic
810	#95	C₂³×C₆₇	1	1	yes	characteristic
811	#95	C₂³×C₆₇	1	2	yes	—
812	#95	C₂³×C₆₇	1	2	yes	—
813	#95	C₂³×C₆₇	1	2	yes	—
814	#95	C₂³×C₆₇	1	2	yes	—
815	#95	C₂³×C₆₇	1	1	yes	characteristic
816	#95	C₂³×C₆₇	1	1	yes	characteristic
817	#95	C₂³×C₆₇	1	1	yes	characteristic
818	#95	C₂³×C₆₇	1	1	yes	characteristic
819	#95	C₂³×C₆₇	1	1	yes	characteristic
820	#95	C₂³×C₆₇	1	1	yes	characteristic
821	#95	C₂³×C₆₇	1	2	yes	—
822	#95	C₂³×C₆₇	1	2	yes	—
823	#95	C₂³×C₆₇	1	2	yes	—
824	C₂⁴	—	2	4	no	—
825	C₂⁴	—	2	4	no	—
826	C₂⁴	—	2	4	no	—
827	C₂⁴	—	4	2	no	—
828	C₂⁴	—	4	2	no	—
829	C₂⁴	—	4	2	no	—
830	C₂⁴	—	4	2	no	—
831	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
832	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
833	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
834	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
835	C₂×Q₈	—	2	4	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×Q₈	—	4	2	no	—
838	C₂×D₄	—	2	4	no	—
839	C₂×D₄	—	2	4	no	—
840	C₂×D₄	—	2	4	no	—
841	C₂×D₄	—	2	4	no	—
842	C₂×D₄	—	2	4	no	—
843	C₂×D₄	—	2	4	no	—
844	C₂×D₄	—	2	4	no	—
845	C₂×D₄	—	2	4	no	—
846	C₂×D₄	—	2	4	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	4	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	4	2	no	—
856	C₂×D₄	—	4	2	no	—
857	C₂×D₄	—	4	2	no	—
858	C₂×D₄	—	4	2	no	—
859	C₂×D₄	—	4	2	no	—
860	C₂×D₄	—	4	2	no	—
861	C₂×D₄	—	4	2	no	—
862	C₂×D₄	—	4	2	no	—
863	C₂×D₄	—	4	16	no	—
864	C₂×D₄	#41×C₆₇	1	4	yes	—
865	C₂×D₄	#41×C₆₇	1	4	yes	—
866	C₂²×C₄	—	2	4	no	—
867	C₂²×C₄	—	2	4	no	—
868	C₂²×C₄	—	2	4	no	—
869	C₂²×C₄	—	2	4	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	4	no	—
874	C₂²×C₄	—	2	4	no	—
875	C₂²×C₄	—	2	4	no	—
876	C₂²×C₄	—	4	2	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	4	2	no	—
879	C₂²×C₄	—	4	2	no	—
880	C₂²×C₄	—	4	2	no	—
881	C₂²×C₄	—	4	2	no	—
882	C₂²×C₄	—	4	2	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
892	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
893	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
894	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
895	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
899	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
903	C₄⋊C₄	—	2	4	no	—
904	C₄⋊C₄	—	2	4	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	2	4	no	—
907	C₄⋊C₄	—	2	4	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	4	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	4	2	no	—
916	C₄⋊C₄	—	4	2	no	—
917	C₄⋊C₄	—	4	1	no	—
918	C₄⋊C₄	—	4	1	no	—
919	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	complemented
920	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	complemented
921	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	complemented
922	C₂²⋊C₄	—	2	4	no	—
923	C₂²⋊C₄	—	2	4	no	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	2	4	no	—
926	C₂²⋊C₄	—	2	4	no	—
927	C₂²⋊C₄	—	2	4	no	—
928	C₂²⋊C₄	—	2	4	no	—
929	C₂²⋊C₄	—	2	4	no	—
930	C₂²⋊C₄	—	2	4	no	—
931	C₂²⋊C₄	—	2	4	no	—
932	C₂²⋊C₄	—	2	4	no	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	4	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	—	4	2	no	—
941	C₂²⋊C₄	—	4	2	no	—
942	C₂²⋊C₄	—	4	2	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	1	no	—
947	C₂²⋊C₄	—	4	1	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	—	4	2	no	—
951	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
952	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
953	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
954	C₄²	—	2	4	no	—
955	C₄²	—	2	4	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	4	1	no	—
964	C₄²	—	4	1	no	—
965	C₄²	C₂×D₄×C₆₇	1	4	yes	complemented
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	2	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	2	no	—
976	C₂³	—	2	2	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	2	no	—
979	C₂³	—	2	2	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	1	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	2	2	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	2	no	—
991	C₂³	—	4	8	no	—
992	C₂³	—	4	8	no	—
993	C₂³	—	4	8	no	—
994	C₂³	—	8	4	no	—
995	C₂³	—	8	4	no	—
996	C₂³	—	8	4	no	—
997	C₂³	—	8	4	no	—
998	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
999	C₂³	C₂×#41×C₆₇	1	4	yes	—
1000	C₂³	C₂×#41×C₆₇	1	4	yes	—
1001	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1002	Q₈	—	8	4	no	—
1003	D₄	—	2	8	no	—
1004	D₄	—	2	8	no	—
1005	D₄	—	4	8	no	—
1006	D₄	—	4	8	no	—
1007	D₄	—	4	8	no	—
1008	D₄	—	4	8	no	—
1009	D₄	—	4	4	no	—
1010	D₄	—	8	4	no	—
1011	D₄	—	8	4	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	4	8	no	—
1060	C₂×C₄	—	4	8	no	—
1061	C₂×C₄	—	4	4	no	—
1062	C₂×C₄	—	8	4	no	—
1063	C₂×C₄	—	8	4	no	—
1064	C₂×C₄	—	8	4	no	—
1065	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1067	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1071	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1072	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1073	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1074	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1075	C₂²	—	2	4	no	—
1076	C₂²	—	2	4	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	2	no	—
1079	C₂²	—	2	4	no	—
1080	C₂²	—	2	4	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	4	no	—
1083	C₂²	—	2	4	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	8	16	no	—
1104	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1105	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1106	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1107	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1108	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1109	C₂²	#585×C₆₇	1	1	yes	characteristic
1110	C₂²	#585×C₆₇	1	1	yes	characteristic
1111	C₄	—	2	2	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	2	2	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	2	no	—
1124	C₄	—	4	2	no	—
1125	C₄	—	4	2	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	#551×C₆₇	1	4	yes	complemented
1130	C₂	—	4	2	no	—
1131	C₂	—	4	4	no	—
1132	C₂	—	4	4	no	—
1133	C₂	—	8	2	no	—
1134	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1135	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1136	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
1137	C₂	C₆₇×#3498	1	1	yes	characteristic
1138	C₂	C₆₇×#3513	1	1	yes	characteristic
1139	C₂	C₆₇×#3514	1	1	yes	characteristic
1140	C₂	C₆₇×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2433	C₂
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×#551×C₆₇	C₂	semidirect
2. C₆₇×#2696	C₂	semidirect
3. C₆₇×#2685	C₂	semidirect
4. C₆₇×#2598	C₂	semidirect
5. C₆₇×#2542	C₂	semidirect
6. C₆₇×#2496	C₂	semidirect
7. C₆₇×#2491	C₂	semidirect
8. C₆₇×#2472	C₂	semidirect
9. C₆₇×#2471	C₂	semidirect
10. C₆₇×#2463	C₂	semidirect
11. C₆₇×#2452	C₂	semidirect
12. C₆₇×#2445	C₂	semidirect
13. C₆₇×#2445	C₂	semidirect
15. C₆₇×#2422	C₂	semidirect
16. C₆₇×#2418	C₂	semidirect
17. C₆₇×#2366	C₂	semidirect
18. C₆₇×#2354	C₂	semidirect
19. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
20. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
21. C₄×#127×C₆₇	C₂	semidirect
22. C₄×#126×C₆₇	C₂	semidirect
23. C₆₇×#2293	C₂	semidirect
26. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
33. C₂×#123×C₆₇	C₂²	semidirect
34. C₂×#123×C₆₇	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
36. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
37. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
45. C₂×C₄×D₄×C₆₇	C₂²	semidirect
46. C₂×C₄×D₄×C₆₇	C₂²	semidirect
47. C₂×C₄×D₄×C₆₇	C₂²	semidirect
48. C₂×C₄×D₄×C₆₇	C₂²	semidirect
49. C₂×#117×C₆₇	C₂²	semidirect
50. C₂×#117×C₆₇	C₂²	semidirect
53. #400×C₆₇	C₂²	semidirect
54. #399×C₆₇	C₂²	semidirect
55. #399×C₆₇	C₂²	semidirect
57. #397×C₆₇	C₂²	semidirect
58. #396×C₆₇	C₂²	semidirect
61. #394×C₆₇	C₂²	semidirect
62. #394×C₆₇	C₂²	semidirect
63. #394×C₆₇	C₂²	semidirect
64. #394×C₆₇	C₂²	semidirect
65. #393×C₆₇	C₂²	semidirect
66. #393×C₆₇	C₂²	semidirect
75. #390×C₆₇	C₂²	semidirect
76. #390×C₆₇	C₂²	semidirect
77. #390×C₆₇	C₂²	semidirect
78. #390×C₆₇	C₂²	semidirect
79. #390×C₆₇	C₂²	semidirect
80. #390×C₆₇	C₂²	semidirect
81. #389×C₆₇	C₂²	semidirect
82. #389×C₆₇	C₂²	semidirect
83. #389×C₆₇	C₂²	semidirect
87. #388×C₆₇	C₂²	semidirect
88. #388×C₆₇	C₂²	semidirect
89. #388×C₆₇	C₂²	semidirect
90. #388×C₆₇	C₂²	semidirect
91. #388×C₆₇	C₂²	semidirect
92. #387×C₆₇	C₂²	semidirect
93. #387×C₆₇	C₂²	semidirect
94. #387×C₆₇	C₂²	semidirect
95. #387×C₆₇	C₂²	semidirect
100. #386×C₆₇	C₂²	semidirect
101. #386×C₆₇	C₂²	semidirect
102. #386×C₆₇	C₂²	semidirect
103. #386×C₆₇	C₂²	semidirect
104. #385×C₆₇	C₂²	semidirect
105. #385×C₆₇	C₂²	semidirect
106. #384×C₆₇	C₂²	semidirect
107. #384×C₆₇	C₂²	semidirect
108. #383×C₆₇	C₂²	semidirect
111. #380×C₆₇	C₂²	semidirect
114. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
115. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
116. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
117. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
118. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
123. C₄³×C₆₇	C₂²	semidirect
148. #126×C₆₇	D₄	semidirect
348. C₄⋊C₄×C₆₇	C₂×D₄	semidirect
349. C₄⋊C₄×C₆₇	C₂×D₄	semidirect
350. C₄⋊C₄×C₆₇	C₂×D₄	semidirect
394. C₄²×C₆₇	C₂×D₄	semidirect
558. C₄×C₆₇	#551	semidirect
559. #59476	C₆₇	direct (N × H)
571. C₂×#551	C₂×C₆₇	semidirect
572. #2696	C₂×C₆₇	semidirect
573. #2685	C₂×C₆₇	semidirect
574. #2598	C₂×C₆₇	semidirect
575. #2542	C₂×C₆₇	semidirect
576. #2496	C₂×C₆₇	semidirect
577. #2491	C₂×C₆₇	semidirect
578. #2472	C₂×C₆₇	semidirect
579. #2471	C₂×C₆₇	semidirect
580. #2463	C₂×C₆₇	semidirect
581. #2452	C₂×C₆₇	semidirect
582. #2445	C₂×C₆₇	semidirect
583. #2445	C₂×C₆₇	semidirect
585. #2422	C₂×C₆₇	semidirect
586. #2418	C₂×C₆₇	semidirect
587. #2366	C₂×C₆₇	semidirect
588. #2354	C₂×C₆₇	semidirect
589. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
590. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
591. C₄×#127	C₂×C₆₇	semidirect
592. C₄×#126	C₂×C₆₇	semidirect
593. #2293	C₂×C₆₇	semidirect
594. C₆₇	#59476	direct (N × H)
597. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
604. C₂×#123	C₂²×C₆₇	semidirect
605. C₂×#123	C₂²×C₆₇	semidirect
606. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
607. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
608. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
616. C₂×C₄×D₄	C₂²×C₆₇	semidirect
617. C₂×C₄×D₄	C₂²×C₆₇	semidirect
618. C₂×C₄×D₄	C₂²×C₆₇	semidirect
619. C₂×C₄×D₄	C₂²×C₆₇	semidirect
620. C₂×#117	C₂²×C₆₇	semidirect
621. C₂×#117	C₂²×C₆₇	semidirect
624. #400	C₂²×C₆₇	semidirect
625. #399	C₂²×C₆₇	semidirect
626. #399	C₂²×C₆₇	semidirect
628. #397	C₂²×C₆₇	semidirect
629. #396	C₂²×C₆₇	semidirect
632. #394	C₂²×C₆₇	semidirect
633. #394	C₂²×C₆₇	semidirect
634. #394	C₂²×C₆₇	semidirect
635. #394	C₂²×C₆₇	semidirect
636. #393	C₂²×C₆₇	semidirect
637. #393	C₂²×C₆₇	semidirect
646. #390	C₂²×C₆₇	semidirect
647. #390	C₂²×C₆₇	semidirect
648. #390	C₂²×C₆₇	semidirect
649. #390	C₂²×C₆₇	semidirect
650. #390	C₂²×C₆₇	semidirect
651. #390	C₂²×C₆₇	semidirect
652. #389	C₂²×C₆₇	semidirect
653. #389	C₂²×C₆₇	semidirect
654. #389	C₂²×C₆₇	semidirect
658. #388	C₂²×C₆₇	semidirect
659. #388	C₂²×C₆₇	semidirect
660. #388	C₂²×C₆₇	semidirect
661. #388	C₂²×C₆₇	semidirect
662. #388	C₂²×C₆₇	semidirect
663. #387	C₂²×C₆₇	semidirect
664. #387	C₂²×C₆₇	semidirect
665. #387	C₂²×C₆₇	semidirect
666. #387	C₂²×C₆₇	semidirect
671. #386	C₂²×C₆₇	semidirect
672. #386	C₂²×C₆₇	semidirect
673. #386	C₂²×C₆₇	semidirect
674. #386	C₂²×C₆₇	semidirect
675. #385	C₂²×C₆₇	semidirect
676. #385	C₂²×C₆₇	semidirect
677. #384	C₂²×C₆₇	semidirect
678. #384	C₂²×C₆₇	semidirect
679. #383	C₂²×C₆₇	semidirect
682. #380	C₂²×C₆₇	semidirect
685. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
686. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
687. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
688. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
689. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
693. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
694. C₄³	C₂²×C₆₇	semidirect
719. #126	D₄×C₆₇	semidirect
919. C₄⋊C₄	C₂×D₄×C₆₇	semidirect
920. C₄⋊C₄	C₂×D₄×C₆₇	semidirect
921. C₄⋊C₄	C₂×D₄×C₆₇	semidirect
965. C₄²	C₂×D₄×C₆₇	semidirect
1129. C₄	#551×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#551×C₆₇	2
C₆₇×#2696	2
C₆₇×#2685	2
C₆₇×#2598	2
C₆₇×#2542	2
C₆₇×#2496	2
C₆₇×#2491	2
C₆₇×#2472	2
C₆₇×#2471	2
C₆₇×#2463	2
C₆₇×#2452	2
C₆₇×#2445	2
C₆₇×#2433	2
C₆₇×#2422	2
C₆₇×#2418	2
C₆₇×#2366	2
C₆₇×#2354	2
D₄×C₂²⋊C₄×C₆₇	2
C₄×#127×C₆₇	2
C₄×#126×C₆₇	2
C₆₇×#2293	2
#59476	67

Subgroups — C67×#59476 #30738727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59476 #30738727